Z3---4.15.1.UNS-Prf.s

%------------------------------------------------------------------------------
% File     : Z3---4.15.1
% Problem  : SWV865-1 : TPTP v9.0.0. Released v4.1.0.
% Transfm  : none
% Format   : tptp
% Command  : run_E %s %d THM

% Computer : n013.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Sat Jun 21 05:36:14 AM UTC 2025

% Result   : Unsatisfiable 24.89s 25.06s
% Output   : Proof 24.93s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : SWV865-1 : TPTP v9.0.0. Released v4.1.0.
% 0.03/0.12  % Command    : run_E %s %d THM
% 0.12/0.33  % Computer : n013.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit   : 300
% 0.12/0.33  % WCLimit    : 300
% 0.12/0.33  % DateTime   : Fri Jun 20 10:58:38 EDT 2025
% 0.12/0.33  % CPUTime    : 
% 24.89/25.06  % SZS status Unsatisfiable
% 24.89/25.06  % SZS output start Proof
% 24.89/25.06  tff(c_Natural_Oevalc_type, type, (
% 24.89/25.06     c_Natural_Oevalc: ( $i * $i * $i ) > $o)).
% 24.89/25.06  tff(v_s_H_type, type, (
% 24.89/25.06     v_s_H: $i)).
% 24.89/25.06  tff(c_Natural_Osko__Natural__Xevalc__elim__cases__4__1_type, type, (
% 24.89/25.06     c_Natural_Osko__Natural__Xevalc__elim__cases__4__1: ( $i * $i * $i * $i ) > $i)).
% 24.89/25.06  tff(v_Z_type, type, (
% 24.89/25.06     v_Z: $i)).
% 24.89/25.06  tff(c_Com_Ocom_OSKIP_type, type, (
% 24.89/25.06     c_Com_Ocom_OSKIP: $i)).
% 24.89/25.06  tff(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2_type, type, (
% 24.89/25.06     v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2: $i)).
% 24.89/25.06  tff(v_Z_H_type, type, (
% 24.89/25.06     v_Z_H: $i > $i)).
% 24.89/25.06  tff(c_Com_Ocom_OSemi_type, type, (
% 24.89/25.06     c_Com_Ocom_OSemi: ( $i * $i ) > $i)).
% 24.89/25.06  tff(v_s_type, type, (
% 24.89/25.06     v_s: $i)).
% 24.89/25.06  tff(v_c_type, type, (
% 24.89/25.06     v_c: $i)).
% 24.89/25.06  tff(hAPP_type, type, (
% 24.89/25.06     hAPP: ( $i * $i ) > $i)).
% 24.89/25.06  tff(v_t_type, type, (
% 24.89/25.06     v_t: $i)).
% 24.89/25.06  tff(c_Natural_Osko__Natural__Xevalc__evaln__1__1_type, type, (
% 24.89/25.06     c_Natural_Osko__Natural__Xevalc__evaln__1__1: ( $i * $i * $i ) > $i)).
% 24.89/25.06  tff(1,plain,
% 24.89/25.06      (^[V_s: $i] : refl(c_Natural_Oevalc(c_Com_Ocom_OSKIP, V_s, V_s) <=> c_Natural_Oevalc(c_Com_Ocom_OSKIP, V_s, V_s))),
% 24.89/25.06      inference(bind,[status(th)],[])).
% 24.89/25.06  tff(2,plain,
% 24.89/25.06      (![V_s: $i] : c_Natural_Oevalc(c_Com_Ocom_OSKIP, V_s, V_s) <=> ![V_s: $i] : c_Natural_Oevalc(c_Com_Ocom_OSKIP, V_s, V_s)),
% 24.89/25.06      inference(quant_intro,[status(thm)],[1])).
% 24.89/25.06  tff(3,plain,
% 24.89/25.06      (![V_s: $i] : c_Natural_Oevalc(c_Com_Ocom_OSKIP, V_s, V_s) <=> ![V_s: $i] : c_Natural_Oevalc(c_Com_Ocom_OSKIP, V_s, V_s)),
% 24.89/25.06      inference(rewrite,[status(thm)],[])).
% 24.89/25.06  tff(4,axiom,(![V_s: $i] : c_Natural_Oevalc(c_Com_Ocom_OSKIP, V_s, V_s)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_evalc_OSkip_0')).
% 24.89/25.06  tff(5,plain,
% 24.89/25.06      (![V_s: $i] : c_Natural_Oevalc(c_Com_Ocom_OSKIP, V_s, V_s)),
% 24.89/25.06      inference(modus_ponens,[status(thm)],[4, 3])).
% 24.89/25.06  tff(6,plain,(
% 24.89/25.06      ![V_s: $i] : c_Natural_Oevalc(c_Com_Ocom_OSKIP, V_s, V_s)),
% 24.89/25.06      inference(skolemize,[status(sab)],[5])).
% 24.89/25.06  tff(7,plain,
% 24.89/25.06      (![V_s: $i] : c_Natural_Oevalc(c_Com_Ocom_OSKIP, V_s, V_s)),
% 24.89/25.06      inference(modus_ponens,[status(thm)],[6, 2])).
% 24.89/25.06  tff(8,plain,
% 24.89/25.06      ((~![V_s: $i] : c_Natural_Oevalc(c_Com_Ocom_OSKIP, V_s, V_s)) | c_Natural_Oevalc(c_Com_Ocom_OSKIP, v_Z, v_Z)),
% 24.89/25.06      inference(quant_inst,[status(thm)],[])).
% 24.89/25.06  tff(9,plain,
% 24.89/25.06      (c_Natural_Oevalc(c_Com_Ocom_OSKIP, v_Z, v_Z)),
% 24.89/25.06      inference(unit_resolution,[status(thm)],[8, 7])).
% 24.89/25.06  tff(10,plain,
% 24.89/25.06      (^[V_s0: $i, V_s2: $i, V_c0: $i, V_c1: $i, V_s1: $i] : refl(((~c_Natural_Oevalc(V_c0, V_s0, V_s1)) | (~c_Natural_Oevalc(V_c1, V_s1, V_s2)) | c_Natural_Oevalc(c_Com_Ocom_OSemi(V_c0, V_c1), V_s0, V_s2)) <=> ((~c_Natural_Oevalc(V_c0, V_s0, V_s1)) | (~c_Natural_Oevalc(V_c1, V_s1, V_s2)) | c_Natural_Oevalc(c_Com_Ocom_OSemi(V_c0, V_c1), V_s0, V_s2)))),
% 24.89/25.06      inference(bind,[status(th)],[])).
% 24.89/25.06  tff(11,plain,
% 24.89/25.06      (![V_s0: $i, V_s2: $i, V_c0: $i, V_c1: $i, V_s1: $i] : ((~c_Natural_Oevalc(V_c0, V_s0, V_s1)) | (~c_Natural_Oevalc(V_c1, V_s1, V_s2)) | c_Natural_Oevalc(c_Com_Ocom_OSemi(V_c0, V_c1), V_s0, V_s2)) <=> ![V_s0: $i, V_s2: $i, V_c0: $i, V_c1: $i, V_s1: $i] : ((~c_Natural_Oevalc(V_c0, V_s0, V_s1)) | (~c_Natural_Oevalc(V_c1, V_s1, V_s2)) | c_Natural_Oevalc(c_Com_Ocom_OSemi(V_c0, V_c1), V_s0, V_s2))),
% 24.89/25.06      inference(quant_intro,[status(thm)],[10])).
% 24.89/25.06  tff(12,plain,
% 24.89/25.06      (![V_s0: $i, V_s2: $i, V_c0: $i, V_c1: $i, V_s1: $i] : ((~c_Natural_Oevalc(V_c0, V_s0, V_s1)) | (~c_Natural_Oevalc(V_c1, V_s1, V_s2)) | c_Natural_Oevalc(c_Com_Ocom_OSemi(V_c0, V_c1), V_s0, V_s2)) <=> ![V_s0: $i, V_s2: $i, V_c0: $i, V_c1: $i, V_s1: $i] : ((~c_Natural_Oevalc(V_c0, V_s0, V_s1)) | (~c_Natural_Oevalc(V_c1, V_s1, V_s2)) | c_Natural_Oevalc(c_Com_Ocom_OSemi(V_c0, V_c1), V_s0, V_s2))),
% 24.89/25.06      inference(rewrite,[status(thm)],[])).
% 24.89/25.06  tff(13,plain,
% 24.89/25.06      (^[V_s0: $i, V_s2: $i, V_c0: $i, V_c1: $i, V_s1: $i] : trans(monotonicity(rewrite((c_Natural_Oevalc(c_Com_Ocom_OSemi(V_c0, V_c1), V_s0, V_s2) | (~c_Natural_Oevalc(V_c1, V_s1, V_s2))) <=> ((~c_Natural_Oevalc(V_c1, V_s1, V_s2)) | c_Natural_Oevalc(c_Com_Ocom_OSemi(V_c0, V_c1), V_s0, V_s2))), (((c_Natural_Oevalc(c_Com_Ocom_OSemi(V_c0, V_c1), V_s0, V_s2) | (~c_Natural_Oevalc(V_c1, V_s1, V_s2))) | (~c_Natural_Oevalc(V_c0, V_s0, V_s1))) <=> (((~c_Natural_Oevalc(V_c1, V_s1, V_s2)) | c_Natural_Oevalc(c_Com_Ocom_OSemi(V_c0, V_c1), V_s0, V_s2)) | (~c_Natural_Oevalc(V_c0, V_s0, V_s1))))), rewrite((((~c_Natural_Oevalc(V_c1, V_s1, V_s2)) | c_Natural_Oevalc(c_Com_Ocom_OSemi(V_c0, V_c1), V_s0, V_s2)) | (~c_Natural_Oevalc(V_c0, V_s0, V_s1))) <=> ((~c_Natural_Oevalc(V_c0, V_s0, V_s1)) | (~c_Natural_Oevalc(V_c1, V_s1, V_s2)) | c_Natural_Oevalc(c_Com_Ocom_OSemi(V_c0, V_c1), V_s0, V_s2))), (((c_Natural_Oevalc(c_Com_Ocom_OSemi(V_c0, V_c1), V_s0, V_s2) | (~c_Natural_Oevalc(V_c1, V_s1, V_s2))) | (~c_Natural_Oevalc(V_c0, V_s0, V_s1))) <=> ((~c_Natural_Oevalc(V_c0, V_s0, V_s1)) | (~c_Natural_Oevalc(V_c1, V_s1, V_s2)) | c_Natural_Oevalc(c_Com_Ocom_OSemi(V_c0, V_c1), V_s0, V_s2))))),
% 24.89/25.06      inference(bind,[status(th)],[])).
% 24.89/25.06  tff(14,plain,
% 24.89/25.06      (![V_s0: $i, V_s2: $i, V_c0: $i, V_c1: $i, V_s1: $i] : ((c_Natural_Oevalc(c_Com_Ocom_OSemi(V_c0, V_c1), V_s0, V_s2) | (~c_Natural_Oevalc(V_c1, V_s1, V_s2))) | (~c_Natural_Oevalc(V_c0, V_s0, V_s1))) <=> ![V_s0: $i, V_s2: $i, V_c0: $i, V_c1: $i, V_s1: $i] : ((~c_Natural_Oevalc(V_c0, V_s0, V_s1)) | (~c_Natural_Oevalc(V_c1, V_s1, V_s2)) | c_Natural_Oevalc(c_Com_Ocom_OSemi(V_c0, V_c1), V_s0, V_s2))),
% 24.89/25.06      inference(quant_intro,[status(thm)],[13])).
% 24.89/25.06  tff(15,axiom,(![V_s0: $i, V_s2: $i, V_c0: $i, V_c1: $i, V_s1: $i] : ((c_Natural_Oevalc(c_Com_Ocom_OSemi(V_c0, V_c1), V_s0, V_s2) | (~c_Natural_Oevalc(V_c1, V_s1, V_s2))) | (~c_Natural_Oevalc(V_c0, V_s0, V_s1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_evalc_OSemi_0')).
% 24.89/25.06  tff(16,plain,
% 24.89/25.06      (![V_s0: $i, V_s2: $i, V_c0: $i, V_c1: $i, V_s1: $i] : ((~c_Natural_Oevalc(V_c0, V_s0, V_s1)) | (~c_Natural_Oevalc(V_c1, V_s1, V_s2)) | c_Natural_Oevalc(c_Com_Ocom_OSemi(V_c0, V_c1), V_s0, V_s2))),
% 24.89/25.06      inference(modus_ponens,[status(thm)],[15, 14])).
% 24.89/25.06  tff(17,plain,
% 24.89/25.06      (![V_s0: $i, V_s2: $i, V_c0: $i, V_c1: $i, V_s1: $i] : ((~c_Natural_Oevalc(V_c0, V_s0, V_s1)) | (~c_Natural_Oevalc(V_c1, V_s1, V_s2)) | c_Natural_Oevalc(c_Com_Ocom_OSemi(V_c0, V_c1), V_s0, V_s2))),
% 24.89/25.06      inference(modus_ponens,[status(thm)],[16, 12])).
% 24.89/25.06  tff(18,plain,(
% 24.89/25.06      ![V_s0: $i, V_s2: $i, V_c0: $i, V_c1: $i, V_s1: $i] : ((~c_Natural_Oevalc(V_c0, V_s0, V_s1)) | (~c_Natural_Oevalc(V_c1, V_s1, V_s2)) | c_Natural_Oevalc(c_Com_Ocom_OSemi(V_c0, V_c1), V_s0, V_s2))),
% 24.89/25.06      inference(skolemize,[status(sab)],[17])).
% 24.89/25.06  tff(19,plain,
% 24.89/25.06      (![V_s0: $i, V_s2: $i, V_c0: $i, V_c1: $i, V_s1: $i] : ((~c_Natural_Oevalc(V_c0, V_s0, V_s1)) | (~c_Natural_Oevalc(V_c1, V_s1, V_s2)) | c_Natural_Oevalc(c_Com_Ocom_OSemi(V_c0, V_c1), V_s0, V_s2))),
% 24.89/25.06      inference(modus_ponens,[status(thm)],[18, 11])).
% 24.89/25.06  tff(20,plain,
% 24.89/25.06      (((~![V_s0: $i, V_s2: $i, V_c0: $i, V_c1: $i, V_s1: $i] : ((~c_Natural_Oevalc(V_c0, V_s0, V_s1)) | (~c_Natural_Oevalc(V_c1, V_s1, V_s2)) | c_Natural_Oevalc(c_Com_Ocom_OSemi(V_c0, V_c1), V_s0, V_s2))) | ((~c_Natural_Oevalc(c_Com_Ocom_OSKIP, v_Z, v_Z)) | c_Natural_Oevalc(c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP), v_Z, v_Z))) <=> ((~![V_s0: $i, V_s2: $i, V_c0: $i, V_c1: $i, V_s1: $i] : ((~c_Natural_Oevalc(V_c0, V_s0, V_s1)) | (~c_Natural_Oevalc(V_c1, V_s1, V_s2)) | c_Natural_Oevalc(c_Com_Ocom_OSemi(V_c0, V_c1), V_s0, V_s2))) | (~c_Natural_Oevalc(c_Com_Ocom_OSKIP, v_Z, v_Z)) | c_Natural_Oevalc(c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP), v_Z, v_Z))),
% 24.89/25.06      inference(rewrite,[status(thm)],[])).
% 24.89/25.06  tff(21,plain,
% 24.89/25.06      (((~c_Natural_Oevalc(c_Com_Ocom_OSKIP, v_Z, v_Z)) | (~c_Natural_Oevalc(c_Com_Ocom_OSKIP, v_Z, v_Z)) | c_Natural_Oevalc(c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP), v_Z, v_Z)) <=> ((~c_Natural_Oevalc(c_Com_Ocom_OSKIP, v_Z, v_Z)) | c_Natural_Oevalc(c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP), v_Z, v_Z))),
% 24.89/25.06      inference(rewrite,[status(thm)],[])).
% 24.89/25.06  tff(22,plain,
% 24.89/25.06      (((~![V_s0: $i, V_s2: $i, V_c0: $i, V_c1: $i, V_s1: $i] : ((~c_Natural_Oevalc(V_c0, V_s0, V_s1)) | (~c_Natural_Oevalc(V_c1, V_s1, V_s2)) | c_Natural_Oevalc(c_Com_Ocom_OSemi(V_c0, V_c1), V_s0, V_s2))) | ((~c_Natural_Oevalc(c_Com_Ocom_OSKIP, v_Z, v_Z)) | (~c_Natural_Oevalc(c_Com_Ocom_OSKIP, v_Z, v_Z)) | c_Natural_Oevalc(c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP), v_Z, v_Z))) <=> ((~![V_s0: $i, V_s2: $i, V_c0: $i, V_c1: $i, V_s1: $i] : ((~c_Natural_Oevalc(V_c0, V_s0, V_s1)) | (~c_Natural_Oevalc(V_c1, V_s1, V_s2)) | c_Natural_Oevalc(c_Com_Ocom_OSemi(V_c0, V_c1), V_s0, V_s2))) | ((~c_Natural_Oevalc(c_Com_Ocom_OSKIP, v_Z, v_Z)) | c_Natural_Oevalc(c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP), v_Z, v_Z)))),
% 24.89/25.06      inference(monotonicity,[status(thm)],[21])).
% 24.89/25.06  tff(23,plain,
% 24.89/25.06      (((~![V_s0: $i, V_s2: $i, V_c0: $i, V_c1: $i, V_s1: $i] : ((~c_Natural_Oevalc(V_c0, V_s0, V_s1)) | (~c_Natural_Oevalc(V_c1, V_s1, V_s2)) | c_Natural_Oevalc(c_Com_Ocom_OSemi(V_c0, V_c1), V_s0, V_s2))) | ((~c_Natural_Oevalc(c_Com_Ocom_OSKIP, v_Z, v_Z)) | (~c_Natural_Oevalc(c_Com_Ocom_OSKIP, v_Z, v_Z)) | c_Natural_Oevalc(c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP), v_Z, v_Z))) <=> ((~![V_s0: $i, V_s2: $i, V_c0: $i, V_c1: $i, V_s1: $i] : ((~c_Natural_Oevalc(V_c0, V_s0, V_s1)) | (~c_Natural_Oevalc(V_c1, V_s1, V_s2)) | c_Natural_Oevalc(c_Com_Ocom_OSemi(V_c0, V_c1), V_s0, V_s2))) | (~c_Natural_Oevalc(c_Com_Ocom_OSKIP, v_Z, v_Z)) | c_Natural_Oevalc(c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP), v_Z, v_Z))),
% 24.89/25.06      inference(transitivity,[status(thm)],[22, 20])).
% 24.89/25.06  tff(24,plain,
% 24.89/25.06      ((~![V_s0: $i, V_s2: $i, V_c0: $i, V_c1: $i, V_s1: $i] : ((~c_Natural_Oevalc(V_c0, V_s0, V_s1)) | (~c_Natural_Oevalc(V_c1, V_s1, V_s2)) | c_Natural_Oevalc(c_Com_Ocom_OSemi(V_c0, V_c1), V_s0, V_s2))) | ((~c_Natural_Oevalc(c_Com_Ocom_OSKIP, v_Z, v_Z)) | (~c_Natural_Oevalc(c_Com_Ocom_OSKIP, v_Z, v_Z)) | c_Natural_Oevalc(c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP), v_Z, v_Z))),
% 24.89/25.06      inference(quant_inst,[status(thm)],[])).
% 24.89/25.06  tff(25,plain,
% 24.89/25.06      ((~![V_s0: $i, V_s2: $i, V_c0: $i, V_c1: $i, V_s1: $i] : ((~c_Natural_Oevalc(V_c0, V_s0, V_s1)) | (~c_Natural_Oevalc(V_c1, V_s1, V_s2)) | c_Natural_Oevalc(c_Com_Ocom_OSemi(V_c0, V_c1), V_s0, V_s2))) | (~c_Natural_Oevalc(c_Com_Ocom_OSKIP, v_Z, v_Z)) | c_Natural_Oevalc(c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP), v_Z, v_Z)),
% 24.89/25.06      inference(modus_ponens,[status(thm)],[24, 23])).
% 24.89/25.06  tff(26,plain,
% 24.89/25.06      (c_Natural_Oevalc(c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP), v_Z, v_Z)),
% 24.89/25.06      inference(unit_resolution,[status(thm)],[25, 19, 9])).
% 24.89/25.06  tff(27,plain,
% 24.89/25.06      (^[V_t: $i, V_c2: $i, V_c1: $i, V_s: $i] : refl(((~c_Natural_Oevalc(c_Com_Ocom_OSemi(V_c1, V_c2), V_s, V_t)) | c_Natural_Oevalc(V_c2, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(V_c1, V_c2, V_s, V_t), V_t)) <=> ((~c_Natural_Oevalc(c_Com_Ocom_OSemi(V_c1, V_c2), V_s, V_t)) | c_Natural_Oevalc(V_c2, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(V_c1, V_c2, V_s, V_t), V_t)))),
% 24.89/25.06      inference(bind,[status(th)],[])).
% 24.89/25.06  tff(28,plain,
% 24.89/25.06      (![V_t: $i, V_c2: $i, V_c1: $i, V_s: $i] : ((~c_Natural_Oevalc(c_Com_Ocom_OSemi(V_c1, V_c2), V_s, V_t)) | c_Natural_Oevalc(V_c2, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(V_c1, V_c2, V_s, V_t), V_t)) <=> ![V_t: $i, V_c2: $i, V_c1: $i, V_s: $i] : ((~c_Natural_Oevalc(c_Com_Ocom_OSemi(V_c1, V_c2), V_s, V_t)) | c_Natural_Oevalc(V_c2, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(V_c1, V_c2, V_s, V_t), V_t))),
% 24.89/25.06      inference(quant_intro,[status(thm)],[27])).
% 24.89/25.06  tff(29,plain,
% 24.89/25.06      (![V_t: $i, V_c2: $i, V_c1: $i, V_s: $i] : ((~c_Natural_Oevalc(c_Com_Ocom_OSemi(V_c1, V_c2), V_s, V_t)) | c_Natural_Oevalc(V_c2, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(V_c1, V_c2, V_s, V_t), V_t)) <=> ![V_t: $i, V_c2: $i, V_c1: $i, V_s: $i] : ((~c_Natural_Oevalc(c_Com_Ocom_OSemi(V_c1, V_c2), V_s, V_t)) | c_Natural_Oevalc(V_c2, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(V_c1, V_c2, V_s, V_t), V_t))),
% 24.89/25.06      inference(rewrite,[status(thm)],[])).
% 24.89/25.06  tff(30,plain,
% 24.89/25.06      (^[V_t: $i, V_c2: $i, V_c1: $i, V_s: $i] : rewrite((c_Natural_Oevalc(V_c2, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(V_c1, V_c2, V_s, V_t), V_t) | (~c_Natural_Oevalc(c_Com_Ocom_OSemi(V_c1, V_c2), V_s, V_t))) <=> ((~c_Natural_Oevalc(c_Com_Ocom_OSemi(V_c1, V_c2), V_s, V_t)) | c_Natural_Oevalc(V_c2, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(V_c1, V_c2, V_s, V_t), V_t)))),
% 24.89/25.06      inference(bind,[status(th)],[])).
% 24.89/25.06  tff(31,plain,
% 24.89/25.06      (![V_t: $i, V_c2: $i, V_c1: $i, V_s: $i] : (c_Natural_Oevalc(V_c2, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(V_c1, V_c2, V_s, V_t), V_t) | (~c_Natural_Oevalc(c_Com_Ocom_OSemi(V_c1, V_c2), V_s, V_t))) <=> ![V_t: $i, V_c2: $i, V_c1: $i, V_s: $i] : ((~c_Natural_Oevalc(c_Com_Ocom_OSemi(V_c1, V_c2), V_s, V_t)) | c_Natural_Oevalc(V_c2, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(V_c1, V_c2, V_s, V_t), V_t))),
% 24.89/25.06      inference(quant_intro,[status(thm)],[30])).
% 24.89/25.06  tff(32,axiom,(![V_t: $i, V_c2: $i, V_c1: $i, V_s: $i] : (c_Natural_Oevalc(V_c2, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(V_c1, V_c2, V_s, V_t), V_t) | (~c_Natural_Oevalc(c_Com_Ocom_OSemi(V_c1, V_c2), V_s, V_t)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_evalc__elim__cases_I4_J_1')).
% 24.89/25.06  tff(33,plain,
% 24.89/25.06      (![V_t: $i, V_c2: $i, V_c1: $i, V_s: $i] : ((~c_Natural_Oevalc(c_Com_Ocom_OSemi(V_c1, V_c2), V_s, V_t)) | c_Natural_Oevalc(V_c2, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(V_c1, V_c2, V_s, V_t), V_t))),
% 24.89/25.06      inference(modus_ponens,[status(thm)],[32, 31])).
% 24.89/25.06  tff(34,plain,
% 24.89/25.06      (![V_t: $i, V_c2: $i, V_c1: $i, V_s: $i] : ((~c_Natural_Oevalc(c_Com_Ocom_OSemi(V_c1, V_c2), V_s, V_t)) | c_Natural_Oevalc(V_c2, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(V_c1, V_c2, V_s, V_t), V_t))),
% 24.89/25.06      inference(modus_ponens,[status(thm)],[33, 29])).
% 24.89/25.06  tff(35,plain,(
% 24.89/25.06      ![V_t: $i, V_c2: $i, V_c1: $i, V_s: $i] : ((~c_Natural_Oevalc(c_Com_Ocom_OSemi(V_c1, V_c2), V_s, V_t)) | c_Natural_Oevalc(V_c2, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(V_c1, V_c2, V_s, V_t), V_t))),
% 24.89/25.06      inference(skolemize,[status(sab)],[34])).
% 24.89/25.06  tff(36,plain,
% 24.89/25.06      (![V_t: $i, V_c2: $i, V_c1: $i, V_s: $i] : ((~c_Natural_Oevalc(c_Com_Ocom_OSemi(V_c1, V_c2), V_s, V_t)) | c_Natural_Oevalc(V_c2, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(V_c1, V_c2, V_s, V_t), V_t))),
% 24.89/25.06      inference(modus_ponens,[status(thm)],[35, 28])).
% 24.89/25.06  tff(37,plain,
% 24.89/25.06      (((~![V_t: $i, V_c2: $i, V_c1: $i, V_s: $i] : ((~c_Natural_Oevalc(c_Com_Ocom_OSemi(V_c1, V_c2), V_s, V_t)) | c_Natural_Oevalc(V_c2, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(V_c1, V_c2, V_s, V_t), V_t))) | ((~c_Natural_Oevalc(c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP), v_Z, v_Z)) | c_Natural_Oevalc(c_Com_Ocom_OSKIP, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z))) <=> ((~![V_t: $i, V_c2: $i, V_c1: $i, V_s: $i] : ((~c_Natural_Oevalc(c_Com_Ocom_OSemi(V_c1, V_c2), V_s, V_t)) | c_Natural_Oevalc(V_c2, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(V_c1, V_c2, V_s, V_t), V_t))) | (~c_Natural_Oevalc(c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP), v_Z, v_Z)) | c_Natural_Oevalc(c_Com_Ocom_OSKIP, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z))),
% 24.89/25.06      inference(rewrite,[status(thm)],[])).
% 24.89/25.06  tff(38,plain,
% 24.89/25.06      ((~![V_t: $i, V_c2: $i, V_c1: $i, V_s: $i] : ((~c_Natural_Oevalc(c_Com_Ocom_OSemi(V_c1, V_c2), V_s, V_t)) | c_Natural_Oevalc(V_c2, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(V_c1, V_c2, V_s, V_t), V_t))) | ((~c_Natural_Oevalc(c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP), v_Z, v_Z)) | c_Natural_Oevalc(c_Com_Ocom_OSKIP, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z))),
% 24.89/25.06      inference(quant_inst,[status(thm)],[])).
% 24.89/25.06  tff(39,plain,
% 24.89/25.06      ((~![V_t: $i, V_c2: $i, V_c1: $i, V_s: $i] : ((~c_Natural_Oevalc(c_Com_Ocom_OSemi(V_c1, V_c2), V_s, V_t)) | c_Natural_Oevalc(V_c2, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(V_c1, V_c2, V_s, V_t), V_t))) | (~c_Natural_Oevalc(c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP), v_Z, v_Z)) | c_Natural_Oevalc(c_Com_Ocom_OSKIP, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z)),
% 24.89/25.06      inference(modus_ponens,[status(thm)],[38, 37])).
% 24.89/25.06  tff(40,plain,
% 24.89/25.06      (c_Natural_Oevalc(c_Com_Ocom_OSKIP, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z)),
% 24.89/25.06      inference(unit_resolution,[status(thm)],[39, 36, 26])).
% 24.89/25.06  tff(41,plain,
% 24.89/25.06      (^[V_t: $i, V_s: $i] : refl(((V_t = V_s) | (~c_Natural_Oevalc(c_Com_Ocom_OSKIP, V_s, V_t))) <=> ((V_t = V_s) | (~c_Natural_Oevalc(c_Com_Ocom_OSKIP, V_s, V_t))))),
% 24.89/25.06      inference(bind,[status(th)],[])).
% 24.89/25.06  tff(42,plain,
% 24.89/25.06      (![V_t: $i, V_s: $i] : ((V_t = V_s) | (~c_Natural_Oevalc(c_Com_Ocom_OSKIP, V_s, V_t))) <=> ![V_t: $i, V_s: $i] : ((V_t = V_s) | (~c_Natural_Oevalc(c_Com_Ocom_OSKIP, V_s, V_t)))),
% 24.89/25.06      inference(quant_intro,[status(thm)],[41])).
% 24.89/25.06  tff(43,plain,
% 24.89/25.06      (![V_t: $i, V_s: $i] : ((V_t = V_s) | (~c_Natural_Oevalc(c_Com_Ocom_OSKIP, V_s, V_t))) <=> ![V_t: $i, V_s: $i] : ((V_t = V_s) | (~c_Natural_Oevalc(c_Com_Ocom_OSKIP, V_s, V_t)))),
% 24.89/25.06      inference(rewrite,[status(thm)],[])).
% 24.89/25.06  tff(44,axiom,(![V_t: $i, V_s: $i] : ((V_t = V_s) | (~c_Natural_Oevalc(c_Com_Ocom_OSKIP, V_s, V_t)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_evalc__elim__cases_I1_J_0')).
% 24.89/25.06  tff(45,plain,
% 24.89/25.06      (![V_t: $i, V_s: $i] : ((V_t = V_s) | (~c_Natural_Oevalc(c_Com_Ocom_OSKIP, V_s, V_t)))),
% 24.89/25.06      inference(modus_ponens,[status(thm)],[44, 43])).
% 24.89/25.06  tff(46,plain,(
% 24.89/25.06      ![V_t: $i, V_s: $i] : ((V_t = V_s) | (~c_Natural_Oevalc(c_Com_Ocom_OSKIP, V_s, V_t)))),
% 24.89/25.06      inference(skolemize,[status(sab)],[45])).
% 24.89/25.06  tff(47,plain,
% 24.89/25.06      (![V_t: $i, V_s: $i] : ((V_t = V_s) | (~c_Natural_Oevalc(c_Com_Ocom_OSKIP, V_s, V_t)))),
% 24.89/25.06      inference(modus_ponens,[status(thm)],[46, 42])).
% 24.89/25.06  tff(48,plain,
% 24.89/25.06      (((~![V_t: $i, V_s: $i] : ((V_t = V_s) | (~c_Natural_Oevalc(c_Com_Ocom_OSKIP, V_s, V_t)))) | ((~c_Natural_Oevalc(c_Com_Ocom_OSKIP, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z)) | (v_Z = c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z)))) <=> ((~![V_t: $i, V_s: $i] : ((V_t = V_s) | (~c_Natural_Oevalc(c_Com_Ocom_OSKIP, V_s, V_t)))) | (~c_Natural_Oevalc(c_Com_Ocom_OSKIP, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z)) | (v_Z = c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z)))),
% 24.89/25.06      inference(rewrite,[status(thm)],[])).
% 24.89/25.06  tff(49,plain,
% 24.89/25.06      (((v_Z = c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z)) | (~c_Natural_Oevalc(c_Com_Ocom_OSKIP, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z))) <=> ((~c_Natural_Oevalc(c_Com_Ocom_OSKIP, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z)) | (v_Z = c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z)))),
% 24.89/25.06      inference(rewrite,[status(thm)],[])).
% 24.89/25.06  tff(50,plain,
% 24.89/25.06      (((~![V_t: $i, V_s: $i] : ((V_t = V_s) | (~c_Natural_Oevalc(c_Com_Ocom_OSKIP, V_s, V_t)))) | ((v_Z = c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z)) | (~c_Natural_Oevalc(c_Com_Ocom_OSKIP, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z)))) <=> ((~![V_t: $i, V_s: $i] : ((V_t = V_s) | (~c_Natural_Oevalc(c_Com_Ocom_OSKIP, V_s, V_t)))) | ((~c_Natural_Oevalc(c_Com_Ocom_OSKIP, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z)) | (v_Z = c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z))))),
% 24.89/25.06      inference(monotonicity,[status(thm)],[49])).
% 24.89/25.06  tff(51,plain,
% 24.89/25.06      (((~![V_t: $i, V_s: $i] : ((V_t = V_s) | (~c_Natural_Oevalc(c_Com_Ocom_OSKIP, V_s, V_t)))) | ((v_Z = c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z)) | (~c_Natural_Oevalc(c_Com_Ocom_OSKIP, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z)))) <=> ((~![V_t: $i, V_s: $i] : ((V_t = V_s) | (~c_Natural_Oevalc(c_Com_Ocom_OSKIP, V_s, V_t)))) | (~c_Natural_Oevalc(c_Com_Ocom_OSKIP, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z)) | (v_Z = c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z)))),
% 24.89/25.06      inference(transitivity,[status(thm)],[50, 48])).
% 24.89/25.06  tff(52,plain,
% 24.89/25.06      ((~![V_t: $i, V_s: $i] : ((V_t = V_s) | (~c_Natural_Oevalc(c_Com_Ocom_OSKIP, V_s, V_t)))) | ((v_Z = c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z)) | (~c_Natural_Oevalc(c_Com_Ocom_OSKIP, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z)))),
% 24.89/25.06      inference(quant_inst,[status(thm)],[])).
% 24.89/25.06  tff(53,plain,
% 24.89/25.06      ((~![V_t: $i, V_s: $i] : ((V_t = V_s) | (~c_Natural_Oevalc(c_Com_Ocom_OSKIP, V_s, V_t)))) | (~c_Natural_Oevalc(c_Com_Ocom_OSKIP, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z)) | (v_Z = c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z))),
% 24.89/25.06      inference(modus_ponens,[status(thm)],[52, 51])).
% 24.89/25.06  tff(54,plain,
% 24.89/25.06      (v_Z = c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z)),
% 24.89/25.06      inference(unit_resolution,[status(thm)],[53, 47, 40])).
% 24.89/25.06  tff(55,plain,
% 24.89/25.06      (c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z) = v_Z),
% 24.89/25.06      inference(symmetry,[status(thm)],[54])).
% 24.89/25.06  tff(56,plain,
% 24.89/25.06      ((c_Com_Ocom_OSemi(v_s_H, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP)) = c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z))) <=> (c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z)) = c_Com_Ocom_OSemi(v_s_H, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP)))),
% 24.89/25.06      inference(commutativity,[status(thm)],[])).
% 24.89/25.06  tff(57,plain,
% 24.89/25.06      ((c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z)) = c_Com_Ocom_OSemi(v_s_H, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP))) <=> (c_Com_Ocom_OSemi(v_s_H, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP)) = c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z)))),
% 24.89/25.06      inference(symmetry,[status(thm)],[56])).
% 24.89/25.06  tff(58,plain,
% 24.89/25.06      (c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP))))) <=> c_Natural_Oevalc(v_c, v_Z, v_Z_H(v_Z_H(c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP)))))),
% 24.89/25.06      inference(monotonicity,[status(thm)],[55])).
% 24.89/25.06  tff(59,plain,
% 24.89/25.06      (c_Natural_Oevalc(v_c, v_Z, v_Z_H(v_Z_H(c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP))))) <=> c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP)))))),
% 24.89/25.06      inference(symmetry,[status(thm)],[58])).
% 24.89/25.06  tff(60,assumption,(c_Natural_Oevalc(v_c, v_Z, v_Z_H(c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP))))), introduced(assumption)).
% 24.89/25.06  tff(61,assumption,(v_Z_H(c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP))) = v_s_H), introduced(assumption)).
% 24.89/25.06  tff(62,plain,
% 24.89/25.06      (c_Natural_Oevalc(v_c, v_Z, v_Z_H(c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP)))) <=> c_Natural_Oevalc(v_c, v_Z, v_s_H)),
% 24.89/25.06      inference(monotonicity,[status(thm)],[61])).
% 24.89/25.06  tff(63,plain,
% 24.89/25.06      (c_Natural_Oevalc(v_c, v_Z, v_s_H) <=> c_Natural_Oevalc(v_c, v_Z, v_Z_H(c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP))))),
% 24.89/25.06      inference(symmetry,[status(thm)],[62])).
% 24.89/25.06  tff(64,plain,
% 24.89/25.06      ((~c_Natural_Oevalc(v_c, v_Z, v_s_H)) <=> (~c_Natural_Oevalc(v_c, v_Z, v_Z_H(c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP)))))),
% 24.89/25.07      inference(monotonicity,[status(thm)],[63])).
% 24.89/25.07  tff(65,plain,
% 24.89/25.07      ((~c_Natural_Oevalc(v_c, v_Z, v_s_H)) <=> (~c_Natural_Oevalc(v_c, v_Z, v_s_H))),
% 24.89/25.07      inference(rewrite,[status(thm)],[])).
% 24.89/25.07  tff(66,axiom,(~c_Natural_Oevalc(v_c, v_Z, v_s_H)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_1')).
% 24.89/25.07  tff(67,plain,
% 24.89/25.07      (~c_Natural_Oevalc(v_c, v_Z, v_s_H)),
% 24.89/25.07      inference(modus_ponens,[status(thm)],[66, 65])).
% 24.89/25.07  tff(68,plain,
% 24.89/25.07      (~c_Natural_Oevalc(v_c, v_Z, v_Z_H(c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP))))),
% 24.89/25.07      inference(modus_ponens,[status(thm)],[67, 64])).
% 24.89/25.07  tff(69,plain,
% 24.89/25.07      ($false),
% 24.89/25.07      inference(unit_resolution,[status(thm)],[60, 68])).
% 24.89/25.07  tff(70,plain,((~(v_Z_H(c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP))) = v_s_H)) | (~c_Natural_Oevalc(v_c, v_Z, v_Z_H(c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP)))))), inference(lemma,lemma(discharge,[]))).
% 24.89/25.07  tff(71,plain,
% 24.89/25.07      (~(v_Z_H(c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP))) = v_s_H)),
% 24.89/25.07      inference(unit_resolution,[status(thm)],[70, 60])).
% 24.89/25.07  tff(72,plain,
% 24.89/25.07      (^[V_Z_Ha: $i] : refl(((V_Z_Ha = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(V_Z_Ha))) <=> ((V_Z_Ha = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(V_Z_Ha))))),
% 24.89/25.07      inference(bind,[status(th)],[])).
% 24.89/25.07  tff(73,plain,
% 24.89/25.07      (![V_Z_Ha: $i] : ((V_Z_Ha = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(V_Z_Ha))) <=> ![V_Z_Ha: $i] : ((V_Z_Ha = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(V_Z_Ha)))),
% 24.89/25.07      inference(quant_intro,[status(thm)],[72])).
% 24.89/25.07  tff(74,plain,
% 24.89/25.07      (![V_Z_Ha: $i] : ((V_Z_Ha = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(V_Z_Ha))) <=> ![V_Z_Ha: $i] : ((V_Z_Ha = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(V_Z_Ha)))),
% 24.89/25.07      inference(rewrite,[status(thm)],[])).
% 24.89/25.07  tff(75,axiom,(![V_Z_Ha: $i] : ((V_Z_Ha = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(V_Z_Ha)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_3')).
% 24.89/25.07  tff(76,plain,
% 24.89/25.07      (![V_Z_Ha: $i] : ((V_Z_Ha = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(V_Z_Ha)))),
% 24.89/25.07      inference(modus_ponens,[status(thm)],[75, 74])).
% 24.89/25.07  tff(77,plain,(
% 24.89/25.07      ![V_Z_Ha: $i] : ((V_Z_Ha = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(V_Z_Ha)))),
% 24.89/25.07      inference(skolemize,[status(sab)],[76])).
% 24.89/25.07  tff(78,plain,
% 24.89/25.07      (![V_Z_Ha: $i] : ((V_Z_Ha = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(V_Z_Ha)))),
% 24.89/25.07      inference(modus_ponens,[status(thm)],[77, 73])).
% 24.89/25.07  tff(79,plain,
% 24.89/25.07      (((~![V_Z_Ha: $i] : ((V_Z_Ha = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(V_Z_Ha)))) | ((v_Z_H(c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP))) = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(v_Z_H(c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP))))))) <=> ((~![V_Z_Ha: $i] : ((V_Z_Ha = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(V_Z_Ha)))) | (v_Z_H(c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP))) = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(v_Z_H(c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP))))))),
% 24.89/25.07      inference(rewrite,[status(thm)],[])).
% 24.89/25.07  tff(80,plain,
% 24.89/25.07      ((~![V_Z_Ha: $i] : ((V_Z_Ha = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(V_Z_Ha)))) | ((v_Z_H(c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP))) = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(v_Z_H(c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP))))))),
% 24.89/25.07      inference(quant_inst,[status(thm)],[])).
% 24.89/25.07  tff(81,plain,
% 24.89/25.07      ((~![V_Z_Ha: $i] : ((V_Z_Ha = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(V_Z_Ha)))) | (v_Z_H(c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP))) = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(v_Z_H(c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP)))))),
% 24.89/25.07      inference(modus_ponens,[status(thm)],[80, 79])).
% 24.89/25.07  tff(82,plain,
% 24.89/25.07      (c_Natural_Oevalc(v_c, v_Z, v_Z_H(v_Z_H(c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP)))))),
% 24.89/25.07      inference(unit_resolution,[status(thm)],[81, 78, 71])).
% 24.89/25.07  tff(83,plain,
% 24.89/25.07      (c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP)))))),
% 24.89/25.07      inference(modus_ponens,[status(thm)],[82, 59])).
% 24.89/25.07  tff(84,plain,
% 24.89/25.07      (^[V_Z_Ha: $i] : refl(((~(V_Z_Ha = v_Z_H(V_Z_Ha))) | (V_Z_Ha = v_s_H)) <=> ((~(V_Z_Ha = v_Z_H(V_Z_Ha))) | (V_Z_Ha = v_s_H)))),
% 24.89/25.07      inference(bind,[status(th)],[])).
% 24.89/25.07  tff(85,plain,
% 24.89/25.07      (![V_Z_Ha: $i] : ((~(V_Z_Ha = v_Z_H(V_Z_Ha))) | (V_Z_Ha = v_s_H)) <=> ![V_Z_Ha: $i] : ((~(V_Z_Ha = v_Z_H(V_Z_Ha))) | (V_Z_Ha = v_s_H))),
% 24.89/25.07      inference(quant_intro,[status(thm)],[84])).
% 24.89/25.07  tff(86,plain,
% 24.89/25.07      (![V_Z_Ha: $i] : ((~(V_Z_Ha = v_Z_H(V_Z_Ha))) | (V_Z_Ha = v_s_H)) <=> ![V_Z_Ha: $i] : ((~(V_Z_Ha = v_Z_H(V_Z_Ha))) | (V_Z_Ha = v_s_H))),
% 24.89/25.07      inference(rewrite,[status(thm)],[])).
% 24.89/25.07  tff(87,axiom,(![V_Z_Ha: $i] : ((~(V_Z_Ha = v_Z_H(V_Z_Ha))) | (V_Z_Ha = v_s_H))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_4')).
% 24.89/25.07  tff(88,plain,
% 24.89/25.07      (![V_Z_Ha: $i] : ((~(V_Z_Ha = v_Z_H(V_Z_Ha))) | (V_Z_Ha = v_s_H))),
% 24.89/25.07      inference(modus_ponens,[status(thm)],[87, 86])).
% 24.89/25.07  tff(89,plain,(
% 24.89/25.07      ![V_Z_Ha: $i] : ((~(V_Z_Ha = v_Z_H(V_Z_Ha))) | (V_Z_Ha = v_s_H))),
% 24.89/25.07      inference(skolemize,[status(sab)],[88])).
% 24.89/25.07  tff(90,plain,
% 24.89/25.07      (![V_Z_Ha: $i] : ((~(V_Z_Ha = v_Z_H(V_Z_Ha))) | (V_Z_Ha = v_s_H))),
% 24.89/25.07      inference(modus_ponens,[status(thm)],[89, 85])).
% 24.89/25.07  tff(91,plain,
% 24.89/25.07      (((~![V_Z_Ha: $i] : ((~(V_Z_Ha = v_Z_H(V_Z_Ha))) | (V_Z_Ha = v_s_H))) | ((~(v_Z_H(c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP))) = v_Z_H(v_Z_H(c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP)))))) | (v_Z_H(c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP))) = v_s_H))) <=> ((~![V_Z_Ha: $i] : ((~(V_Z_Ha = v_Z_H(V_Z_Ha))) | (V_Z_Ha = v_s_H))) | (~(v_Z_H(c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP))) = v_Z_H(v_Z_H(c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP)))))) | (v_Z_H(c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP))) = v_s_H))),
% 24.89/25.07      inference(rewrite,[status(thm)],[])).
% 24.89/25.07  tff(92,plain,
% 24.89/25.07      ((~![V_Z_Ha: $i] : ((~(V_Z_Ha = v_Z_H(V_Z_Ha))) | (V_Z_Ha = v_s_H))) | ((~(v_Z_H(c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP))) = v_Z_H(v_Z_H(c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP)))))) | (v_Z_H(c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP))) = v_s_H))),
% 24.89/25.07      inference(quant_inst,[status(thm)],[])).
% 24.89/25.07  tff(93,plain,
% 24.89/25.07      ((~![V_Z_Ha: $i] : ((~(V_Z_Ha = v_Z_H(V_Z_Ha))) | (V_Z_Ha = v_s_H))) | (~(v_Z_H(c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP))) = v_Z_H(v_Z_H(c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP)))))) | (v_Z_H(c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP))) = v_s_H)),
% 24.89/25.07      inference(modus_ponens,[status(thm)],[92, 91])).
% 24.89/25.07  tff(94,plain,
% 24.89/25.07      ((~(v_Z_H(c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP))) = v_Z_H(v_Z_H(c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP)))))) | (v_Z_H(c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP))) = v_s_H)),
% 24.89/25.07      inference(unit_resolution,[status(thm)],[93, 90])).
% 24.89/25.07  tff(95,plain,
% 24.89/25.07      (~(v_Z_H(c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP))) = v_Z_H(v_Z_H(c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP)))))),
% 24.89/25.07      inference(unit_resolution,[status(thm)],[94, 71])).
% 24.89/25.07  tff(96,plain,
% 24.89/25.07      (c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP)))) <=> c_Natural_Oevalc(v_c, v_Z, v_Z_H(c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP))))),
% 24.89/25.07      inference(monotonicity,[status(thm)],[55])).
% 24.89/25.07  tff(97,plain,
% 24.89/25.07      (c_Natural_Oevalc(v_c, v_Z, v_Z_H(c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP)))) <=> c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP))))),
% 24.89/25.07      inference(symmetry,[status(thm)],[96])).
% 24.89/25.07  tff(98,plain,
% 24.89/25.07      (c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP))))),
% 24.89/25.07      inference(modus_ponens,[status(thm)],[60, 97])).
% 24.89/25.07  tff(99,plain,
% 24.89/25.07      (^[V_c: $i, V_u: $i, V_t: $i, V_s: $i] : refl(((~c_Natural_Oevalc(V_c, V_s, V_t)) | (~c_Natural_Oevalc(V_c, V_s, V_u)) | (V_u = V_t)) <=> ((~c_Natural_Oevalc(V_c, V_s, V_t)) | (~c_Natural_Oevalc(V_c, V_s, V_u)) | (V_u = V_t)))),
% 24.89/25.07      inference(bind,[status(th)],[])).
% 24.89/25.07  tff(100,plain,
% 24.89/25.07      (![V_c: $i, V_u: $i, V_t: $i, V_s: $i] : ((~c_Natural_Oevalc(V_c, V_s, V_t)) | (~c_Natural_Oevalc(V_c, V_s, V_u)) | (V_u = V_t)) <=> ![V_c: $i, V_u: $i, V_t: $i, V_s: $i] : ((~c_Natural_Oevalc(V_c, V_s, V_t)) | (~c_Natural_Oevalc(V_c, V_s, V_u)) | (V_u = V_t))),
% 24.89/25.07      inference(quant_intro,[status(thm)],[99])).
% 24.89/25.07  tff(101,plain,
% 24.89/25.07      (![V_c: $i, V_u: $i, V_t: $i, V_s: $i] : ((~c_Natural_Oevalc(V_c, V_s, V_t)) | (~c_Natural_Oevalc(V_c, V_s, V_u)) | (V_u = V_t)) <=> ![V_c: $i, V_u: $i, V_t: $i, V_s: $i] : ((~c_Natural_Oevalc(V_c, V_s, V_t)) | (~c_Natural_Oevalc(V_c, V_s, V_u)) | (V_u = V_t))),
% 24.89/25.07      inference(rewrite,[status(thm)],[])).
% 24.89/25.07  tff(102,plain,
% 24.89/25.07      (^[V_c: $i, V_u: $i, V_t: $i, V_s: $i] : trans(monotonicity(rewrite(((V_u = V_t) | (~c_Natural_Oevalc(V_c, V_s, V_u))) <=> ((~c_Natural_Oevalc(V_c, V_s, V_u)) | (V_u = V_t))), ((((V_u = V_t) | (~c_Natural_Oevalc(V_c, V_s, V_u))) | (~c_Natural_Oevalc(V_c, V_s, V_t))) <=> (((~c_Natural_Oevalc(V_c, V_s, V_u)) | (V_u = V_t)) | (~c_Natural_Oevalc(V_c, V_s, V_t))))), rewrite((((~c_Natural_Oevalc(V_c, V_s, V_u)) | (V_u = V_t)) | (~c_Natural_Oevalc(V_c, V_s, V_t))) <=> ((~c_Natural_Oevalc(V_c, V_s, V_t)) | (~c_Natural_Oevalc(V_c, V_s, V_u)) | (V_u = V_t))), ((((V_u = V_t) | (~c_Natural_Oevalc(V_c, V_s, V_u))) | (~c_Natural_Oevalc(V_c, V_s, V_t))) <=> ((~c_Natural_Oevalc(V_c, V_s, V_t)) | (~c_Natural_Oevalc(V_c, V_s, V_u)) | (V_u = V_t))))),
% 24.89/25.07      inference(bind,[status(th)],[])).
% 24.89/25.07  tff(103,plain,
% 24.89/25.07      (![V_c: $i, V_u: $i, V_t: $i, V_s: $i] : (((V_u = V_t) | (~c_Natural_Oevalc(V_c, V_s, V_u))) | (~c_Natural_Oevalc(V_c, V_s, V_t))) <=> ![V_c: $i, V_u: $i, V_t: $i, V_s: $i] : ((~c_Natural_Oevalc(V_c, V_s, V_t)) | (~c_Natural_Oevalc(V_c, V_s, V_u)) | (V_u = V_t))),
% 24.89/25.07      inference(quant_intro,[status(thm)],[102])).
% 24.89/25.07  tff(104,axiom,(![V_c: $i, V_u: $i, V_t: $i, V_s: $i] : (((V_u = V_t) | (~c_Natural_Oevalc(V_c, V_s, V_u))) | (~c_Natural_Oevalc(V_c, V_s, V_t)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_com__det_0')).
% 24.89/25.07  tff(105,plain,
% 24.89/25.07      (![V_c: $i, V_u: $i, V_t: $i, V_s: $i] : ((~c_Natural_Oevalc(V_c, V_s, V_t)) | (~c_Natural_Oevalc(V_c, V_s, V_u)) | (V_u = V_t))),
% 24.89/25.07      inference(modus_ponens,[status(thm)],[104, 103])).
% 24.89/25.07  tff(106,plain,
% 24.89/25.07      (![V_c: $i, V_u: $i, V_t: $i, V_s: $i] : ((~c_Natural_Oevalc(V_c, V_s, V_t)) | (~c_Natural_Oevalc(V_c, V_s, V_u)) | (V_u = V_t))),
% 24.89/25.07      inference(modus_ponens,[status(thm)],[105, 101])).
% 24.89/25.07  tff(107,plain,(
% 24.89/25.07      ![V_c: $i, V_u: $i, V_t: $i, V_s: $i] : ((~c_Natural_Oevalc(V_c, V_s, V_t)) | (~c_Natural_Oevalc(V_c, V_s, V_u)) | (V_u = V_t))),
% 24.89/25.07      inference(skolemize,[status(sab)],[106])).
% 24.89/25.07  tff(108,plain,
% 24.89/25.07      (![V_c: $i, V_u: $i, V_t: $i, V_s: $i] : ((~c_Natural_Oevalc(V_c, V_s, V_t)) | (~c_Natural_Oevalc(V_c, V_s, V_u)) | (V_u = V_t))),
% 24.89/25.07      inference(modus_ponens,[status(thm)],[107, 100])).
% 24.89/25.07  tff(109,plain,
% 24.89/25.07      (((~![V_c: $i, V_u: $i, V_t: $i, V_s: $i] : ((~c_Natural_Oevalc(V_c, V_s, V_t)) | (~c_Natural_Oevalc(V_c, V_s, V_u)) | (V_u = V_t))) | ((~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP))))) | (~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP)))))) | (v_Z_H(c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP))) = v_Z_H(v_Z_H(c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP))))))) <=> ((~![V_c: $i, V_u: $i, V_t: $i, V_s: $i] : ((~c_Natural_Oevalc(V_c, V_s, V_t)) | (~c_Natural_Oevalc(V_c, V_s, V_u)) | (V_u = V_t))) | (~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP))))) | (~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP)))))) | (v_Z_H(c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP))) = v_Z_H(v_Z_H(c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP))))))),
% 24.89/25.07      inference(rewrite,[status(thm)],[])).
% 24.89/25.07  tff(110,plain,
% 24.89/25.07      (((~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP)))))) | (~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP))))) | (v_Z_H(c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP))) = v_Z_H(v_Z_H(c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP)))))) <=> ((~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP))))) | (~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP)))))) | (v_Z_H(c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP))) = v_Z_H(v_Z_H(c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP))))))),
% 24.89/25.07      inference(rewrite,[status(thm)],[])).
% 24.89/25.07  tff(111,plain,
% 24.89/25.07      (((~![V_c: $i, V_u: $i, V_t: $i, V_s: $i] : ((~c_Natural_Oevalc(V_c, V_s, V_t)) | (~c_Natural_Oevalc(V_c, V_s, V_u)) | (V_u = V_t))) | ((~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP)))))) | (~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP))))) | (v_Z_H(c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP))) = v_Z_H(v_Z_H(c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP))))))) <=> ((~![V_c: $i, V_u: $i, V_t: $i, V_s: $i] : ((~c_Natural_Oevalc(V_c, V_s, V_t)) | (~c_Natural_Oevalc(V_c, V_s, V_u)) | (V_u = V_t))) | ((~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP))))) | (~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP)))))) | (v_Z_H(c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP))) = v_Z_H(v_Z_H(c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP)))))))),
% 24.89/25.07      inference(monotonicity,[status(thm)],[110])).
% 24.89/25.07  tff(112,plain,
% 24.89/25.07      (((~![V_c: $i, V_u: $i, V_t: $i, V_s: $i] : ((~c_Natural_Oevalc(V_c, V_s, V_t)) | (~c_Natural_Oevalc(V_c, V_s, V_u)) | (V_u = V_t))) | ((~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP)))))) | (~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP))))) | (v_Z_H(c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP))) = v_Z_H(v_Z_H(c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP))))))) <=> ((~![V_c: $i, V_u: $i, V_t: $i, V_s: $i] : ((~c_Natural_Oevalc(V_c, V_s, V_t)) | (~c_Natural_Oevalc(V_c, V_s, V_u)) | (V_u = V_t))) | (~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP))))) | (~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP)))))) | (v_Z_H(c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP))) = v_Z_H(v_Z_H(c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP))))))),
% 24.89/25.07      inference(transitivity,[status(thm)],[111, 109])).
% 24.89/25.07  tff(113,plain,
% 24.89/25.07      ((~![V_c: $i, V_u: $i, V_t: $i, V_s: $i] : ((~c_Natural_Oevalc(V_c, V_s, V_t)) | (~c_Natural_Oevalc(V_c, V_s, V_u)) | (V_u = V_t))) | ((~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP)))))) | (~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP))))) | (v_Z_H(c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP))) = v_Z_H(v_Z_H(c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP))))))),
% 24.89/25.07      inference(quant_inst,[status(thm)],[])).
% 24.89/25.07  tff(114,plain,
% 24.89/25.07      ((~![V_c: $i, V_u: $i, V_t: $i, V_s: $i] : ((~c_Natural_Oevalc(V_c, V_s, V_t)) | (~c_Natural_Oevalc(V_c, V_s, V_u)) | (V_u = V_t))) | (~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP))))) | (~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP)))))) | (v_Z_H(c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP))) = v_Z_H(v_Z_H(c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP)))))),
% 24.89/25.07      inference(modus_ponens,[status(thm)],[113, 112])).
% 24.89/25.07  tff(115,plain,
% 24.89/25.07      (~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP)))))),
% 24.89/25.07      inference(unit_resolution,[status(thm)],[114, 108, 98, 95])).
% 24.89/25.07  tff(116,plain,
% 24.89/25.07      ($false),
% 24.89/25.07      inference(unit_resolution,[status(thm)],[115, 83])).
% 24.89/25.07  tff(117,plain,(~c_Natural_Oevalc(v_c, v_Z, v_Z_H(c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP))))), inference(lemma,lemma(discharge,[]))).
% 24.89/25.07  tff(118,plain,
% 24.89/25.07      (((~![V_Z_Ha: $i] : ((V_Z_Ha = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(V_Z_Ha)))) | ((c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP)) = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP)))))) <=> ((~![V_Z_Ha: $i] : ((V_Z_Ha = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(V_Z_Ha)))) | (c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP)) = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP)))))),
% 24.89/25.07      inference(rewrite,[status(thm)],[])).
% 24.89/25.07  tff(119,plain,
% 24.89/25.07      ((~![V_Z_Ha: $i] : ((V_Z_Ha = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(V_Z_Ha)))) | ((c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP)) = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP)))))),
% 24.89/25.07      inference(quant_inst,[status(thm)],[])).
% 24.89/25.07  tff(120,plain,
% 24.89/25.07      ((~![V_Z_Ha: $i] : ((V_Z_Ha = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(V_Z_Ha)))) | (c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP)) = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP))))),
% 24.89/25.07      inference(modus_ponens,[status(thm)],[119, 118])).
% 24.89/25.07  tff(121,plain,
% 24.89/25.07      ((c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP)) = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP))))),
% 24.89/25.07      inference(unit_resolution,[status(thm)],[120, 78])).
% 24.89/25.07  tff(122,plain,
% 24.89/25.07      (c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP)) = v_s_H),
% 24.89/25.07      inference(unit_resolution,[status(thm)],[121, 117])).
% 24.89/25.07  tff(123,plain,
% 24.89/25.07      (c_Natural_Oevalc(v_c, v_Z, v_Z_H(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2)) <=> c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2))),
% 24.89/25.07      inference(monotonicity,[status(thm)],[54])).
% 24.89/25.07  tff(124,plain,
% 24.89/25.07      (c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2)) <=> c_Natural_Oevalc(v_c, v_Z, v_Z_H(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2))),
% 24.89/25.07      inference(symmetry,[status(thm)],[123])).
% 24.89/25.07  tff(125,plain,
% 24.89/25.07      (c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_t)) <=> c_Natural_Oevalc(v_c, v_Z, v_Z_H(v_t))),
% 24.89/25.07      inference(monotonicity,[status(thm)],[55])).
% 24.89/25.07  tff(126,plain,
% 24.89/25.07      (c_Natural_Oevalc(v_c, v_Z, v_Z_H(v_t)) <=> c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_t))),
% 24.89/25.07      inference(symmetry,[status(thm)],[125])).
% 24.89/25.07  tff(127,assumption,(c_Natural_Oevalc(v_c, v_Z, v_Z_H(v_t))), introduced(assumption)).
% 24.89/25.07  tff(128,plain,
% 24.89/25.07      (c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_t))),
% 24.89/25.07      inference(modus_ponens,[status(thm)],[127, 126])).
% 24.89/25.07  tff(129,plain,
% 24.89/25.07      (c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(v_t))) <=> c_Natural_Oevalc(v_c, v_Z, v_Z_H(v_Z_H(v_t)))),
% 24.89/25.07      inference(monotonicity,[status(thm)],[55])).
% 24.89/25.07  tff(130,plain,
% 24.89/25.07      (c_Natural_Oevalc(v_c, v_Z, v_Z_H(v_Z_H(v_t))) <=> c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(v_t)))),
% 24.89/25.07      inference(symmetry,[status(thm)],[129])).
% 24.89/25.07  tff(131,assumption,(~(v_Z_H(v_t) = v_s_H)), introduced(assumption)).
% 24.89/25.07  tff(132,plain,
% 24.89/25.07      (((~![V_Z_Ha: $i] : ((V_Z_Ha = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(V_Z_Ha)))) | ((v_Z_H(v_t) = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(v_Z_H(v_t))))) <=> ((~![V_Z_Ha: $i] : ((V_Z_Ha = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(V_Z_Ha)))) | (v_Z_H(v_t) = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(v_Z_H(v_t))))),
% 24.89/25.07      inference(rewrite,[status(thm)],[])).
% 24.89/25.07  tff(133,plain,
% 24.89/25.07      ((~![V_Z_Ha: $i] : ((V_Z_Ha = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(V_Z_Ha)))) | ((v_Z_H(v_t) = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(v_Z_H(v_t))))),
% 24.89/25.07      inference(quant_inst,[status(thm)],[])).
% 24.89/25.07  tff(134,plain,
% 24.89/25.07      ((~![V_Z_Ha: $i] : ((V_Z_Ha = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(V_Z_Ha)))) | (v_Z_H(v_t) = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(v_Z_H(v_t)))),
% 24.89/25.07      inference(modus_ponens,[status(thm)],[133, 132])).
% 24.89/25.07  tff(135,plain,
% 24.89/25.07      (c_Natural_Oevalc(v_c, v_Z, v_Z_H(v_Z_H(v_t)))),
% 24.89/25.07      inference(unit_resolution,[status(thm)],[134, 78, 131])).
% 24.89/25.07  tff(136,plain,
% 24.89/25.07      (c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(v_t)))),
% 24.89/25.07      inference(modus_ponens,[status(thm)],[135, 130])).
% 24.89/25.07  tff(137,assumption,(c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_t))), introduced(assumption)).
% 24.89/25.07  tff(138,plain,
% 24.89/25.07      (((~![V_Z_Ha: $i] : ((~(V_Z_Ha = v_Z_H(V_Z_Ha))) | (V_Z_Ha = v_s_H))) | ((~(v_Z_H(v_t) = v_Z_H(v_Z_H(v_t)))) | (v_Z_H(v_t) = v_s_H))) <=> ((~![V_Z_Ha: $i] : ((~(V_Z_Ha = v_Z_H(V_Z_Ha))) | (V_Z_Ha = v_s_H))) | (~(v_Z_H(v_t) = v_Z_H(v_Z_H(v_t)))) | (v_Z_H(v_t) = v_s_H))),
% 24.89/25.07      inference(rewrite,[status(thm)],[])).
% 24.89/25.07  tff(139,plain,
% 24.89/25.07      ((~![V_Z_Ha: $i] : ((~(V_Z_Ha = v_Z_H(V_Z_Ha))) | (V_Z_Ha = v_s_H))) | ((~(v_Z_H(v_t) = v_Z_H(v_Z_H(v_t)))) | (v_Z_H(v_t) = v_s_H))),
% 24.89/25.07      inference(quant_inst,[status(thm)],[])).
% 24.89/25.07  tff(140,plain,
% 24.89/25.07      ((~![V_Z_Ha: $i] : ((~(V_Z_Ha = v_Z_H(V_Z_Ha))) | (V_Z_Ha = v_s_H))) | (~(v_Z_H(v_t) = v_Z_H(v_Z_H(v_t)))) | (v_Z_H(v_t) = v_s_H)),
% 24.89/25.07      inference(modus_ponens,[status(thm)],[139, 138])).
% 24.89/25.07  tff(141,plain,
% 24.89/25.07      ((~(v_Z_H(v_t) = v_Z_H(v_Z_H(v_t)))) | (v_Z_H(v_t) = v_s_H)),
% 24.89/25.07      inference(unit_resolution,[status(thm)],[140, 90])).
% 24.89/25.07  tff(142,plain,
% 24.89/25.07      (~(v_Z_H(v_t) = v_Z_H(v_Z_H(v_t)))),
% 24.89/25.07      inference(unit_resolution,[status(thm)],[141, 131])).
% 24.89/25.07  tff(143,plain,
% 24.89/25.07      (((~![V_c: $i, V_u: $i, V_t: $i, V_s: $i] : ((~c_Natural_Oevalc(V_c, V_s, V_t)) | (~c_Natural_Oevalc(V_c, V_s, V_u)) | (V_u = V_t))) | ((v_Z_H(v_t) = v_Z_H(v_Z_H(v_t))) | (~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_t))) | (~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(v_t)))))) <=> ((~![V_c: $i, V_u: $i, V_t: $i, V_s: $i] : ((~c_Natural_Oevalc(V_c, V_s, V_t)) | (~c_Natural_Oevalc(V_c, V_s, V_u)) | (V_u = V_t))) | (v_Z_H(v_t) = v_Z_H(v_Z_H(v_t))) | (~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_t))) | (~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(v_t)))))),
% 24.89/25.07      inference(rewrite,[status(thm)],[])).
% 24.89/25.07  tff(144,plain,
% 24.89/25.07      (((~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(v_t)))) | (~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_t))) | (v_Z_H(v_t) = v_Z_H(v_Z_H(v_t)))) <=> ((v_Z_H(v_t) = v_Z_H(v_Z_H(v_t))) | (~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_t))) | (~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(v_t)))))),
% 24.89/25.07      inference(rewrite,[status(thm)],[])).
% 24.89/25.07  tff(145,plain,
% 24.89/25.07      (((~![V_c: $i, V_u: $i, V_t: $i, V_s: $i] : ((~c_Natural_Oevalc(V_c, V_s, V_t)) | (~c_Natural_Oevalc(V_c, V_s, V_u)) | (V_u = V_t))) | ((~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(v_t)))) | (~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_t))) | (v_Z_H(v_t) = v_Z_H(v_Z_H(v_t))))) <=> ((~![V_c: $i, V_u: $i, V_t: $i, V_s: $i] : ((~c_Natural_Oevalc(V_c, V_s, V_t)) | (~c_Natural_Oevalc(V_c, V_s, V_u)) | (V_u = V_t))) | ((v_Z_H(v_t) = v_Z_H(v_Z_H(v_t))) | (~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_t))) | (~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(v_t))))))),
% 24.89/25.07      inference(monotonicity,[status(thm)],[144])).
% 24.89/25.07  tff(146,plain,
% 24.89/25.07      (((~![V_c: $i, V_u: $i, V_t: $i, V_s: $i] : ((~c_Natural_Oevalc(V_c, V_s, V_t)) | (~c_Natural_Oevalc(V_c, V_s, V_u)) | (V_u = V_t))) | ((~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(v_t)))) | (~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_t))) | (v_Z_H(v_t) = v_Z_H(v_Z_H(v_t))))) <=> ((~![V_c: $i, V_u: $i, V_t: $i, V_s: $i] : ((~c_Natural_Oevalc(V_c, V_s, V_t)) | (~c_Natural_Oevalc(V_c, V_s, V_u)) | (V_u = V_t))) | (v_Z_H(v_t) = v_Z_H(v_Z_H(v_t))) | (~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_t))) | (~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(v_t)))))),
% 24.89/25.07      inference(transitivity,[status(thm)],[145, 143])).
% 24.89/25.07  tff(147,plain,
% 24.89/25.07      ((~![V_c: $i, V_u: $i, V_t: $i, V_s: $i] : ((~c_Natural_Oevalc(V_c, V_s, V_t)) | (~c_Natural_Oevalc(V_c, V_s, V_u)) | (V_u = V_t))) | ((~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(v_t)))) | (~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_t))) | (v_Z_H(v_t) = v_Z_H(v_Z_H(v_t))))),
% 24.89/25.07      inference(quant_inst,[status(thm)],[])).
% 24.89/25.07  tff(148,plain,
% 24.89/25.07      ((~![V_c: $i, V_u: $i, V_t: $i, V_s: $i] : ((~c_Natural_Oevalc(V_c, V_s, V_t)) | (~c_Natural_Oevalc(V_c, V_s, V_u)) | (V_u = V_t))) | (v_Z_H(v_t) = v_Z_H(v_Z_H(v_t))) | (~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_t))) | (~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(v_t))))),
% 24.89/25.07      inference(modus_ponens,[status(thm)],[147, 146])).
% 24.89/25.07  tff(149,plain,
% 24.89/25.07      (~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(v_t)))),
% 24.89/25.07      inference(unit_resolution,[status(thm)],[148, 108, 142, 137])).
% 24.89/25.07  tff(150,plain,
% 24.89/25.07      ($false),
% 24.89/25.07      inference(unit_resolution,[status(thm)],[149, 136])).
% 24.89/25.07  tff(151,plain,((v_Z_H(v_t) = v_s_H) | (~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_t)))), inference(lemma,lemma(discharge,[]))).
% 24.89/25.07  tff(152,plain,
% 24.89/25.07      (v_Z_H(v_t) = v_s_H),
% 24.89/25.07      inference(unit_resolution,[status(thm)],[151, 128])).
% 24.89/25.07  tff(153,plain,
% 24.89/25.07      (v_s_H = v_Z_H(v_t)),
% 24.89/25.07      inference(symmetry,[status(thm)],[152])).
% 24.89/25.07  tff(154,plain,
% 24.89/25.07      (c_Natural_Oevalc(v_c, v_Z, v_s_H) <=> c_Natural_Oevalc(v_c, v_Z, v_Z_H(v_t))),
% 24.89/25.07      inference(monotonicity,[status(thm)],[153])).
% 24.89/25.07  tff(155,plain,
% 24.89/25.07      (c_Natural_Oevalc(v_c, v_Z, v_Z_H(v_t)) <=> c_Natural_Oevalc(v_c, v_Z, v_s_H)),
% 24.89/25.07      inference(symmetry,[status(thm)],[154])).
% 24.89/25.07  tff(156,plain,
% 24.89/25.07      (c_Natural_Oevalc(v_c, v_Z, v_s_H)),
% 24.89/25.07      inference(modus_ponens,[status(thm)],[127, 155])).
% 24.89/25.07  tff(157,plain,
% 24.89/25.07      ($false),
% 24.89/25.07      inference(unit_resolution,[status(thm)],[67, 156])).
% 24.89/25.07  tff(158,plain,(~c_Natural_Oevalc(v_c, v_Z, v_Z_H(v_t))), inference(lemma,lemma(discharge,[]))).
% 24.89/25.07  tff(159,plain,
% 24.89/25.07      (((~![V_Z_Ha: $i] : ((V_Z_Ha = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(V_Z_Ha)))) | ((v_t = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(v_t)))) <=> ((~![V_Z_Ha: $i] : ((V_Z_Ha = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(V_Z_Ha)))) | (v_t = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(v_t)))),
% 24.89/25.07      inference(rewrite,[status(thm)],[])).
% 24.89/25.07  tff(160,plain,
% 24.89/25.07      ((~![V_Z_Ha: $i] : ((V_Z_Ha = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(V_Z_Ha)))) | ((v_t = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(v_t)))),
% 24.89/25.07      inference(quant_inst,[status(thm)],[])).
% 24.89/25.07  tff(161,plain,
% 24.89/25.07      ((~![V_Z_Ha: $i] : ((V_Z_Ha = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(V_Z_Ha)))) | (v_t = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(v_t))),
% 24.89/25.07      inference(modus_ponens,[status(thm)],[160, 159])).
% 24.89/25.07  tff(162,plain,
% 24.89/25.07      ((v_t = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(v_t))),
% 24.89/25.07      inference(unit_resolution,[status(thm)],[161, 78])).
% 24.89/25.07  tff(163,plain,
% 24.89/25.07      (v_t = v_s_H),
% 24.89/25.07      inference(unit_resolution,[status(thm)],[162, 158])).
% 24.89/25.07  tff(164,plain,
% 24.89/25.07      (v_s_H = v_t),
% 24.89/25.07      inference(symmetry,[status(thm)],[163])).
% 24.89/25.07  tff(165,assumption,(~(v_Z_H(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2) = v_Z_H(v_Z_H(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2)))), introduced(assumption)).
% 24.89/25.07  tff(166,plain,
% 24.89/25.07      (c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(v_Z_H(v_t)))) <=> c_Natural_Oevalc(v_c, v_Z, v_Z_H(v_Z_H(v_Z_H(v_t))))),
% 24.89/25.07      inference(monotonicity,[status(thm)],[55])).
% 24.89/25.07  tff(167,plain,
% 24.89/25.07      (c_Natural_Oevalc(v_c, v_Z, v_Z_H(v_Z_H(v_Z_H(v_t)))) <=> c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(v_Z_H(v_t))))),
% 24.89/25.07      inference(symmetry,[status(thm)],[166])).
% 24.89/25.07  tff(168,assumption,(c_Natural_Oevalc(v_c, v_Z, v_Z_H(v_Z_H(v_t)))), introduced(assumption)).
% 24.89/25.07  tff(169,assumption,(v_Z_H(v_Z_H(v_t)) = v_s_H), introduced(assumption)).
% 24.89/25.07  tff(170,plain,
% 24.89/25.07      (v_s_H = v_Z_H(v_Z_H(v_t))),
% 24.89/25.07      inference(symmetry,[status(thm)],[169])).
% 24.89/25.07  tff(171,plain,
% 24.89/25.07      (c_Natural_Oevalc(v_c, v_Z, v_s_H) <=> c_Natural_Oevalc(v_c, v_Z, v_Z_H(v_Z_H(v_t)))),
% 24.89/25.07      inference(monotonicity,[status(thm)],[170])).
% 24.89/25.07  tff(172,plain,
% 24.89/25.07      (c_Natural_Oevalc(v_c, v_Z, v_Z_H(v_Z_H(v_t))) <=> c_Natural_Oevalc(v_c, v_Z, v_s_H)),
% 24.89/25.07      inference(symmetry,[status(thm)],[171])).
% 24.89/25.07  tff(173,plain,
% 24.89/25.07      (c_Natural_Oevalc(v_c, v_Z, v_s_H)),
% 24.89/25.07      inference(modus_ponens,[status(thm)],[168, 172])).
% 24.89/25.07  tff(174,plain,
% 24.89/25.07      ($false),
% 24.89/25.07      inference(unit_resolution,[status(thm)],[67, 173])).
% 24.89/25.07  tff(175,plain,((~(v_Z_H(v_Z_H(v_t)) = v_s_H)) | (~c_Natural_Oevalc(v_c, v_Z, v_Z_H(v_Z_H(v_t))))), inference(lemma,lemma(discharge,[]))).
% 24.89/25.07  tff(176,plain,
% 24.89/25.07      (~(v_Z_H(v_Z_H(v_t)) = v_s_H)),
% 24.89/25.07      inference(unit_resolution,[status(thm)],[175, 168])).
% 24.89/25.07  tff(177,plain,
% 24.89/25.07      (((~![V_Z_Ha: $i] : ((V_Z_Ha = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(V_Z_Ha)))) | ((v_Z_H(v_Z_H(v_t)) = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(v_Z_H(v_Z_H(v_t)))))) <=> ((~![V_Z_Ha: $i] : ((V_Z_Ha = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(V_Z_Ha)))) | (v_Z_H(v_Z_H(v_t)) = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(v_Z_H(v_Z_H(v_t)))))),
% 24.89/25.07      inference(rewrite,[status(thm)],[])).
% 24.89/25.07  tff(178,plain,
% 24.89/25.07      ((~![V_Z_Ha: $i] : ((V_Z_Ha = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(V_Z_Ha)))) | ((v_Z_H(v_Z_H(v_t)) = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(v_Z_H(v_Z_H(v_t)))))),
% 24.89/25.07      inference(quant_inst,[status(thm)],[])).
% 24.89/25.07  tff(179,plain,
% 24.89/25.07      ((~![V_Z_Ha: $i] : ((V_Z_Ha = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(V_Z_Ha)))) | (v_Z_H(v_Z_H(v_t)) = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(v_Z_H(v_Z_H(v_t))))),
% 24.89/25.08      inference(modus_ponens,[status(thm)],[178, 177])).
% 24.89/25.08  tff(180,plain,
% 24.89/25.08      ((v_Z_H(v_Z_H(v_t)) = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(v_Z_H(v_Z_H(v_t))))),
% 24.89/25.08      inference(unit_resolution,[status(thm)],[179, 78])).
% 24.89/25.08  tff(181,plain,
% 24.89/25.08      (c_Natural_Oevalc(v_c, v_Z, v_Z_H(v_Z_H(v_Z_H(v_t))))),
% 24.89/25.08      inference(unit_resolution,[status(thm)],[180, 176])).
% 24.89/25.08  tff(182,plain,
% 24.89/25.08      (c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(v_Z_H(v_t))))),
% 24.89/25.08      inference(modus_ponens,[status(thm)],[181, 167])).
% 24.89/25.08  tff(183,plain,
% 24.89/25.08      (((~![V_Z_Ha: $i] : ((~(V_Z_Ha = v_Z_H(V_Z_Ha))) | (V_Z_Ha = v_s_H))) | ((~(v_Z_H(v_Z_H(v_t)) = v_Z_H(v_Z_H(v_Z_H(v_t))))) | (v_Z_H(v_Z_H(v_t)) = v_s_H))) <=> ((~![V_Z_Ha: $i] : ((~(V_Z_Ha = v_Z_H(V_Z_Ha))) | (V_Z_Ha = v_s_H))) | (~(v_Z_H(v_Z_H(v_t)) = v_Z_H(v_Z_H(v_Z_H(v_t))))) | (v_Z_H(v_Z_H(v_t)) = v_s_H))),
% 24.89/25.08      inference(rewrite,[status(thm)],[])).
% 24.89/25.08  tff(184,plain,
% 24.89/25.08      ((~![V_Z_Ha: $i] : ((~(V_Z_Ha = v_Z_H(V_Z_Ha))) | (V_Z_Ha = v_s_H))) | ((~(v_Z_H(v_Z_H(v_t)) = v_Z_H(v_Z_H(v_Z_H(v_t))))) | (v_Z_H(v_Z_H(v_t)) = v_s_H))),
% 24.89/25.08      inference(quant_inst,[status(thm)],[])).
% 24.89/25.08  tff(185,plain,
% 24.89/25.08      ((~![V_Z_Ha: $i] : ((~(V_Z_Ha = v_Z_H(V_Z_Ha))) | (V_Z_Ha = v_s_H))) | (~(v_Z_H(v_Z_H(v_t)) = v_Z_H(v_Z_H(v_Z_H(v_t))))) | (v_Z_H(v_Z_H(v_t)) = v_s_H)),
% 24.89/25.08      inference(modus_ponens,[status(thm)],[184, 183])).
% 24.89/25.08  tff(186,plain,
% 24.89/25.08      (~(v_Z_H(v_Z_H(v_t)) = v_Z_H(v_Z_H(v_Z_H(v_t))))),
% 24.89/25.08      inference(unit_resolution,[status(thm)],[185, 90, 176])).
% 24.89/25.08  tff(187,plain,
% 24.89/25.08      (c_Natural_Oevalc(v_c, v_Z, v_Z_H(v_Z_H(v_t))) <=> c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(v_t)))),
% 24.89/25.08      inference(monotonicity,[status(thm)],[54])).
% 24.89/25.08  tff(188,plain,
% 24.89/25.08      (c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(v_t)))),
% 24.89/25.08      inference(modus_ponens,[status(thm)],[168, 187])).
% 24.89/25.08  tff(189,plain,
% 24.89/25.08      (((~![V_c: $i, V_u: $i, V_t: $i, V_s: $i] : ((~c_Natural_Oevalc(V_c, V_s, V_t)) | (~c_Natural_Oevalc(V_c, V_s, V_u)) | (V_u = V_t))) | ((~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(v_t)))) | (~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(v_Z_H(v_t))))) | (v_Z_H(v_Z_H(v_t)) = v_Z_H(v_Z_H(v_Z_H(v_t)))))) <=> ((~![V_c: $i, V_u: $i, V_t: $i, V_s: $i] : ((~c_Natural_Oevalc(V_c, V_s, V_t)) | (~c_Natural_Oevalc(V_c, V_s, V_u)) | (V_u = V_t))) | (~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(v_t)))) | (~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(v_Z_H(v_t))))) | (v_Z_H(v_Z_H(v_t)) = v_Z_H(v_Z_H(v_Z_H(v_t)))))),
% 24.89/25.08      inference(rewrite,[status(thm)],[])).
% 24.89/25.08  tff(190,plain,
% 24.89/25.08      (((~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(v_Z_H(v_t))))) | (~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(v_t)))) | (v_Z_H(v_Z_H(v_t)) = v_Z_H(v_Z_H(v_Z_H(v_t))))) <=> ((~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(v_t)))) | (~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(v_Z_H(v_t))))) | (v_Z_H(v_Z_H(v_t)) = v_Z_H(v_Z_H(v_Z_H(v_t)))))),
% 24.89/25.08      inference(rewrite,[status(thm)],[])).
% 24.89/25.08  tff(191,plain,
% 24.89/25.08      (((~![V_c: $i, V_u: $i, V_t: $i, V_s: $i] : ((~c_Natural_Oevalc(V_c, V_s, V_t)) | (~c_Natural_Oevalc(V_c, V_s, V_u)) | (V_u = V_t))) | ((~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(v_Z_H(v_t))))) | (~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(v_t)))) | (v_Z_H(v_Z_H(v_t)) = v_Z_H(v_Z_H(v_Z_H(v_t)))))) <=> ((~![V_c: $i, V_u: $i, V_t: $i, V_s: $i] : ((~c_Natural_Oevalc(V_c, V_s, V_t)) | (~c_Natural_Oevalc(V_c, V_s, V_u)) | (V_u = V_t))) | ((~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(v_t)))) | (~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(v_Z_H(v_t))))) | (v_Z_H(v_Z_H(v_t)) = v_Z_H(v_Z_H(v_Z_H(v_t))))))),
% 24.89/25.08      inference(monotonicity,[status(thm)],[190])).
% 24.89/25.08  tff(192,plain,
% 24.89/25.08      (((~![V_c: $i, V_u: $i, V_t: $i, V_s: $i] : ((~c_Natural_Oevalc(V_c, V_s, V_t)) | (~c_Natural_Oevalc(V_c, V_s, V_u)) | (V_u = V_t))) | ((~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(v_Z_H(v_t))))) | (~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(v_t)))) | (v_Z_H(v_Z_H(v_t)) = v_Z_H(v_Z_H(v_Z_H(v_t)))))) <=> ((~![V_c: $i, V_u: $i, V_t: $i, V_s: $i] : ((~c_Natural_Oevalc(V_c, V_s, V_t)) | (~c_Natural_Oevalc(V_c, V_s, V_u)) | (V_u = V_t))) | (~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(v_t)))) | (~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(v_Z_H(v_t))))) | (v_Z_H(v_Z_H(v_t)) = v_Z_H(v_Z_H(v_Z_H(v_t)))))),
% 24.89/25.08      inference(transitivity,[status(thm)],[191, 189])).
% 24.89/25.08  tff(193,plain,
% 24.89/25.08      ((~![V_c: $i, V_u: $i, V_t: $i, V_s: $i] : ((~c_Natural_Oevalc(V_c, V_s, V_t)) | (~c_Natural_Oevalc(V_c, V_s, V_u)) | (V_u = V_t))) | ((~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(v_Z_H(v_t))))) | (~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(v_t)))) | (v_Z_H(v_Z_H(v_t)) = v_Z_H(v_Z_H(v_Z_H(v_t)))))),
% 24.89/25.08      inference(quant_inst,[status(thm)],[])).
% 24.89/25.08  tff(194,plain,
% 24.89/25.08      ((~![V_c: $i, V_u: $i, V_t: $i, V_s: $i] : ((~c_Natural_Oevalc(V_c, V_s, V_t)) | (~c_Natural_Oevalc(V_c, V_s, V_u)) | (V_u = V_t))) | (~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(v_t)))) | (~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(v_Z_H(v_t))))) | (v_Z_H(v_Z_H(v_t)) = v_Z_H(v_Z_H(v_Z_H(v_t))))),
% 24.89/25.08      inference(modus_ponens,[status(thm)],[193, 192])).
% 24.89/25.08  tff(195,plain,
% 24.89/25.08      ((~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(v_Z_H(v_t))))) | (v_Z_H(v_Z_H(v_t)) = v_Z_H(v_Z_H(v_Z_H(v_t))))),
% 24.89/25.08      inference(unit_resolution,[status(thm)],[194, 108, 188])).
% 24.89/25.08  tff(196,plain,
% 24.89/25.08      (~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(v_Z_H(v_t))))),
% 24.89/25.08      inference(unit_resolution,[status(thm)],[195, 186])).
% 24.89/25.08  tff(197,plain,
% 24.89/25.08      ($false),
% 24.89/25.08      inference(unit_resolution,[status(thm)],[196, 182])).
% 24.89/25.08  tff(198,plain,(~c_Natural_Oevalc(v_c, v_Z, v_Z_H(v_Z_H(v_t)))), inference(lemma,lemma(discharge,[]))).
% 24.89/25.08  tff(199,plain,
% 24.89/25.08      (v_Z_H(v_t) = v_s_H),
% 24.89/25.08      inference(unit_resolution,[status(thm)],[134, 78, 198])).
% 24.89/25.08  tff(200,plain,
% 24.89/25.08      ((~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2))) <=> (~c_Natural_Oevalc(v_c, v_Z, v_Z_H(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2)))),
% 24.89/25.08      inference(monotonicity,[status(thm)],[124])).
% 24.89/25.08  tff(201,plain,
% 24.89/25.08      (c_Natural_Oevalc(v_c, v_Z, v_Z_H(v_Z_H(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2))) <=> c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2)))),
% 24.89/25.08      inference(monotonicity,[status(thm)],[54])).
% 24.89/25.08  tff(202,assumption,(~(v_Z_H(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2) = v_s_H)), introduced(assumption)).
% 24.89/25.08  tff(203,plain,
% 24.89/25.08      (((~![V_Z_Ha: $i] : ((V_Z_Ha = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(V_Z_Ha)))) | ((v_Z_H(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2) = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(v_Z_H(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2))))) <=> ((~![V_Z_Ha: $i] : ((V_Z_Ha = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(V_Z_Ha)))) | (v_Z_H(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2) = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(v_Z_H(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2))))),
% 24.89/25.08      inference(rewrite,[status(thm)],[])).
% 24.89/25.08  tff(204,plain,
% 24.89/25.08      ((~![V_Z_Ha: $i] : ((V_Z_Ha = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(V_Z_Ha)))) | ((v_Z_H(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2) = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(v_Z_H(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2))))),
% 24.89/25.08      inference(quant_inst,[status(thm)],[])).
% 24.89/25.08  tff(205,plain,
% 24.89/25.08      ((~![V_Z_Ha: $i] : ((V_Z_Ha = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(V_Z_Ha)))) | (v_Z_H(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2) = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(v_Z_H(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2)))),
% 24.89/25.08      inference(modus_ponens,[status(thm)],[204, 203])).
% 24.89/25.08  tff(206,plain,
% 24.89/25.08      ((v_Z_H(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2) = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(v_Z_H(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2)))),
% 24.89/25.08      inference(unit_resolution,[status(thm)],[205, 78])).
% 24.89/25.08  tff(207,plain,
% 24.89/25.08      (c_Natural_Oevalc(v_c, v_Z, v_Z_H(v_Z_H(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2)))),
% 24.89/25.08      inference(unit_resolution,[status(thm)],[206, 202])).
% 24.89/25.08  tff(208,plain,
% 24.89/25.08      (c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2)))),
% 24.89/25.08      inference(modus_ponens,[status(thm)],[207, 201])).
% 24.89/25.08  tff(209,assumption,(c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2))), introduced(assumption)).
% 24.89/25.08  tff(210,assumption,(c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2)))), introduced(assumption)).
% 24.89/25.08  tff(211,plain,
% 24.89/25.08      (((~![V_c: $i, V_u: $i, V_t: $i, V_s: $i] : ((~c_Natural_Oevalc(V_c, V_s, V_t)) | (~c_Natural_Oevalc(V_c, V_s, V_u)) | (V_u = V_t))) | ((~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2)))) | (~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2))) | (v_Z_H(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2) = v_Z_H(v_Z_H(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2))))) <=> ((~![V_c: $i, V_u: $i, V_t: $i, V_s: $i] : ((~c_Natural_Oevalc(V_c, V_s, V_t)) | (~c_Natural_Oevalc(V_c, V_s, V_u)) | (V_u = V_t))) | (~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2)))) | (~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2))) | (v_Z_H(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2) = v_Z_H(v_Z_H(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2))))),
% 24.89/25.08      inference(rewrite,[status(thm)],[])).
% 24.89/25.08  tff(212,plain,
% 24.89/25.08      ((~![V_c: $i, V_u: $i, V_t: $i, V_s: $i] : ((~c_Natural_Oevalc(V_c, V_s, V_t)) | (~c_Natural_Oevalc(V_c, V_s, V_u)) | (V_u = V_t))) | ((~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2)))) | (~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2))) | (v_Z_H(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2) = v_Z_H(v_Z_H(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2))))),
% 24.89/25.08      inference(quant_inst,[status(thm)],[])).
% 24.89/25.08  tff(213,plain,
% 24.89/25.08      ((~![V_c: $i, V_u: $i, V_t: $i, V_s: $i] : ((~c_Natural_Oevalc(V_c, V_s, V_t)) | (~c_Natural_Oevalc(V_c, V_s, V_u)) | (V_u = V_t))) | (~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2)))) | (~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2))) | (v_Z_H(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2) = v_Z_H(v_Z_H(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2)))),
% 24.89/25.08      inference(modus_ponens,[status(thm)],[212, 211])).
% 24.89/25.08  tff(214,plain,
% 24.89/25.08      ($false),
% 24.89/25.08      inference(unit_resolution,[status(thm)],[213, 108, 165, 210, 209])).
% 24.89/25.08  tff(215,plain,((~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2))) | (v_Z_H(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2) = v_Z_H(v_Z_H(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2))) | (~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2))))), inference(lemma,lemma(discharge,[]))).
% 24.89/25.08  tff(216,plain,
% 24.89/25.08      (~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2))),
% 24.89/25.08      inference(unit_resolution,[status(thm)],[215, 208, 165])).
% 24.89/25.08  tff(217,plain,
% 24.89/25.08      (~c_Natural_Oevalc(v_c, v_Z, v_Z_H(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2))),
% 24.89/25.08      inference(modus_ponens,[status(thm)],[216, 200])).
% 24.89/25.08  tff(218,plain,
% 24.89/25.08      (((~![V_Z_Ha: $i] : ((V_Z_Ha = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(V_Z_Ha)))) | ((v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2 = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2)))) <=> ((~![V_Z_Ha: $i] : ((V_Z_Ha = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(V_Z_Ha)))) | (v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2 = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2)))),
% 24.89/25.08      inference(rewrite,[status(thm)],[])).
% 24.89/25.08  tff(219,plain,
% 24.89/25.08      ((~![V_Z_Ha: $i] : ((V_Z_Ha = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(V_Z_Ha)))) | ((v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2 = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2)))),
% 24.89/25.08      inference(quant_inst,[status(thm)],[])).
% 24.89/25.08  tff(220,plain,
% 24.89/25.08      ((~![V_Z_Ha: $i] : ((V_Z_Ha = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(V_Z_Ha)))) | (v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2 = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2))),
% 24.89/25.08      inference(modus_ponens,[status(thm)],[219, 218])).
% 24.89/25.08  tff(221,plain,
% 24.89/25.08      ((v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2 = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2))),
% 24.89/25.08      inference(unit_resolution,[status(thm)],[220, 78])).
% 24.89/25.08  tff(222,plain,
% 24.89/25.08      (v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2 = v_s_H),
% 24.89/25.08      inference(unit_resolution,[status(thm)],[221, 217])).
% 24.89/25.08  tff(223,plain,
% 24.89/25.08      (v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2 = v_t),
% 24.89/25.08      inference(transitivity,[status(thm)],[222, 164])).
% 24.89/25.08  tff(224,plain,
% 24.89/25.08      (v_Z_H(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2) = v_Z_H(v_t)),
% 24.89/25.08      inference(monotonicity,[status(thm)],[223])).
% 24.89/25.08  tff(225,plain,
% 24.89/25.08      (v_Z_H(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2) = v_s_H),
% 24.89/25.08      inference(transitivity,[status(thm)],[224, 199])).
% 24.89/25.08  tff(226,plain,
% 24.89/25.08      (c_Natural_Oevalc(c_Com_Ocom_OSKIP, v_s_H, v_Z_H(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2)) <=> c_Natural_Oevalc(c_Com_Ocom_OSKIP, v_s_H, v_s_H)),
% 24.89/25.08      inference(monotonicity,[status(thm)],[225])).
% 24.89/25.08  tff(227,plain,
% 24.89/25.08      (c_Natural_Oevalc(c_Com_Ocom_OSKIP, v_s_H, v_s_H) <=> c_Natural_Oevalc(c_Com_Ocom_OSKIP, v_s_H, v_Z_H(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2))),
% 24.89/25.08      inference(symmetry,[status(thm)],[226])).
% 24.89/25.08  tff(228,plain,
% 24.89/25.08      ((~![V_s: $i] : c_Natural_Oevalc(c_Com_Ocom_OSKIP, V_s, V_s)) | c_Natural_Oevalc(c_Com_Ocom_OSKIP, v_s_H, v_s_H)),
% 24.89/25.08      inference(quant_inst,[status(thm)],[])).
% 24.89/25.08  tff(229,plain,
% 24.89/25.08      (c_Natural_Oevalc(c_Com_Ocom_OSKIP, v_s_H, v_s_H)),
% 24.89/25.08      inference(unit_resolution,[status(thm)],[228, 7])).
% 24.89/25.08  tff(230,plain,
% 24.89/25.08      (c_Natural_Oevalc(c_Com_Ocom_OSKIP, v_s_H, v_Z_H(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2))),
% 24.89/25.08      inference(modus_ponens,[status(thm)],[229, 227])).
% 24.89/25.08  tff(231,plain,
% 24.89/25.08      (((~![V_t: $i, V_s: $i] : ((V_t = V_s) | (~c_Natural_Oevalc(c_Com_Ocom_OSKIP, V_s, V_t)))) | ((v_Z_H(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2) = v_s_H) | (~c_Natural_Oevalc(c_Com_Ocom_OSKIP, v_s_H, v_Z_H(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2))))) <=> ((~![V_t: $i, V_s: $i] : ((V_t = V_s) | (~c_Natural_Oevalc(c_Com_Ocom_OSKIP, V_s, V_t)))) | (v_Z_H(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2) = v_s_H) | (~c_Natural_Oevalc(c_Com_Ocom_OSKIP, v_s_H, v_Z_H(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2))))),
% 24.89/25.08      inference(rewrite,[status(thm)],[])).
% 24.89/25.08  tff(232,plain,
% 24.89/25.08      ((~![V_t: $i, V_s: $i] : ((V_t = V_s) | (~c_Natural_Oevalc(c_Com_Ocom_OSKIP, V_s, V_t)))) | ((v_Z_H(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2) = v_s_H) | (~c_Natural_Oevalc(c_Com_Ocom_OSKIP, v_s_H, v_Z_H(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2))))),
% 24.89/25.08      inference(quant_inst,[status(thm)],[])).
% 24.89/25.08  tff(233,plain,
% 24.89/25.08      ((~![V_t: $i, V_s: $i] : ((V_t = V_s) | (~c_Natural_Oevalc(c_Com_Ocom_OSKIP, V_s, V_t)))) | (v_Z_H(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2) = v_s_H) | (~c_Natural_Oevalc(c_Com_Ocom_OSKIP, v_s_H, v_Z_H(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2)))),
% 24.89/25.08      inference(modus_ponens,[status(thm)],[232, 231])).
% 24.89/25.08  tff(234,plain,
% 24.89/25.08      ((v_Z_H(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2) = v_s_H) | (~c_Natural_Oevalc(c_Com_Ocom_OSKIP, v_s_H, v_Z_H(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2)))),
% 24.89/25.08      inference(unit_resolution,[status(thm)],[233, 47])).
% 24.89/25.08  tff(235,plain,
% 24.89/25.08      (~c_Natural_Oevalc(c_Com_Ocom_OSKIP, v_s_H, v_Z_H(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2))),
% 24.89/25.08      inference(unit_resolution,[status(thm)],[234, 202])).
% 24.89/25.08  tff(236,plain,
% 24.89/25.08      ($false),
% 24.89/25.08      inference(unit_resolution,[status(thm)],[235, 230])).
% 24.89/25.08  tff(237,plain,((v_Z_H(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2) = v_s_H) | (v_Z_H(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2) = v_Z_H(v_Z_H(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2)))), inference(lemma,lemma(discharge,[]))).
% 24.89/25.08  tff(238,plain,
% 24.89/25.08      (v_Z_H(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2) = v_s_H),
% 24.89/25.08      inference(unit_resolution,[status(thm)],[237, 165])).
% 24.89/25.08  tff(239,plain,
% 24.89/25.08      (v_Z_H(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2) = v_t),
% 24.89/25.08      inference(transitivity,[status(thm)],[238, 164])).
% 24.89/25.08  tff(240,plain,
% 24.89/25.08      (v_Z_H(v_Z_H(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2)) = v_Z_H(v_t)),
% 24.89/25.08      inference(monotonicity,[status(thm)],[239])).
% 24.89/25.08  tff(241,plain,
% 24.89/25.08      (v_Z_H(v_t) = v_Z_H(v_Z_H(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2))),
% 24.89/25.08      inference(symmetry,[status(thm)],[240])).
% 24.89/25.08  tff(242,plain,
% 24.89/25.08      (v_s_H = v_Z_H(v_t)),
% 24.89/25.08      inference(symmetry,[status(thm)],[199])).
% 24.89/25.08  tff(243,plain,
% 24.89/25.08      (v_Z_H(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2) = v_Z_H(v_Z_H(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2))),
% 24.89/25.08      inference(transitivity,[status(thm)],[238, 242, 241])).
% 24.89/25.08  tff(244,plain,
% 24.89/25.08      ($false),
% 24.89/25.08      inference(unit_resolution,[status(thm)],[165, 243])).
% 24.89/25.08  tff(245,plain,(v_Z_H(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2) = v_Z_H(v_Z_H(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2))), inference(lemma,lemma(discharge,[]))).
% 24.89/25.08  tff(246,plain,
% 24.89/25.08      (c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2)) <=> c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2)))),
% 24.89/25.08      inference(monotonicity,[status(thm)],[245])).
% 24.89/25.08  tff(247,plain,
% 24.89/25.08      (c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2))) <=> c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2))),
% 24.89/25.08      inference(symmetry,[status(thm)],[246])).
% 24.89/25.08  tff(248,plain,
% 24.89/25.08      (((~![V_Z_Ha: $i] : ((~(V_Z_Ha = v_Z_H(V_Z_Ha))) | (V_Z_Ha = v_s_H))) | ((~(v_Z_H(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2) = v_Z_H(v_Z_H(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2)))) | (v_Z_H(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2) = v_s_H))) <=> ((~![V_Z_Ha: $i] : ((~(V_Z_Ha = v_Z_H(V_Z_Ha))) | (V_Z_Ha = v_s_H))) | (~(v_Z_H(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2) = v_Z_H(v_Z_H(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2)))) | (v_Z_H(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2) = v_s_H))),
% 24.89/25.08      inference(rewrite,[status(thm)],[])).
% 24.89/25.08  tff(249,plain,
% 24.89/25.08      ((~![V_Z_Ha: $i] : ((~(V_Z_Ha = v_Z_H(V_Z_Ha))) | (V_Z_Ha = v_s_H))) | ((~(v_Z_H(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2) = v_Z_H(v_Z_H(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2)))) | (v_Z_H(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2) = v_s_H))),
% 24.89/25.08      inference(quant_inst,[status(thm)],[])).
% 24.89/25.08  tff(250,plain,
% 24.89/25.08      ((~![V_Z_Ha: $i] : ((~(V_Z_Ha = v_Z_H(V_Z_Ha))) | (V_Z_Ha = v_s_H))) | (~(v_Z_H(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2) = v_Z_H(v_Z_H(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2)))) | (v_Z_H(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2) = v_s_H)),
% 24.89/25.08      inference(modus_ponens,[status(thm)],[249, 248])).
% 24.89/25.08  tff(251,plain,
% 24.89/25.08      ((~(v_Z_H(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2) = v_Z_H(v_Z_H(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2)))) | (v_Z_H(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2) = v_s_H)),
% 24.89/25.08      inference(unit_resolution,[status(thm)],[250, 90])).
% 24.89/25.08  tff(252,plain,
% 24.89/25.08      (v_Z_H(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2) = v_s_H),
% 24.89/25.08      inference(unit_resolution,[status(thm)],[251, 245])).
% 24.89/25.08  tff(253,plain,
% 24.89/25.08      (v_Z_H(v_Z_H(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2)) = v_Z_H(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2)),
% 24.89/25.08      inference(symmetry,[status(thm)],[245])).
% 24.89/25.08  tff(254,plain,
% 24.89/25.08      (v_Z_H(v_Z_H(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2)) = v_s_H),
% 24.89/25.08      inference(transitivity,[status(thm)],[253, 252])).
% 24.89/25.08  tff(255,plain,
% 24.89/25.08      (c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2))) <=> c_Natural_Oevalc(v_c, v_Z, v_s_H)),
% 24.89/25.08      inference(monotonicity,[status(thm)],[55, 254])).
% 24.89/25.08  tff(256,plain,
% 24.89/25.08      (c_Natural_Oevalc(v_c, v_Z, v_s_H) <=> c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2)))),
% 24.89/25.08      inference(symmetry,[status(thm)],[255])).
% 24.89/25.08  tff(257,plain,
% 24.89/25.08      (c_Natural_Oevalc(v_c, v_Z, v_s_H) <=> c_Natural_Oevalc(v_c, v_Z, v_Z_H(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2))),
% 24.89/25.08      inference(transitivity,[status(thm)],[256, 247, 124])).
% 24.89/25.08  tff(258,plain,
% 24.89/25.08      ((~c_Natural_Oevalc(v_c, v_Z, v_s_H)) <=> (~c_Natural_Oevalc(v_c, v_Z, v_Z_H(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2)))),
% 24.89/25.08      inference(monotonicity,[status(thm)],[257])).
% 24.89/25.08  tff(259,plain,
% 24.89/25.08      (~c_Natural_Oevalc(v_c, v_Z, v_Z_H(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2))),
% 24.89/25.08      inference(modus_ponens,[status(thm)],[67, 258])).
% 24.89/25.08  tff(260,plain,
% 24.89/25.08      (v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2 = v_s_H),
% 24.89/25.08      inference(unit_resolution,[status(thm)],[221, 259])).
% 24.89/25.08  tff(261,plain,
% 24.89/25.08      (v_s_H = v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2),
% 24.89/25.08      inference(symmetry,[status(thm)],[260])).
% 24.89/25.08  tff(262,plain,
% 24.89/25.08      (c_Com_Ocom_OSemi(v_s_H, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP)) = c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP))),
% 24.89/25.08      inference(monotonicity,[status(thm)],[261])).
% 24.89/25.08  tff(263,plain,
% 24.89/25.08      (c_Com_Ocom_OSemi(v_s_H, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP)) = v_s_H),
% 24.89/25.08      inference(transitivity,[status(thm)],[262, 122])).
% 24.89/25.08  tff(264,plain,
% 24.89/25.08      ((c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z)) = c_Com_Ocom_OSemi(v_s_H, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP))) <=> (c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z)) = v_s_H)),
% 24.89/25.08      inference(monotonicity,[status(thm)],[263])).
% 24.89/25.08  tff(265,plain,
% 24.89/25.08      ((c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z)) = v_s_H) <=> (c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z)) = c_Com_Ocom_OSemi(v_s_H, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP)))),
% 24.89/25.08      inference(symmetry,[status(thm)],[264])).
% 24.89/25.08  tff(266,plain,
% 24.89/25.08      ((c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z)) = v_s_H) <=> (c_Com_Ocom_OSemi(v_s_H, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP)) = c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z)))),
% 24.89/25.08      inference(transitivity,[status(thm)],[265, 57])).
% 24.89/25.08  tff(267,plain,
% 24.89/25.08      ((v_s_H = v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z)))) <=> (v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z))) = v_s_H)),
% 24.89/25.08      inference(commutativity,[status(thm)],[])).
% 24.89/25.08  tff(268,plain,
% 24.89/25.08      (c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H))) <=> c_Natural_Oevalc(v_c, v_Z, v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H)))),
% 24.89/25.08      inference(monotonicity,[status(thm)],[55])).
% 24.89/25.08  tff(269,plain,
% 24.89/25.08      (c_Natural_Oevalc(v_c, v_Z, v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H))) <=> c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H)))),
% 24.89/25.08      inference(symmetry,[status(thm)],[268])).
% 24.89/25.08  tff(270,assumption,(~(v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H)) = v_s_H)), introduced(assumption)).
% 24.89/25.08  tff(271,assumption,(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H) = v_s_H), introduced(assumption)).
% 24.89/25.08  tff(272,plain,
% 24.89/25.08      (c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H) = v_t),
% 24.89/25.08      inference(transitivity,[status(thm)],[271, 164])).
% 24.89/25.08  tff(273,plain,
% 24.89/25.08      (v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H)) = v_Z_H(v_t)),
% 24.89/25.08      inference(monotonicity,[status(thm)],[272])).
% 24.89/25.08  tff(274,plain,
% 24.89/25.08      (v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H)) = v_s_H),
% 24.89/25.08      inference(transitivity,[status(thm)],[273, 199])).
% 24.89/25.08  tff(275,plain,
% 24.89/25.08      ($false),
% 24.89/25.08      inference(unit_resolution,[status(thm)],[270, 274])).
% 24.89/25.08  tff(276,plain,((~(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H) = v_s_H)) | (v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H)) = v_s_H)), inference(lemma,lemma(discharge,[]))).
% 24.89/25.08  tff(277,plain,
% 24.89/25.08      (~(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H) = v_s_H)),
% 24.89/25.08      inference(unit_resolution,[status(thm)],[276, 270])).
% 24.89/25.08  tff(278,plain,
% 24.89/25.08      (((~![V_Z_Ha: $i] : ((V_Z_Ha = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(V_Z_Ha)))) | ((c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H) = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H))))) <=> ((~![V_Z_Ha: $i] : ((V_Z_Ha = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(V_Z_Ha)))) | (c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H) = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H))))),
% 24.89/25.08      inference(rewrite,[status(thm)],[])).
% 24.89/25.08  tff(279,plain,
% 24.89/25.08      ((~![V_Z_Ha: $i] : ((V_Z_Ha = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(V_Z_Ha)))) | ((c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H) = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H))))),
% 24.89/25.08      inference(quant_inst,[status(thm)],[])).
% 24.89/25.08  tff(280,plain,
% 24.89/25.08      ((~![V_Z_Ha: $i] : ((V_Z_Ha = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(V_Z_Ha)))) | (c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H) = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H)))),
% 24.89/25.08      inference(modus_ponens,[status(thm)],[279, 278])).
% 24.89/25.08  tff(281,plain,
% 24.89/25.08      ((c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H) = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H)))),
% 24.89/25.08      inference(unit_resolution,[status(thm)],[280, 78])).
% 24.89/25.08  tff(282,plain,
% 24.89/25.08      (c_Natural_Oevalc(v_c, v_Z, v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H)))),
% 24.89/25.08      inference(unit_resolution,[status(thm)],[281, 277])).
% 24.89/25.08  tff(283,plain,
% 24.89/25.08      (c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H)))),
% 24.89/25.08      inference(modus_ponens,[status(thm)],[282, 269])).
% 24.89/25.08  tff(284,plain,
% 24.89/25.08      (c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H)))) <=> c_Natural_Oevalc(v_c, v_Z, v_Z_H(v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H))))),
% 24.89/25.08      inference(monotonicity,[status(thm)],[55])).
% 24.89/25.08  tff(285,plain,
% 24.89/25.08      (c_Natural_Oevalc(v_c, v_Z, v_Z_H(v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H)))) <=> c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H))))),
% 24.89/25.08      inference(symmetry,[status(thm)],[284])).
% 24.89/25.08  tff(286,plain,
% 24.89/25.08      (((~![V_Z_Ha: $i] : ((V_Z_Ha = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(V_Z_Ha)))) | ((v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H)) = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H)))))) <=> ((~![V_Z_Ha: $i] : ((V_Z_Ha = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(V_Z_Ha)))) | (v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H)) = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H)))))),
% 24.89/25.08      inference(rewrite,[status(thm)],[])).
% 24.89/25.08  tff(287,plain,
% 24.89/25.08      ((~![V_Z_Ha: $i] : ((V_Z_Ha = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(V_Z_Ha)))) | ((v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H)) = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H)))))),
% 24.89/25.08      inference(quant_inst,[status(thm)],[])).
% 24.89/25.08  tff(288,plain,
% 24.89/25.08      ((~![V_Z_Ha: $i] : ((V_Z_Ha = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(V_Z_Ha)))) | (v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H)) = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H))))),
% 24.89/25.08      inference(modus_ponens,[status(thm)],[287, 286])).
% 24.89/25.08  tff(289,plain,
% 24.89/25.08      (c_Natural_Oevalc(v_c, v_Z, v_Z_H(v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H))))),
% 24.89/25.08      inference(unit_resolution,[status(thm)],[288, 78, 270])).
% 24.89/25.08  tff(290,plain,
% 24.89/25.08      (c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H))))),
% 24.89/25.08      inference(modus_ponens,[status(thm)],[289, 285])).
% 24.89/25.08  tff(291,plain,
% 24.89/25.08      (((~![V_Z_Ha: $i] : ((~(V_Z_Ha = v_Z_H(V_Z_Ha))) | (V_Z_Ha = v_s_H))) | ((~(v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H)) = v_Z_H(v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H))))) | (v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H)) = v_s_H))) <=> ((~![V_Z_Ha: $i] : ((~(V_Z_Ha = v_Z_H(V_Z_Ha))) | (V_Z_Ha = v_s_H))) | (~(v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H)) = v_Z_H(v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H))))) | (v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H)) = v_s_H))),
% 24.89/25.08      inference(rewrite,[status(thm)],[])).
% 24.89/25.08  tff(292,plain,
% 24.89/25.08      ((~![V_Z_Ha: $i] : ((~(V_Z_Ha = v_Z_H(V_Z_Ha))) | (V_Z_Ha = v_s_H))) | ((~(v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H)) = v_Z_H(v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H))))) | (v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H)) = v_s_H))),
% 24.89/25.08      inference(quant_inst,[status(thm)],[])).
% 24.89/25.08  tff(293,plain,
% 24.89/25.08      ((~![V_Z_Ha: $i] : ((~(V_Z_Ha = v_Z_H(V_Z_Ha))) | (V_Z_Ha = v_s_H))) | (~(v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H)) = v_Z_H(v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H))))) | (v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H)) = v_s_H)),
% 24.89/25.08      inference(modus_ponens,[status(thm)],[292, 291])).
% 24.89/25.08  tff(294,plain,
% 24.89/25.08      ((~(v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H)) = v_Z_H(v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H))))) | (v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H)) = v_s_H)),
% 24.89/25.08      inference(unit_resolution,[status(thm)],[293, 90])).
% 24.89/25.08  tff(295,plain,
% 24.89/25.08      (~(v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H)) = v_Z_H(v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H))))),
% 24.89/25.08      inference(unit_resolution,[status(thm)],[294, 270])).
% 24.89/25.08  tff(296,plain,
% 24.89/25.08      (((~![V_c: $i, V_u: $i, V_t: $i, V_s: $i] : ((~c_Natural_Oevalc(V_c, V_s, V_t)) | (~c_Natural_Oevalc(V_c, V_s, V_u)) | (V_u = V_t))) | ((v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H)) = v_Z_H(v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H)))) | (~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H)))) | (~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H))))))) <=> ((~![V_c: $i, V_u: $i, V_t: $i, V_s: $i] : ((~c_Natural_Oevalc(V_c, V_s, V_t)) | (~c_Natural_Oevalc(V_c, V_s, V_u)) | (V_u = V_t))) | (v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H)) = v_Z_H(v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H)))) | (~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H)))) | (~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H))))))),
% 24.89/25.08      inference(rewrite,[status(thm)],[])).
% 24.89/25.08  tff(297,plain,
% 24.89/25.08      (((~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H))))) | (~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H)))) | (v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H)) = v_Z_H(v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H))))) <=> ((v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H)) = v_Z_H(v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H)))) | (~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H)))) | (~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H))))))),
% 24.89/25.08      inference(rewrite,[status(thm)],[])).
% 24.89/25.08  tff(298,plain,
% 24.89/25.08      (((~![V_c: $i, V_u: $i, V_t: $i, V_s: $i] : ((~c_Natural_Oevalc(V_c, V_s, V_t)) | (~c_Natural_Oevalc(V_c, V_s, V_u)) | (V_u = V_t))) | ((~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H))))) | (~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H)))) | (v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H)) = v_Z_H(v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H)))))) <=> ((~![V_c: $i, V_u: $i, V_t: $i, V_s: $i] : ((~c_Natural_Oevalc(V_c, V_s, V_t)) | (~c_Natural_Oevalc(V_c, V_s, V_u)) | (V_u = V_t))) | ((v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H)) = v_Z_H(v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H)))) | (~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H)))) | (~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H)))))))),
% 24.89/25.08      inference(monotonicity,[status(thm)],[297])).
% 24.89/25.08  tff(299,plain,
% 24.89/25.08      (((~![V_c: $i, V_u: $i, V_t: $i, V_s: $i] : ((~c_Natural_Oevalc(V_c, V_s, V_t)) | (~c_Natural_Oevalc(V_c, V_s, V_u)) | (V_u = V_t))) | ((~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H))))) | (~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H)))) | (v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H)) = v_Z_H(v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H)))))) <=> ((~![V_c: $i, V_u: $i, V_t: $i, V_s: $i] : ((~c_Natural_Oevalc(V_c, V_s, V_t)) | (~c_Natural_Oevalc(V_c, V_s, V_u)) | (V_u = V_t))) | (v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H)) = v_Z_H(v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H)))) | (~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H)))) | (~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H))))))),
% 24.89/25.08      inference(transitivity,[status(thm)],[298, 296])).
% 24.89/25.08  tff(300,plain,
% 24.89/25.08      ((~![V_c: $i, V_u: $i, V_t: $i, V_s: $i] : ((~c_Natural_Oevalc(V_c, V_s, V_t)) | (~c_Natural_Oevalc(V_c, V_s, V_u)) | (V_u = V_t))) | ((~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H))))) | (~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H)))) | (v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H)) = v_Z_H(v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H)))))),
% 24.89/25.08      inference(quant_inst,[status(thm)],[])).
% 24.89/25.08  tff(301,plain,
% 24.89/25.08      ((~![V_c: $i, V_u: $i, V_t: $i, V_s: $i] : ((~c_Natural_Oevalc(V_c, V_s, V_t)) | (~c_Natural_Oevalc(V_c, V_s, V_u)) | (V_u = V_t))) | (v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H)) = v_Z_H(v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H)))) | (~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H)))) | (~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H)))))),
% 24.89/25.08      inference(modus_ponens,[status(thm)],[300, 299])).
% 24.89/25.08  tff(302,plain,
% 24.89/25.08      (~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H)))),
% 24.89/25.08      inference(unit_resolution,[status(thm)],[301, 108, 295, 290])).
% 24.89/25.08  tff(303,plain,
% 24.89/25.08      ($false),
% 24.89/25.08      inference(unit_resolution,[status(thm)],[302, 283])).
% 24.89/25.08  tff(304,plain,(v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H)) = v_s_H), inference(lemma,lemma(discharge,[]))).
% 24.89/25.08  tff(305,plain,
% 24.89/25.08      ((v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H)) = v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z)))) <=> (v_s_H = v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z))))),
% 24.89/25.09      inference(monotonicity,[status(thm)],[304])).
% 24.89/25.09  tff(306,plain,
% 24.89/25.09      ((v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H)) = v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z)))) <=> (v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z))) = v_s_H)),
% 24.89/25.09      inference(transitivity,[status(thm)],[305, 267])).
% 24.89/25.09  tff(307,plain,
% 24.89/25.09      ((v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z))) = v_s_H) <=> (v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H)) = v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z))))),
% 24.89/25.09      inference(symmetry,[status(thm)],[306])).
% 24.89/25.09  tff(308,plain,
% 24.89/25.09      (c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z)))) <=> c_Natural_Oevalc(v_c, v_Z, v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z))))),
% 24.89/25.09      inference(monotonicity,[status(thm)],[55])).
% 24.89/25.09  tff(309,plain,
% 24.89/25.09      (c_Natural_Oevalc(v_c, v_Z, v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z)))) <=> c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z))))),
% 24.89/25.09      inference(symmetry,[status(thm)],[308])).
% 24.89/25.09  tff(310,assumption,(c_Natural_Oevalc(v_c, v_Z, v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z))))), introduced(assumption)).
% 24.89/25.09  tff(311,plain,
% 24.89/25.09      (c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z))))),
% 24.89/25.09      inference(modus_ponens,[status(thm)],[310, 309])).
% 24.89/25.09  tff(312,plain,
% 24.89/25.09      (c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z))))) <=> c_Natural_Oevalc(v_c, v_Z, v_Z_H(v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z)))))),
% 24.89/25.09      inference(monotonicity,[status(thm)],[55])).
% 24.89/25.09  tff(313,plain,
% 24.89/25.09      (c_Natural_Oevalc(v_c, v_Z, v_Z_H(v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z))))) <=> c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z)))))),
% 24.89/25.09      inference(symmetry,[status(thm)],[312])).
% 24.89/25.09  tff(314,assumption,(~(v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z))) = v_s_H)), introduced(assumption)).
% 24.89/25.09  tff(315,plain,
% 24.89/25.09      (((~![V_Z_Ha: $i] : ((V_Z_Ha = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(V_Z_Ha)))) | ((v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z))) = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z))))))) <=> ((~![V_Z_Ha: $i] : ((V_Z_Ha = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(V_Z_Ha)))) | (v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z))) = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z))))))),
% 24.89/25.09      inference(rewrite,[status(thm)],[])).
% 24.89/25.09  tff(316,plain,
% 24.89/25.09      ((~![V_Z_Ha: $i] : ((V_Z_Ha = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(V_Z_Ha)))) | ((v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z))) = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z))))))),
% 24.89/25.09      inference(quant_inst,[status(thm)],[])).
% 24.89/25.09  tff(317,plain,
% 24.89/25.09      ((~![V_Z_Ha: $i] : ((V_Z_Ha = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(V_Z_Ha)))) | (v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z))) = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z)))))),
% 24.89/25.09      inference(modus_ponens,[status(thm)],[316, 315])).
% 24.89/25.09  tff(318,plain,
% 24.89/25.09      (c_Natural_Oevalc(v_c, v_Z, v_Z_H(v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z)))))),
% 24.89/25.09      inference(unit_resolution,[status(thm)],[317, 78, 314])).
% 24.89/25.09  tff(319,plain,
% 24.89/25.09      (c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z)))))),
% 24.89/25.09      inference(modus_ponens,[status(thm)],[318, 313])).
% 24.89/25.09  tff(320,plain,
% 24.89/25.09      (((~![V_Z_Ha: $i] : ((~(V_Z_Ha = v_Z_H(V_Z_Ha))) | (V_Z_Ha = v_s_H))) | ((~(v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z))) = v_Z_H(v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z)))))) | (v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z))) = v_s_H))) <=> ((~![V_Z_Ha: $i] : ((~(V_Z_Ha = v_Z_H(V_Z_Ha))) | (V_Z_Ha = v_s_H))) | (~(v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z))) = v_Z_H(v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z)))))) | (v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z))) = v_s_H))),
% 24.89/25.09      inference(rewrite,[status(thm)],[])).
% 24.89/25.09  tff(321,plain,
% 24.89/25.09      ((~![V_Z_Ha: $i] : ((~(V_Z_Ha = v_Z_H(V_Z_Ha))) | (V_Z_Ha = v_s_H))) | ((~(v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z))) = v_Z_H(v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z)))))) | (v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z))) = v_s_H))),
% 24.89/25.09      inference(quant_inst,[status(thm)],[])).
% 24.89/25.09  tff(322,plain,
% 24.89/25.09      ((~![V_Z_Ha: $i] : ((~(V_Z_Ha = v_Z_H(V_Z_Ha))) | (V_Z_Ha = v_s_H))) | (~(v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z))) = v_Z_H(v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z)))))) | (v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z))) = v_s_H)),
% 24.89/25.09      inference(modus_ponens,[status(thm)],[321, 320])).
% 24.89/25.09  tff(323,plain,
% 24.89/25.09      ((~(v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z))) = v_Z_H(v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z)))))) | (v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z))) = v_s_H)),
% 24.89/25.09      inference(unit_resolution,[status(thm)],[322, 90])).
% 24.89/25.09  tff(324,plain,
% 24.89/25.09      (~(v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z))) = v_Z_H(v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z)))))),
% 24.89/25.09      inference(unit_resolution,[status(thm)],[323, 314])).
% 24.89/25.09  tff(325,assumption,(c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z))))), introduced(assumption)).
% 24.89/25.09  tff(326,plain,
% 24.89/25.09      (((~![V_c: $i, V_u: $i, V_t: $i, V_s: $i] : ((~c_Natural_Oevalc(V_c, V_s, V_t)) | (~c_Natural_Oevalc(V_c, V_s, V_u)) | (V_u = V_t))) | ((v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z))) = v_Z_H(v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z))))) | (~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z))))) | (~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z)))))))) <=> ((~![V_c: $i, V_u: $i, V_t: $i, V_s: $i] : ((~c_Natural_Oevalc(V_c, V_s, V_t)) | (~c_Natural_Oevalc(V_c, V_s, V_u)) | (V_u = V_t))) | (v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z))) = v_Z_H(v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z))))) | (~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z))))) | (~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z)))))))),
% 24.89/25.09      inference(rewrite,[status(thm)],[])).
% 24.89/25.09  tff(327,plain,
% 24.89/25.09      (((~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z)))))) | (~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z))))) | (v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z))) = v_Z_H(v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z)))))) <=> ((v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z))) = v_Z_H(v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z))))) | (~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z))))) | (~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z)))))))),
% 24.89/25.09      inference(rewrite,[status(thm)],[])).
% 24.89/25.09  tff(328,plain,
% 24.89/25.09      (((~![V_c: $i, V_u: $i, V_t: $i, V_s: $i] : ((~c_Natural_Oevalc(V_c, V_s, V_t)) | (~c_Natural_Oevalc(V_c, V_s, V_u)) | (V_u = V_t))) | ((~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z)))))) | (~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z))))) | (v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z))) = v_Z_H(v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z))))))) <=> ((~![V_c: $i, V_u: $i, V_t: $i, V_s: $i] : ((~c_Natural_Oevalc(V_c, V_s, V_t)) | (~c_Natural_Oevalc(V_c, V_s, V_u)) | (V_u = V_t))) | ((v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z))) = v_Z_H(v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z))))) | (~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z))))) | (~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z))))))))),
% 24.89/25.09      inference(monotonicity,[status(thm)],[327])).
% 24.89/25.09  tff(329,plain,
% 24.89/25.09      (((~![V_c: $i, V_u: $i, V_t: $i, V_s: $i] : ((~c_Natural_Oevalc(V_c, V_s, V_t)) | (~c_Natural_Oevalc(V_c, V_s, V_u)) | (V_u = V_t))) | ((~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z)))))) | (~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z))))) | (v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z))) = v_Z_H(v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z))))))) <=> ((~![V_c: $i, V_u: $i, V_t: $i, V_s: $i] : ((~c_Natural_Oevalc(V_c, V_s, V_t)) | (~c_Natural_Oevalc(V_c, V_s, V_u)) | (V_u = V_t))) | (v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z))) = v_Z_H(v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z))))) | (~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z))))) | (~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z)))))))),
% 24.89/25.09      inference(transitivity,[status(thm)],[328, 326])).
% 24.89/25.09  tff(330,plain,
% 24.89/25.09      ((~![V_c: $i, V_u: $i, V_t: $i, V_s: $i] : ((~c_Natural_Oevalc(V_c, V_s, V_t)) | (~c_Natural_Oevalc(V_c, V_s, V_u)) | (V_u = V_t))) | ((~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z)))))) | (~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z))))) | (v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z))) = v_Z_H(v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z))))))),
% 24.89/25.09      inference(quant_inst,[status(thm)],[])).
% 24.89/25.09  tff(331,plain,
% 24.89/25.09      ((~![V_c: $i, V_u: $i, V_t: $i, V_s: $i] : ((~c_Natural_Oevalc(V_c, V_s, V_t)) | (~c_Natural_Oevalc(V_c, V_s, V_u)) | (V_u = V_t))) | (v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z))) = v_Z_H(v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z))))) | (~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z))))) | (~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z))))))),
% 24.89/25.09      inference(modus_ponens,[status(thm)],[330, 329])).
% 24.89/25.09  tff(332,plain,
% 24.89/25.09      (~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z)))))),
% 24.89/25.09      inference(unit_resolution,[status(thm)],[331, 108, 325, 324])).
% 24.89/25.09  tff(333,plain,
% 24.89/25.09      ($false),
% 24.89/25.09      inference(unit_resolution,[status(thm)],[332, 319])).
% 24.89/25.09  tff(334,plain,((v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z))) = v_s_H) | (~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z)))))), inference(lemma,lemma(discharge,[]))).
% 24.93/25.09  tff(335,plain,
% 24.93/25.09      (v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z))) = v_s_H),
% 24.93/25.09      inference(unit_resolution,[status(thm)],[334, 311])).
% 24.93/25.09  tff(336,plain,
% 24.93/25.09      (v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H)) = v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z)))),
% 24.93/25.09      inference(modus_ponens,[status(thm)],[335, 307])).
% 24.93/25.09  tff(337,assumption,(v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H)) = v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z)))), introduced(assumption)).
% 24.93/25.09  tff(338,plain,
% 24.93/25.09      (v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z))) = v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H))),
% 24.93/25.09      inference(symmetry,[status(thm)],[337])).
% 24.93/25.09  tff(339,plain,
% 24.93/25.09      (v_Z_H(v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z)))) = v_Z_H(v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H)))),
% 24.93/25.09      inference(monotonicity,[status(thm)],[338])).
% 24.93/25.09  tff(340,plain,
% 24.93/25.09      (v_Z_H(v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H))) = v_Z_H(v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z))))),
% 24.93/25.09      inference(symmetry,[status(thm)],[339])).
% 24.93/25.09  tff(341,plain,
% 24.93/25.09      (c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H)))) <=> c_Natural_Oevalc(v_c, v_Z, v_Z_H(v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z)))))),
% 24.93/25.09      inference(monotonicity,[status(thm)],[55, 340])).
% 24.93/25.09  tff(342,plain,
% 24.93/25.09      (c_Natural_Oevalc(v_c, v_Z, v_Z_H(v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z))))) <=> c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H))))),
% 24.93/25.09      inference(symmetry,[status(thm)],[341])).
% 24.93/25.09  tff(343,plain,
% 24.93/25.09      ((v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z))) = v_s_H) <=> (v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H)) = v_s_H)),
% 24.93/25.09      inference(monotonicity,[status(thm)],[338])).
% 24.93/25.09  tff(344,plain,
% 24.93/25.09      ((v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H)) = v_s_H) <=> (v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z))) = v_s_H)),
% 24.93/25.09      inference(symmetry,[status(thm)],[343])).
% 24.93/25.09  tff(345,plain,
% 24.93/25.09      ((~(v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H)) = v_s_H)) <=> (~(v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z))) = v_s_H))),
% 24.93/25.09      inference(monotonicity,[status(thm)],[344])).
% 24.93/25.09  tff(346,plain,
% 24.93/25.09      (~(v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z))) = v_s_H)),
% 24.93/25.09      inference(modus_ponens,[status(thm)],[270, 345])).
% 24.93/25.09  tff(347,plain,
% 24.93/25.09      ((v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z))) = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z)))))),
% 24.93/25.09      inference(unit_resolution,[status(thm)],[317, 78])).
% 24.93/25.09  tff(348,plain,
% 24.93/25.09      (c_Natural_Oevalc(v_c, v_Z, v_Z_H(v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z)))))),
% 24.93/25.09      inference(unit_resolution,[status(thm)],[347, 346])).
% 24.93/25.09  tff(349,plain,
% 24.93/25.09      (c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H))))),
% 24.93/25.09      inference(modus_ponens,[status(thm)],[348, 342])).
% 24.93/25.09  tff(350,plain,
% 24.93/25.09      ((v_Z_H(v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H))) = v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H))) <=> (v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H)) = v_Z_H(v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H))))),
% 24.93/25.09      inference(commutativity,[status(thm)],[])).
% 24.93/25.09  tff(351,plain,
% 24.93/25.09      ((v_Z_H(v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H))) = v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z)))) <=> (v_Z_H(v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H))) = v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H)))),
% 24.93/25.09      inference(monotonicity,[status(thm)],[338])).
% 24.93/25.09  tff(352,plain,
% 24.93/25.09      ((v_Z_H(v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H))) = v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z)))) <=> (v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H)) = v_Z_H(v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H))))),
% 24.93/25.09      inference(transitivity,[status(thm)],[351, 350])).
% 24.93/25.09  tff(353,plain,
% 24.93/25.09      ((v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H)) = v_Z_H(v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H)))) <=> (v_Z_H(v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H))) = v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z))))),
% 24.93/25.09      inference(symmetry,[status(thm)],[352])).
% 24.93/25.09  tff(354,plain,
% 24.93/25.09      ((~(v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H)) = v_Z_H(v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H))))) <=> (~(v_Z_H(v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H))) = v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z)))))),
% 24.93/25.09      inference(monotonicity,[status(thm)],[353])).
% 24.93/25.09  tff(355,plain,
% 24.93/25.09      (~(v_Z_H(v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H))) = v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z))))),
% 24.93/25.09      inference(modus_ponens,[status(thm)],[295, 354])).
% 24.93/25.09  tff(356,plain,
% 24.93/25.09      (((~![V_c: $i, V_u: $i, V_t: $i, V_s: $i] : ((~c_Natural_Oevalc(V_c, V_s, V_t)) | (~c_Natural_Oevalc(V_c, V_s, V_u)) | (V_u = V_t))) | ((~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z))))) | (v_Z_H(v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H))) = v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z)))) | (~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H))))))) <=> ((~![V_c: $i, V_u: $i, V_t: $i, V_s: $i] : ((~c_Natural_Oevalc(V_c, V_s, V_t)) | (~c_Natural_Oevalc(V_c, V_s, V_u)) | (V_u = V_t))) | (~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z))))) | (v_Z_H(v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H))) = v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z)))) | (~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H))))))),
% 24.93/25.09      inference(rewrite,[status(thm)],[])).
% 24.93/25.09  tff(357,plain,
% 24.93/25.09      (((~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z))))) | (~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H))))) | (v_Z_H(v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H))) = v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z))))) <=> ((~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z))))) | (v_Z_H(v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H))) = v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z)))) | (~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H))))))),
% 24.93/25.09      inference(rewrite,[status(thm)],[])).
% 24.93/25.09  tff(358,plain,
% 24.93/25.09      (((~![V_c: $i, V_u: $i, V_t: $i, V_s: $i] : ((~c_Natural_Oevalc(V_c, V_s, V_t)) | (~c_Natural_Oevalc(V_c, V_s, V_u)) | (V_u = V_t))) | ((~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z))))) | (~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H))))) | (v_Z_H(v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H))) = v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z)))))) <=> ((~![V_c: $i, V_u: $i, V_t: $i, V_s: $i] : ((~c_Natural_Oevalc(V_c, V_s, V_t)) | (~c_Natural_Oevalc(V_c, V_s, V_u)) | (V_u = V_t))) | ((~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z))))) | (v_Z_H(v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H))) = v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z)))) | (~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H)))))))),
% 24.93/25.09      inference(monotonicity,[status(thm)],[357])).
% 24.93/25.09  tff(359,plain,
% 24.93/25.09      (((~![V_c: $i, V_u: $i, V_t: $i, V_s: $i] : ((~c_Natural_Oevalc(V_c, V_s, V_t)) | (~c_Natural_Oevalc(V_c, V_s, V_u)) | (V_u = V_t))) | ((~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z))))) | (~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H))))) | (v_Z_H(v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H))) = v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z)))))) <=> ((~![V_c: $i, V_u: $i, V_t: $i, V_s: $i] : ((~c_Natural_Oevalc(V_c, V_s, V_t)) | (~c_Natural_Oevalc(V_c, V_s, V_u)) | (V_u = V_t))) | (~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z))))) | (v_Z_H(v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H))) = v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z)))) | (~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H))))))),
% 24.93/25.09      inference(transitivity,[status(thm)],[358, 356])).
% 24.93/25.09  tff(360,plain,
% 24.93/25.09      ((~![V_c: $i, V_u: $i, V_t: $i, V_s: $i] : ((~c_Natural_Oevalc(V_c, V_s, V_t)) | (~c_Natural_Oevalc(V_c, V_s, V_u)) | (V_u = V_t))) | ((~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z))))) | (~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H))))) | (v_Z_H(v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H))) = v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z)))))),
% 24.93/25.09      inference(quant_inst,[status(thm)],[])).
% 24.93/25.09  tff(361,plain,
% 24.93/25.09      ((~![V_c: $i, V_u: $i, V_t: $i, V_s: $i] : ((~c_Natural_Oevalc(V_c, V_s, V_t)) | (~c_Natural_Oevalc(V_c, V_s, V_u)) | (V_u = V_t))) | (~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z))))) | (v_Z_H(v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H))) = v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z)))) | (~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H)))))),
% 24.93/25.09      inference(modus_ponens,[status(thm)],[360, 359])).
% 24.93/25.09  tff(362,plain,
% 24.93/25.09      ((v_Z_H(v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H))) = v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z)))) | (~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H)))))),
% 24.93/25.09      inference(unit_resolution,[status(thm)],[361, 108, 325])).
% 24.93/25.09  tff(363,plain,
% 24.93/25.09      ($false),
% 24.93/25.09      inference(unit_resolution,[status(thm)],[362, 355, 349])).
% 24.93/25.09  tff(364,plain,((v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H)) = v_s_H) | (~c_Natural_Oevalc(v_c, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z))))) | (~(v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H)) = v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z)))))), inference(lemma,lemma(discharge,[]))).
% 24.93/25.09  tff(365,plain,
% 24.93/25.09      (v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H)) = v_s_H),
% 24.93/25.09      inference(unit_resolution,[status(thm)],[364, 337, 311])).
% 24.93/25.09  tff(366,plain,
% 24.93/25.09      (v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z))) = v_s_H),
% 24.93/25.09      inference(transitivity,[status(thm)],[338, 365])).
% 24.93/25.09  tff(367,plain,
% 24.93/25.09      (c_Natural_Oevalc(v_c, v_Z, v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z)))) <=> c_Natural_Oevalc(v_c, v_Z, v_s_H)),
% 24.93/25.09      inference(monotonicity,[status(thm)],[366])).
% 24.93/25.09  tff(368,plain,
% 24.93/25.09      (c_Natural_Oevalc(v_c, v_Z, v_s_H) <=> c_Natural_Oevalc(v_c, v_Z, v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z))))),
% 24.93/25.09      inference(symmetry,[status(thm)],[367])).
% 24.93/25.09  tff(369,plain,
% 24.93/25.09      ((~c_Natural_Oevalc(v_c, v_Z, v_s_H)) <=> (~c_Natural_Oevalc(v_c, v_Z, v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z)))))),
% 24.93/25.09      inference(monotonicity,[status(thm)],[368])).
% 24.93/25.09  tff(370,plain,
% 24.93/25.09      (~c_Natural_Oevalc(v_c, v_Z, v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z))))),
% 24.93/25.09      inference(modus_ponens,[status(thm)],[67, 369])).
% 24.93/25.09  tff(371,plain,
% 24.93/25.09      ($false),
% 24.93/25.09      inference(unit_resolution,[status(thm)],[310, 370])).
% 24.93/25.09  tff(372,plain,((~(v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H)) = v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z))))) | (~c_Natural_Oevalc(v_c, v_Z, v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z)))))), inference(lemma,lemma(discharge,[]))).
% 24.93/25.09  tff(373,plain,
% 24.93/25.09      (~(v_Z_H(c_Natural_Osko__Natural__Xevalc__evaln__1__1(c_Com_Ocom_OSKIP, v_s_H, v_s_H)) = v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z))))),
% 24.93/25.09      inference(unit_resolution,[status(thm)],[372, 310])).
% 24.93/25.09  tff(374,plain,
% 24.93/25.09      ($false),
% 24.93/25.09      inference(unit_resolution,[status(thm)],[373, 336])).
% 24.93/25.09  tff(375,plain,(~c_Natural_Oevalc(v_c, v_Z, v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z))))), inference(lemma,lemma(discharge,[]))).
% 24.93/25.09  tff(376,plain,
% 24.93/25.09      (((~![V_Z_Ha: $i] : ((V_Z_Ha = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(V_Z_Ha)))) | ((c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z)) = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z)))))) <=> ((~![V_Z_Ha: $i] : ((V_Z_Ha = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(V_Z_Ha)))) | (c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z)) = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z)))))),
% 24.93/25.09      inference(rewrite,[status(thm)],[])).
% 24.93/25.09  tff(377,plain,
% 24.93/25.09      ((~![V_Z_Ha: $i] : ((V_Z_Ha = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(V_Z_Ha)))) | ((c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z)) = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z)))))),
% 24.93/25.09      inference(quant_inst,[status(thm)],[])).
% 24.93/25.09  tff(378,plain,
% 24.93/25.09      ((~![V_Z_Ha: $i] : ((V_Z_Ha = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(V_Z_Ha)))) | (c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z)) = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z))))),
% 24.93/25.09      inference(modus_ponens,[status(thm)],[377, 376])).
% 24.93/25.09  tff(379,plain,
% 24.93/25.09      ((c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z)) = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z))))),
% 24.93/25.09      inference(unit_resolution,[status(thm)],[378, 78])).
% 24.93/25.09  tff(380,plain,
% 24.93/25.09      (c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z)) = v_s_H),
% 24.93/25.09      inference(unit_resolution,[status(thm)],[379, 375])).
% 24.93/25.09  tff(381,plain,
% 24.93/25.09      (c_Com_Ocom_OSemi(v_s_H, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP)) = c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z))),
% 24.93/25.09      inference(modus_ponens,[status(thm)],[380, 266])).
% 24.93/25.09  tff(382,plain,
% 24.93/25.09      (^[V_com1: $i, V_com1_H: $i, V_com2_H: $i, V_com2: $i] : refl(((~(c_Com_Ocom_OSemi(V_com1, V_com2) = c_Com_Ocom_OSemi(V_com1_H, V_com2_H))) | (V_com1 = V_com1_H)) <=> ((~(c_Com_Ocom_OSemi(V_com1, V_com2) = c_Com_Ocom_OSemi(V_com1_H, V_com2_H))) | (V_com1 = V_com1_H)))),
% 24.93/25.09      inference(bind,[status(th)],[])).
% 24.93/25.09  tff(383,plain,
% 24.93/25.09      (![V_com1: $i, V_com1_H: $i, V_com2_H: $i, V_com2: $i] : ((~(c_Com_Ocom_OSemi(V_com1, V_com2) = c_Com_Ocom_OSemi(V_com1_H, V_com2_H))) | (V_com1 = V_com1_H)) <=> ![V_com1: $i, V_com1_H: $i, V_com2_H: $i, V_com2: $i] : ((~(c_Com_Ocom_OSemi(V_com1, V_com2) = c_Com_Ocom_OSemi(V_com1_H, V_com2_H))) | (V_com1 = V_com1_H))),
% 24.93/25.09      inference(quant_intro,[status(thm)],[382])).
% 24.93/25.09  tff(384,plain,
% 24.93/25.09      (![V_com1: $i, V_com1_H: $i, V_com2_H: $i, V_com2: $i] : ((~(c_Com_Ocom_OSemi(V_com1, V_com2) = c_Com_Ocom_OSemi(V_com1_H, V_com2_H))) | (V_com1 = V_com1_H)) <=> ![V_com1: $i, V_com1_H: $i, V_com2_H: $i, V_com2: $i] : ((~(c_Com_Ocom_OSemi(V_com1, V_com2) = c_Com_Ocom_OSemi(V_com1_H, V_com2_H))) | (V_com1 = V_com1_H))),
% 24.93/25.09      inference(rewrite,[status(thm)],[])).
% 24.93/25.09  tff(385,axiom,(![V_com1: $i, V_com1_H: $i, V_com2_H: $i, V_com2: $i] : ((~(c_Com_Ocom_OSemi(V_com1, V_com2) = c_Com_Ocom_OSemi(V_com1_H, V_com2_H))) | (V_com1 = V_com1_H))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_com_Osimps_I3_J_0')).
% 24.93/25.09  tff(386,plain,
% 24.93/25.09      (![V_com1: $i, V_com1_H: $i, V_com2_H: $i, V_com2: $i] : ((~(c_Com_Ocom_OSemi(V_com1, V_com2) = c_Com_Ocom_OSemi(V_com1_H, V_com2_H))) | (V_com1 = V_com1_H))),
% 24.93/25.09      inference(modus_ponens,[status(thm)],[385, 384])).
% 24.93/25.09  tff(387,plain,(
% 24.93/25.09      ![V_com1: $i, V_com1_H: $i, V_com2_H: $i, V_com2: $i] : ((~(c_Com_Ocom_OSemi(V_com1, V_com2) = c_Com_Ocom_OSemi(V_com1_H, V_com2_H))) | (V_com1 = V_com1_H))),
% 24.93/25.09      inference(skolemize,[status(sab)],[386])).
% 24.93/25.09  tff(388,plain,
% 24.93/25.09      (![V_com1: $i, V_com1_H: $i, V_com2_H: $i, V_com2: $i] : ((~(c_Com_Ocom_OSemi(V_com1, V_com2) = c_Com_Ocom_OSemi(V_com1_H, V_com2_H))) | (V_com1 = V_com1_H))),
% 24.93/25.09      inference(modus_ponens,[status(thm)],[387, 383])).
% 24.93/25.09  tff(389,plain,
% 24.93/25.09      (((~![V_com1: $i, V_com1_H: $i, V_com2_H: $i, V_com2: $i] : ((~(c_Com_Ocom_OSemi(V_com1, V_com2) = c_Com_Ocom_OSemi(V_com1_H, V_com2_H))) | (V_com1 = V_com1_H))) | ((~(c_Com_Ocom_OSemi(v_s_H, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP)) = c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z)))) | (v_s_H = v_c))) <=> ((~![V_com1: $i, V_com1_H: $i, V_com2_H: $i, V_com2: $i] : ((~(c_Com_Ocom_OSemi(V_com1, V_com2) = c_Com_Ocom_OSemi(V_com1_H, V_com2_H))) | (V_com1 = V_com1_H))) | (~(c_Com_Ocom_OSemi(v_s_H, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP)) = c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z)))) | (v_s_H = v_c))),
% 24.93/25.09      inference(rewrite,[status(thm)],[])).
% 24.93/25.09  tff(390,plain,
% 24.93/25.09      ((~![V_com1: $i, V_com1_H: $i, V_com2_H: $i, V_com2: $i] : ((~(c_Com_Ocom_OSemi(V_com1, V_com2) = c_Com_Ocom_OSemi(V_com1_H, V_com2_H))) | (V_com1 = V_com1_H))) | ((~(c_Com_Ocom_OSemi(v_s_H, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP)) = c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z)))) | (v_s_H = v_c))),
% 24.93/25.09      inference(quant_inst,[status(thm)],[])).
% 24.93/25.09  tff(391,plain,
% 24.93/25.09      ((~![V_com1: $i, V_com1_H: $i, V_com2_H: $i, V_com2: $i] : ((~(c_Com_Ocom_OSemi(V_com1, V_com2) = c_Com_Ocom_OSemi(V_com1_H, V_com2_H))) | (V_com1 = V_com1_H))) | (~(c_Com_Ocom_OSemi(v_s_H, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP)) = c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z)))) | (v_s_H = v_c)),
% 24.93/25.09      inference(modus_ponens,[status(thm)],[390, 389])).
% 24.93/25.09  tff(392,plain,
% 24.93/25.09      ((~(c_Com_Ocom_OSemi(v_s_H, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP)) = c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z)))) | (v_s_H = v_c)),
% 24.93/25.09      inference(unit_resolution,[status(thm)],[391, 388])).
% 24.93/25.10  tff(393,plain,
% 24.93/25.10      (v_s_H = v_c),
% 24.93/25.10      inference(unit_resolution,[status(thm)],[392, 381])).
% 24.93/25.10  tff(394,plain,
% 24.93/25.10      (c_Natural_Oevalc(v_s_H, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(c_Com_Ocom_OSemi(v_s, c_Com_Ocom_OSKIP)))) <=> c_Natural_Oevalc(v_c, v_Z, v_Z_H(v_Z_H(c_Com_Ocom_OSemi(v_s, c_Com_Ocom_OSKIP))))),
% 24.93/25.10      inference(monotonicity,[status(thm)],[393, 55])).
% 24.93/25.10  tff(395,plain,
% 24.93/25.10      (c_Natural_Oevalc(v_c, v_Z, v_Z_H(v_Z_H(c_Com_Ocom_OSemi(v_s, c_Com_Ocom_OSKIP)))) <=> c_Natural_Oevalc(v_s_H, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(c_Com_Ocom_OSemi(v_s, c_Com_Ocom_OSKIP))))),
% 24.93/25.10      inference(symmetry,[status(thm)],[394])).
% 24.93/25.10  tff(396,assumption,(~(v_Z_H(c_Com_Ocom_OSemi(v_s, c_Com_Ocom_OSKIP)) = v_s_H)), introduced(assumption)).
% 24.93/25.10  tff(397,plain,
% 24.93/25.10      (((~![V_Z_Ha: $i] : ((V_Z_Ha = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(V_Z_Ha)))) | ((v_Z_H(c_Com_Ocom_OSemi(v_s, c_Com_Ocom_OSKIP)) = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(v_Z_H(c_Com_Ocom_OSemi(v_s, c_Com_Ocom_OSKIP)))))) <=> ((~![V_Z_Ha: $i] : ((V_Z_Ha = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(V_Z_Ha)))) | (v_Z_H(c_Com_Ocom_OSemi(v_s, c_Com_Ocom_OSKIP)) = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(v_Z_H(c_Com_Ocom_OSemi(v_s, c_Com_Ocom_OSKIP)))))),
% 24.93/25.10      inference(rewrite,[status(thm)],[])).
% 24.93/25.10  tff(398,plain,
% 24.93/25.10      ((~![V_Z_Ha: $i] : ((V_Z_Ha = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(V_Z_Ha)))) | ((v_Z_H(c_Com_Ocom_OSemi(v_s, c_Com_Ocom_OSKIP)) = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(v_Z_H(c_Com_Ocom_OSemi(v_s, c_Com_Ocom_OSKIP)))))),
% 24.93/25.10      inference(quant_inst,[status(thm)],[])).
% 24.93/25.10  tff(399,plain,
% 24.93/25.10      ((~![V_Z_Ha: $i] : ((V_Z_Ha = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(V_Z_Ha)))) | (v_Z_H(c_Com_Ocom_OSemi(v_s, c_Com_Ocom_OSKIP)) = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(v_Z_H(c_Com_Ocom_OSemi(v_s, c_Com_Ocom_OSKIP))))),
% 24.93/25.10      inference(modus_ponens,[status(thm)],[398, 397])).
% 24.93/25.10  tff(400,plain,
% 24.93/25.10      (c_Natural_Oevalc(v_c, v_Z, v_Z_H(v_Z_H(c_Com_Ocom_OSemi(v_s, c_Com_Ocom_OSKIP))))),
% 24.93/25.10      inference(unit_resolution,[status(thm)],[399, 78, 396])).
% 24.93/25.10  tff(401,plain,
% 24.93/25.10      (c_Natural_Oevalc(v_s_H, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(c_Com_Ocom_OSemi(v_s, c_Com_Ocom_OSKIP))))),
% 24.93/25.10      inference(modus_ponens,[status(thm)],[400, 395])).
% 24.93/25.10  tff(402,plain,
% 24.93/25.10      (c_Natural_Oevalc(v_s_H, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(c_Com_Ocom_OSemi(v_s, c_Com_Ocom_OSKIP))) <=> c_Natural_Oevalc(v_c, v_Z, v_Z_H(c_Com_Ocom_OSemi(v_s, c_Com_Ocom_OSKIP)))),
% 24.93/25.10      inference(monotonicity,[status(thm)],[393, 55])).
% 24.93/25.10  tff(403,plain,
% 24.93/25.10      (c_Natural_Oevalc(v_c, v_Z, v_Z_H(c_Com_Ocom_OSemi(v_s, c_Com_Ocom_OSKIP))) <=> c_Natural_Oevalc(v_s_H, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(c_Com_Ocom_OSemi(v_s, c_Com_Ocom_OSKIP)))),
% 24.93/25.10      inference(symmetry,[status(thm)],[402])).
% 24.93/25.10  tff(404,plain,
% 24.93/25.10      ((v_s_H = c_Com_Ocom_OSemi(v_s, c_Com_Ocom_OSKIP)) <=> (c_Com_Ocom_OSemi(v_s, c_Com_Ocom_OSKIP) = v_s_H)),
% 24.93/25.10      inference(commutativity,[status(thm)],[])).
% 24.93/25.10  tff(405,plain,
% 24.93/25.10      (v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2 = v_c),
% 24.93/25.10      inference(transitivity,[status(thm)],[260, 393])).
% 24.93/25.10  tff(406,plain,
% 24.93/25.10      (c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2, hAPP(v_s, v_Z)) = c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z))),
% 24.93/25.10      inference(monotonicity,[status(thm)],[405])).
% 24.93/25.10  tff(407,plain,
% 24.93/25.10      (c_Com_Ocom_OSemi(v_s_H, hAPP(v_s, v_Z)) = c_Com_Ocom_OSemi(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2, hAPP(v_s, v_Z))),
% 24.93/25.10      inference(monotonicity,[status(thm)],[261])).
% 24.93/25.10  tff(408,plain,
% 24.93/25.10      (c_Com_Ocom_OSemi(v_s_H, hAPP(v_s, v_Z)) = v_s_H),
% 24.93/25.10      inference(transitivity,[status(thm)],[407, 406, 380])).
% 24.93/25.10  tff(409,plain,
% 24.93/25.10      ((c_Com_Ocom_OSemi(v_s_H, hAPP(v_s, v_Z)) = c_Com_Ocom_OSemi(v_s, c_Com_Ocom_OSKIP)) <=> (v_s_H = c_Com_Ocom_OSemi(v_s, c_Com_Ocom_OSKIP))),
% 24.93/25.10      inference(monotonicity,[status(thm)],[408])).
% 24.93/25.10  tff(410,plain,
% 24.93/25.10      ((c_Com_Ocom_OSemi(v_s_H, hAPP(v_s, v_Z)) = c_Com_Ocom_OSemi(v_s, c_Com_Ocom_OSKIP)) <=> (c_Com_Ocom_OSemi(v_s, c_Com_Ocom_OSKIP) = v_s_H)),
% 24.93/25.10      inference(transitivity,[status(thm)],[409, 404])).
% 24.93/25.10  tff(411,plain,
% 24.93/25.10      ((~(c_Com_Ocom_OSemi(v_s_H, hAPP(v_s, v_Z)) = c_Com_Ocom_OSemi(v_s, c_Com_Ocom_OSKIP))) <=> (~(c_Com_Ocom_OSemi(v_s, c_Com_Ocom_OSKIP) = v_s_H))),
% 24.93/25.10      inference(monotonicity,[status(thm)],[410])).
% 24.93/25.10  tff(412,plain,
% 24.93/25.10      ((hAPP(v_s, v_Z) = c_Com_Ocom_OSKIP) <=> (c_Com_Ocom_OSKIP = hAPP(v_s, v_Z))),
% 24.93/25.10      inference(commutativity,[status(thm)],[])).
% 24.93/25.10  tff(413,plain,
% 24.93/25.10      ((c_Com_Ocom_OSKIP = hAPP(v_s, v_Z)) <=> (hAPP(v_s, v_Z) = c_Com_Ocom_OSKIP)),
% 24.93/25.10      inference(symmetry,[status(thm)],[412])).
% 24.93/25.10  tff(414,plain,
% 24.93/25.10      (^[V_com1: $i, V_com1_H: $i, V_com2_H: $i, V_com2: $i] : refl(((~(c_Com_Ocom_OSemi(V_com1, V_com2) = c_Com_Ocom_OSemi(V_com1_H, V_com2_H))) | (V_com2 = V_com2_H)) <=> ((~(c_Com_Ocom_OSemi(V_com1, V_com2) = c_Com_Ocom_OSemi(V_com1_H, V_com2_H))) | (V_com2 = V_com2_H)))),
% 24.93/25.10      inference(bind,[status(th)],[])).
% 24.93/25.10  tff(415,plain,
% 24.93/25.10      (![V_com1: $i, V_com1_H: $i, V_com2_H: $i, V_com2: $i] : ((~(c_Com_Ocom_OSemi(V_com1, V_com2) = c_Com_Ocom_OSemi(V_com1_H, V_com2_H))) | (V_com2 = V_com2_H)) <=> ![V_com1: $i, V_com1_H: $i, V_com2_H: $i, V_com2: $i] : ((~(c_Com_Ocom_OSemi(V_com1, V_com2) = c_Com_Ocom_OSemi(V_com1_H, V_com2_H))) | (V_com2 = V_com2_H))),
% 24.93/25.10      inference(quant_intro,[status(thm)],[414])).
% 24.93/25.10  tff(416,plain,
% 24.93/25.10      (![V_com1: $i, V_com1_H: $i, V_com2_H: $i, V_com2: $i] : ((~(c_Com_Ocom_OSemi(V_com1, V_com2) = c_Com_Ocom_OSemi(V_com1_H, V_com2_H))) | (V_com2 = V_com2_H)) <=> ![V_com1: $i, V_com1_H: $i, V_com2_H: $i, V_com2: $i] : ((~(c_Com_Ocom_OSemi(V_com1, V_com2) = c_Com_Ocom_OSemi(V_com1_H, V_com2_H))) | (V_com2 = V_com2_H))),
% 24.93/25.10      inference(rewrite,[status(thm)],[])).
% 24.93/25.10  tff(417,axiom,(![V_com1: $i, V_com1_H: $i, V_com2_H: $i, V_com2: $i] : ((~(c_Com_Ocom_OSemi(V_com1, V_com2) = c_Com_Ocom_OSemi(V_com1_H, V_com2_H))) | (V_com2 = V_com2_H))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_com_Osimps_I3_J_1')).
% 24.93/25.10  tff(418,plain,
% 24.93/25.10      (![V_com1: $i, V_com1_H: $i, V_com2_H: $i, V_com2: $i] : ((~(c_Com_Ocom_OSemi(V_com1, V_com2) = c_Com_Ocom_OSemi(V_com1_H, V_com2_H))) | (V_com2 = V_com2_H))),
% 24.93/25.10      inference(modus_ponens,[status(thm)],[417, 416])).
% 24.93/25.10  tff(419,plain,(
% 24.93/25.10      ![V_com1: $i, V_com1_H: $i, V_com2_H: $i, V_com2: $i] : ((~(c_Com_Ocom_OSemi(V_com1, V_com2) = c_Com_Ocom_OSemi(V_com1_H, V_com2_H))) | (V_com2 = V_com2_H))),
% 24.93/25.10      inference(skolemize,[status(sab)],[418])).
% 24.93/25.10  tff(420,plain,
% 24.93/25.10      (![V_com1: $i, V_com1_H: $i, V_com2_H: $i, V_com2: $i] : ((~(c_Com_Ocom_OSemi(V_com1, V_com2) = c_Com_Ocom_OSemi(V_com1_H, V_com2_H))) | (V_com2 = V_com2_H))),
% 24.93/25.10      inference(modus_ponens,[status(thm)],[419, 415])).
% 24.93/25.10  tff(421,plain,
% 24.93/25.10      (((~![V_com1: $i, V_com1_H: $i, V_com2_H: $i, V_com2: $i] : ((~(c_Com_Ocom_OSemi(V_com1, V_com2) = c_Com_Ocom_OSemi(V_com1_H, V_com2_H))) | (V_com2 = V_com2_H))) | ((~(c_Com_Ocom_OSemi(v_s_H, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP)) = c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z)))) | (c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP) = hAPP(v_s, v_Z)))) <=> ((~![V_com1: $i, V_com1_H: $i, V_com2_H: $i, V_com2: $i] : ((~(c_Com_Ocom_OSemi(V_com1, V_com2) = c_Com_Ocom_OSemi(V_com1_H, V_com2_H))) | (V_com2 = V_com2_H))) | (~(c_Com_Ocom_OSemi(v_s_H, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP)) = c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z)))) | (c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP) = hAPP(v_s, v_Z)))),
% 24.93/25.10      inference(rewrite,[status(thm)],[])).
% 24.93/25.10  tff(422,plain,
% 24.93/25.10      ((~![V_com1: $i, V_com1_H: $i, V_com2_H: $i, V_com2: $i] : ((~(c_Com_Ocom_OSemi(V_com1, V_com2) = c_Com_Ocom_OSemi(V_com1_H, V_com2_H))) | (V_com2 = V_com2_H))) | ((~(c_Com_Ocom_OSemi(v_s_H, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP)) = c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z)))) | (c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP) = hAPP(v_s, v_Z)))),
% 24.93/25.10      inference(quant_inst,[status(thm)],[])).
% 24.93/25.10  tff(423,plain,
% 24.93/25.10      ((~![V_com1: $i, V_com1_H: $i, V_com2_H: $i, V_com2: $i] : ((~(c_Com_Ocom_OSemi(V_com1, V_com2) = c_Com_Ocom_OSemi(V_com1_H, V_com2_H))) | (V_com2 = V_com2_H))) | (~(c_Com_Ocom_OSemi(v_s_H, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP)) = c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z)))) | (c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP) = hAPP(v_s, v_Z))),
% 24.93/25.10      inference(modus_ponens,[status(thm)],[422, 421])).
% 24.93/25.10  tff(424,plain,
% 24.93/25.10      ((~(c_Com_Ocom_OSemi(v_s_H, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP)) = c_Com_Ocom_OSemi(v_c, hAPP(v_s, v_Z)))) | (c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP) = hAPP(v_s, v_Z))),
% 24.93/25.10      inference(unit_resolution,[status(thm)],[423, 420])).
% 24.93/25.10  tff(425,plain,
% 24.93/25.10      (c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP) = hAPP(v_s, v_Z)),
% 24.93/25.10      inference(unit_resolution,[status(thm)],[424, 381])).
% 24.93/25.10  tff(426,plain,
% 24.93/25.10      ((c_Com_Ocom_OSKIP = c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP)) <=> (c_Com_Ocom_OSKIP = hAPP(v_s, v_Z))),
% 24.93/25.10      inference(monotonicity,[status(thm)],[425])).
% 24.93/25.10  tff(427,plain,
% 24.93/25.10      ((c_Com_Ocom_OSKIP = c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP)) <=> (hAPP(v_s, v_Z) = c_Com_Ocom_OSKIP)),
% 24.93/25.10      inference(transitivity,[status(thm)],[426, 413])).
% 24.93/25.10  tff(428,plain,
% 24.93/25.10      ((~(c_Com_Ocom_OSKIP = c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP))) <=> (~(hAPP(v_s, v_Z) = c_Com_Ocom_OSKIP))),
% 24.93/25.10      inference(monotonicity,[status(thm)],[427])).
% 24.93/25.10  tff(429,plain,
% 24.93/25.10      (^[V_com1_H: $i, V_com2_H: $i] : refl((~(c_Com_Ocom_OSKIP = c_Com_Ocom_OSemi(V_com1_H, V_com2_H))) <=> (~(c_Com_Ocom_OSKIP = c_Com_Ocom_OSemi(V_com1_H, V_com2_H))))),
% 24.93/25.10      inference(bind,[status(th)],[])).
% 24.93/25.10  tff(430,plain,
% 24.93/25.10      (![V_com1_H: $i, V_com2_H: $i] : (~(c_Com_Ocom_OSKIP = c_Com_Ocom_OSemi(V_com1_H, V_com2_H))) <=> ![V_com1_H: $i, V_com2_H: $i] : (~(c_Com_Ocom_OSKIP = c_Com_Ocom_OSemi(V_com1_H, V_com2_H)))),
% 24.93/25.10      inference(quant_intro,[status(thm)],[429])).
% 24.93/25.10  tff(431,plain,
% 24.93/25.10      (![V_com1_H: $i, V_com2_H: $i] : (~(c_Com_Ocom_OSKIP = c_Com_Ocom_OSemi(V_com1_H, V_com2_H))) <=> ![V_com1_H: $i, V_com2_H: $i] : (~(c_Com_Ocom_OSKIP = c_Com_Ocom_OSemi(V_com1_H, V_com2_H)))),
% 24.93/25.10      inference(rewrite,[status(thm)],[])).
% 24.93/25.10  tff(432,axiom,(![V_com1_H: $i, V_com2_H: $i] : (~(c_Com_Ocom_OSKIP = c_Com_Ocom_OSemi(V_com1_H, V_com2_H)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_com_Osimps_I12_J_0')).
% 24.93/25.10  tff(433,plain,
% 24.93/25.10      (![V_com1_H: $i, V_com2_H: $i] : (~(c_Com_Ocom_OSKIP = c_Com_Ocom_OSemi(V_com1_H, V_com2_H)))),
% 24.93/25.10      inference(modus_ponens,[status(thm)],[432, 431])).
% 24.93/25.10  tff(434,plain,(
% 24.93/25.10      ![V_com1_H: $i, V_com2_H: $i] : (~(c_Com_Ocom_OSKIP = c_Com_Ocom_OSemi(V_com1_H, V_com2_H)))),
% 24.93/25.10      inference(skolemize,[status(sab)],[433])).
% 24.93/25.10  tff(435,plain,
% 24.93/25.10      (![V_com1_H: $i, V_com2_H: $i] : (~(c_Com_Ocom_OSKIP = c_Com_Ocom_OSemi(V_com1_H, V_com2_H)))),
% 24.93/25.10      inference(modus_ponens,[status(thm)],[434, 430])).
% 24.93/25.10  tff(436,plain,
% 24.93/25.10      ((~![V_com1_H: $i, V_com2_H: $i] : (~(c_Com_Ocom_OSKIP = c_Com_Ocom_OSemi(V_com1_H, V_com2_H)))) | (~(c_Com_Ocom_OSKIP = c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP)))),
% 24.93/25.10      inference(quant_inst,[status(thm)],[])).
% 24.93/25.10  tff(437,plain,
% 24.93/25.10      (~(c_Com_Ocom_OSKIP = c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP))),
% 24.93/25.10      inference(unit_resolution,[status(thm)],[436, 435])).
% 24.93/25.10  tff(438,plain,
% 24.93/25.10      (~(hAPP(v_s, v_Z) = c_Com_Ocom_OSKIP)),
% 24.93/25.10      inference(modus_ponens,[status(thm)],[437, 428])).
% 24.93/25.10  tff(439,plain,
% 24.93/25.10      (((~![V_com1: $i, V_com1_H: $i, V_com2_H: $i, V_com2: $i] : ((~(c_Com_Ocom_OSemi(V_com1, V_com2) = c_Com_Ocom_OSemi(V_com1_H, V_com2_H))) | (V_com2 = V_com2_H))) | ((~(c_Com_Ocom_OSemi(v_s_H, hAPP(v_s, v_Z)) = c_Com_Ocom_OSemi(v_s, c_Com_Ocom_OSKIP))) | (hAPP(v_s, v_Z) = c_Com_Ocom_OSKIP))) <=> ((~![V_com1: $i, V_com1_H: $i, V_com2_H: $i, V_com2: $i] : ((~(c_Com_Ocom_OSemi(V_com1, V_com2) = c_Com_Ocom_OSemi(V_com1_H, V_com2_H))) | (V_com2 = V_com2_H))) | (~(c_Com_Ocom_OSemi(v_s_H, hAPP(v_s, v_Z)) = c_Com_Ocom_OSemi(v_s, c_Com_Ocom_OSKIP))) | (hAPP(v_s, v_Z) = c_Com_Ocom_OSKIP))),
% 24.93/25.10      inference(rewrite,[status(thm)],[])).
% 24.93/25.10  tff(440,plain,
% 24.93/25.10      ((~![V_com1: $i, V_com1_H: $i, V_com2_H: $i, V_com2: $i] : ((~(c_Com_Ocom_OSemi(V_com1, V_com2) = c_Com_Ocom_OSemi(V_com1_H, V_com2_H))) | (V_com2 = V_com2_H))) | ((~(c_Com_Ocom_OSemi(v_s_H, hAPP(v_s, v_Z)) = c_Com_Ocom_OSemi(v_s, c_Com_Ocom_OSKIP))) | (hAPP(v_s, v_Z) = c_Com_Ocom_OSKIP))),
% 24.93/25.10      inference(quant_inst,[status(thm)],[])).
% 24.93/25.10  tff(441,plain,
% 24.93/25.10      ((~![V_com1: $i, V_com1_H: $i, V_com2_H: $i, V_com2: $i] : ((~(c_Com_Ocom_OSemi(V_com1, V_com2) = c_Com_Ocom_OSemi(V_com1_H, V_com2_H))) | (V_com2 = V_com2_H))) | (~(c_Com_Ocom_OSemi(v_s_H, hAPP(v_s, v_Z)) = c_Com_Ocom_OSemi(v_s, c_Com_Ocom_OSKIP))) | (hAPP(v_s, v_Z) = c_Com_Ocom_OSKIP)),
% 24.93/25.10      inference(modus_ponens,[status(thm)],[440, 439])).
% 24.93/25.10  tff(442,plain,
% 24.93/25.10      (~(c_Com_Ocom_OSemi(v_s_H, hAPP(v_s, v_Z)) = c_Com_Ocom_OSemi(v_s, c_Com_Ocom_OSKIP))),
% 24.93/25.10      inference(unit_resolution,[status(thm)],[441, 420, 438])).
% 24.93/25.10  tff(443,plain,
% 24.93/25.10      (~(c_Com_Ocom_OSemi(v_s, c_Com_Ocom_OSKIP) = v_s_H)),
% 24.93/25.10      inference(modus_ponens,[status(thm)],[442, 411])).
% 24.93/25.10  tff(444,plain,
% 24.93/25.10      (((~![V_Z_Ha: $i] : ((V_Z_Ha = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(V_Z_Ha)))) | ((c_Com_Ocom_OSemi(v_s, c_Com_Ocom_OSKIP) = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(c_Com_Ocom_OSemi(v_s, c_Com_Ocom_OSKIP))))) <=> ((~![V_Z_Ha: $i] : ((V_Z_Ha = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(V_Z_Ha)))) | (c_Com_Ocom_OSemi(v_s, c_Com_Ocom_OSKIP) = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(c_Com_Ocom_OSemi(v_s, c_Com_Ocom_OSKIP))))),
% 24.93/25.10      inference(rewrite,[status(thm)],[])).
% 24.93/25.10  tff(445,plain,
% 24.93/25.10      ((~![V_Z_Ha: $i] : ((V_Z_Ha = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(V_Z_Ha)))) | ((c_Com_Ocom_OSemi(v_s, c_Com_Ocom_OSKIP) = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(c_Com_Ocom_OSemi(v_s, c_Com_Ocom_OSKIP))))),
% 24.93/25.10      inference(quant_inst,[status(thm)],[])).
% 24.93/25.10  tff(446,plain,
% 24.93/25.10      ((~![V_Z_Ha: $i] : ((V_Z_Ha = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(V_Z_Ha)))) | (c_Com_Ocom_OSemi(v_s, c_Com_Ocom_OSKIP) = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(c_Com_Ocom_OSemi(v_s, c_Com_Ocom_OSKIP)))),
% 24.93/25.10      inference(modus_ponens,[status(thm)],[445, 444])).
% 24.93/25.10  tff(447,plain,
% 24.93/25.10      ((c_Com_Ocom_OSemi(v_s, c_Com_Ocom_OSKIP) = v_s_H) | c_Natural_Oevalc(v_c, v_Z, v_Z_H(c_Com_Ocom_OSemi(v_s, c_Com_Ocom_OSKIP)))),
% 24.93/25.10      inference(unit_resolution,[status(thm)],[446, 78])).
% 24.93/25.10  tff(448,plain,
% 24.93/25.10      (c_Natural_Oevalc(v_c, v_Z, v_Z_H(c_Com_Ocom_OSemi(v_s, c_Com_Ocom_OSKIP)))),
% 24.93/25.10      inference(unit_resolution,[status(thm)],[447, 443])).
% 24.93/25.10  tff(449,plain,
% 24.93/25.10      (c_Natural_Oevalc(v_s_H, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(c_Com_Ocom_OSemi(v_s, c_Com_Ocom_OSKIP)))),
% 24.93/25.10      inference(modus_ponens,[status(thm)],[448, 403])).
% 24.93/25.10  tff(450,plain,
% 24.93/25.10      (((~![V_Z_Ha: $i] : ((~(V_Z_Ha = v_Z_H(V_Z_Ha))) | (V_Z_Ha = v_s_H))) | ((~(v_Z_H(c_Com_Ocom_OSemi(v_s, c_Com_Ocom_OSKIP)) = v_Z_H(v_Z_H(c_Com_Ocom_OSemi(v_s, c_Com_Ocom_OSKIP))))) | (v_Z_H(c_Com_Ocom_OSemi(v_s, c_Com_Ocom_OSKIP)) = v_s_H))) <=> ((~![V_Z_Ha: $i] : ((~(V_Z_Ha = v_Z_H(V_Z_Ha))) | (V_Z_Ha = v_s_H))) | (~(v_Z_H(c_Com_Ocom_OSemi(v_s, c_Com_Ocom_OSKIP)) = v_Z_H(v_Z_H(c_Com_Ocom_OSemi(v_s, c_Com_Ocom_OSKIP))))) | (v_Z_H(c_Com_Ocom_OSemi(v_s, c_Com_Ocom_OSKIP)) = v_s_H))),
% 24.93/25.10      inference(rewrite,[status(thm)],[])).
% 24.93/25.10  tff(451,plain,
% 24.93/25.10      ((~![V_Z_Ha: $i] : ((~(V_Z_Ha = v_Z_H(V_Z_Ha))) | (V_Z_Ha = v_s_H))) | ((~(v_Z_H(c_Com_Ocom_OSemi(v_s, c_Com_Ocom_OSKIP)) = v_Z_H(v_Z_H(c_Com_Ocom_OSemi(v_s, c_Com_Ocom_OSKIP))))) | (v_Z_H(c_Com_Ocom_OSemi(v_s, c_Com_Ocom_OSKIP)) = v_s_H))),
% 24.93/25.10      inference(quant_inst,[status(thm)],[])).
% 24.93/25.10  tff(452,plain,
% 24.93/25.10      ((~![V_Z_Ha: $i] : ((~(V_Z_Ha = v_Z_H(V_Z_Ha))) | (V_Z_Ha = v_s_H))) | (~(v_Z_H(c_Com_Ocom_OSemi(v_s, c_Com_Ocom_OSKIP)) = v_Z_H(v_Z_H(c_Com_Ocom_OSemi(v_s, c_Com_Ocom_OSKIP))))) | (v_Z_H(c_Com_Ocom_OSemi(v_s, c_Com_Ocom_OSKIP)) = v_s_H)),
% 24.93/25.10      inference(modus_ponens,[status(thm)],[451, 450])).
% 24.93/25.10  tff(453,plain,
% 24.93/25.10      ((~(v_Z_H(c_Com_Ocom_OSemi(v_s, c_Com_Ocom_OSKIP)) = v_Z_H(v_Z_H(c_Com_Ocom_OSemi(v_s, c_Com_Ocom_OSKIP))))) | (v_Z_H(c_Com_Ocom_OSemi(v_s, c_Com_Ocom_OSKIP)) = v_s_H)),
% 24.93/25.10      inference(unit_resolution,[status(thm)],[452, 90])).
% 24.93/25.10  tff(454,plain,
% 24.93/25.10      (~(v_Z_H(c_Com_Ocom_OSemi(v_s, c_Com_Ocom_OSKIP)) = v_Z_H(v_Z_H(c_Com_Ocom_OSemi(v_s, c_Com_Ocom_OSKIP))))),
% 24.93/25.10      inference(unit_resolution,[status(thm)],[453, 396])).
% 24.93/25.10  tff(455,plain,
% 24.93/25.10      (((~![V_c: $i, V_u: $i, V_t: $i, V_s: $i] : ((~c_Natural_Oevalc(V_c, V_s, V_t)) | (~c_Natural_Oevalc(V_c, V_s, V_u)) | (V_u = V_t))) | ((~c_Natural_Oevalc(v_s_H, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(c_Com_Ocom_OSemi(v_s, c_Com_Ocom_OSKIP)))) | (v_Z_H(c_Com_Ocom_OSemi(v_s, c_Com_Ocom_OSKIP)) = v_Z_H(v_Z_H(c_Com_Ocom_OSemi(v_s, c_Com_Ocom_OSKIP)))) | (~c_Natural_Oevalc(v_s_H, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(c_Com_Ocom_OSemi(v_s, c_Com_Ocom_OSKIP))))))) <=> ((~![V_c: $i, V_u: $i, V_t: $i, V_s: $i] : ((~c_Natural_Oevalc(V_c, V_s, V_t)) | (~c_Natural_Oevalc(V_c, V_s, V_u)) | (V_u = V_t))) | (~c_Natural_Oevalc(v_s_H, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(c_Com_Ocom_OSemi(v_s, c_Com_Ocom_OSKIP)))) | (v_Z_H(c_Com_Ocom_OSemi(v_s, c_Com_Ocom_OSKIP)) = v_Z_H(v_Z_H(c_Com_Ocom_OSemi(v_s, c_Com_Ocom_OSKIP)))) | (~c_Natural_Oevalc(v_s_H, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(c_Com_Ocom_OSemi(v_s, c_Com_Ocom_OSKIP))))))),
% 24.93/25.10      inference(rewrite,[status(thm)],[])).
% 24.93/25.10  tff(456,plain,
% 24.93/25.10      (((~c_Natural_Oevalc(v_s_H, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(c_Com_Ocom_OSemi(v_s, c_Com_Ocom_OSKIP))))) | (~c_Natural_Oevalc(v_s_H, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(c_Com_Ocom_OSemi(v_s, c_Com_Ocom_OSKIP)))) | (v_Z_H(c_Com_Ocom_OSemi(v_s, c_Com_Ocom_OSKIP)) = v_Z_H(v_Z_H(c_Com_Ocom_OSemi(v_s, c_Com_Ocom_OSKIP))))) <=> ((~c_Natural_Oevalc(v_s_H, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(c_Com_Ocom_OSemi(v_s, c_Com_Ocom_OSKIP)))) | (v_Z_H(c_Com_Ocom_OSemi(v_s, c_Com_Ocom_OSKIP)) = v_Z_H(v_Z_H(c_Com_Ocom_OSemi(v_s, c_Com_Ocom_OSKIP)))) | (~c_Natural_Oevalc(v_s_H, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(c_Com_Ocom_OSemi(v_s, c_Com_Ocom_OSKIP))))))),
% 24.93/25.10      inference(rewrite,[status(thm)],[])).
% 24.93/25.10  tff(457,plain,
% 24.93/25.10      (((~![V_c: $i, V_u: $i, V_t: $i, V_s: $i] : ((~c_Natural_Oevalc(V_c, V_s, V_t)) | (~c_Natural_Oevalc(V_c, V_s, V_u)) | (V_u = V_t))) | ((~c_Natural_Oevalc(v_s_H, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(c_Com_Ocom_OSemi(v_s, c_Com_Ocom_OSKIP))))) | (~c_Natural_Oevalc(v_s_H, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(c_Com_Ocom_OSemi(v_s, c_Com_Ocom_OSKIP)))) | (v_Z_H(c_Com_Ocom_OSemi(v_s, c_Com_Ocom_OSKIP)) = v_Z_H(v_Z_H(c_Com_Ocom_OSemi(v_s, c_Com_Ocom_OSKIP)))))) <=> ((~![V_c: $i, V_u: $i, V_t: $i, V_s: $i] : ((~c_Natural_Oevalc(V_c, V_s, V_t)) | (~c_Natural_Oevalc(V_c, V_s, V_u)) | (V_u = V_t))) | ((~c_Natural_Oevalc(v_s_H, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(c_Com_Ocom_OSemi(v_s, c_Com_Ocom_OSKIP)))) | (v_Z_H(c_Com_Ocom_OSemi(v_s, c_Com_Ocom_OSKIP)) = v_Z_H(v_Z_H(c_Com_Ocom_OSemi(v_s, c_Com_Ocom_OSKIP)))) | (~c_Natural_Oevalc(v_s_H, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(c_Com_Ocom_OSemi(v_s, c_Com_Ocom_OSKIP)))))))),
% 24.93/25.10      inference(monotonicity,[status(thm)],[456])).
% 24.93/25.10  tff(458,plain,
% 24.93/25.10      (((~![V_c: $i, V_u: $i, V_t: $i, V_s: $i] : ((~c_Natural_Oevalc(V_c, V_s, V_t)) | (~c_Natural_Oevalc(V_c, V_s, V_u)) | (V_u = V_t))) | ((~c_Natural_Oevalc(v_s_H, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(c_Com_Ocom_OSemi(v_s, c_Com_Ocom_OSKIP))))) | (~c_Natural_Oevalc(v_s_H, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(c_Com_Ocom_OSemi(v_s, c_Com_Ocom_OSKIP)))) | (v_Z_H(c_Com_Ocom_OSemi(v_s, c_Com_Ocom_OSKIP)) = v_Z_H(v_Z_H(c_Com_Ocom_OSemi(v_s, c_Com_Ocom_OSKIP)))))) <=> ((~![V_c: $i, V_u: $i, V_t: $i, V_s: $i] : ((~c_Natural_Oevalc(V_c, V_s, V_t)) | (~c_Natural_Oevalc(V_c, V_s, V_u)) | (V_u = V_t))) | (~c_Natural_Oevalc(v_s_H, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(c_Com_Ocom_OSemi(v_s, c_Com_Ocom_OSKIP)))) | (v_Z_H(c_Com_Ocom_OSemi(v_s, c_Com_Ocom_OSKIP)) = v_Z_H(v_Z_H(c_Com_Ocom_OSemi(v_s, c_Com_Ocom_OSKIP)))) | (~c_Natural_Oevalc(v_s_H, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(c_Com_Ocom_OSemi(v_s, c_Com_Ocom_OSKIP))))))),
% 24.93/25.10      inference(transitivity,[status(thm)],[457, 455])).
% 24.93/25.10  tff(459,plain,
% 24.93/25.10      ((~![V_c: $i, V_u: $i, V_t: $i, V_s: $i] : ((~c_Natural_Oevalc(V_c, V_s, V_t)) | (~c_Natural_Oevalc(V_c, V_s, V_u)) | (V_u = V_t))) | ((~c_Natural_Oevalc(v_s_H, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(c_Com_Ocom_OSemi(v_s, c_Com_Ocom_OSKIP))))) | (~c_Natural_Oevalc(v_s_H, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(c_Com_Ocom_OSemi(v_s, c_Com_Ocom_OSKIP)))) | (v_Z_H(c_Com_Ocom_OSemi(v_s, c_Com_Ocom_OSKIP)) = v_Z_H(v_Z_H(c_Com_Ocom_OSemi(v_s, c_Com_Ocom_OSKIP)))))),
% 24.93/25.10      inference(quant_inst,[status(thm)],[])).
% 24.93/25.10  tff(460,plain,
% 24.93/25.10      ((~![V_c: $i, V_u: $i, V_t: $i, V_s: $i] : ((~c_Natural_Oevalc(V_c, V_s, V_t)) | (~c_Natural_Oevalc(V_c, V_s, V_u)) | (V_u = V_t))) | (~c_Natural_Oevalc(v_s_H, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(c_Com_Ocom_OSemi(v_s, c_Com_Ocom_OSKIP)))) | (v_Z_H(c_Com_Ocom_OSemi(v_s, c_Com_Ocom_OSKIP)) = v_Z_H(v_Z_H(c_Com_Ocom_OSemi(v_s, c_Com_Ocom_OSKIP)))) | (~c_Natural_Oevalc(v_s_H, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(c_Com_Ocom_OSemi(v_s, c_Com_Ocom_OSKIP)))))),
% 24.93/25.10      inference(modus_ponens,[status(thm)],[459, 458])).
% 24.93/25.10  tff(461,plain,
% 24.93/25.10      (~c_Natural_Oevalc(v_s_H, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_Z_H(v_Z_H(c_Com_Ocom_OSemi(v_s, c_Com_Ocom_OSKIP))))),
% 24.93/25.10      inference(unit_resolution,[status(thm)],[460, 108, 454, 449])).
% 24.93/25.10  tff(462,plain,
% 24.93/25.10      ($false),
% 24.93/25.10      inference(unit_resolution,[status(thm)],[461, 401])).
% 24.93/25.10  tff(463,plain,(v_Z_H(c_Com_Ocom_OSemi(v_s, c_Com_Ocom_OSKIP)) = v_s_H), inference(lemma,lemma(discharge,[]))).
% 24.93/25.10  tff(464,plain,
% 24.93/25.10      (v_s_H = v_Z_H(c_Com_Ocom_OSemi(v_s, c_Com_Ocom_OSKIP))),
% 24.93/25.10      inference(symmetry,[status(thm)],[463])).
% 24.93/25.10  tff(465,plain,
% 24.93/25.10      (c_Natural_Oevalc(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_s_H) <=> c_Natural_Oevalc(v_c, v_Z, v_Z_H(c_Com_Ocom_OSemi(v_s, c_Com_Ocom_OSKIP)))),
% 24.93/25.10      inference(monotonicity,[status(thm)],[405, 55, 464])).
% 24.93/25.10  tff(466,plain,
% 24.93/25.10      (c_Natural_Oevalc(v_c, v_Z, v_Z_H(c_Com_Ocom_OSemi(v_s, c_Com_Ocom_OSKIP))) <=> c_Natural_Oevalc(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_s_H)),
% 24.93/25.10      inference(symmetry,[status(thm)],[465])).
% 24.93/25.10  tff(467,plain,
% 24.93/25.10      (c_Natural_Oevalc(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_s_H)),
% 24.93/25.10      inference(modus_ponens,[status(thm)],[448, 466])).
% 24.93/25.10  tff(468,plain,
% 24.93/25.10      (v_c = v_s_H),
% 24.93/25.10      inference(symmetry,[status(thm)],[393])).
% 24.93/25.10  tff(469,plain,
% 24.93/25.10      (v_c = v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2),
% 24.93/25.10      inference(transitivity,[status(thm)],[468, 261])).
% 24.93/25.10  tff(470,plain,
% 24.93/25.10      (c_Natural_Oevalc(v_c, v_Z, v_s_H) <=> c_Natural_Oevalc(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_s_H)),
% 24.93/25.11      inference(monotonicity,[status(thm)],[469, 54])).
% 24.93/25.11  tff(471,plain,
% 24.93/25.11      ((~c_Natural_Oevalc(v_c, v_Z, v_s_H)) <=> (~c_Natural_Oevalc(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_s_H))),
% 24.93/25.11      inference(monotonicity,[status(thm)],[470])).
% 24.93/25.11  tff(472,plain,
% 24.93/25.11      (~c_Natural_Oevalc(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2, c_Natural_Osko__Natural__Xevalc__elim__cases__4__1(c_Com_Ocom_OSKIP, c_Com_Ocom_OSKIP, v_Z, v_Z), v_s_H)),
% 24.93/25.11      inference(modus_ponens,[status(thm)],[67, 471])).
% 24.93/25.11  tff(473,plain,
% 24.93/25.11      ($false),
% 24.93/25.11      inference(unit_resolution,[status(thm)],[472, 467])).
% 24.93/25.11  % SZS output end Proof
% 24.93/25.12  % E exiting
%------------------------------------------------------------------------------