%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWW302+1 : TPTP v9.0.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.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 05:36:48 AM UTC 2025
% Result : Theorem 18.06s 18.23s
% Output : Proof 18.40s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.12 % Problem : SWW302+1 : TPTP v9.0.0. Released v5.2.0.
% 0.02/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n001.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 11:29:35 EDT 2025
% 0.11/0.33 % CPUTime :
% 18.06/18.23 % SZS status Theorem
% 18.06/18.23 % SZS output start Proof
% 18.06/18.23 tff(v_Q_H_type, type, (
% 18.06/18.23 v_Q_H: ( $i * $i ) > $o)).
% 18.06/18.23 tff(tptp_fun_B_s_H_514_type, type, (
% 18.06/18.23 tptp_fun_B_s_H_514: $i)).
% 18.06/18.23 tff(tptp_fun_B_Z_513_type, type, (
% 18.06/18.23 tptp_fun_B_Z_513: $i)).
% 18.06/18.23 tff(v_Q_type, type, (
% 18.06/18.23 v_Q: ( $i * $i ) > $o)).
% 18.06/18.23 tff(v_P_type, type, (
% 18.06/18.23 v_P: ( $i * $i ) > $o)).
% 18.06/18.23 tff(tptp_fun_B_s_512_type, type, (
% 18.06/18.23 tptp_fun_B_s_512: $i)).
% 18.06/18.23 tff(1,plain,
% 18.06/18.23 ((v_P(B_Z!513, B_s!512) & (![B_Z_H: $i] : ((~v_P(B_Z_H, B_s!512)) | v_Q_H(B_Z_H, B_s_H!514)) & (~v_Q(B_Z!513, B_s_H!514)))) <=> (v_P(B_Z!513, B_s!512) & ![B_Z_H: $i] : ((~v_P(B_Z_H, B_s!512)) | v_Q_H(B_Z_H, B_s_H!514)) & (~v_Q(B_Z!513, B_s_H!514)))),
% 18.06/18.23 inference(rewrite,[status(thm)],[])).
% 18.06/18.23 tff(2,plain,
% 18.06/18.23 ((![B_Z_H: $i] : ((~v_P(B_Z_H, B_s!512)) | v_Q_H(B_Z_H, B_s_H!514)) & (~v_Q(B_Z!513, B_s_H!514))) <=> (![B_Z_H: $i] : ((~v_P(B_Z_H, B_s!512)) | v_Q_H(B_Z_H, B_s_H!514)) & (~v_Q(B_Z!513, B_s_H!514)))),
% 18.06/18.23 inference(rewrite,[status(thm)],[])).
% 18.06/18.23 tff(3,plain,
% 18.06/18.23 ((v_P(B_Z!513, B_s!512) & (![B_Z_H: $i] : ((~v_P(B_Z_H, B_s!512)) | v_Q_H(B_Z_H, B_s_H!514)) & (~v_Q(B_Z!513, B_s_H!514)))) <=> (v_P(B_Z!513, B_s!512) & (![B_Z_H: $i] : ((~v_P(B_Z_H, B_s!512)) | v_Q_H(B_Z_H, B_s_H!514)) & (~v_Q(B_Z!513, B_s_H!514))))),
% 18.06/18.23 inference(monotonicity,[status(thm)],[2])).
% 18.06/18.23 tff(4,plain,
% 18.06/18.23 ((v_P(B_Z!513, B_s!512) & (![B_Z_H: $i] : ((~v_P(B_Z_H, B_s!512)) | v_Q_H(B_Z_H, B_s_H!514)) & (~v_Q(B_Z!513, B_s_H!514)))) <=> (v_P(B_Z!513, B_s!512) & ![B_Z_H: $i] : ((~v_P(B_Z_H, B_s!512)) | v_Q_H(B_Z_H, B_s_H!514)) & (~v_Q(B_Z!513, B_s_H!514)))),
% 18.06/18.23 inference(transitivity,[status(thm)],[3, 1])).
% 18.06/18.23 tff(5,plain,
% 18.06/18.23 ((~![B_Z: $i, B_s: $i] : ((~v_P(B_Z, B_s)) | ![B_s_H: $i] : ((~![B_Z_H: $i] : ((~v_P(B_Z_H, B_s)) | v_Q_H(B_Z_H, B_s_H))) | v_Q(B_Z, B_s_H)))) <=> (~![B_Z: $i, B_s: $i] : ((~v_P(B_Z, B_s)) | ![B_s_H: $i] : ((~![B_Z_H: $i] : ((~v_P(B_Z_H, B_s)) | v_Q_H(B_Z_H, B_s_H))) | v_Q(B_Z, B_s_H))))),
% 18.06/18.23 inference(rewrite,[status(thm)],[])).
% 18.06/18.23 tff(6,plain,
% 18.06/18.23 ((~![B_Z: $i, B_s: $i] : (v_P(B_Z, B_s) => ![B_s_H: $i] : (![B_Z_H: $i] : (v_P(B_Z_H, B_s) => v_Q_H(B_Z_H, B_s_H)) => v_Q(B_Z, B_s_H)))) <=> (~![B_Z: $i, B_s: $i] : ((~v_P(B_Z, B_s)) | ![B_s_H: $i] : ((~![B_Z_H: $i] : ((~v_P(B_Z_H, B_s)) | v_Q_H(B_Z_H, B_s_H))) | v_Q(B_Z, B_s_H))))),
% 18.06/18.23 inference(rewrite,[status(thm)],[])).
% 18.06/18.23 tff(7,axiom,(~![B_Z: $i, B_s: $i] : (v_P(B_Z, B_s) => ![B_s_H: $i] : (![B_Z_H: $i] : (v_P(B_Z_H, B_s) => v_Q_H(B_Z_H, B_s_H)) => v_Q(B_Z, B_s_H)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','conj_1')).
% 18.06/18.23 tff(8,plain,
% 18.06/18.23 (~![B_Z: $i, B_s: $i] : ((~v_P(B_Z, B_s)) | ![B_s_H: $i] : ((~![B_Z_H: $i] : ((~v_P(B_Z_H, B_s)) | v_Q_H(B_Z_H, B_s_H))) | v_Q(B_Z, B_s_H)))),
% 18.06/18.23 inference(modus_ponens,[status(thm)],[7, 6])).
% 18.06/18.23 tff(9,plain,
% 18.06/18.23 (~![B_Z: $i, B_s: $i] : ((~v_P(B_Z, B_s)) | ![B_s_H: $i] : ((~![B_Z_H: $i] : ((~v_P(B_Z_H, B_s)) | v_Q_H(B_Z_H, B_s_H))) | v_Q(B_Z, B_s_H)))),
% 18.06/18.23 inference(modus_ponens,[status(thm)],[8, 5])).
% 18.06/18.23 tff(10,plain,
% 18.06/18.23 (~![B_Z: $i, B_s: $i] : ((~v_P(B_Z, B_s)) | ![B_s_H: $i] : ((~![B_Z_H: $i] : ((~v_P(B_Z_H, B_s)) | v_Q_H(B_Z_H, B_s_H))) | v_Q(B_Z, B_s_H)))),
% 18.06/18.23 inference(modus_ponens,[status(thm)],[9, 5])).
% 18.06/18.23 tff(11,plain,
% 18.06/18.23 (~![B_Z: $i, B_s: $i] : ((~v_P(B_Z, B_s)) | ![B_s_H: $i] : ((~![B_Z_H: $i] : ((~v_P(B_Z_H, B_s)) | v_Q_H(B_Z_H, B_s_H))) | v_Q(B_Z, B_s_H)))),
% 18.06/18.23 inference(modus_ponens,[status(thm)],[10, 5])).
% 18.06/18.23 tff(12,plain,
% 18.06/18.23 (v_P(B_Z!513, B_s!512) & ![B_Z_H: $i] : ((~v_P(B_Z_H, B_s!512)) | v_Q_H(B_Z_H, B_s_H!514)) & (~v_Q(B_Z!513, B_s_H!514))),
% 18.06/18.23 inference(modus_ponens,[status(thm)],[11, 4])).
% 18.06/18.23 tff(13,plain,
% 18.06/18.23 (~v_Q(B_Z!513, B_s_H!514)),
% 18.06/18.23 inference(and_elim,[status(thm)],[12])).
% 18.06/18.23 tff(14,plain,
% 18.06/18.23 (^[B_Z: $i, B_s: $i] : refl(((~v_Q_H(B_Z, B_s)) | v_Q(B_Z, B_s)) <=> ((~v_Q_H(B_Z, B_s)) | v_Q(B_Z, B_s)))),
% 18.06/18.23 inference(bind,[status(th)],[])).
% 18.06/18.23 tff(15,plain,
% 18.06/18.23 (![B_Z: $i, B_s: $i] : ((~v_Q_H(B_Z, B_s)) | v_Q(B_Z, B_s)) <=> ![B_Z: $i, B_s: $i] : ((~v_Q_H(B_Z, B_s)) | v_Q(B_Z, B_s))),
% 18.06/18.23 inference(quant_intro,[status(thm)],[14])).
% 18.06/18.23 tff(16,plain,
% 18.06/18.23 (![B_Z: $i, B_s: $i] : ((~v_Q_H(B_Z, B_s)) | v_Q(B_Z, B_s)) <=> ![B_Z: $i, B_s: $i] : ((~v_Q_H(B_Z, B_s)) | v_Q(B_Z, B_s))),
% 18.40/18.63 inference(rewrite,[status(thm)],[])).
% 18.40/18.63 tff(17,plain,
% 18.40/18.63 (^[B_Z: $i, B_s: $i] : rewrite((v_Q_H(B_Z, B_s) => v_Q(B_Z, B_s)) <=> ((~v_Q_H(B_Z, B_s)) | v_Q(B_Z, B_s)))),
% 18.40/18.63 inference(bind,[status(th)],[])).
% 18.40/18.63 tff(18,plain,
% 18.40/18.63 (![B_Z: $i, B_s: $i] : (v_Q_H(B_Z, B_s) => v_Q(B_Z, B_s)) <=> ![B_Z: $i, B_s: $i] : ((~v_Q_H(B_Z, B_s)) | v_Q(B_Z, B_s))),
% 18.40/18.63 inference(quant_intro,[status(thm)],[17])).
% 18.40/18.63 tff(19,axiom,(![B_Z: $i, B_s: $i] : (v_Q_H(B_Z, B_s) => v_Q(B_Z, B_s))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','conj_0')).
% 18.40/18.63 tff(20,plain,
% 18.40/18.63 (![B_Z: $i, B_s: $i] : ((~v_Q_H(B_Z, B_s)) | v_Q(B_Z, B_s))),
% 18.40/18.63 inference(modus_ponens,[status(thm)],[19, 18])).
% 18.40/18.63 tff(21,plain,
% 18.40/18.63 (![B_Z: $i, B_s: $i] : ((~v_Q_H(B_Z, B_s)) | v_Q(B_Z, B_s))),
% 18.40/18.63 inference(modus_ponens,[status(thm)],[20, 16])).
% 18.40/18.63 tff(22,plain,(
% 18.40/18.63 ![B_Z: $i, B_s: $i] : ((~v_Q_H(B_Z, B_s)) | v_Q(B_Z, B_s))),
% 18.40/18.63 inference(skolemize,[status(sab)],[21])).
% 18.40/18.63 tff(23,plain,
% 18.40/18.63 (![B_Z: $i, B_s: $i] : ((~v_Q_H(B_Z, B_s)) | v_Q(B_Z, B_s))),
% 18.40/18.63 inference(modus_ponens,[status(thm)],[22, 15])).
% 18.40/18.63 tff(24,plain,
% 18.40/18.63 (((~![B_Z: $i, B_s: $i] : ((~v_Q_H(B_Z, B_s)) | v_Q(B_Z, B_s))) | ((~v_Q_H(B_Z!513, B_s_H!514)) | v_Q(B_Z!513, B_s_H!514))) <=> ((~![B_Z: $i, B_s: $i] : ((~v_Q_H(B_Z, B_s)) | v_Q(B_Z, B_s))) | (~v_Q_H(B_Z!513, B_s_H!514)) | v_Q(B_Z!513, B_s_H!514))),
% 18.40/18.63 inference(rewrite,[status(thm)],[])).
% 18.40/18.63 tff(25,plain,
% 18.40/18.63 ((~![B_Z: $i, B_s: $i] : ((~v_Q_H(B_Z, B_s)) | v_Q(B_Z, B_s))) | ((~v_Q_H(B_Z!513, B_s_H!514)) | v_Q(B_Z!513, B_s_H!514))),
% 18.40/18.63 inference(quant_inst,[status(thm)],[])).
% 18.40/18.63 tff(26,plain,
% 18.40/18.63 ((~![B_Z: $i, B_s: $i] : ((~v_Q_H(B_Z, B_s)) | v_Q(B_Z, B_s))) | (~v_Q_H(B_Z!513, B_s_H!514)) | v_Q(B_Z!513, B_s_H!514)),
% 18.40/18.63 inference(modus_ponens,[status(thm)],[25, 24])).
% 18.40/18.63 tff(27,plain,
% 18.40/18.63 (~v_Q_H(B_Z!513, B_s_H!514)),
% 18.40/18.63 inference(unit_resolution,[status(thm)],[26, 23, 13])).
% 18.40/18.63 tff(28,plain,
% 18.40/18.63 (^[B_Z_H: $i] : refl(((~v_P(B_Z_H, B_s!512)) | v_Q_H(B_Z_H, B_s_H!514)) <=> ((~v_P(B_Z_H, B_s!512)) | v_Q_H(B_Z_H, B_s_H!514)))),
% 18.40/18.63 inference(bind,[status(th)],[])).
% 18.40/18.63 tff(29,plain,
% 18.40/18.63 (![B_Z_H: $i] : ((~v_P(B_Z_H, B_s!512)) | v_Q_H(B_Z_H, B_s_H!514)) <=> ![B_Z_H: $i] : ((~v_P(B_Z_H, B_s!512)) | v_Q_H(B_Z_H, B_s_H!514))),
% 18.40/18.63 inference(quant_intro,[status(thm)],[28])).
% 18.40/18.63 tff(30,plain,
% 18.40/18.63 (![B_Z_H: $i] : ((~v_P(B_Z_H, B_s!512)) | v_Q_H(B_Z_H, B_s_H!514))),
% 18.40/18.63 inference(and_elim,[status(thm)],[12])).
% 18.40/18.63 tff(31,plain,
% 18.40/18.63 (![B_Z_H: $i] : ((~v_P(B_Z_H, B_s!512)) | v_Q_H(B_Z_H, B_s_H!514))),
% 18.40/18.63 inference(modus_ponens,[status(thm)],[30, 29])).
% 18.40/18.63 tff(32,plain,
% 18.40/18.63 (v_P(B_Z!513, B_s!512)),
% 18.40/18.63 inference(and_elim,[status(thm)],[12])).
% 18.40/18.63 tff(33,plain,
% 18.40/18.63 (((~![B_Z_H: $i] : ((~v_P(B_Z_H, B_s!512)) | v_Q_H(B_Z_H, B_s_H!514))) | ((~v_P(B_Z!513, B_s!512)) | v_Q_H(B_Z!513, B_s_H!514))) <=> ((~![B_Z_H: $i] : ((~v_P(B_Z_H, B_s!512)) | v_Q_H(B_Z_H, B_s_H!514))) | (~v_P(B_Z!513, B_s!512)) | v_Q_H(B_Z!513, B_s_H!514))),
% 18.40/18.63 inference(rewrite,[status(thm)],[])).
% 18.40/18.63 tff(34,plain,
% 18.40/18.63 ((~![B_Z_H: $i] : ((~v_P(B_Z_H, B_s!512)) | v_Q_H(B_Z_H, B_s_H!514))) | ((~v_P(B_Z!513, B_s!512)) | v_Q_H(B_Z!513, B_s_H!514))),
% 18.40/18.63 inference(quant_inst,[status(thm)],[])).
% 18.40/18.63 tff(35,plain,
% 18.40/18.63 ((~![B_Z_H: $i] : ((~v_P(B_Z_H, B_s!512)) | v_Q_H(B_Z_H, B_s_H!514))) | (~v_P(B_Z!513, B_s!512)) | v_Q_H(B_Z!513, B_s_H!514)),
% 18.40/18.63 inference(modus_ponens,[status(thm)],[34, 33])).
% 18.40/18.63 tff(36,plain,
% 18.40/18.63 ($false),
% 18.40/18.63 inference(unit_resolution,[status(thm)],[35, 32, 31, 27])).
% 18.40/18.63 % SZS output end Proof
% 18.40/18.65 % E exiting
%------------------------------------------------------------------------------