%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : DAT333_3 : TPTP v9.0.0. Released v8.2.0.
% 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 05:04:49 AM UTC 2025
% Result : Theorem 0.11s 0.38s
% Output : Proof 0.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : DAT333_3 : TPTP v9.0.0. Released v8.2.0.
% 0.08/0.12 % 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 : Thu Jun 19 13:36:03 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.11/0.38 % SZS status Theorem
% 0.11/0.38 % SZS output start Proof
% 0.11/0.38 tff(teach_type, type, (
% 0.11/0.38 teach: ( |'$ki_world'| * $i * $i ) > $o)).
% 0.11/0.38 tff(math_type, type, (
% 0.11/0.38 math: $i)).
% 0.11/0.38 tff(john_type, type, (
% 0.11/0.38 john: $i)).
% 0.11/0.38 tff(tptp_fun_W_3_type, type, (
% 0.11/0.38 tptp_fun_W_3: $i > |'$ki_world'|)).
% 0.11/0.38 tff(psych_type, type, (
% 0.11/0.38 psych: $i)).
% 0.11/0.38 tff(sue_type, type, (
% 0.11/0.38 sue: $i)).
% 0.11/0.38 tff(mary_type, type, (
% 0.11/0.38 mary: $i)).
% 0.11/0.38 tff(cs_type, type, (
% 0.11/0.38 cs: $i)).
% 0.11/0.38 tff(tptp_fun_X_2_type, type, (
% 0.11/0.38 tptp_fun_X_2: |'$ki_world'| > $i)).
% 0.11/0.38 tff(tptp_fun___ki_exists_in_world__i__type, type, (
% 0.11/0.38 tptp_fun___ki_exists_in_world__i_: ( |'$ki_world'| * $i ) > $o)).
% 0.11/0.38 tff(tptp_fun___ki_accessible__type, type, (
% 0.11/0.38 tptp_fun___ki_accessible_: ( |'$ki_world'| * |'$ki_world'| ) > $o)).
% 0.11/0.38 tff(tptp_fun___ki_local_world__type, type, (
% 0.11/0.38 tptp_fun___ki_local_world_: |'$ki_world'|)).
% 0.11/0.38 tff(1,assumption,(~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, math)), introduced(assumption)).
% 0.11/0.38 tff(2,plain,
% 0.11/0.38 (^[W: |'$ki_world'|, X: $i] : refl(tptp_fun___ki_exists_in_world__i_(W, X) <=> tptp_fun___ki_exists_in_world__i_(W, X))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(3,plain,
% 0.11/0.38 (![W: |'$ki_world'|, X: $i] : tptp_fun___ki_exists_in_world__i_(W, X) <=> ![W: |'$ki_world'|, X: $i] : tptp_fun___ki_exists_in_world__i_(W, X)),
% 0.11/0.38 inference(quant_intro,[status(thm)],[2])).
% 0.11/0.38 tff(4,plain,
% 0.11/0.38 (![W: |'$ki_world'|, X: $i] : tptp_fun___ki_exists_in_world__i_(W, X) <=> ![W: |'$ki_world'|, X: $i] : tptp_fun___ki_exists_in_world__i_(W, X)),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(5,axiom,(![W: |'$ki_world'|, X: $i] : tptp_fun___ki_exists_in_world__i_(W, X)), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''$ki_exists_in_world_$i_const'')).
% 0.11/0.38 tff(6,plain,
% 0.11/0.38 (![W: |'$ki_world'|, X: $i] : tptp_fun___ki_exists_in_world__i_(W, X)),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.11/0.38 tff(7,plain,(
% 0.11/0.38 ![W: |'$ki_world'|, X: $i] : tptp_fun___ki_exists_in_world__i_(W, X)),
% 0.11/0.38 inference(skolemize,[status(sab)],[6])).
% 0.11/0.38 tff(8,plain,
% 0.11/0.38 (![W: |'$ki_world'|, X: $i] : tptp_fun___ki_exists_in_world__i_(W, X)),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.11/0.38 tff(9,plain,
% 0.11/0.38 ((~![W: |'$ki_world'|, X: $i] : tptp_fun___ki_exists_in_world__i_(W, X)) | tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, math)),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(10,plain,
% 0.11/0.38 ($false),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.11/0.38 tff(11,plain,(tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, math)), inference(lemma,lemma(discharge,[]))).
% 0.11/0.38 tff(12,plain,
% 0.11/0.38 (^[X: $i] : refl(((~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X)) | (~((~tptp_fun___ki_accessible_(|'$ki_local_world'|, tptp_fun_W_3(X))) | teach(tptp_fun_W_3(X), john, X)))) <=> ((~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X)) | (~((~tptp_fun___ki_accessible_(|'$ki_local_world'|, tptp_fun_W_3(X))) | teach(tptp_fun_W_3(X), john, X)))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(13,plain,
% 0.11/0.38 (![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X)) | (~((~tptp_fun___ki_accessible_(|'$ki_local_world'|, tptp_fun_W_3(X))) | teach(tptp_fun_W_3(X), john, X)))) <=> ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X)) | (~((~tptp_fun___ki_accessible_(|'$ki_local_world'|, tptp_fun_W_3(X))) | teach(tptp_fun_W_3(X), john, X))))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[12])).
% 0.11/0.38 tff(14,plain,
% 0.11/0.38 ((~?[X: $i] : (tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X) & ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | teach(W, john, X)))) <=> (~?[X: $i] : (tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X) & ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | teach(W, john, X))))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(15,plain,
% 0.11/0.38 ((~?[X: $i] : (tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X) & ![W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => teach(W, john, X)))) <=> (~?[X: $i] : (tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X) & ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | teach(W, john, X))))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(16,axiom,(~?[X: $i] : (tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X) & ![W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => teach(W, john, X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','verify')).
% 0.11/0.38 tff(17,plain,
% 0.11/0.38 (~?[X: $i] : (tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X) & ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | teach(W, john, X)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.11/0.38 tff(18,plain,
% 0.11/0.38 (~?[X: $i] : (tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X) & ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | teach(W, john, X)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[17, 14])).
% 0.11/0.38 tff(19,plain,
% 0.11/0.38 (~?[X: $i] : (tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X) & ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | teach(W, john, X)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.11/0.38 tff(20,plain,
% 0.11/0.38 (~?[X: $i] : (tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X) & ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | teach(W, john, X)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[19, 14])).
% 0.11/0.38 tff(21,plain,
% 0.11/0.38 (^[X: $i] : nnf_neg(refl($oeq((~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X)), (~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X)))), sk($oeq((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | teach(W, john, X))), (~((~tptp_fun___ki_accessible_(|'$ki_local_world'|, tptp_fun_W_3(X))) | teach(tptp_fun_W_3(X), john, X))))), $oeq((~(tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X) & ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | teach(W, john, X)))), ((~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X)) | (~((~tptp_fun___ki_accessible_(|'$ki_local_world'|, tptp_fun_W_3(X))) | teach(tptp_fun_W_3(X), john, X))))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(22,plain,(
% 0.11/0.38 ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X)) | (~((~tptp_fun___ki_accessible_(|'$ki_local_world'|, tptp_fun_W_3(X))) | teach(tptp_fun_W_3(X), john, X))))),
% 0.11/0.38 inference(nnf-neg,[status(sab)],[20, 21])).
% 0.11/0.38 tff(23,plain,
% 0.11/0.38 (![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X)) | (~((~tptp_fun___ki_accessible_(|'$ki_local_world'|, tptp_fun_W_3(X))) | teach(tptp_fun_W_3(X), john, X))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[22, 13])).
% 0.11/0.38 tff(24,plain,
% 0.11/0.38 (((~![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X)) | (~((~tptp_fun___ki_accessible_(|'$ki_local_world'|, tptp_fun_W_3(X))) | teach(tptp_fun_W_3(X), john, X))))) | ((~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, math)) | (~((~tptp_fun___ki_accessible_(|'$ki_local_world'|, tptp_fun_W_3(math))) | teach(tptp_fun_W_3(math), john, math))))) <=> ((~![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X)) | (~((~tptp_fun___ki_accessible_(|'$ki_local_world'|, tptp_fun_W_3(X))) | teach(tptp_fun_W_3(X), john, X))))) | (~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, math)) | (~((~tptp_fun___ki_accessible_(|'$ki_local_world'|, tptp_fun_W_3(math))) | teach(tptp_fun_W_3(math), john, math))))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(25,plain,
% 0.11/0.38 ((~![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X)) | (~((~tptp_fun___ki_accessible_(|'$ki_local_world'|, tptp_fun_W_3(X))) | teach(tptp_fun_W_3(X), john, X))))) | ((~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, math)) | (~((~tptp_fun___ki_accessible_(|'$ki_local_world'|, tptp_fun_W_3(math))) | teach(tptp_fun_W_3(math), john, math))))),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(26,plain,
% 0.11/0.38 ((~![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, X)) | (~((~tptp_fun___ki_accessible_(|'$ki_local_world'|, tptp_fun_W_3(X))) | teach(tptp_fun_W_3(X), john, X))))) | (~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, math)) | (~((~tptp_fun___ki_accessible_(|'$ki_local_world'|, tptp_fun_W_3(math))) | teach(tptp_fun_W_3(math), john, math)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.11/0.38 tff(27,plain,
% 0.11/0.38 ((~tptp_fun___ki_exists_in_world__i_(|'$ki_local_world'|, math)) | (~((~tptp_fun___ki_accessible_(|'$ki_local_world'|, tptp_fun_W_3(math))) | teach(tptp_fun_W_3(math), john, math)))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[26, 23])).
% 0.11/0.38 tff(28,plain,
% 0.11/0.38 (~((~tptp_fun___ki_accessible_(|'$ki_local_world'|, tptp_fun_W_3(math))) | teach(tptp_fun_W_3(math), john, math))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[27, 11])).
% 0.11/0.38 tff(29,plain,
% 0.11/0.38 (((~tptp_fun___ki_accessible_(|'$ki_local_world'|, tptp_fun_W_3(math))) | teach(tptp_fun_W_3(math), john, math)) | (~teach(tptp_fun_W_3(math), john, math))),
% 0.11/0.38 inference(tautology,[status(thm)],[])).
% 0.11/0.38 tff(30,plain,
% 0.11/0.38 (~teach(tptp_fun_W_3(math), john, math)),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[29, 28])).
% 0.11/0.38 tff(31,plain,
% 0.11/0.38 (((~tptp_fun___ki_exists_in_world__i_(tptp_fun_W_3(math), tptp_fun_X_2(tptp_fun_W_3(math)))) | (~teach(tptp_fun_W_3(math), tptp_fun_X_2(tptp_fun_W_3(math)), cs)) | (~teach(tptp_fun_W_3(math), mary, psych)) | (~teach(tptp_fun_W_3(math), sue, psych)) | (~teach(tptp_fun_W_3(math), john, math))) | teach(tptp_fun_W_3(math), john, math)),
% 0.11/0.38 inference(tautology,[status(thm)],[])).
% 0.11/0.38 tff(32,plain,
% 0.11/0.38 ((~tptp_fun___ki_exists_in_world__i_(tptp_fun_W_3(math), tptp_fun_X_2(tptp_fun_W_3(math)))) | (~teach(tptp_fun_W_3(math), tptp_fun_X_2(tptp_fun_W_3(math)), cs)) | (~teach(tptp_fun_W_3(math), mary, psych)) | (~teach(tptp_fun_W_3(math), sue, psych)) | (~teach(tptp_fun_W_3(math), john, math))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[31, 30])).
% 0.11/0.38 tff(33,plain,
% 0.11/0.38 (((~tptp_fun___ki_accessible_(|'$ki_local_world'|, tptp_fun_W_3(math))) | teach(tptp_fun_W_3(math), john, math)) | tptp_fun___ki_accessible_(|'$ki_local_world'|, tptp_fun_W_3(math))),
% 0.11/0.38 inference(tautology,[status(thm)],[])).
% 0.11/0.38 tff(34,plain,
% 0.11/0.38 (tptp_fun___ki_accessible_(|'$ki_local_world'|, tptp_fun_W_3(math))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[33, 28])).
% 0.11/0.38 tff(35,plain,
% 0.11/0.38 (^[W: |'$ki_world'|] : refl(((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~((~teach(W, john, math)) | (~tptp_fun___ki_exists_in_world__i_(W, tptp_fun_X_2(W))) | (~teach(W, tptp_fun_X_2(W), cs)) | (~teach(W, mary, psych)) | (~teach(W, sue, psych))))) <=> ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~((~teach(W, john, math)) | (~tptp_fun___ki_exists_in_world__i_(W, tptp_fun_X_2(W))) | (~teach(W, tptp_fun_X_2(W), cs)) | (~teach(W, mary, psych)) | (~teach(W, sue, psych))))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(36,plain,
% 0.11/0.38 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~((~teach(W, john, math)) | (~tptp_fun___ki_exists_in_world__i_(W, tptp_fun_X_2(W))) | (~teach(W, tptp_fun_X_2(W), cs)) | (~teach(W, mary, psych)) | (~teach(W, sue, psych))))) <=> ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~((~teach(W, john, math)) | (~tptp_fun___ki_exists_in_world__i_(W, tptp_fun_X_2(W))) | (~teach(W, tptp_fun_X_2(W), cs)) | (~teach(W, mary, psych)) | (~teach(W, sue, psych)))))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[35])).
% 0.11/0.38 tff(37,plain,
% 0.11/0.38 (^[W: |'$ki_world'|] : rewrite(((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (teach(W, john, math) & tptp_fun___ki_exists_in_world__i_(W, tptp_fun_X_2(W)) & teach(W, tptp_fun_X_2(W), cs) & teach(W, mary, psych) & teach(W, sue, psych))) <=> ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~((~teach(W, john, math)) | (~tptp_fun___ki_exists_in_world__i_(W, tptp_fun_X_2(W))) | (~teach(W, tptp_fun_X_2(W), cs)) | (~teach(W, mary, psych)) | (~teach(W, sue, psych))))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(38,plain,
% 0.11/0.38 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (teach(W, john, math) & tptp_fun___ki_exists_in_world__i_(W, tptp_fun_X_2(W)) & teach(W, tptp_fun_X_2(W), cs) & teach(W, mary, psych) & teach(W, sue, psych))) <=> ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~((~teach(W, john, math)) | (~tptp_fun___ki_exists_in_world__i_(W, tptp_fun_X_2(W))) | (~teach(W, tptp_fun_X_2(W), cs)) | (~teach(W, mary, psych)) | (~teach(W, sue, psych)))))),
% 0.11/0.39 inference(quant_intro,[status(thm)],[37])).
% 0.11/0.39 tff(39,plain,
% 0.11/0.39 (^[W: |'$ki_world'|] : rewrite(((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (teach(W, john, math) & (tptp_fun___ki_exists_in_world__i_(W, tptp_fun_X_2(W)) & teach(W, tptp_fun_X_2(W), cs)) & teach(W, mary, psych) & teach(W, sue, psych))) <=> ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (teach(W, john, math) & tptp_fun___ki_exists_in_world__i_(W, tptp_fun_X_2(W)) & teach(W, tptp_fun_X_2(W), cs) & teach(W, mary, psych) & teach(W, sue, psych))))),
% 0.11/0.39 inference(bind,[status(th)],[])).
% 0.11/0.39 tff(40,plain,
% 0.11/0.39 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (teach(W, john, math) & (tptp_fun___ki_exists_in_world__i_(W, tptp_fun_X_2(W)) & teach(W, tptp_fun_X_2(W), cs)) & teach(W, mary, psych) & teach(W, sue, psych))) <=> ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (teach(W, john, math) & tptp_fun___ki_exists_in_world__i_(W, tptp_fun_X_2(W)) & teach(W, tptp_fun_X_2(W), cs) & teach(W, mary, psych) & teach(W, sue, psych)))),
% 0.11/0.39 inference(quant_intro,[status(thm)],[39])).
% 0.11/0.39 tff(41,plain,
% 0.11/0.39 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (teach(W, john, math) & ?[X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & teach(W, X, cs)) & teach(W, mary, psych) & teach(W, sue, psych))) <=> ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (teach(W, john, math) & ?[X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & teach(W, X, cs)) & teach(W, mary, psych) & teach(W, sue, psych)))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(42,plain,
% 0.11/0.39 (^[W: |'$ki_world'|] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((teach(W, john, math) & ?[X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & teach(W, X, cs))) <=> (teach(W, john, math) & ?[X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & teach(W, X, cs)))), (((teach(W, john, math) & ?[X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & teach(W, X, cs))) & teach(W, mary, psych)) <=> ((teach(W, john, math) & ?[X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & teach(W, X, cs))) & teach(W, mary, psych)))), rewrite(((teach(W, john, math) & ?[X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & teach(W, X, cs))) & teach(W, mary, psych)) <=> (teach(W, john, math) & ?[X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & teach(W, X, cs)) & teach(W, mary, psych))), (((teach(W, john, math) & ?[X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & teach(W, X, cs))) & teach(W, mary, psych)) <=> (teach(W, john, math) & ?[X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & teach(W, X, cs)) & teach(W, mary, psych)))), ((((teach(W, john, math) & ?[X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & teach(W, X, cs))) & teach(W, mary, psych)) & teach(W, sue, psych)) <=> ((teach(W, john, math) & ?[X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & teach(W, X, cs)) & teach(W, mary, psych)) & teach(W, sue, psych)))), rewrite(((teach(W, john, math) & ?[X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & teach(W, X, cs)) & teach(W, mary, psych)) & teach(W, sue, psych)) <=> (teach(W, john, math) & ?[X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & teach(W, X, cs)) & teach(W, mary, psych) & teach(W, sue, psych))), ((((teach(W, john, math) & ?[X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & teach(W, X, cs))) & teach(W, mary, psych)) & teach(W, sue, psych)) <=> (teach(W, john, math) & ?[X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & teach(W, X, cs)) & teach(W, mary, psych) & teach(W, sue, psych)))), ((tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => (((teach(W, john, math) & ?[X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & teach(W, X, cs))) & teach(W, mary, psych)) & teach(W, sue, psych))) <=> (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => (teach(W, john, math) & ?[X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & teach(W, X, cs)) & teach(W, mary, psych) & teach(W, sue, psych))))), rewrite((tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => (teach(W, john, math) & ?[X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & teach(W, X, cs)) & teach(W, mary, psych) & teach(W, sue, psych))) <=> ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (teach(W, john, math) & ?[X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & teach(W, X, cs)) & teach(W, mary, psych) & teach(W, sue, psych)))), ((tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => (((teach(W, john, math) & ?[X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & teach(W, X, cs))) & teach(W, mary, psych)) & teach(W, sue, psych))) <=> ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (teach(W, john, math) & ?[X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & teach(W, X, cs)) & teach(W, mary, psych) & teach(W, sue, psych)))))),
% 0.11/0.39 inference(bind,[status(th)],[])).
% 0.11/0.39 tff(43,plain,
% 0.11/0.39 (![W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => (((teach(W, john, math) & ?[X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & teach(W, X, cs))) & teach(W, mary, psych)) & teach(W, sue, psych))) <=> ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (teach(W, john, math) & ?[X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & teach(W, X, cs)) & teach(W, mary, psych) & teach(W, sue, psych)))),
% 0.11/0.39 inference(quant_intro,[status(thm)],[42])).
% 0.11/0.39 tff(44,axiom,(![W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => (((teach(W, john, math) & ?[X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & teach(W, X, cs))) & teach(W, mary, psych)) & teach(W, sue, psych)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','db')).
% 0.11/0.39 tff(45,plain,
% 0.11/0.39 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (teach(W, john, math) & ?[X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & teach(W, X, cs)) & teach(W, mary, psych) & teach(W, sue, psych)))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.11/0.39 tff(46,plain,
% 0.11/0.39 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (teach(W, john, math) & ?[X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & teach(W, X, cs)) & teach(W, mary, psych) & teach(W, sue, psych)))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[45, 41])).
% 0.11/0.39 tff(47,plain,(
% 0.11/0.39 ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (teach(W, john, math) & (tptp_fun___ki_exists_in_world__i_(W, tptp_fun_X_2(W)) & teach(W, tptp_fun_X_2(W), cs)) & teach(W, mary, psych) & teach(W, sue, psych)))),
% 0.11/0.39 inference(skolemize,[status(sab)],[46])).
% 0.11/0.39 tff(48,plain,
% 0.11/0.39 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (teach(W, john, math) & tptp_fun___ki_exists_in_world__i_(W, tptp_fun_X_2(W)) & teach(W, tptp_fun_X_2(W), cs) & teach(W, mary, psych) & teach(W, sue, psych)))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[47, 40])).
% 0.11/0.39 tff(49,plain,
% 0.11/0.39 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~((~teach(W, john, math)) | (~tptp_fun___ki_exists_in_world__i_(W, tptp_fun_X_2(W))) | (~teach(W, tptp_fun_X_2(W), cs)) | (~teach(W, mary, psych)) | (~teach(W, sue, psych)))))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[48, 38])).
% 0.11/0.39 tff(50,plain,
% 0.11/0.39 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~((~teach(W, john, math)) | (~tptp_fun___ki_exists_in_world__i_(W, tptp_fun_X_2(W))) | (~teach(W, tptp_fun_X_2(W), cs)) | (~teach(W, mary, psych)) | (~teach(W, sue, psych)))))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[49, 36])).
% 0.11/0.39 tff(51,plain,
% 0.11/0.39 (((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~((~teach(W, john, math)) | (~tptp_fun___ki_exists_in_world__i_(W, tptp_fun_X_2(W))) | (~teach(W, tptp_fun_X_2(W), cs)) | (~teach(W, mary, psych)) | (~teach(W, sue, psych)))))) | ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, tptp_fun_W_3(math))) | (~((~tptp_fun___ki_exists_in_world__i_(tptp_fun_W_3(math), tptp_fun_X_2(tptp_fun_W_3(math)))) | (~teach(tptp_fun_W_3(math), tptp_fun_X_2(tptp_fun_W_3(math)), cs)) | (~teach(tptp_fun_W_3(math), mary, psych)) | (~teach(tptp_fun_W_3(math), sue, psych)) | (~teach(tptp_fun_W_3(math), john, math)))))) <=> ((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~((~teach(W, john, math)) | (~tptp_fun___ki_exists_in_world__i_(W, tptp_fun_X_2(W))) | (~teach(W, tptp_fun_X_2(W), cs)) | (~teach(W, mary, psych)) | (~teach(W, sue, psych)))))) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, tptp_fun_W_3(math))) | (~((~tptp_fun___ki_exists_in_world__i_(tptp_fun_W_3(math), tptp_fun_X_2(tptp_fun_W_3(math)))) | (~teach(tptp_fun_W_3(math), tptp_fun_X_2(tptp_fun_W_3(math)), cs)) | (~teach(tptp_fun_W_3(math), mary, psych)) | (~teach(tptp_fun_W_3(math), sue, psych)) | (~teach(tptp_fun_W_3(math), john, math)))))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(52,plain,
% 0.11/0.39 (((~tptp_fun___ki_accessible_(|'$ki_local_world'|, tptp_fun_W_3(math))) | (~((~teach(tptp_fun_W_3(math), john, math)) | (~tptp_fun___ki_exists_in_world__i_(tptp_fun_W_3(math), tptp_fun_X_2(tptp_fun_W_3(math)))) | (~teach(tptp_fun_W_3(math), tptp_fun_X_2(tptp_fun_W_3(math)), cs)) | (~teach(tptp_fun_W_3(math), mary, psych)) | (~teach(tptp_fun_W_3(math), sue, psych))))) <=> ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, tptp_fun_W_3(math))) | (~((~tptp_fun___ki_exists_in_world__i_(tptp_fun_W_3(math), tptp_fun_X_2(tptp_fun_W_3(math)))) | (~teach(tptp_fun_W_3(math), tptp_fun_X_2(tptp_fun_W_3(math)), cs)) | (~teach(tptp_fun_W_3(math), mary, psych)) | (~teach(tptp_fun_W_3(math), sue, psych)) | (~teach(tptp_fun_W_3(math), john, math)))))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(53,plain,
% 0.11/0.39 (((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~((~teach(W, john, math)) | (~tptp_fun___ki_exists_in_world__i_(W, tptp_fun_X_2(W))) | (~teach(W, tptp_fun_X_2(W), cs)) | (~teach(W, mary, psych)) | (~teach(W, sue, psych)))))) | ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, tptp_fun_W_3(math))) | (~((~teach(tptp_fun_W_3(math), john, math)) | (~tptp_fun___ki_exists_in_world__i_(tptp_fun_W_3(math), tptp_fun_X_2(tptp_fun_W_3(math)))) | (~teach(tptp_fun_W_3(math), tptp_fun_X_2(tptp_fun_W_3(math)), cs)) | (~teach(tptp_fun_W_3(math), mary, psych)) | (~teach(tptp_fun_W_3(math), sue, psych)))))) <=> ((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~((~teach(W, john, math)) | (~tptp_fun___ki_exists_in_world__i_(W, tptp_fun_X_2(W))) | (~teach(W, tptp_fun_X_2(W), cs)) | (~teach(W, mary, psych)) | (~teach(W, sue, psych)))))) | ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, tptp_fun_W_3(math))) | (~((~tptp_fun___ki_exists_in_world__i_(tptp_fun_W_3(math), tptp_fun_X_2(tptp_fun_W_3(math)))) | (~teach(tptp_fun_W_3(math), tptp_fun_X_2(tptp_fun_W_3(math)), cs)) | (~teach(tptp_fun_W_3(math), mary, psych)) | (~teach(tptp_fun_W_3(math), sue, psych)) | (~teach(tptp_fun_W_3(math), john, math))))))),
% 0.11/0.39 inference(monotonicity,[status(thm)],[52])).
% 0.11/0.39 tff(54,plain,
% 0.11/0.39 (((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~((~teach(W, john, math)) | (~tptp_fun___ki_exists_in_world__i_(W, tptp_fun_X_2(W))) | (~teach(W, tptp_fun_X_2(W), cs)) | (~teach(W, mary, psych)) | (~teach(W, sue, psych)))))) | ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, tptp_fun_W_3(math))) | (~((~teach(tptp_fun_W_3(math), john, math)) | (~tptp_fun___ki_exists_in_world__i_(tptp_fun_W_3(math), tptp_fun_X_2(tptp_fun_W_3(math)))) | (~teach(tptp_fun_W_3(math), tptp_fun_X_2(tptp_fun_W_3(math)), cs)) | (~teach(tptp_fun_W_3(math), mary, psych)) | (~teach(tptp_fun_W_3(math), sue, psych)))))) <=> ((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~((~teach(W, john, math)) | (~tptp_fun___ki_exists_in_world__i_(W, tptp_fun_X_2(W))) | (~teach(W, tptp_fun_X_2(W), cs)) | (~teach(W, mary, psych)) | (~teach(W, sue, psych)))))) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, tptp_fun_W_3(math))) | (~((~tptp_fun___ki_exists_in_world__i_(tptp_fun_W_3(math), tptp_fun_X_2(tptp_fun_W_3(math)))) | (~teach(tptp_fun_W_3(math), tptp_fun_X_2(tptp_fun_W_3(math)), cs)) | (~teach(tptp_fun_W_3(math), mary, psych)) | (~teach(tptp_fun_W_3(math), sue, psych)) | (~teach(tptp_fun_W_3(math), john, math)))))),
% 0.11/0.40 inference(transitivity,[status(thm)],[53, 51])).
% 0.11/0.40 tff(55,plain,
% 0.11/0.40 ((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~((~teach(W, john, math)) | (~tptp_fun___ki_exists_in_world__i_(W, tptp_fun_X_2(W))) | (~teach(W, tptp_fun_X_2(W), cs)) | (~teach(W, mary, psych)) | (~teach(W, sue, psych)))))) | ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, tptp_fun_W_3(math))) | (~((~teach(tptp_fun_W_3(math), john, math)) | (~tptp_fun___ki_exists_in_world__i_(tptp_fun_W_3(math), tptp_fun_X_2(tptp_fun_W_3(math)))) | (~teach(tptp_fun_W_3(math), tptp_fun_X_2(tptp_fun_W_3(math)), cs)) | (~teach(tptp_fun_W_3(math), mary, psych)) | (~teach(tptp_fun_W_3(math), sue, psych)))))),
% 0.11/0.40 inference(quant_inst,[status(thm)],[])).
% 0.11/0.40 tff(56,plain,
% 0.11/0.40 ((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~((~teach(W, john, math)) | (~tptp_fun___ki_exists_in_world__i_(W, tptp_fun_X_2(W))) | (~teach(W, tptp_fun_X_2(W), cs)) | (~teach(W, mary, psych)) | (~teach(W, sue, psych)))))) | (~tptp_fun___ki_accessible_(|'$ki_local_world'|, tptp_fun_W_3(math))) | (~((~tptp_fun___ki_exists_in_world__i_(tptp_fun_W_3(math), tptp_fun_X_2(tptp_fun_W_3(math)))) | (~teach(tptp_fun_W_3(math), tptp_fun_X_2(tptp_fun_W_3(math)), cs)) | (~teach(tptp_fun_W_3(math), mary, psych)) | (~teach(tptp_fun_W_3(math), sue, psych)) | (~teach(tptp_fun_W_3(math), john, math))))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.11/0.40 tff(57,plain,
% 0.11/0.40 ($false),
% 0.11/0.40 inference(unit_resolution,[status(thm)],[56, 50, 34, 32])).
% 0.11/0.40 % SZS output end Proof
% 0.11/0.40 % E exiting
%------------------------------------------------------------------------------