%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : DAT334_21 : TPTP v9.0.0. Released v8.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.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 05:04:50 AM UTC 2025
% Result : Theorem 0.11s 0.36s
% Output : Proof 0.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : DAT334_21 : TPTP v9.0.0. Released v8.2.0.
% 0.07/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n009.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Thu Jun 19 13:31:33 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.11/0.36 % SZS status Theorem
% 0.11/0.36 % SZS output start Proof
% 0.11/0.36 tff(teach_type, type, (
% 0.11/0.36 teach: ( |'$ki_world'| * $i * $i ) > $o)).
% 0.11/0.36 tff(cs_type, type, (
% 0.11/0.36 cs: $i)).
% 0.11/0.36 tff(tptp_fun_X_2_type, type, (
% 0.11/0.36 tptp_fun_X_2: |'$ki_world'| > $i)).
% 0.11/0.36 tff(tptp_fun_W_3_type, type, (
% 0.11/0.36 tptp_fun_W_3: |'$ki_world'|)).
% 0.11/0.36 tff(psych_type, type, (
% 0.11/0.36 psych: $i)).
% 0.11/0.36 tff(sue_type, type, (
% 0.11/0.36 sue: $i)).
% 0.11/0.36 tff(mary_type, type, (
% 0.11/0.36 mary: $i)).
% 0.11/0.36 tff(tptp_fun___ki_exists_in_world__i__type, type, (
% 0.11/0.36 tptp_fun___ki_exists_in_world__i_: ( |'$ki_world'| * $i ) > $o)).
% 0.11/0.36 tff(math_type, type, (
% 0.11/0.36 math: $i)).
% 0.11/0.36 tff(john_type, type, (
% 0.11/0.36 john: $i)).
% 0.11/0.36 tff(tptp_fun___ki_accessible__type, type, (
% 0.11/0.36 tptp_fun___ki_accessible_: ( |'$ki_world'| * |'$ki_world'| ) > $o)).
% 0.11/0.36 tff(tptp_fun___ki_local_world__type, type, (
% 0.11/0.36 tptp_fun___ki_local_world_: |'$ki_world'|)).
% 0.11/0.36 tff(1,plain,
% 0.11/0.36 ((tptp_fun___ki_accessible_(|'$ki_local_world'|, W!3) & ![X: $i] : (~(tptp_fun___ki_exists_in_world__i_(W!3, X) & teach(W!3, X, cs)))) <=> (tptp_fun___ki_accessible_(|'$ki_local_world'|, W!3) & ![X: $i] : (~(tptp_fun___ki_exists_in_world__i_(W!3, X) & teach(W!3, X, cs))))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(2,plain,
% 0.11/0.36 ((~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ?[X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & teach(W, X, cs)))) <=> (~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ?[X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & teach(W, X, cs))))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(3,plain,
% 0.11/0.36 ((~![W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => ?[X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & teach(W, X, cs)))) <=> (~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ?[X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & teach(W, X, cs))))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(4,axiom,(~![W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => ?[X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & teach(W, X, cs)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','verify')).
% 0.11/0.36 tff(5,plain,
% 0.11/0.36 (~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ?[X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & teach(W, X, cs)))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.11/0.36 tff(6,plain,
% 0.11/0.36 (~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ?[X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & teach(W, X, cs)))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[5, 2])).
% 0.11/0.36 tff(7,plain,
% 0.11/0.36 (~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ?[X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & teach(W, X, cs)))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.11/0.36 tff(8,plain,
% 0.11/0.36 (~![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ?[X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & teach(W, X, cs)))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[7, 2])).
% 0.11/0.36 tff(9,plain,
% 0.11/0.36 (tptp_fun___ki_accessible_(|'$ki_local_world'|, W!3) & ![X: $i] : (~(tptp_fun___ki_exists_in_world__i_(W!3, X) & teach(W!3, X, cs)))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[8, 1])).
% 0.11/0.36 tff(10,plain,
% 0.11/0.36 (tptp_fun___ki_accessible_(|'$ki_local_world'|, W!3)),
% 0.11/0.36 inference(and_elim,[status(thm)],[9])).
% 0.11/0.36 tff(11,plain,
% 0.11/0.36 (^[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_(|'$ki_local_world'|, W)) | (~((~teach(W, john, math)) | (~tptp_fun___ki_exists_in_world__i_(W, tptp_fun_X_2(W))) | (~teach(W, tptp_fun_X_2(W), cs)) | (~teach(W, mary, psych)) | (~teach(W, sue, psych))))))),
% 0.11/0.36 inference(bind,[status(th)],[])).
% 0.11/0.36 tff(12,plain,
% 0.11/0.36 (![W: |'$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_(|'$ki_local_world'|, W)) | (~((~teach(W, john, math)) | (~tptp_fun___ki_exists_in_world__i_(W, tptp_fun_X_2(W))) | (~teach(W, tptp_fun_X_2(W), cs)) | (~teach(W, mary, psych)) | (~teach(W, sue, psych)))))),
% 0.11/0.36 inference(quant_intro,[status(thm)],[11])).
% 0.11/0.36 tff(13,plain,
% 0.11/0.36 (^[W: |'$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))))))),
% 0.11/0.36 inference(bind,[status(th)],[])).
% 0.11/0.36 tff(14,plain,
% 0.11/0.36 (![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)))))),
% 0.11/0.36 inference(quant_intro,[status(thm)],[13])).
% 0.11/0.36 tff(15,plain,
% 0.11/0.36 (^[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_(|'$ki_local_world'|, W)) | (teach(W, john, math) & tptp_fun___ki_exists_in_world__i_(W, tptp_fun_X_2(W)) & teach(W, tptp_fun_X_2(W), cs) & teach(W, mary, psych) & teach(W, sue, psych))))),
% 0.11/0.36 inference(bind,[status(th)],[])).
% 0.11/0.36 tff(16,plain,
% 0.11/0.36 (![W: |'$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_(|'$ki_local_world'|, W)) | (teach(W, john, math) & tptp_fun___ki_exists_in_world__i_(W, tptp_fun_X_2(W)) & teach(W, tptp_fun_X_2(W), cs) & teach(W, mary, psych) & teach(W, sue, psych)))),
% 0.11/0.36 inference(quant_intro,[status(thm)],[15])).
% 0.11/0.36 tff(17,plain,
% 0.11/0.36 (![W: |'$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: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & teach(W, X, cs)) & teach(W, mary, psych) & teach(W, sue, psych)))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(18,plain,
% 0.11/0.36 (^[W: |'$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: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & teach(W, X, cs)) & teach(W, mary, psych) & teach(W, sue, psych)))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(19,plain,
% 0.11/0.37 (![W: |'$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: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & teach(W, X, cs)) & teach(W, mary, psych) & teach(W, sue, psych)))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[18])).
% 0.11/0.37 tff(20,axiom,(![W: |'$ki_world'|] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => (((teach(W, john, math) & ?[X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & teach(W, X, cs))) & teach(W, mary, psych)) & teach(W, sue, psych)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','db')).
% 0.11/0.37 tff(21,plain,
% 0.11/0.37 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (teach(W, john, math) & ?[X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & teach(W, X, cs)) & teach(W, mary, psych) & teach(W, sue, psych)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.11/0.37 tff(22,plain,
% 0.11/0.37 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (teach(W, john, math) & ?[X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & teach(W, X, cs)) & teach(W, mary, psych) & teach(W, sue, psych)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[21, 17])).
% 0.11/0.37 tff(23,plain,(
% 0.11/0.37 ![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (teach(W, john, math) & (tptp_fun___ki_exists_in_world__i_(W, tptp_fun_X_2(W)) & teach(W, tptp_fun_X_2(W), cs)) & teach(W, mary, psych) & teach(W, sue, psych)))),
% 0.11/0.37 inference(skolemize,[status(sab)],[22])).
% 0.11/0.37 tff(24,plain,
% 0.11/0.37 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (teach(W, john, math) & tptp_fun___ki_exists_in_world__i_(W, tptp_fun_X_2(W)) & teach(W, tptp_fun_X_2(W), cs) & teach(W, mary, psych) & teach(W, sue, psych)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[23, 16])).
% 0.11/0.37 tff(25,plain,
% 0.11/0.37 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~((~teach(W, john, math)) | (~tptp_fun___ki_exists_in_world__i_(W, tptp_fun_X_2(W))) | (~teach(W, tptp_fun_X_2(W), cs)) | (~teach(W, mary, psych)) | (~teach(W, sue, psych)))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[24, 14])).
% 0.11/0.37 tff(26,plain,
% 0.11/0.37 (![W: |'$ki_world'|] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~((~teach(W, john, math)) | (~tptp_fun___ki_exists_in_world__i_(W, tptp_fun_X_2(W))) | (~teach(W, tptp_fun_X_2(W), cs)) | (~teach(W, mary, psych)) | (~teach(W, sue, psych)))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[25, 12])).
% 0.11/0.37 tff(27,plain,
% 0.11/0.37 (((~![W: |'$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'|, W!3)) | (~((~teach(W!3, john, math)) | (~tptp_fun___ki_exists_in_world__i_(W!3, tptp_fun_X_2(W!3))) | (~teach(W!3, tptp_fun_X_2(W!3), cs)) | (~teach(W!3, mary, psych)) | (~teach(W!3, 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_(|'$ki_local_world'|, W!3)) | (~((~teach(W!3, john, math)) | (~tptp_fun___ki_exists_in_world__i_(W!3, tptp_fun_X_2(W!3))) | (~teach(W!3, tptp_fun_X_2(W!3), cs)) | (~teach(W!3, mary, psych)) | (~teach(W!3, sue, psych)))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(28,plain,
% 0.11/0.37 ((~![W: |'$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'|, W!3)) | (~((~teach(W!3, john, math)) | (~tptp_fun___ki_exists_in_world__i_(W!3, tptp_fun_X_2(W!3))) | (~teach(W!3, tptp_fun_X_2(W!3), cs)) | (~teach(W!3, mary, psych)) | (~teach(W!3, sue, psych)))))),
% 0.11/0.37 inference(quant_inst,[status(thm)],[])).
% 0.11/0.37 tff(29,plain,
% 0.11/0.37 ((~![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'|, W!3)) | (~((~teach(W!3, john, math)) | (~tptp_fun___ki_exists_in_world__i_(W!3, tptp_fun_X_2(W!3))) | (~teach(W!3, tptp_fun_X_2(W!3), cs)) | (~teach(W!3, mary, psych)) | (~teach(W!3, sue, psych))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.11/0.37 tff(30,plain,
% 0.11/0.37 (~((~teach(W!3, john, math)) | (~tptp_fun___ki_exists_in_world__i_(W!3, tptp_fun_X_2(W!3))) | (~teach(W!3, tptp_fun_X_2(W!3), cs)) | (~teach(W!3, mary, psych)) | (~teach(W!3, sue, psych)))),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[29, 26, 10])).
% 0.11/0.37 tff(31,plain,
% 0.11/0.37 (((~teach(W!3, john, math)) | (~tptp_fun___ki_exists_in_world__i_(W!3, tptp_fun_X_2(W!3))) | (~teach(W!3, tptp_fun_X_2(W!3), cs)) | (~teach(W!3, mary, psych)) | (~teach(W!3, sue, psych))) | teach(W!3, tptp_fun_X_2(W!3), cs)),
% 0.11/0.37 inference(tautology,[status(thm)],[])).
% 0.11/0.37 tff(32,plain,
% 0.11/0.37 (teach(W!3, tptp_fun_X_2(W!3), cs)),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[31, 30])).
% 0.11/0.37 tff(33,plain,
% 0.11/0.37 (((~teach(W!3, john, math)) | (~tptp_fun___ki_exists_in_world__i_(W!3, tptp_fun_X_2(W!3))) | (~teach(W!3, tptp_fun_X_2(W!3), cs)) | (~teach(W!3, mary, psych)) | (~teach(W!3, sue, psych))) | tptp_fun___ki_exists_in_world__i_(W!3, tptp_fun_X_2(W!3))),
% 0.11/0.37 inference(tautology,[status(thm)],[])).
% 0.11/0.37 tff(34,plain,
% 0.11/0.37 (tptp_fun___ki_exists_in_world__i_(W!3, tptp_fun_X_2(W!3))),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[33, 30])).
% 0.11/0.37 tff(35,plain,
% 0.11/0.37 (^[X: $i] : refl(((~tptp_fun___ki_exists_in_world__i_(W!3, X)) | (~teach(W!3, X, cs))) <=> ((~tptp_fun___ki_exists_in_world__i_(W!3, X)) | (~teach(W!3, X, cs))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(36,plain,
% 0.11/0.37 (![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!3, X)) | (~teach(W!3, X, cs))) <=> ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!3, X)) | (~teach(W!3, X, cs)))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[35])).
% 0.11/0.37 tff(37,plain,
% 0.11/0.37 (^[X: $i] : trans(monotonicity(rewrite((tptp_fun___ki_exists_in_world__i_(W!3, X) & teach(W!3, X, cs)) <=> (~((~tptp_fun___ki_exists_in_world__i_(W!3, X)) | (~teach(W!3, X, cs))))), ((~(tptp_fun___ki_exists_in_world__i_(W!3, X) & teach(W!3, X, cs))) <=> (~(~((~tptp_fun___ki_exists_in_world__i_(W!3, X)) | (~teach(W!3, X, cs))))))), rewrite((~(~((~tptp_fun___ki_exists_in_world__i_(W!3, X)) | (~teach(W!3, X, cs))))) <=> ((~tptp_fun___ki_exists_in_world__i_(W!3, X)) | (~teach(W!3, X, cs)))), ((~(tptp_fun___ki_exists_in_world__i_(W!3, X) & teach(W!3, X, cs))) <=> ((~tptp_fun___ki_exists_in_world__i_(W!3, X)) | (~teach(W!3, X, cs)))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(38,plain,
% 0.11/0.37 (![X: $i] : (~(tptp_fun___ki_exists_in_world__i_(W!3, X) & teach(W!3, X, cs))) <=> ![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!3, X)) | (~teach(W!3, X, cs)))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[37])).
% 0.11/0.37 tff(39,plain,
% 0.11/0.37 (![X: $i] : (~(tptp_fun___ki_exists_in_world__i_(W!3, X) & teach(W!3, X, cs)))),
% 0.11/0.37 inference(and_elim,[status(thm)],[9])).
% 0.11/0.37 tff(40,plain,
% 0.11/0.37 (![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!3, X)) | (~teach(W!3, X, cs)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.11/0.37 tff(41,plain,
% 0.11/0.37 (![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!3, X)) | (~teach(W!3, X, cs)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[40, 36])).
% 0.11/0.37 tff(42,plain,
% 0.11/0.37 (((~![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!3, X)) | (~teach(W!3, X, cs)))) | ((~tptp_fun___ki_exists_in_world__i_(W!3, tptp_fun_X_2(W!3))) | (~teach(W!3, tptp_fun_X_2(W!3), cs)))) <=> ((~![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!3, X)) | (~teach(W!3, X, cs)))) | (~tptp_fun___ki_exists_in_world__i_(W!3, tptp_fun_X_2(W!3))) | (~teach(W!3, tptp_fun_X_2(W!3), cs)))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(43,plain,
% 0.11/0.37 ((~![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!3, X)) | (~teach(W!3, X, cs)))) | ((~tptp_fun___ki_exists_in_world__i_(W!3, tptp_fun_X_2(W!3))) | (~teach(W!3, tptp_fun_X_2(W!3), cs)))),
% 0.11/0.37 inference(quant_inst,[status(thm)],[])).
% 0.11/0.37 tff(44,plain,
% 0.11/0.37 ((~![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!3, X)) | (~teach(W!3, X, cs)))) | (~tptp_fun___ki_exists_in_world__i_(W!3, tptp_fun_X_2(W!3))) | (~teach(W!3, tptp_fun_X_2(W!3), cs))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.11/0.37 tff(45,plain,
% 0.11/0.37 ($false),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[44, 41, 34, 32])).
% 0.11/0.37 % SZS output end Proof
% 0.11/0.37 % E exiting
%------------------------------------------------------------------------------