TSTP Solution File: DAT334_21 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : DAT334_21 : TPTP v8.2.0. Released v8.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n006.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 : Mon May 22 15:24:26 EDT 2023
% Result : Theorem 0.19s 0.39s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : DAT334_21 : TPTP v8.2.0. Released v8.2.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n006.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon May 22 11:02:50 EDT 2023
% 0.19/0.34 % CPUTime :
% 0.19/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.19/0.34 Usage: tptp [options] [-file:]file
% 0.19/0.34 -h, -? prints this message.
% 0.19/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.19/0.34 -m, -model generate model.
% 0.19/0.34 -p, -proof generate proof.
% 0.19/0.34 -c, -core generate unsat core of named formulas.
% 0.19/0.34 -st, -statistics display statistics.
% 0.19/0.34 -t:timeout set timeout (in second).
% 0.19/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.19/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.19/0.34 -<param>:<value> configuration parameter and value.
% 0.19/0.34 -o:<output-file> file to place output in.
% 0.19/0.39 % SZS status Theorem
% 0.19/0.39 % SZS output start Proof
% 0.19/0.39 tff(teach_type, type, (
% 0.19/0.39 teach: ( '$ki_world' * $i * $i ) > $o)).
% 0.19/0.39 tff(cs_type, type, (
% 0.19/0.39 cs: $i)).
% 0.19/0.39 tff(tptp_fun_X_2_type, type, (
% 0.19/0.39 tptp_fun_X_2: '$ki_world' > $i)).
% 0.19/0.39 tff(tptp_fun_W_3_type, type, (
% 0.19/0.39 tptp_fun_W_3: '$ki_world')).
% 0.19/0.39 tff(psych_type, type, (
% 0.19/0.39 psych: $i)).
% 0.19/0.39 tff(sue_type, type, (
% 0.19/0.39 sue: $i)).
% 0.19/0.39 tff(mary_type, type, (
% 0.19/0.39 mary: $i)).
% 0.19/0.39 tff(tptp_fun___ki_exists_in_world__i__type, type, (
% 0.19/0.39 tptp_fun___ki_exists_in_world__i_: ( '$ki_world' * $i ) > $o)).
% 0.19/0.39 tff(math_type, type, (
% 0.19/0.39 math: $i)).
% 0.19/0.39 tff(john_type, type, (
% 0.19/0.39 john: $i)).
% 0.19/0.39 tff(tptp_fun___ki_accessible__type, type, (
% 0.19/0.39 tptp_fun___ki_accessible_: ( '$ki_world' * '$ki_world' ) > $o)).
% 0.19/0.39 tff(tptp_fun___ki_local_world__type, type, (
% 0.19/0.39 tptp_fun___ki_local_world_: '$ki_world')).
% 0.19/0.39 tff(1,plain,
% 0.19/0.39 (((~(~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: $i] : (~(tptp_fun___ki_exists_in_world__i_(W!3, X) & teach(W!3, X, cs))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(2,plain,
% 0.19/0.39 ((~![W: '$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: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & teach(W, X, cs))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(3,plain,
% 0.19/0.39 ((~![W: '$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: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & teach(W, X, cs))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(4,axiom,(~![W: '$ki_world'] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => ?[X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & teach(W, X, cs)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','verify')).
% 0.19/0.39 tff(5,plain,
% 0.19/0.39 (~![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ?[X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & teach(W, X, cs)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.19/0.39 tff(6,plain,
% 0.19/0.39 (~![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ?[X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & teach(W, X, cs)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[5, 2])).
% 0.19/0.39 tff(7,plain,
% 0.19/0.39 (~![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ?[X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & teach(W, X, cs)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.19/0.39 tff(8,plain,
% 0.19/0.39 (~![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ?[X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & teach(W, X, cs)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[7, 2])).
% 0.19/0.39 tff(9,plain,
% 0.19/0.39 (~![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ?[X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & teach(W, X, cs)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[8, 2])).
% 0.19/0.39 tff(10,plain,
% 0.19/0.39 (~![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ?[X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & teach(W, X, cs)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.19/0.39 tff(11,plain,
% 0.19/0.39 (~![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | ?[X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & teach(W, X, cs)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[10, 2])).
% 0.19/0.39 tff(12,plain,
% 0.19/0.39 (tptp_fun___ki_accessible_(|'$ki_local_world'|, W!3) & ![X: $i] : (~(tptp_fun___ki_exists_in_world__i_(W!3, X) & teach(W!3, X, cs)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[11, 1])).
% 0.19/0.39 tff(13,plain,
% 0.19/0.39 (tptp_fun___ki_accessible_(|'$ki_local_world'|, W!3)),
% 0.19/0.39 inference(and_elim,[status(thm)],[12])).
% 0.19/0.39 tff(14,plain,
% 0.19/0.39 (^[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_(|'$ki_local_world'|, W)) | (~((~teach(W, john, math)) | (~tptp_fun___ki_exists_in_world__i_(W, tptp_fun_X_2(W))) | (~teach(W, tptp_fun_X_2(W), cs)) | (~teach(W, mary, psych)) | (~teach(W, sue, psych))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(15,plain,
% 0.19/0.39 (![W: '$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_(|'$ki_local_world'|, W)) | (~((~teach(W, john, math)) | (~tptp_fun___ki_exists_in_world__i_(W, tptp_fun_X_2(W))) | (~teach(W, tptp_fun_X_2(W), cs)) | (~teach(W, mary, psych)) | (~teach(W, sue, psych)))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[14])).
% 0.19/0.39 tff(16,plain,
% 0.19/0.39 (^[W: '$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))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(17,plain,
% 0.19/0.39 (![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)))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[16])).
% 0.19/0.39 tff(18,plain,
% 0.19/0.39 (^[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_(|'$ki_local_world'|, W)) | (teach(W, john, math) & tptp_fun___ki_exists_in_world__i_(W, tptp_fun_X_2(W)) & teach(W, tptp_fun_X_2(W), cs) & teach(W, mary, psych) & teach(W, sue, psych))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(19,plain,
% 0.19/0.39 (![W: '$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_(|'$ki_local_world'|, W)) | (teach(W, john, math) & tptp_fun___ki_exists_in_world__i_(W, tptp_fun_X_2(W)) & teach(W, tptp_fun_X_2(W), cs) & teach(W, mary, psych) & teach(W, sue, psych)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[18])).
% 0.19/0.39 tff(20,plain,
% 0.19/0.39 (![W: '$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: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & teach(W, X, cs)) & teach(W, mary, psych) & teach(W, sue, psych)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(21,plain,
% 0.19/0.39 (^[W: '$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: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & teach(W, X, cs)) & teach(W, mary, psych) & teach(W, sue, psych)))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(22,plain,
% 0.19/0.39 (![W: '$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: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & teach(W, X, cs)) & teach(W, mary, psych) & teach(W, sue, psych)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[21])).
% 0.19/0.39 tff(23,axiom,(![W: '$ki_world'] : (tptp_fun___ki_accessible_(|'$ki_local_world'|, W) => (((teach(W, john, math) & ?[X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & teach(W, X, cs))) & teach(W, mary, psych)) & teach(W, sue, psych)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','db')).
% 0.19/0.39 tff(24,plain,
% 0.19/0.39 (![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (teach(W, john, math) & ?[X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & teach(W, X, cs)) & teach(W, mary, psych) & teach(W, sue, psych)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.19/0.39 tff(25,plain,
% 0.19/0.39 (![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (teach(W, john, math) & ?[X: $i] : (tptp_fun___ki_exists_in_world__i_(W, X) & teach(W, X, cs)) & teach(W, mary, psych) & teach(W, sue, psych)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[24, 20])).
% 0.19/0.40 tff(26,plain,(
% 0.19/0.40 ![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (teach(W, john, math) & (tptp_fun___ki_exists_in_world__i_(W, tptp_fun_X_2(W)) & teach(W, tptp_fun_X_2(W), cs)) & teach(W, mary, psych) & teach(W, sue, psych)))),
% 0.19/0.40 inference(skolemize,[status(sab)],[25])).
% 0.19/0.40 tff(27,plain,
% 0.19/0.40 (![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (teach(W, john, math) & tptp_fun___ki_exists_in_world__i_(W, tptp_fun_X_2(W)) & teach(W, tptp_fun_X_2(W), cs) & teach(W, mary, psych) & teach(W, sue, psych)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[26, 19])).
% 0.19/0.40 tff(28,plain,
% 0.19/0.40 (![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~((~teach(W, john, math)) | (~tptp_fun___ki_exists_in_world__i_(W, tptp_fun_X_2(W))) | (~teach(W, tptp_fun_X_2(W), cs)) | (~teach(W, mary, psych)) | (~teach(W, sue, psych)))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[27, 17])).
% 0.19/0.40 tff(29,plain,
% 0.19/0.40 (![W: '$ki_world'] : ((~tptp_fun___ki_accessible_(|'$ki_local_world'|, W)) | (~((~teach(W, john, math)) | (~tptp_fun___ki_exists_in_world__i_(W, tptp_fun_X_2(W))) | (~teach(W, tptp_fun_X_2(W), cs)) | (~teach(W, mary, psych)) | (~teach(W, sue, psych)))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[28, 15])).
% 0.19/0.40 tff(30,plain,
% 0.19/0.40 (((~![W: '$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'|, 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_(|'$ki_local_world'|, W!3)) | (~((~teach(W!3, john, math)) | (~tptp_fun___ki_exists_in_world__i_(W!3, tptp_fun_X_2(W!3))) | (~teach(W!3, tptp_fun_X_2(W!3), cs)) | (~teach(W!3, mary, psych)) | (~teach(W!3, sue, psych)))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(31,plain,
% 0.19/0.40 ((~![W: '$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'|, 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)))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(32,plain,
% 0.19/0.40 ((~![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'|, 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))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.19/0.40 tff(33,plain,
% 0.19/0.40 (~((~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)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[32, 29, 13])).
% 0.19/0.40 tff(34,plain,
% 0.19/0.40 (((~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)),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(35,plain,
% 0.19/0.40 (teach(W!3, tptp_fun_X_2(W!3), cs)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[34, 33])).
% 0.19/0.40 tff(36,plain,
% 0.19/0.40 (((~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))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(37,plain,
% 0.19/0.40 (tptp_fun___ki_exists_in_world__i_(W!3, tptp_fun_X_2(W!3))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[36, 33])).
% 0.19/0.40 tff(38,plain,
% 0.19/0.40 (^[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))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(39,plain,
% 0.19/0.40 (![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)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[38])).
% 0.19/0.40 tff(40,plain,
% 0.19/0.40 (^[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)))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(41,plain,
% 0.19/0.40 (![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)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[40])).
% 0.19/0.40 tff(42,plain,
% 0.19/0.40 (![X: $i] : (~(tptp_fun___ki_exists_in_world__i_(W!3, X) & teach(W!3, X, cs)))),
% 0.19/0.40 inference(and_elim,[status(thm)],[12])).
% 0.19/0.40 tff(43,plain,
% 0.19/0.40 (![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!3, X)) | (~teach(W!3, X, cs)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.19/0.40 tff(44,plain,
% 0.19/0.40 (![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!3, X)) | (~teach(W!3, X, cs)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[43, 39])).
% 0.19/0.40 tff(45,plain,
% 0.19/0.40 (((~![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)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(46,plain,
% 0.19/0.40 ((~![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)))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(47,plain,
% 0.19/0.40 ((~![X: $i] : ((~tptp_fun___ki_exists_in_world__i_(W!3, X)) | (~teach(W!3, X, cs)))) | (~tptp_fun___ki_exists_in_world__i_(W!3, tptp_fun_X_2(W!3))) | (~teach(W!3, tptp_fun_X_2(W!3), cs))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.19/0.40 tff(48,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[47, 44, 37, 35])).
% 0.19/0.40 % SZS output end Proof
%------------------------------------------------------------------------------