%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN920+1 : TPTP v9.0.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.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 05:41:00 AM UTC 2025
% Result : Theorem 0.19s 0.36s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.11 % Problem : SYN920+1 : TPTP v9.0.0. Released v3.1.0.
% 0.02/0.11 % Command : run_E %s %d THM
% 0.12/0.32 % Computer : n007.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Fri Jun 20 13:02:35 EDT 2025
% 0.12/0.32 % CPUTime :
% 0.19/0.36 % SZS status Theorem
% 0.19/0.36 % SZS output start Proof
% 0.19/0.36 tff(h_type, type, (
% 0.19/0.36 h: $i > $o)).
% 0.19/0.36 tff(tptp_fun_X_1_type, type, (
% 0.19/0.36 tptp_fun_X_1: $i)).
% 0.19/0.36 tff(f_type, type, (
% 0.19/0.36 f: $i > $o)).
% 0.19/0.36 tff(g_type, type, (
% 0.19/0.36 g: $i > $o)).
% 0.19/0.36 tff(tptp_fun_X_0_type, type, (
% 0.19/0.36 tptp_fun_X_0: $i)).
% 0.19/0.36 tff(1,assumption,(~(h(X!0) | (~f(X!0)) | (~g(X!0)))), introduced(assumption)).
% 0.19/0.36 tff(2,plain,
% 0.19/0.36 ((h(X!0) | (~f(X!0)) | (~g(X!0))) | g(X!0)),
% 0.19/0.36 inference(tautology,[status(thm)],[])).
% 0.19/0.36 tff(3,plain,
% 0.19/0.36 (g(X!0)),
% 0.19/0.36 inference(unit_resolution,[status(thm)],[2, 1])).
% 0.19/0.36 tff(4,plain,
% 0.19/0.36 ((h(X!0) | (~f(X!0)) | (~g(X!0))) | f(X!0)),
% 0.19/0.36 inference(tautology,[status(thm)],[])).
% 0.19/0.36 tff(5,plain,
% 0.19/0.36 (f(X!0)),
% 0.19/0.36 inference(unit_resolution,[status(thm)],[4, 1])).
% 0.19/0.36 tff(6,plain,
% 0.19/0.36 ((h(X!0) | (~f(X!0)) | (~g(X!0))) | (~h(X!0))),
% 0.19/0.36 inference(tautology,[status(thm)],[])).
% 0.19/0.36 tff(7,plain,
% 0.19/0.36 (~h(X!0)),
% 0.19/0.36 inference(unit_resolution,[status(thm)],[6, 1])).
% 0.19/0.36 tff(8,plain,
% 0.19/0.36 (^[V: $i] : refl(((~g(V)) | h(V) | (~f(V))) <=> ((~g(V)) | h(V) | (~f(V))))),
% 0.19/0.36 inference(bind,[status(th)],[])).
% 0.19/0.36 tff(9,plain,
% 0.19/0.36 (![V: $i] : ((~g(V)) | h(V) | (~f(V))) <=> ![V: $i] : ((~g(V)) | h(V) | (~f(V)))),
% 0.19/0.36 inference(quant_intro,[status(thm)],[8])).
% 0.19/0.36 tff(10,plain,
% 0.19/0.36 (^[V: $i] : trans(monotonicity(rewrite((f(V) & g(V) & (~h(V))) <=> (~((~g(V)) | h(V) | (~f(V))))), ((~(f(V) & g(V) & (~h(V)))) <=> (~(~((~g(V)) | h(V) | (~f(V))))))), rewrite((~(~((~g(V)) | h(V) | (~f(V))))) <=> ((~g(V)) | h(V) | (~f(V)))), ((~(f(V) & g(V) & (~h(V)))) <=> ((~g(V)) | h(V) | (~f(V)))))),
% 0.19/0.36 inference(bind,[status(th)],[])).
% 0.19/0.36 tff(11,plain,
% 0.19/0.36 (![V: $i] : (~(f(V) & g(V) & (~h(V)))) <=> ![V: $i] : ((~g(V)) | h(V) | (~f(V)))),
% 0.19/0.36 inference(quant_intro,[status(thm)],[10])).
% 0.19/0.36 tff(12,plain,
% 0.19/0.36 ((~?[V: $i] : (f(V) & g(V) & (~h(V)))) <=> (~?[V: $i] : (f(V) & g(V) & (~h(V))))),
% 0.19/0.36 inference(rewrite,[status(thm)],[])).
% 0.19/0.36 tff(13,plain,
% 0.19/0.36 ((~(((![X: $i] : ((f(X) & g(X)) => h(X)) => ?[X: $i] : (f(X) & (~g(X)))) & (![W: $i] : (f(W) => g(W)) | ![Z: $i] : (f(Z) => h(Z)))) => (![R: $i] : ((f(R) & h(R)) => g(R)) => ?[V: $i] : ((f(V) & g(V)) & (~h(V)))))) <=> (~(?[V: $i] : (f(V) & g(V) & (~h(V))) | (~![R: $i] : (g(R) | (~(f(R) & h(R))))) | (~(((~![X: $i] : (h(X) | (~(f(X) & g(X))))) | ?[X: $i] : (f(X) & (~g(X)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))))))),
% 0.19/0.36 inference(rewrite,[status(thm)],[])).
% 0.19/0.36 tff(14,axiom,(~(((![X: $i] : ((f(X) & g(X)) => h(X)) => ?[X: $i] : (f(X) & (~g(X)))) & (![W: $i] : (f(W) => g(W)) | ![Z: $i] : (f(Z) => h(Z)))) => (![R: $i] : ((f(R) & h(R)) => g(R)) => ?[V: $i] : ((f(V) & g(V)) & (~h(V)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this')).
% 0.19/0.36 tff(15,plain,
% 0.19/0.36 (~(?[V: $i] : (f(V) & g(V) & (~h(V))) | (~![R: $i] : (g(R) | (~(f(R) & h(R))))) | (~(((~![X: $i] : (h(X) | (~(f(X) & g(X))))) | ?[X: $i] : (f(X) & (~g(X)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z)))))))),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.19/0.36 tff(16,plain,
% 0.19/0.36 (~?[V: $i] : (f(V) & g(V) & (~h(V)))),
% 0.19/0.36 inference(or_elim,[status(thm)],[15])).
% 0.19/0.36 tff(17,plain,
% 0.19/0.36 (~?[V: $i] : (f(V) & g(V) & (~h(V)))),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.19/0.36 tff(18,plain,
% 0.19/0.36 (~?[V: $i] : (f(V) & g(V) & (~h(V)))),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[17, 12])).
% 0.19/0.36 tff(19,plain,
% 0.19/0.36 (~?[V: $i] : (f(V) & g(V) & (~h(V)))),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[18, 12])).
% 0.19/0.36 tff(20,plain,
% 0.19/0.36 (^[V: $i] : refl($oeq((~(f(V) & g(V) & (~h(V)))), (~(f(V) & g(V) & (~h(V))))))),
% 0.19/0.36 inference(bind,[status(th)],[])).
% 0.19/0.36 tff(21,plain,(
% 0.19/0.36 ![V: $i] : (~(f(V) & g(V) & (~h(V))))),
% 0.19/0.36 inference(nnf-neg,[status(sab)],[19, 20])).
% 0.19/0.36 tff(22,plain,
% 0.19/0.36 (![V: $i] : ((~g(V)) | h(V) | (~f(V)))),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[21, 11])).
% 0.19/0.36 tff(23,plain,
% 0.19/0.36 (![V: $i] : ((~g(V)) | h(V) | (~f(V)))),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[22, 9])).
% 0.19/0.36 tff(24,plain,
% 0.19/0.36 (((~![V: $i] : ((~g(V)) | h(V) | (~f(V)))) | (h(X!0) | (~f(X!0)) | (~g(X!0)))) <=> ((~![V: $i] : ((~g(V)) | h(V) | (~f(V)))) | h(X!0) | (~f(X!0)) | (~g(X!0)))),
% 0.19/0.36 inference(rewrite,[status(thm)],[])).
% 0.19/0.36 tff(25,plain,
% 0.19/0.36 (((~g(X!0)) | h(X!0) | (~f(X!0))) <=> (h(X!0) | (~f(X!0)) | (~g(X!0)))),
% 0.19/0.36 inference(rewrite,[status(thm)],[])).
% 0.19/0.36 tff(26,plain,
% 0.19/0.36 (((~![V: $i] : ((~g(V)) | h(V) | (~f(V)))) | ((~g(X!0)) | h(X!0) | (~f(X!0)))) <=> ((~![V: $i] : ((~g(V)) | h(V) | (~f(V)))) | (h(X!0) | (~f(X!0)) | (~g(X!0))))),
% 0.19/0.36 inference(monotonicity,[status(thm)],[25])).
% 0.19/0.36 tff(27,plain,
% 0.19/0.36 (((~![V: $i] : ((~g(V)) | h(V) | (~f(V)))) | ((~g(X!0)) | h(X!0) | (~f(X!0)))) <=> ((~![V: $i] : ((~g(V)) | h(V) | (~f(V)))) | h(X!0) | (~f(X!0)) | (~g(X!0)))),
% 0.19/0.36 inference(transitivity,[status(thm)],[26, 24])).
% 0.19/0.36 tff(28,plain,
% 0.19/0.36 ((~![V: $i] : ((~g(V)) | h(V) | (~f(V)))) | ((~g(X!0)) | h(X!0) | (~f(X!0)))),
% 0.19/0.36 inference(quant_inst,[status(thm)],[])).
% 0.19/0.36 tff(29,plain,
% 0.19/0.36 ((~![V: $i] : ((~g(V)) | h(V) | (~f(V)))) | h(X!0) | (~f(X!0)) | (~g(X!0))),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.19/0.36 tff(30,plain,
% 0.19/0.36 ($false),
% 0.19/0.36 inference(unit_resolution,[status(thm)],[29, 23, 7, 5, 3])).
% 0.19/0.36 tff(31,plain,(h(X!0) | (~f(X!0)) | (~g(X!0))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.36 tff(32,plain,
% 0.19/0.36 (((~(h(X!0) | (~f(X!0)) | (~g(X!0)))) | (~(g(X!1) | (~f(X!1))))) <=> ((~(g(X!1) | (~f(X!1)))) | (~(h(X!0) | (~f(X!0)) | (~g(X!0)))))),
% 0.19/0.36 inference(rewrite,[status(thm)],[])).
% 0.19/0.36 tff(33,plain,
% 0.19/0.36 ((f(X!1) & (~g(X!1))) <=> (~(g(X!1) | (~f(X!1))))),
% 0.19/0.36 inference(rewrite,[status(thm)],[])).
% 0.19/0.36 tff(34,plain,
% 0.19/0.36 ((~(h(X!0) | (~(f(X!0) & g(X!0))))) <=> (~(h(X!0) | (~f(X!0)) | (~g(X!0))))),
% 0.19/0.36 inference(rewrite,[status(thm)],[])).
% 0.19/0.36 tff(35,plain,
% 0.19/0.36 (((~(h(X!0) | (~(f(X!0) & g(X!0))))) | (f(X!1) & (~g(X!1)))) <=> ((~(h(X!0) | (~f(X!0)) | (~g(X!0)))) | (~(g(X!1) | (~f(X!1)))))),
% 0.19/0.36 inference(monotonicity,[status(thm)],[34, 33])).
% 0.19/0.36 tff(36,plain,
% 0.19/0.36 (((~(h(X!0) | (~(f(X!0) & g(X!0))))) | (f(X!1) & (~g(X!1)))) <=> ((~(g(X!1) | (~f(X!1)))) | (~(h(X!0) | (~f(X!0)) | (~g(X!0)))))),
% 0.19/0.36 inference(transitivity,[status(thm)],[35, 32])).
% 0.19/0.36 tff(37,plain,
% 0.19/0.36 (((~![X: $i] : (h(X) | (~(f(X) & g(X))))) | ?[X: $i] : (f(X) & (~g(X)))) <=> ((~![X: $i] : (h(X) | (~(f(X) & g(X))))) | ?[X: $i] : (f(X) & (~g(X))))),
% 0.19/0.36 inference(rewrite,[status(thm)],[])).
% 0.19/0.36 tff(38,plain,
% 0.19/0.36 (((~![X: $i] : (h(X) | (~(f(X) & g(X))))) | ?[X: $i] : (f(X) & (~g(X)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))),
% 0.19/0.36 inference(or_elim,[status(thm)],[15])).
% 0.19/0.36 tff(39,plain,
% 0.19/0.36 ((~![X: $i] : (h(X) | (~(f(X) & g(X))))) | ?[X: $i] : (f(X) & (~g(X)))),
% 0.19/0.36 inference(and_elim,[status(thm)],[38])).
% 0.19/0.36 tff(40,plain,
% 0.19/0.36 ((~![X: $i] : (h(X) | (~(f(X) & g(X))))) | ?[X: $i] : (f(X) & (~g(X)))),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[39, 37])).
% 0.19/0.36 tff(41,plain,
% 0.19/0.36 ((~![X: $i] : (h(X) | (~(f(X) & g(X))))) | ?[X: $i] : (f(X) & (~g(X)))),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[40, 37])).
% 0.19/0.36 tff(42,plain,
% 0.19/0.36 ((~![X: $i] : (h(X) | (~(f(X) & g(X))))) | ?[X: $i] : (f(X) & (~g(X)))),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[41, 37])).
% 0.19/0.36 Proof display could not be completed: monotonicity rule is not handled
% 0.19/0.36 % E exiting
%------------------------------------------------------------------------------