%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN918+1 : TPTP v9.0.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.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 0.20s 0.38s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SYN918+1 : TPTP v9.0.0. Released v3.1.0.
% 0.03/0.13 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n011.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 13:01:12 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.20/0.38 % SZS status Theorem
% 0.20/0.38 % SZS output start Proof
% 0.20/0.38 tff(g_type, type, (
% 0.20/0.38 g: $i > $o)).
% 0.20/0.38 tff(elem_1_type, type, (
% 0.20/0.38 elem_1: $i)).
% 0.20/0.38 tff(h_type, type, (
% 0.20/0.38 h: $i > $o)).
% 0.20/0.38 tff(f_type, type, (
% 0.20/0.38 f: $i > $o)).
% 0.20/0.38 tff(tptp_fun_Y_0_type, type, (
% 0.20/0.38 tptp_fun_Y_0: $i)).
% 0.20/0.38 tff(1,assumption,(~(g(Y!0) | (~f(Y!0)))), introduced(assumption)).
% 0.20/0.38 tff(2,plain,
% 0.20/0.38 ((g(Y!0) | (~f(Y!0))) | f(Y!0)),
% 0.20/0.38 inference(tautology,[status(thm)],[])).
% 0.20/0.38 tff(3,plain,
% 0.20/0.38 (f(Y!0)),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[2, 1])).
% 0.20/0.38 tff(4,plain,
% 0.20/0.38 ((g(Y!0) | (~f(Y!0))) | (~g(Y!0))),
% 0.20/0.38 inference(tautology,[status(thm)],[])).
% 0.20/0.38 tff(5,plain,
% 0.20/0.38 (~g(Y!0)),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[4, 1])).
% 0.20/0.38 tff(6,assumption,(![Z: $i] : (h(Z) | (~f(Z)))), introduced(assumption)).
% 0.20/0.38 tff(7,plain,
% 0.20/0.38 (^[R: $i] : refl((g(R) | (~h(R)) | (~f(R))) <=> (g(R) | (~h(R)) | (~f(R))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(8,plain,
% 0.20/0.38 (![R: $i] : (g(R) | (~h(R)) | (~f(R))) <=> ![R: $i] : (g(R) | (~h(R)) | (~f(R)))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[7])).
% 0.20/0.38 tff(9,plain,
% 0.20/0.38 (^[R: $i] : trans(monotonicity(trans(monotonicity(rewrite((f(R) & h(R)) <=> (~((~f(R)) | (~h(R))))), ((~(f(R) & h(R))) <=> (~(~((~f(R)) | (~h(R))))))), rewrite((~(~((~f(R)) | (~h(R))))) <=> ((~f(R)) | (~h(R)))), ((~(f(R) & h(R))) <=> ((~f(R)) | (~h(R))))), ((g(R) | (~(f(R) & h(R)))) <=> (g(R) | ((~f(R)) | (~h(R)))))), rewrite((g(R) | ((~f(R)) | (~h(R)))) <=> (g(R) | (~h(R)) | (~f(R)))), ((g(R) | (~(f(R) & h(R)))) <=> (g(R) | (~h(R)) | (~f(R)))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(10,plain,
% 0.20/0.38 (![R: $i] : (g(R) | (~(f(R) & h(R)))) <=> ![R: $i] : (g(R) | (~h(R)) | (~f(R)))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[9])).
% 0.20/0.38 tff(11,plain,
% 0.20/0.38 (![R: $i] : (g(R) | (~(f(R) & h(R)))) <=> ![R: $i] : (g(R) | (~(f(R) & h(R))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(12,plain,
% 0.20/0.38 ((~((![X: $i] : (((f(X) & g(X)) => h(X)) => ?[Y: $i] : (f(Y) & (~g(Y)))) & (![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))))) | ?[Y: $i] : (f(Y) & (~g(Y)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(13,axiom,(~((![X: $i] : (((f(X) & g(X)) => h(X)) => ?[Y: $i] : (f(Y) & (~g(Y)))) & (![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')).
% 0.20/0.38 tff(14,plain,
% 0.20/0.38 (~(?[V: $i] : (f(V) & g(V) & (~h(V))) | (~![R: $i] : (g(R) | (~(f(R) & h(R))))) | (~(![X: $i] : ((~(h(X) | (~(f(X) & g(X))))) | ?[Y: $i] : (f(Y) & (~g(Y)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z)))))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.20/0.38 tff(15,plain,
% 0.20/0.38 (![R: $i] : (g(R) | (~(f(R) & h(R))))),
% 0.20/0.38 inference(or_elim,[status(thm)],[14])).
% 0.20/0.38 tff(16,plain,
% 0.20/0.38 (![R: $i] : (g(R) | (~(f(R) & h(R))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.20/0.38 tff(17,plain,(
% 0.20/0.38 ![R: $i] : (g(R) | (~(f(R) & h(R))))),
% 0.20/0.38 inference(skolemize,[status(sab)],[16])).
% 0.20/0.38 tff(18,plain,
% 0.20/0.38 (![R: $i] : (g(R) | (~h(R)) | (~f(R)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[17, 10])).
% 0.20/0.38 tff(19,plain,
% 0.20/0.38 (![R: $i] : (g(R) | (~h(R)) | (~f(R)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[18, 8])).
% 0.20/0.38 tff(20,plain,
% 0.20/0.38 (((~![R: $i] : (g(R) | (~h(R)) | (~f(R)))) | (g(Y!0) | (~f(Y!0)) | (~h(Y!0)))) <=> ((~![R: $i] : (g(R) | (~h(R)) | (~f(R)))) | g(Y!0) | (~f(Y!0)) | (~h(Y!0)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(21,plain,
% 0.20/0.38 ((g(Y!0) | (~h(Y!0)) | (~f(Y!0))) <=> (g(Y!0) | (~f(Y!0)) | (~h(Y!0)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(22,plain,
% 0.20/0.38 (((~![R: $i] : (g(R) | (~h(R)) | (~f(R)))) | (g(Y!0) | (~h(Y!0)) | (~f(Y!0)))) <=> ((~![R: $i] : (g(R) | (~h(R)) | (~f(R)))) | (g(Y!0) | (~f(Y!0)) | (~h(Y!0))))),
% 0.20/0.38 inference(monotonicity,[status(thm)],[21])).
% 0.20/0.38 tff(23,plain,
% 0.20/0.38 (((~![R: $i] : (g(R) | (~h(R)) | (~f(R)))) | (g(Y!0) | (~h(Y!0)) | (~f(Y!0)))) <=> ((~![R: $i] : (g(R) | (~h(R)) | (~f(R)))) | g(Y!0) | (~f(Y!0)) | (~h(Y!0)))),
% 0.20/0.38 inference(transitivity,[status(thm)],[22, 20])).
% 0.20/0.38 tff(24,plain,
% 0.20/0.38 ((~![R: $i] : (g(R) | (~h(R)) | (~f(R)))) | (g(Y!0) | (~h(Y!0)) | (~f(Y!0)))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(25,plain,
% 0.20/0.38 ((~![R: $i] : (g(R) | (~h(R)) | (~f(R)))) | g(Y!0) | (~f(Y!0)) | (~h(Y!0))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.20/0.38 tff(26,plain,
% 0.20/0.38 (~h(Y!0)),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[25, 19, 5, 3])).
% 0.20/0.38 tff(27,plain,
% 0.20/0.38 (((~![Z: $i] : (h(Z) | (~f(Z)))) | (h(Y!0) | (~f(Y!0)))) <=> ((~![Z: $i] : (h(Z) | (~f(Z)))) | h(Y!0) | (~f(Y!0)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(28,plain,
% 0.20/0.38 ((~![Z: $i] : (h(Z) | (~f(Z)))) | (h(Y!0) | (~f(Y!0)))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(29,plain,
% 0.20/0.38 ((~![Z: $i] : (h(Z) | (~f(Z)))) | h(Y!0) | (~f(Y!0))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.20/0.38 tff(30,plain,
% 0.20/0.38 ($false),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[29, 6, 3, 26])).
% 0.20/0.38 tff(31,plain,((g(Y!0) | (~f(Y!0))) | (~![Z: $i] : (h(Z) | (~f(Z))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.38 tff(32,plain,
% 0.20/0.38 (g(Y!0) | (~f(Y!0))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[31, 6])).
% 0.20/0.38 tff(33,plain,
% 0.20/0.38 (^[X: $i] : refl(((~(h(X) | (~g(X)) | (~f(X)))) | (~(g(Y!0) | (~f(Y!0))))) <=> ((~(h(X) | (~g(X)) | (~f(X)))) | (~(g(Y!0) | (~f(Y!0))))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(34,plain,
% 0.20/0.38 (![X: $i] : ((~(h(X) | (~g(X)) | (~f(X)))) | (~(g(Y!0) | (~f(Y!0))))) <=> ![X: $i] : ((~(h(X) | (~g(X)) | (~f(X)))) | (~(g(Y!0) | (~f(Y!0)))))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[33])).
% 0.20/0.38 tff(35,plain,
% 0.20/0.38 (^[X: $i] : trans(monotonicity(rewrite((~(h(X) | (~(f(X) & g(X))))) <=> (~(h(X) | (~g(X)) | (~f(X))))), rewrite((f(Y!0) & (~g(Y!0))) <=> (~(g(Y!0) | (~f(Y!0))))), (((~(h(X) | (~(f(X) & g(X))))) | (f(Y!0) & (~g(Y!0)))) <=> ((~(h(X) | (~g(X)) | (~f(X)))) | (~(g(Y!0) | (~f(Y!0))))))), rewrite(((~(h(X) | (~g(X)) | (~f(X)))) | (~(g(Y!0) | (~f(Y!0))))) <=> ((~(h(X) | (~g(X)) | (~f(X)))) | (~(g(Y!0) | (~f(Y!0)))))), (((~(h(X) | (~(f(X) & g(X))))) | (f(Y!0) & (~g(Y!0)))) <=> ((~(h(X) | (~g(X)) | (~f(X)))) | (~(g(Y!0) | (~f(Y!0)))))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(36,plain,
% 0.20/0.38 (![X: $i] : ((~(h(X) | (~(f(X) & g(X))))) | (f(Y!0) & (~g(Y!0)))) <=> ![X: $i] : ((~(h(X) | (~g(X)) | (~f(X)))) | (~(g(Y!0) | (~f(Y!0)))))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[35])).
% 0.20/0.38 tff(37,plain,
% 0.20/0.38 (![X: $i] : ((~(h(X) | (~(f(X) & g(X))))) | ?[Y: $i] : (f(Y) & (~g(Y)))) <=> ![X: $i] : ((~(h(X) | (~(f(X) & g(X))))) | ?[Y: $i] : (f(Y) & (~g(Y))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(38,plain,
% 0.20/0.38 (![X: $i] : ((~(h(X) | (~(f(X) & g(X))))) | ?[Y: $i] : (f(Y) & (~g(Y)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))),
% 0.20/0.38 inference(or_elim,[status(thm)],[14])).
% 0.20/0.38 tff(39,plain,
% 0.20/0.38 (![X: $i] : ((~(h(X) | (~(f(X) & g(X))))) | ?[Y: $i] : (f(Y) & (~g(Y))))),
% 0.20/0.38 inference(and_elim,[status(thm)],[38])).
% 0.20/0.38 tff(40,plain,
% 0.20/0.38 (![X: $i] : ((~(h(X) | (~(f(X) & g(X))))) | ?[Y: $i] : (f(Y) & (~g(Y))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[39, 37])).
% 0.20/0.38 tff(41,plain,(
% 0.20/0.38 ![X: $i] : ((~(h(X) | (~(f(X) & g(X))))) | (f(Y!0) & (~g(Y!0))))),
% 0.20/0.38 inference(skolemize,[status(sab)],[40])).
% 0.20/0.38 tff(42,plain,
% 0.20/0.38 (![X: $i] : ((~(h(X) | (~g(X)) | (~f(X)))) | (~(g(Y!0) | (~f(Y!0)))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[41, 36])).
% 0.20/0.38 tff(43,plain,
% 0.20/0.38 (![X: $i] : ((~(h(X) | (~g(X)) | (~f(X)))) | (~(g(Y!0) | (~f(Y!0)))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[42, 34])).
% 0.20/0.38 tff(44,plain,
% 0.20/0.38 (((~![X: $i] : ((~(h(X) | (~g(X)) | (~f(X)))) | (~(g(Y!0) | (~f(Y!0)))))) | ((~(g(Y!0) | (~f(Y!0)))) | (~((~f(elem!1)) | h(elem!1) | (~g(elem!1)))))) <=> ((~![X: $i] : ((~(h(X) | (~g(X)) | (~f(X)))) | (~(g(Y!0) | (~f(Y!0)))))) | (~(g(Y!0) | (~f(Y!0)))) | (~((~f(elem!1)) | h(elem!1) | (~g(elem!1)))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(45,plain,
% 0.20/0.38 (((~((~f(elem!1)) | h(elem!1) | (~g(elem!1)))) | (~(g(Y!0) | (~f(Y!0))))) <=> ((~(g(Y!0) | (~f(Y!0)))) | (~((~f(elem!1)) | h(elem!1) | (~g(elem!1)))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(46,plain,
% 0.20/0.39 ((~(h(elem!1) | (~g(elem!1)) | (~f(elem!1)))) <=> (~((~f(elem!1)) | h(elem!1) | (~g(elem!1))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(47,plain,
% 0.20/0.39 (((~(h(elem!1) | (~g(elem!1)) | (~f(elem!1)))) | (~(g(Y!0) | (~f(Y!0))))) <=> ((~((~f(elem!1)) | h(elem!1) | (~g(elem!1)))) | (~(g(Y!0) | (~f(Y!0)))))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[46])).
% 0.20/0.39 tff(48,plain,
% 0.20/0.39 (((~(h(elem!1) | (~g(elem!1)) | (~f(elem!1)))) | (~(g(Y!0) | (~f(Y!0))))) <=> ((~(g(Y!0) | (~f(Y!0)))) | (~((~f(elem!1)) | h(elem!1) | (~g(elem!1)))))),
% 0.20/0.39 inference(transitivity,[status(thm)],[47, 45])).
% 0.20/0.39 tff(49,plain,
% 0.20/0.39 (((~![X: $i] : ((~(h(X) | (~g(X)) | (~f(X)))) | (~(g(Y!0) | (~f(Y!0)))))) | ((~(h(elem!1) | (~g(elem!1)) | (~f(elem!1)))) | (~(g(Y!0) | (~f(Y!0)))))) <=> ((~![X: $i] : ((~(h(X) | (~g(X)) | (~f(X)))) | (~(g(Y!0) | (~f(Y!0)))))) | ((~(g(Y!0) | (~f(Y!0)))) | (~((~f(elem!1)) | h(elem!1) | (~g(elem!1))))))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[48])).
% 0.20/0.39 tff(50,plain,
% 0.20/0.39 (((~![X: $i] : ((~(h(X) | (~g(X)) | (~f(X)))) | (~(g(Y!0) | (~f(Y!0)))))) | ((~(h(elem!1) | (~g(elem!1)) | (~f(elem!1)))) | (~(g(Y!0) | (~f(Y!0)))))) <=> ((~![X: $i] : ((~(h(X) | (~g(X)) | (~f(X)))) | (~(g(Y!0) | (~f(Y!0)))))) | (~(g(Y!0) | (~f(Y!0)))) | (~((~f(elem!1)) | h(elem!1) | (~g(elem!1)))))),
% 0.20/0.39 inference(transitivity,[status(thm)],[49, 44])).
% 0.20/0.39 tff(51,plain,
% 0.20/0.39 ((~![X: $i] : ((~(h(X) | (~g(X)) | (~f(X)))) | (~(g(Y!0) | (~f(Y!0)))))) | ((~(h(elem!1) | (~g(elem!1)) | (~f(elem!1)))) | (~(g(Y!0) | (~f(Y!0)))))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(52,plain,
% 0.20/0.39 ((~![X: $i] : ((~(h(X) | (~g(X)) | (~f(X)))) | (~(g(Y!0) | (~f(Y!0)))))) | (~(g(Y!0) | (~f(Y!0)))) | (~((~f(elem!1)) | h(elem!1) | (~g(elem!1))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.20/0.39 tff(53,plain,
% 0.20/0.39 ((~(g(Y!0) | (~f(Y!0)))) | (~((~f(elem!1)) | h(elem!1) | (~g(elem!1))))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[52, 43])).
% 0.20/0.39 tff(54,plain,
% 0.20/0.39 (~((~f(elem!1)) | h(elem!1) | (~g(elem!1)))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[53, 32])).
% 0.20/0.39 tff(55,plain,
% 0.20/0.39 (((~f(elem!1)) | h(elem!1) | (~g(elem!1))) | (~h(elem!1))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(56,plain,
% 0.20/0.39 (~h(elem!1)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[55, 54])).
% 0.20/0.39 tff(57,plain,
% 0.20/0.39 (((~f(elem!1)) | h(elem!1) | (~g(elem!1))) | f(elem!1)),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(58,plain,
% 0.20/0.39 (f(elem!1)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[57, 54])).
% 0.20/0.39 tff(59,plain,
% 0.20/0.39 (((~![Z: $i] : (h(Z) | (~f(Z)))) | (h(elem!1) | (~f(elem!1)))) <=> ((~![Z: $i] : (h(Z) | (~f(Z)))) | h(elem!1) | (~f(elem!1)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(60,plain,
% 0.20/0.39 ((~![Z: $i] : (h(Z) | (~f(Z)))) | (h(elem!1) | (~f(elem!1)))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(61,plain,
% 0.20/0.39 ((~![Z: $i] : (h(Z) | (~f(Z)))) | h(elem!1) | (~f(elem!1))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.20/0.39 tff(62,plain,
% 0.20/0.39 ($false),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[61, 6, 58, 56])).
% 0.20/0.39 tff(63,plain,(~![Z: $i] : (h(Z) | (~f(Z)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.39 tff(64,plain,
% 0.20/0.39 ((![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z)))) <=> (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(65,plain,
% 0.20/0.39 ((![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z)))) <=> (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(66,plain,
% 0.20/0.39 (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z)))),
% 0.20/0.39 inference(and_elim,[status(thm)],[38])).
% 0.20/0.39 tff(67,plain,
% 0.20/0.39 (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.20/0.39 tff(68,plain,
% 0.20/0.39 (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[67, 65])).
% 0.20/0.39 tff(69,plain,
% 0.20/0.39 (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[68, 65])).
% 0.20/0.39 Proof display could not be completed: monotonicity rule is not handled
% 0.20/0.39 % E exiting
%------------------------------------------------------------------------------