%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN939+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 05:41:02 AM UTC 2025
% Result : Theorem 0.12s 0.38s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SYN939+1 : TPTP v9.0.0. Released v3.1.0.
% 0.12/0.12 % 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 13:01:42 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.12/0.38 % SZS status Theorem
% 0.12/0.38 % SZS output start Proof
% 0.12/0.38 tff(q_type, type, (
% 0.12/0.38 q: $i > $o)).
% 0.12/0.38 tff(f_type, type, (
% 0.12/0.38 f: $i > $i)).
% 0.12/0.38 tff(tptp_fun_C_1_type, type, (
% 0.12/0.38 tptp_fun_C_1: $i)).
% 0.12/0.38 tff(r_type, type, (
% 0.12/0.38 r: $i > $o)).
% 0.12/0.38 tff(tptp_fun_B_0_type, type, (
% 0.12/0.38 tptp_fun_B_0: $i)).
% 0.12/0.38 tff(p_type, type, (
% 0.12/0.38 p: $i > $o)).
% 0.12/0.38 tff(elem_2_type, type, (
% 0.12/0.38 elem_2: $i)).
% 0.12/0.38 tff(1,assumption,(~q(f(C!1))), introduced(assumption)).
% 0.12/0.38 tff(2,plain,
% 0.12/0.38 (^[Z: $i] : refl(q(f(Z)) <=> q(f(Z)))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(3,plain,
% 0.12/0.38 (![Z: $i] : q(f(Z)) <=> ![Z: $i] : q(f(Z))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[2])).
% 0.12/0.38 tff(4,plain,
% 0.12/0.38 ((![Z: $i] : q(f(Z)) & ![X: $i, Y: $i] : (~((p(X) | (~p(f(Y)))) & ((~r(Y)) | (r(B!0) & r(C!1))) & q(X)))) <=> (![Z: $i] : q(f(Z)) & ![X: $i, Y: $i] : (~((p(X) | (~p(f(Y)))) & ((~r(Y)) | (r(B!0) & r(C!1))) & q(X))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(5,plain,
% 0.12/0.38 ((~![C: $i, B: $i] : ((~![Z: $i] : q(f(Z))) | ?[X: $i, Y: $i] : ((p(X) | (~p(f(Y)))) & ((~r(Y)) | (r(B) & r(C))) & q(X)))) <=> (~![C: $i, B: $i] : ((~![Z: $i] : q(f(Z))) | ?[X: $i, Y: $i] : ((p(X) | (~p(f(Y)))) & ((~r(Y)) | (r(B) & r(C))) & q(X))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(6,plain,
% 0.12/0.38 ((~![C: $i, B: $i] : (![Z: $i] : q(f(Z)) => ?[X: $i, Y: $i] : (((p(f(Y)) => p(X)) & (r(Y) => (r(B) & r(C)))) & q(X)))) <=> (~![C: $i, B: $i] : ((~![Z: $i] : q(f(Z))) | ?[X: $i, Y: $i] : ((p(X) | (~p(f(Y)))) & ((~r(Y)) | (r(B) & r(C))) & q(X))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(7,axiom,(~![C: $i, B: $i] : (![Z: $i] : q(f(Z)) => ?[X: $i, Y: $i] : (((p(f(Y)) => p(X)) & (r(Y) => (r(B) & r(C)))) & q(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this')).
% 0.12/0.38 tff(8,plain,
% 0.12/0.38 (~![C: $i, B: $i] : ((~![Z: $i] : q(f(Z))) | ?[X: $i, Y: $i] : ((p(X) | (~p(f(Y)))) & ((~r(Y)) | (r(B) & r(C))) & q(X)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.12/0.38 tff(9,plain,
% 0.12/0.38 (~![C: $i, B: $i] : ((~![Z: $i] : q(f(Z))) | ?[X: $i, Y: $i] : ((p(X) | (~p(f(Y)))) & ((~r(Y)) | (r(B) & r(C))) & q(X)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[8, 5])).
% 0.12/0.38 tff(10,plain,
% 0.12/0.38 (~![C: $i, B: $i] : ((~![Z: $i] : q(f(Z))) | ?[X: $i, Y: $i] : ((p(X) | (~p(f(Y)))) & ((~r(Y)) | (r(B) & r(C))) & q(X)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.12/0.38 tff(11,plain,
% 0.12/0.38 (~![C: $i, B: $i] : ((~![Z: $i] : q(f(Z))) | ?[X: $i, Y: $i] : ((p(X) | (~p(f(Y)))) & ((~r(Y)) | (r(B) & r(C))) & q(X)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[10, 5])).
% 0.12/0.38 tff(12,plain,
% 0.12/0.38 (![Z: $i] : q(f(Z)) & ![X: $i, Y: $i] : (~((p(X) | (~p(f(Y)))) & ((~r(Y)) | (r(B!0) & r(C!1))) & q(X)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.12/0.38 tff(13,plain,
% 0.12/0.38 (![Z: $i] : q(f(Z))),
% 0.12/0.38 inference(and_elim,[status(thm)],[12])).
% 0.12/0.38 tff(14,plain,
% 0.12/0.38 (![Z: $i] : q(f(Z))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[13, 3])).
% 0.12/0.38 tff(15,plain,
% 0.12/0.38 ((~![Z: $i] : q(f(Z))) | q(f(C!1))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(16,plain,
% 0.12/0.38 ($false),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[15, 14, 1])).
% 0.12/0.38 tff(17,plain,(q(f(C!1))), inference(lemma,lemma(discharge,[]))).
% 0.12/0.38 tff(18,assumption,(~q(f(B!0))), introduced(assumption)).
% 0.12/0.38 tff(19,plain,
% 0.12/0.38 ((~![Z: $i] : q(f(Z))) | q(f(B!0))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(20,plain,
% 0.12/0.38 ($false),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[19, 14, 18])).
% 0.12/0.38 tff(21,plain,(q(f(B!0))), inference(lemma,lemma(discharge,[]))).
% 0.12/0.38 tff(22,assumption,((~r(B!0)) | (~((~r(B!0)) | (~r(C!1))))), introduced(assumption)).
% 0.12/0.38 tff(23,plain,
% 0.12/0.38 (^[X: $i, Y: $i] : refl(((~(p(X) | (~p(f(Y))))) | (~((~r(Y)) | (~((~r(B!0)) | (~r(C!1)))))) | (~q(X))) <=> ((~(p(X) | (~p(f(Y))))) | (~((~r(Y)) | (~((~r(B!0)) | (~r(C!1)))))) | (~q(X))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(24,plain,
% 0.12/0.38 (![X: $i, Y: $i] : ((~(p(X) | (~p(f(Y))))) | (~((~r(Y)) | (~((~r(B!0)) | (~r(C!1)))))) | (~q(X))) <=> ![X: $i, Y: $i] : ((~(p(X) | (~p(f(Y))))) | (~((~r(Y)) | (~((~r(B!0)) | (~r(C!1)))))) | (~q(X)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[23])).
% 0.12/0.38 tff(25,plain,
% 0.12/0.38 (^[X: $i, Y: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~r(Y)) | (r(B!0) & r(C!1))) <=> ((~r(Y)) | (~((~r(B!0)) | (~r(C!1)))))), (((p(X) | (~p(f(Y)))) & ((~r(Y)) | (r(B!0) & r(C!1))) & q(X)) <=> ((p(X) | (~p(f(Y)))) & ((~r(Y)) | (~((~r(B!0)) | (~r(C!1))))) & q(X)))), rewrite(((p(X) | (~p(f(Y)))) & ((~r(Y)) | (~((~r(B!0)) | (~r(C!1))))) & q(X)) <=> (~((~(p(X) | (~p(f(Y))))) | (~((~r(Y)) | (~((~r(B!0)) | (~r(C!1)))))) | (~q(X))))), (((p(X) | (~p(f(Y)))) & ((~r(Y)) | (r(B!0) & r(C!1))) & q(X)) <=> (~((~(p(X) | (~p(f(Y))))) | (~((~r(Y)) | (~((~r(B!0)) | (~r(C!1)))))) | (~q(X)))))), ((~((p(X) | (~p(f(Y)))) & ((~r(Y)) | (r(B!0) & r(C!1))) & q(X))) <=> (~(~((~(p(X) | (~p(f(Y))))) | (~((~r(Y)) | (~((~r(B!0)) | (~r(C!1)))))) | (~q(X))))))), rewrite((~(~((~(p(X) | (~p(f(Y))))) | (~((~r(Y)) | (~((~r(B!0)) | (~r(C!1)))))) | (~q(X))))) <=> ((~(p(X) | (~p(f(Y))))) | (~((~r(Y)) | (~((~r(B!0)) | (~r(C!1)))))) | (~q(X)))), ((~((p(X) | (~p(f(Y)))) & ((~r(Y)) | (r(B!0) & r(C!1))) & q(X))) <=> ((~(p(X) | (~p(f(Y))))) | (~((~r(Y)) | (~((~r(B!0)) | (~r(C!1)))))) | (~q(X)))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(26,plain,
% 0.12/0.39 (![X: $i, Y: $i] : (~((p(X) | (~p(f(Y)))) & ((~r(Y)) | (r(B!0) & r(C!1))) & q(X))) <=> ![X: $i, Y: $i] : ((~(p(X) | (~p(f(Y))))) | (~((~r(Y)) | (~((~r(B!0)) | (~r(C!1)))))) | (~q(X)))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[25])).
% 0.12/0.39 tff(27,plain,
% 0.12/0.39 (![X: $i, Y: $i] : (~((p(X) | (~p(f(Y)))) & ((~r(Y)) | (r(B!0) & r(C!1))) & q(X)))),
% 0.12/0.39 inference(and_elim,[status(thm)],[12])).
% 0.12/0.39 tff(28,plain,
% 0.12/0.39 (![X: $i, Y: $i] : ((~(p(X) | (~p(f(Y))))) | (~((~r(Y)) | (~((~r(B!0)) | (~r(C!1)))))) | (~q(X)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.12/0.39 tff(29,plain,
% 0.12/0.39 (![X: $i, Y: $i] : ((~(p(X) | (~p(f(Y))))) | (~((~r(Y)) | (~((~r(B!0)) | (~r(C!1)))))) | (~q(X)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.12/0.39 tff(30,plain,
% 0.12/0.39 (((~![X: $i, Y: $i] : ((~(p(X) | (~p(f(Y))))) | (~((~r(Y)) | (~((~r(B!0)) | (~r(C!1)))))) | (~q(X)))) | ((~((~r(B!0)) | (~((~r(B!0)) | (~r(C!1)))))) | (~q(f(B!0))))) <=> ((~![X: $i, Y: $i] : ((~(p(X) | (~p(f(Y))))) | (~((~r(Y)) | (~((~r(B!0)) | (~r(C!1)))))) | (~q(X)))) | (~((~r(B!0)) | (~((~r(B!0)) | (~r(C!1)))))) | (~q(f(B!0))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(31,plain,
% 0.12/0.39 (($false | (~((~r(B!0)) | (~((~r(B!0)) | (~r(C!1)))))) | (~q(f(B!0)))) <=> ((~((~r(B!0)) | (~((~r(B!0)) | (~r(C!1)))))) | (~q(f(B!0))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(32,plain,
% 0.12/0.39 ((~$true) <=> $false),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(33,plain,
% 0.12/0.39 ((p(f(B!0)) | (~p(f(B!0)))) <=> $true),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(34,plain,
% 0.12/0.39 ((~(p(f(B!0)) | (~p(f(B!0))))) <=> (~$true)),
% 0.12/0.39 inference(monotonicity,[status(thm)],[33])).
% 0.12/0.39 tff(35,plain,
% 0.12/0.39 ((~(p(f(B!0)) | (~p(f(B!0))))) <=> $false),
% 0.12/0.39 inference(transitivity,[status(thm)],[34, 32])).
% 0.12/0.39 tff(36,plain,
% 0.12/0.39 (((~(p(f(B!0)) | (~p(f(B!0))))) | (~((~r(B!0)) | (~((~r(B!0)) | (~r(C!1)))))) | (~q(f(B!0)))) <=> ($false | (~((~r(B!0)) | (~((~r(B!0)) | (~r(C!1)))))) | (~q(f(B!0))))),
% 0.12/0.39 inference(monotonicity,[status(thm)],[35])).
% 0.12/0.39 tff(37,plain,
% 0.12/0.39 (((~(p(f(B!0)) | (~p(f(B!0))))) | (~((~r(B!0)) | (~((~r(B!0)) | (~r(C!1)))))) | (~q(f(B!0)))) <=> ((~((~r(B!0)) | (~((~r(B!0)) | (~r(C!1)))))) | (~q(f(B!0))))),
% 0.12/0.39 inference(transitivity,[status(thm)],[36, 31])).
% 0.12/0.39 tff(38,plain,
% 0.12/0.39 (((~![X: $i, Y: $i] : ((~(p(X) | (~p(f(Y))))) | (~((~r(Y)) | (~((~r(B!0)) | (~r(C!1)))))) | (~q(X)))) | ((~(p(f(B!0)) | (~p(f(B!0))))) | (~((~r(B!0)) | (~((~r(B!0)) | (~r(C!1)))))) | (~q(f(B!0))))) <=> ((~![X: $i, Y: $i] : ((~(p(X) | (~p(f(Y))))) | (~((~r(Y)) | (~((~r(B!0)) | (~r(C!1)))))) | (~q(X)))) | ((~((~r(B!0)) | (~((~r(B!0)) | (~r(C!1)))))) | (~q(f(B!0)))))),
% 0.12/0.39 inference(monotonicity,[status(thm)],[37])).
% 0.12/0.39 tff(39,plain,
% 0.12/0.39 (((~![X: $i, Y: $i] : ((~(p(X) | (~p(f(Y))))) | (~((~r(Y)) | (~((~r(B!0)) | (~r(C!1)))))) | (~q(X)))) | ((~(p(f(B!0)) | (~p(f(B!0))))) | (~((~r(B!0)) | (~((~r(B!0)) | (~r(C!1)))))) | (~q(f(B!0))))) <=> ((~![X: $i, Y: $i] : ((~(p(X) | (~p(f(Y))))) | (~((~r(Y)) | (~((~r(B!0)) | (~r(C!1)))))) | (~q(X)))) | (~((~r(B!0)) | (~((~r(B!0)) | (~r(C!1)))))) | (~q(f(B!0))))),
% 0.12/0.39 inference(transitivity,[status(thm)],[38, 30])).
% 0.12/0.39 tff(40,plain,
% 0.12/0.39 ((~![X: $i, Y: $i] : ((~(p(X) | (~p(f(Y))))) | (~((~r(Y)) | (~((~r(B!0)) | (~r(C!1)))))) | (~q(X)))) | ((~(p(f(B!0)) | (~p(f(B!0))))) | (~((~r(B!0)) | (~((~r(B!0)) | (~r(C!1)))))) | (~q(f(B!0))))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(41,plain,
% 0.12/0.39 ((~![X: $i, Y: $i] : ((~(p(X) | (~p(f(Y))))) | (~((~r(Y)) | (~((~r(B!0)) | (~r(C!1)))))) | (~q(X)))) | (~((~r(B!0)) | (~((~r(B!0)) | (~r(C!1)))))) | (~q(f(B!0)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.12/0.39 tff(42,plain,
% 0.12/0.39 ($false),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[41, 29, 22, 21])).
% 0.12/0.39 tff(43,plain,(~((~r(B!0)) | (~((~r(B!0)) | (~r(C!1)))))), inference(lemma,lemma(discharge,[]))).
% 0.12/0.39 tff(44,plain,
% 0.12/0.39 (((~r(B!0)) | (~((~r(B!0)) | (~r(C!1))))) | r(B!0)),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(45,plain,
% 0.12/0.39 (r(B!0)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[44, 43])).
% 0.12/0.39 tff(46,plain,
% 0.12/0.39 ((~![Z: $i] : q(f(Z))) | q(f(elem!2))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(47,plain,
% 0.12/0.39 (q(f(elem!2))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[46, 14])).
% 0.12/0.39 tff(48,plain,
% 0.12/0.39 (((~![X: $i, Y: $i] : ((~(p(X) | (~p(f(Y))))) | (~((~r(Y)) | (~((~r(B!0)) | (~r(C!1)))))) | (~q(X)))) | ((~((~r(elem!2)) | (~((~r(B!0)) | (~r(C!1)))))) | (~q(f(elem!2))))) <=> ((~![X: $i, Y: $i] : ((~(p(X) | (~p(f(Y))))) | (~((~r(Y)) | (~((~r(B!0)) | (~r(C!1)))))) | (~q(X)))) | (~((~r(elem!2)) | (~((~r(B!0)) | (~r(C!1)))))) | (~q(f(elem!2))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(49,plain,
% 0.12/0.39 (($false | (~((~r(elem!2)) | (~((~r(B!0)) | (~r(C!1)))))) | (~q(f(elem!2)))) <=> ((~((~r(elem!2)) | (~((~r(B!0)) | (~r(C!1)))))) | (~q(f(elem!2))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(50,plain,
% 0.12/0.39 ((p(f(elem!2)) | (~p(f(elem!2)))) <=> $true),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(51,plain,
% 0.12/0.39 ((~(p(f(elem!2)) | (~p(f(elem!2))))) <=> (~$true)),
% 0.12/0.39 inference(monotonicity,[status(thm)],[50])).
% 0.12/0.39 tff(52,plain,
% 0.12/0.39 ((~(p(f(elem!2)) | (~p(f(elem!2))))) <=> $false),
% 0.12/0.39 inference(transitivity,[status(thm)],[51, 32])).
% 0.12/0.39 tff(53,plain,
% 0.12/0.39 (((~(p(f(elem!2)) | (~p(f(elem!2))))) | (~((~r(elem!2)) | (~((~r(B!0)) | (~r(C!1)))))) | (~q(f(elem!2)))) <=> ($false | (~((~r(elem!2)) | (~((~r(B!0)) | (~r(C!1)))))) | (~q(f(elem!2))))),
% 0.12/0.39 inference(monotonicity,[status(thm)],[52])).
% 0.12/0.39 tff(54,plain,
% 0.12/0.39 (((~(p(f(elem!2)) | (~p(f(elem!2))))) | (~((~r(elem!2)) | (~((~r(B!0)) | (~r(C!1)))))) | (~q(f(elem!2)))) <=> ((~((~r(elem!2)) | (~((~r(B!0)) | (~r(C!1)))))) | (~q(f(elem!2))))),
% 0.12/0.39 inference(transitivity,[status(thm)],[53, 49])).
% 0.12/0.39 tff(55,plain,
% 0.12/0.39 (((~![X: $i, Y: $i] : ((~(p(X) | (~p(f(Y))))) | (~((~r(Y)) | (~((~r(B!0)) | (~r(C!1)))))) | (~q(X)))) | ((~(p(f(elem!2)) | (~p(f(elem!2))))) | (~((~r(elem!2)) | (~((~r(B!0)) | (~r(C!1)))))) | (~q(f(elem!2))))) <=> ((~![X: $i, Y: $i] : ((~(p(X) | (~p(f(Y))))) | (~((~r(Y)) | (~((~r(B!0)) | (~r(C!1)))))) | (~q(X)))) | ((~((~r(elem!2)) | (~((~r(B!0)) | (~r(C!1)))))) | (~q(f(elem!2)))))),
% 0.12/0.39 inference(monotonicity,[status(thm)],[54])).
% 0.12/0.39 tff(56,plain,
% 0.12/0.39 (((~![X: $i, Y: $i] : ((~(p(X) | (~p(f(Y))))) | (~((~r(Y)) | (~((~r(B!0)) | (~r(C!1)))))) | (~q(X)))) | ((~(p(f(elem!2)) | (~p(f(elem!2))))) | (~((~r(elem!2)) | (~((~r(B!0)) | (~r(C!1)))))) | (~q(f(elem!2))))) <=> ((~![X: $i, Y: $i] : ((~(p(X) | (~p(f(Y))))) | (~((~r(Y)) | (~((~r(B!0)) | (~r(C!1)))))) | (~q(X)))) | (~((~r(elem!2)) | (~((~r(B!0)) | (~r(C!1)))))) | (~q(f(elem!2))))),
% 0.12/0.39 inference(transitivity,[status(thm)],[55, 48])).
% 0.12/0.39 tff(57,plain,
% 0.12/0.39 ((~![X: $i, Y: $i] : ((~(p(X) | (~p(f(Y))))) | (~((~r(Y)) | (~((~r(B!0)) | (~r(C!1)))))) | (~q(X)))) | ((~(p(f(elem!2)) | (~p(f(elem!2))))) | (~((~r(elem!2)) | (~((~r(B!0)) | (~r(C!1)))))) | (~q(f(elem!2))))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(58,plain,
% 0.12/0.39 ((~![X: $i, Y: $i] : ((~(p(X) | (~p(f(Y))))) | (~((~r(Y)) | (~((~r(B!0)) | (~r(C!1)))))) | (~q(X)))) | (~((~r(elem!2)) | (~((~r(B!0)) | (~r(C!1)))))) | (~q(f(elem!2)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.12/0.39 tff(59,plain,
% 0.12/0.39 (~((~r(elem!2)) | (~((~r(B!0)) | (~r(C!1)))))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[58, 29, 47])).
% 0.12/0.39 tff(60,plain,
% 0.12/0.39 (((~r(elem!2)) | (~((~r(B!0)) | (~r(C!1))))) | ((~r(B!0)) | (~r(C!1)))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(61,plain,
% 0.12/0.39 ((~r(B!0)) | (~r(C!1))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[60, 59])).
% 0.12/0.39 tff(62,plain,
% 0.12/0.39 ((~((~r(B!0)) | (~r(C!1)))) | (~r(B!0)) | (~r(C!1))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(63,plain,
% 0.12/0.39 ((~r(B!0)) | (~r(C!1))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[62, 61])).
% 0.12/0.39 tff(64,plain,
% 0.12/0.39 (~r(C!1)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[63, 45])).
% 0.12/0.39 tff(65,plain,
% 0.12/0.39 (((~r(C!1)) | (~((~r(B!0)) | (~r(C!1))))) | r(C!1)),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(66,plain,
% 0.12/0.39 ((~r(C!1)) | (~((~r(B!0)) | (~r(C!1))))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[65, 64])).
% 0.12/0.39 tff(67,plain,
% 0.12/0.39 (((~![X: $i, Y: $i] : ((~(p(X) | (~p(f(Y))))) | (~((~r(Y)) | (~((~r(B!0)) | (~r(C!1)))))) | (~q(X)))) | ((~((~r(C!1)) | (~((~r(B!0)) | (~r(C!1)))))) | (~q(f(C!1))))) <=> ((~![X: $i, Y: $i] : ((~(p(X) | (~p(f(Y))))) | (~((~r(Y)) | (~((~r(B!0)) | (~r(C!1)))))) | (~q(X)))) | (~((~r(C!1)) | (~((~r(B!0)) | (~r(C!1)))))) | (~q(f(C!1))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(68,plain,
% 0.12/0.39 (($false | (~((~r(C!1)) | (~((~r(B!0)) | (~r(C!1)))))) | (~q(f(C!1)))) <=> ((~((~r(C!1)) | (~((~r(B!0)) | (~r(C!1)))))) | (~q(f(C!1))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(69,plain,
% 0.12/0.39 ((p(f(C!1)) | (~p(f(C!1)))) <=> $true),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(70,plain,
% 0.12/0.39 ((~(p(f(C!1)) | (~p(f(C!1))))) <=> (~$true)),
% 0.12/0.39 inference(monotonicity,[status(thm)],[69])).
% 0.12/0.39 tff(71,plain,
% 0.12/0.39 ((~(p(f(C!1)) | (~p(f(C!1))))) <=> $false),
% 0.12/0.39 inference(transitivity,[status(thm)],[70, 32])).
% 0.12/0.39 tff(72,plain,
% 0.12/0.39 (((~(p(f(C!1)) | (~p(f(C!1))))) | (~((~r(C!1)) | (~((~r(B!0)) | (~r(C!1)))))) | (~q(f(C!1)))) <=> ($false | (~((~r(C!1)) | (~((~r(B!0)) | (~r(C!1)))))) | (~q(f(C!1))))),
% 0.12/0.39 inference(monotonicity,[status(thm)],[71])).
% 0.12/0.39 tff(73,plain,
% 0.12/0.39 (((~(p(f(C!1)) | (~p(f(C!1))))) | (~((~r(C!1)) | (~((~r(B!0)) | (~r(C!1)))))) | (~q(f(C!1)))) <=> ((~((~r(C!1)) | (~((~r(B!0)) | (~r(C!1)))))) | (~q(f(C!1))))),
% 0.12/0.39 inference(transitivity,[status(thm)],[72, 68])).
% 0.12/0.39 tff(74,plain,
% 0.12/0.39 (((~![X: $i, Y: $i] : ((~(p(X) | (~p(f(Y))))) | (~((~r(Y)) | (~((~r(B!0)) | (~r(C!1)))))) | (~q(X)))) | ((~(p(f(C!1)) | (~p(f(C!1))))) | (~((~r(C!1)) | (~((~r(B!0)) | (~r(C!1)))))) | (~q(f(C!1))))) <=> ((~![X: $i, Y: $i] : ((~(p(X) | (~p(f(Y))))) | (~((~r(Y)) | (~((~r(B!0)) | (~r(C!1)))))) | (~q(X)))) | ((~((~r(C!1)) | (~((~r(B!0)) | (~r(C!1)))))) | (~q(f(C!1)))))),
% 0.12/0.39 inference(monotonicity,[status(thm)],[73])).
% 0.12/0.39 tff(75,plain,
% 0.12/0.39 (((~![X: $i, Y: $i] : ((~(p(X) | (~p(f(Y))))) | (~((~r(Y)) | (~((~r(B!0)) | (~r(C!1)))))) | (~q(X)))) | ((~(p(f(C!1)) | (~p(f(C!1))))) | (~((~r(C!1)) | (~((~r(B!0)) | (~r(C!1)))))) | (~q(f(C!1))))) <=> ((~![X: $i, Y: $i] : ((~(p(X) | (~p(f(Y))))) | (~((~r(Y)) | (~((~r(B!0)) | (~r(C!1)))))) | (~q(X)))) | (~((~r(C!1)) | (~((~r(B!0)) | (~r(C!1)))))) | (~q(f(C!1))))),
% 0.12/0.39 inference(transitivity,[status(thm)],[74, 67])).
% 0.12/0.39 tff(76,plain,
% 0.12/0.39 ((~![X: $i, Y: $i] : ((~(p(X) | (~p(f(Y))))) | (~((~r(Y)) | (~((~r(B!0)) | (~r(C!1)))))) | (~q(X)))) | ((~(p(f(C!1)) | (~p(f(C!1))))) | (~((~r(C!1)) | (~((~r(B!0)) | (~r(C!1)))))) | (~q(f(C!1))))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(77,plain,
% 0.12/0.39 ((~![X: $i, Y: $i] : ((~(p(X) | (~p(f(Y))))) | (~((~r(Y)) | (~((~r(B!0)) | (~r(C!1)))))) | (~q(X)))) | (~((~r(C!1)) | (~((~r(B!0)) | (~r(C!1)))))) | (~q(f(C!1)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.12/0.39 tff(78,plain,
% 0.12/0.39 ($false),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[77, 29, 66, 17])).
% 0.12/0.39 % SZS output end Proof
% 0.12/0.39 % E exiting
%------------------------------------------------------------------------------