%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN940+1 : TPTP v9.0.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.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 0.11s 0.37s
% Output : Proof 0.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SYN940+1 : TPTP v9.0.0. Released v3.1.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n004.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 13:01:07 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.11/0.37 % SZS status Theorem
% 0.11/0.37 % SZS output start Proof
% 0.11/0.37 tff(q_type, type, (
% 0.11/0.37 q: $i > $o)).
% 0.11/0.37 tff(f_type, type, (
% 0.11/0.37 f: $i > $i)).
% 0.11/0.37 tff(elem_2_type, type, (
% 0.11/0.37 elem_2: $i)).
% 0.11/0.37 tff(r_type, type, (
% 0.11/0.37 r: $i > $o)).
% 0.11/0.37 tff(tptp_fun_C_0_type, type, (
% 0.11/0.37 tptp_fun_C_0: $i)).
% 0.11/0.37 tff(tptp_fun_B_1_type, type, (
% 0.11/0.37 tptp_fun_B_1: $i)).
% 0.11/0.37 tff(p_type, type, (
% 0.11/0.37 p: $i > $o)).
% 0.11/0.37 tff(1,assumption,(p(f(elem!2))), introduced(assumption)).
% 0.11/0.37 tff(2,plain,
% 0.11/0.37 (^[Z: $i] : refl(q(f(Z)) <=> q(f(Z)))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(3,plain,
% 0.11/0.37 (![Z: $i] : q(f(Z)) <=> ![Z: $i] : q(f(Z))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[2])).
% 0.11/0.37 tff(4,plain,
% 0.11/0.37 ((![Z: $i] : q(f(Z)) & ![X: $i, Y: $i] : (~(((~p(f(Y))) | (p(X) & ((~r(Y)) | (r(B!1) & r(C!0))))) & q(X)))) <=> (![Z: $i] : q(f(Z)) & ![X: $i, Y: $i] : (~(((~p(f(Y))) | (p(X) & ((~r(Y)) | (r(B!1) & r(C!0))))) & q(X))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(5,plain,
% 0.11/0.37 ((~![B: $i, C: $i] : ((~![Z: $i] : q(f(Z))) | ?[X: $i, Y: $i] : (((~p(f(Y))) | (p(X) & ((~r(Y)) | (r(B) & r(C))))) & q(X)))) <=> (~![B: $i, C: $i] : ((~![Z: $i] : q(f(Z))) | ?[X: $i, Y: $i] : (((~p(f(Y))) | (p(X) & ((~r(Y)) | (r(B) & r(C))))) & q(X))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(6,plain,
% 0.11/0.37 ((~![B: $i, C: $i] : (![Z: $i] : q(f(Z)) => ?[X: $i, Y: $i] : ((p(f(Y)) => (p(X) & (r(Y) => (r(B) & r(C))))) & q(X)))) <=> (~![B: $i, C: $i] : ((~![Z: $i] : q(f(Z))) | ?[X: $i, Y: $i] : (((~p(f(Y))) | (p(X) & ((~r(Y)) | (r(B) & r(C))))) & q(X))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(7,axiom,(~![B: $i, C: $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/sandbox/benchmark/theBenchmark.p','prove_this')).
% 0.11/0.37 tff(8,plain,
% 0.11/0.37 (~![B: $i, C: $i] : ((~![Z: $i] : q(f(Z))) | ?[X: $i, Y: $i] : (((~p(f(Y))) | (p(X) & ((~r(Y)) | (r(B) & r(C))))) & q(X)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.11/0.37 tff(9,plain,
% 0.11/0.37 (~![B: $i, C: $i] : ((~![Z: $i] : q(f(Z))) | ?[X: $i, Y: $i] : (((~p(f(Y))) | (p(X) & ((~r(Y)) | (r(B) & r(C))))) & q(X)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[8, 5])).
% 0.11/0.37 tff(10,plain,
% 0.11/0.37 (~![B: $i, C: $i] : ((~![Z: $i] : q(f(Z))) | ?[X: $i, Y: $i] : (((~p(f(Y))) | (p(X) & ((~r(Y)) | (r(B) & r(C))))) & q(X)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.11/0.37 tff(11,plain,
% 0.11/0.37 (~![B: $i, C: $i] : ((~![Z: $i] : q(f(Z))) | ?[X: $i, Y: $i] : (((~p(f(Y))) | (p(X) & ((~r(Y)) | (r(B) & r(C))))) & q(X)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[10, 5])).
% 0.11/0.37 tff(12,plain,
% 0.11/0.37 (![Z: $i] : q(f(Z)) & ![X: $i, Y: $i] : (~(((~p(f(Y))) | (p(X) & ((~r(Y)) | (r(B!1) & r(C!0))))) & q(X)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.11/0.37 tff(13,plain,
% 0.11/0.37 (![Z: $i] : q(f(Z))),
% 0.11/0.37 inference(and_elim,[status(thm)],[12])).
% 0.11/0.37 tff(14,plain,
% 0.11/0.37 (![Z: $i] : q(f(Z))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[13, 3])).
% 0.11/0.37 tff(15,plain,
% 0.11/0.37 ((~![Z: $i] : q(f(Z))) | q(f(elem!2))),
% 0.11/0.37 inference(quant_inst,[status(thm)],[])).
% 0.11/0.37 tff(16,plain,
% 0.11/0.37 (q(f(elem!2))),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[15, 14])).
% 0.11/0.37 tff(17,plain,
% 0.11/0.37 (^[X: $i, Y: $i] : refl(((~((~p(f(Y))) | (~((~p(X)) | (~((~r(Y)) | (~((~r(B!1)) | (~r(C!0)))))))))) | (~q(X))) <=> ((~((~p(f(Y))) | (~((~p(X)) | (~((~r(Y)) | (~((~r(B!1)) | (~r(C!0)))))))))) | (~q(X))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(18,plain,
% 0.11/0.37 (![X: $i, Y: $i] : ((~((~p(f(Y))) | (~((~p(X)) | (~((~r(Y)) | (~((~r(B!1)) | (~r(C!0)))))))))) | (~q(X))) <=> ![X: $i, Y: $i] : ((~((~p(f(Y))) | (~((~p(X)) | (~((~r(Y)) | (~((~r(B!1)) | (~r(C!0)))))))))) | (~q(X)))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[17])).
% 0.11/0.37 tff(19,plain,
% 0.11/0.37 (^[X: $i, Y: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~p(f(Y))) | (p(X) & ((~r(Y)) | (r(B!1) & r(C!0))))) <=> ((~p(f(Y))) | (~((~p(X)) | (~((~r(Y)) | (~((~r(B!1)) | (~r(C!0)))))))))), ((((~p(f(Y))) | (p(X) & ((~r(Y)) | (r(B!1) & r(C!0))))) & q(X)) <=> (((~p(f(Y))) | (~((~p(X)) | (~((~r(Y)) | (~((~r(B!1)) | (~r(C!0))))))))) & q(X)))), rewrite((((~p(f(Y))) | (~((~p(X)) | (~((~r(Y)) | (~((~r(B!1)) | (~r(C!0))))))))) & q(X)) <=> (~((~((~p(f(Y))) | (~((~p(X)) | (~((~r(Y)) | (~((~r(B!1)) | (~r(C!0)))))))))) | (~q(X))))), ((((~p(f(Y))) | (p(X) & ((~r(Y)) | (r(B!1) & r(C!0))))) & q(X)) <=> (~((~((~p(f(Y))) | (~((~p(X)) | (~((~r(Y)) | (~((~r(B!1)) | (~r(C!0)))))))))) | (~q(X)))))), ((~(((~p(f(Y))) | (p(X) & ((~r(Y)) | (r(B!1) & r(C!0))))) & q(X))) <=> (~(~((~((~p(f(Y))) | (~((~p(X)) | (~((~r(Y)) | (~((~r(B!1)) | (~r(C!0)))))))))) | (~q(X))))))), rewrite((~(~((~((~p(f(Y))) | (~((~p(X)) | (~((~r(Y)) | (~((~r(B!1)) | (~r(C!0)))))))))) | (~q(X))))) <=> ((~((~p(f(Y))) | (~((~p(X)) | (~((~r(Y)) | (~((~r(B!1)) | (~r(C!0)))))))))) | (~q(X)))), ((~(((~p(f(Y))) | (p(X) & ((~r(Y)) | (r(B!1) & r(C!0))))) & q(X))) <=> ((~((~p(f(Y))) | (~((~p(X)) | (~((~r(Y)) | (~((~r(B!1)) | (~r(C!0)))))))))) | (~q(X)))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(20,plain,
% 0.11/0.37 (![X: $i, Y: $i] : (~(((~p(f(Y))) | (p(X) & ((~r(Y)) | (r(B!1) & r(C!0))))) & q(X))) <=> ![X: $i, Y: $i] : ((~((~p(f(Y))) | (~((~p(X)) | (~((~r(Y)) | (~((~r(B!1)) | (~r(C!0)))))))))) | (~q(X)))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[19])).
% 0.11/0.37 tff(21,plain,
% 0.11/0.37 (![X: $i, Y: $i] : (~(((~p(f(Y))) | (p(X) & ((~r(Y)) | (r(B!1) & r(C!0))))) & q(X)))),
% 0.11/0.37 inference(and_elim,[status(thm)],[12])).
% 0.11/0.37 tff(22,plain,
% 0.11/0.37 (![X: $i, Y: $i] : ((~((~p(f(Y))) | (~((~p(X)) | (~((~r(Y)) | (~((~r(B!1)) | (~r(C!0)))))))))) | (~q(X)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.11/0.37 tff(23,plain,
% 0.11/0.37 (![X: $i, Y: $i] : ((~((~p(f(Y))) | (~((~p(X)) | (~((~r(Y)) | (~((~r(B!1)) | (~r(C!0)))))))))) | (~q(X)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[22, 18])).
% 0.11/0.37 tff(24,plain,
% 0.11/0.37 (((~![X: $i, Y: $i] : ((~((~p(f(Y))) | (~((~p(X)) | (~((~r(Y)) | (~((~r(B!1)) | (~r(C!0)))))))))) | (~q(X)))) | ((~q(f(elem!2))) | (~((~p(f(C!0))) | (~((~p(f(elem!2))) | (~((~r(C!0)) | (~((~r(B!1)) | (~r(C!0)))))))))))) <=> ((~![X: $i, Y: $i] : ((~((~p(f(Y))) | (~((~p(X)) | (~((~r(Y)) | (~((~r(B!1)) | (~r(C!0)))))))))) | (~q(X)))) | (~q(f(elem!2))) | (~((~p(f(C!0))) | (~((~p(f(elem!2))) | (~((~r(C!0)) | (~((~r(B!1)) | (~r(C!0)))))))))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(25,plain,
% 0.11/0.37 (((~((~p(f(C!0))) | (~((~p(f(elem!2))) | (~((~r(C!0)) | (~((~r(B!1)) | (~r(C!0)))))))))) | (~q(f(elem!2)))) <=> ((~q(f(elem!2))) | (~((~p(f(C!0))) | (~((~p(f(elem!2))) | (~((~r(C!0)) | (~((~r(B!1)) | (~r(C!0)))))))))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(26,plain,
% 0.11/0.37 (((~![X: $i, Y: $i] : ((~((~p(f(Y))) | (~((~p(X)) | (~((~r(Y)) | (~((~r(B!1)) | (~r(C!0)))))))))) | (~q(X)))) | ((~((~p(f(C!0))) | (~((~p(f(elem!2))) | (~((~r(C!0)) | (~((~r(B!1)) | (~r(C!0)))))))))) | (~q(f(elem!2))))) <=> ((~![X: $i, Y: $i] : ((~((~p(f(Y))) | (~((~p(X)) | (~((~r(Y)) | (~((~r(B!1)) | (~r(C!0)))))))))) | (~q(X)))) | ((~q(f(elem!2))) | (~((~p(f(C!0))) | (~((~p(f(elem!2))) | (~((~r(C!0)) | (~((~r(B!1)) | (~r(C!0))))))))))))),
% 0.11/0.37 inference(monotonicity,[status(thm)],[25])).
% 0.11/0.37 tff(27,plain,
% 0.11/0.37 (((~![X: $i, Y: $i] : ((~((~p(f(Y))) | (~((~p(X)) | (~((~r(Y)) | (~((~r(B!1)) | (~r(C!0)))))))))) | (~q(X)))) | ((~((~p(f(C!0))) | (~((~p(f(elem!2))) | (~((~r(C!0)) | (~((~r(B!1)) | (~r(C!0)))))))))) | (~q(f(elem!2))))) <=> ((~![X: $i, Y: $i] : ((~((~p(f(Y))) | (~((~p(X)) | (~((~r(Y)) | (~((~r(B!1)) | (~r(C!0)))))))))) | (~q(X)))) | (~q(f(elem!2))) | (~((~p(f(C!0))) | (~((~p(f(elem!2))) | (~((~r(C!0)) | (~((~r(B!1)) | (~r(C!0)))))))))))),
% 0.11/0.37 inference(transitivity,[status(thm)],[26, 24])).
% 0.11/0.37 tff(28,plain,
% 0.11/0.37 ((~![X: $i, Y: $i] : ((~((~p(f(Y))) | (~((~p(X)) | (~((~r(Y)) | (~((~r(B!1)) | (~r(C!0)))))))))) | (~q(X)))) | ((~((~p(f(C!0))) | (~((~p(f(elem!2))) | (~((~r(C!0)) | (~((~r(B!1)) | (~r(C!0)))))))))) | (~q(f(elem!2))))),
% 0.11/0.37 inference(quant_inst,[status(thm)],[])).
% 0.11/0.37 tff(29,plain,
% 0.11/0.37 ((~![X: $i, Y: $i] : ((~((~p(f(Y))) | (~((~p(X)) | (~((~r(Y)) | (~((~r(B!1)) | (~r(C!0)))))))))) | (~q(X)))) | (~q(f(elem!2))) | (~((~p(f(C!0))) | (~((~p(f(elem!2))) | (~((~r(C!0)) | (~((~r(B!1)) | (~r(C!0))))))))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.11/0.37 tff(30,plain,
% 0.11/0.37 ((~q(f(elem!2))) | (~((~p(f(C!0))) | (~((~p(f(elem!2))) | (~((~r(C!0)) | (~((~r(B!1)) | (~r(C!0))))))))))),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[29, 23])).
% 0.11/0.37 tff(31,plain,
% 0.11/0.38 (~((~p(f(C!0))) | (~((~p(f(elem!2))) | (~((~r(C!0)) | (~((~r(B!1)) | (~r(C!0)))))))))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[30, 16])).
% 0.11/0.38 tff(32,plain,
% 0.11/0.38 (((~p(f(C!0))) | (~((~p(f(elem!2))) | (~((~r(C!0)) | (~((~r(B!1)) | (~r(C!0))))))))) | ((~p(f(elem!2))) | (~((~r(C!0)) | (~((~r(B!1)) | (~r(C!0)))))))),
% 0.11/0.38 inference(tautology,[status(thm)],[])).
% 0.11/0.38 tff(33,plain,
% 0.11/0.38 ((~p(f(elem!2))) | (~((~r(C!0)) | (~((~r(B!1)) | (~r(C!0))))))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[32, 31])).
% 0.11/0.38 tff(34,plain,
% 0.11/0.38 ((~((~p(f(elem!2))) | (~((~r(C!0)) | (~((~r(B!1)) | (~r(C!0)))))))) | (~p(f(elem!2))) | (~((~r(C!0)) | (~((~r(B!1)) | (~r(C!0))))))),
% 0.11/0.38 inference(tautology,[status(thm)],[])).
% 0.11/0.38 tff(35,plain,
% 0.11/0.38 (~((~r(C!0)) | (~((~r(B!1)) | (~r(C!0)))))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[34, 33, 1])).
% 0.11/0.38 tff(36,plain,
% 0.11/0.38 (((~r(C!0)) | (~((~r(B!1)) | (~r(C!0))))) | ((~r(B!1)) | (~r(C!0)))),
% 0.11/0.38 inference(tautology,[status(thm)],[])).
% 0.11/0.38 tff(37,plain,
% 0.11/0.38 ((~r(B!1)) | (~r(C!0))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[36, 35])).
% 0.11/0.38 tff(38,plain,
% 0.11/0.38 (((~r(C!0)) | (~((~r(B!1)) | (~r(C!0))))) | r(C!0)),
% 0.11/0.38 inference(tautology,[status(thm)],[])).
% 0.11/0.38 tff(39,plain,
% 0.11/0.38 (r(C!0)),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[38, 35])).
% 0.11/0.38 tff(40,plain,
% 0.11/0.38 (((~![X: $i, Y: $i] : ((~((~p(f(Y))) | (~((~p(X)) | (~((~r(Y)) | (~((~r(B!1)) | (~r(C!0)))))))))) | (~q(X)))) | ((~q(f(elem!2))) | (~((~p(f(B!1))) | (~((~p(f(elem!2))) | (~((~r(B!1)) | (~((~r(B!1)) | (~r(C!0)))))))))))) <=> ((~![X: $i, Y: $i] : ((~((~p(f(Y))) | (~((~p(X)) | (~((~r(Y)) | (~((~r(B!1)) | (~r(C!0)))))))))) | (~q(X)))) | (~q(f(elem!2))) | (~((~p(f(B!1))) | (~((~p(f(elem!2))) | (~((~r(B!1)) | (~((~r(B!1)) | (~r(C!0)))))))))))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(41,plain,
% 0.11/0.38 (((~((~p(f(B!1))) | (~((~p(f(elem!2))) | (~((~r(B!1)) | (~((~r(B!1)) | (~r(C!0)))))))))) | (~q(f(elem!2)))) <=> ((~q(f(elem!2))) | (~((~p(f(B!1))) | (~((~p(f(elem!2))) | (~((~r(B!1)) | (~((~r(B!1)) | (~r(C!0)))))))))))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(42,plain,
% 0.11/0.38 (((~![X: $i, Y: $i] : ((~((~p(f(Y))) | (~((~p(X)) | (~((~r(Y)) | (~((~r(B!1)) | (~r(C!0)))))))))) | (~q(X)))) | ((~((~p(f(B!1))) | (~((~p(f(elem!2))) | (~((~r(B!1)) | (~((~r(B!1)) | (~r(C!0)))))))))) | (~q(f(elem!2))))) <=> ((~![X: $i, Y: $i] : ((~((~p(f(Y))) | (~((~p(X)) | (~((~r(Y)) | (~((~r(B!1)) | (~r(C!0)))))))))) | (~q(X)))) | ((~q(f(elem!2))) | (~((~p(f(B!1))) | (~((~p(f(elem!2))) | (~((~r(B!1)) | (~((~r(B!1)) | (~r(C!0))))))))))))),
% 0.11/0.38 inference(monotonicity,[status(thm)],[41])).
% 0.11/0.38 tff(43,plain,
% 0.11/0.38 (((~![X: $i, Y: $i] : ((~((~p(f(Y))) | (~((~p(X)) | (~((~r(Y)) | (~((~r(B!1)) | (~r(C!0)))))))))) | (~q(X)))) | ((~((~p(f(B!1))) | (~((~p(f(elem!2))) | (~((~r(B!1)) | (~((~r(B!1)) | (~r(C!0)))))))))) | (~q(f(elem!2))))) <=> ((~![X: $i, Y: $i] : ((~((~p(f(Y))) | (~((~p(X)) | (~((~r(Y)) | (~((~r(B!1)) | (~r(C!0)))))))))) | (~q(X)))) | (~q(f(elem!2))) | (~((~p(f(B!1))) | (~((~p(f(elem!2))) | (~((~r(B!1)) | (~((~r(B!1)) | (~r(C!0)))))))))))),
% 0.11/0.38 inference(transitivity,[status(thm)],[42, 40])).
% 0.11/0.38 tff(44,plain,
% 0.11/0.38 ((~![X: $i, Y: $i] : ((~((~p(f(Y))) | (~((~p(X)) | (~((~r(Y)) | (~((~r(B!1)) | (~r(C!0)))))))))) | (~q(X)))) | ((~((~p(f(B!1))) | (~((~p(f(elem!2))) | (~((~r(B!1)) | (~((~r(B!1)) | (~r(C!0)))))))))) | (~q(f(elem!2))))),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(45,plain,
% 0.11/0.38 ((~![X: $i, Y: $i] : ((~((~p(f(Y))) | (~((~p(X)) | (~((~r(Y)) | (~((~r(B!1)) | (~r(C!0)))))))))) | (~q(X)))) | (~q(f(elem!2))) | (~((~p(f(B!1))) | (~((~p(f(elem!2))) | (~((~r(B!1)) | (~((~r(B!1)) | (~r(C!0))))))))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.11/0.38 tff(46,plain,
% 0.11/0.38 ((~q(f(elem!2))) | (~((~p(f(B!1))) | (~((~p(f(elem!2))) | (~((~r(B!1)) | (~((~r(B!1)) | (~r(C!0))))))))))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[45, 23])).
% 0.11/0.38 tff(47,plain,
% 0.11/0.38 (~((~p(f(B!1))) | (~((~p(f(elem!2))) | (~((~r(B!1)) | (~((~r(B!1)) | (~r(C!0)))))))))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[46, 16])).
% 0.11/0.38 tff(48,plain,
% 0.11/0.38 (((~p(f(B!1))) | (~((~p(f(elem!2))) | (~((~r(B!1)) | (~((~r(B!1)) | (~r(C!0))))))))) | ((~p(f(elem!2))) | (~((~r(B!1)) | (~((~r(B!1)) | (~r(C!0)))))))),
% 0.11/0.38 inference(tautology,[status(thm)],[])).
% 0.11/0.38 tff(49,plain,
% 0.11/0.38 ((~p(f(elem!2))) | (~((~r(B!1)) | (~((~r(B!1)) | (~r(C!0))))))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[48, 47])).
% 0.11/0.38 tff(50,plain,
% 0.11/0.38 ((~((~p(f(elem!2))) | (~((~r(B!1)) | (~((~r(B!1)) | (~r(C!0)))))))) | (~p(f(elem!2))) | (~((~r(B!1)) | (~((~r(B!1)) | (~r(C!0))))))),
% 0.11/0.38 inference(tautology,[status(thm)],[])).
% 0.11/0.38 tff(51,plain,
% 0.11/0.38 (~((~r(B!1)) | (~((~r(B!1)) | (~r(C!0)))))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[50, 49, 1])).
% 0.11/0.38 tff(52,plain,
% 0.11/0.38 (((~r(B!1)) | (~((~r(B!1)) | (~r(C!0))))) | r(B!1)),
% 0.11/0.38 inference(tautology,[status(thm)],[])).
% 0.11/0.38 tff(53,plain,
% 0.11/0.38 (r(B!1)),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[52, 51])).
% 0.11/0.38 tff(54,plain,
% 0.11/0.38 ((~((~r(B!1)) | (~r(C!0)))) | (~r(B!1)) | (~r(C!0))),
% 0.11/0.38 inference(tautology,[status(thm)],[])).
% 0.11/0.38 tff(55,plain,
% 0.11/0.38 ($false),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[54, 53, 39, 37])).
% 0.11/0.38 tff(56,plain,(~p(f(elem!2))), inference(lemma,lemma(discharge,[]))).
% 0.11/0.38 tff(57,plain,
% 0.11/0.38 (((~p(f(elem!2))) | (~((~p(f(elem!2))) | (~((~r(elem!2)) | (~((~r(B!1)) | (~r(C!0))))))))) | p(f(elem!2))),
% 0.11/0.38 inference(tautology,[status(thm)],[])).
% 0.11/0.38 tff(58,plain,
% 0.11/0.38 ((~p(f(elem!2))) | (~((~p(f(elem!2))) | (~((~r(elem!2)) | (~((~r(B!1)) | (~r(C!0))))))))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[57, 56])).
% 0.11/0.38 tff(59,plain,
% 0.11/0.38 (((~![X: $i, Y: $i] : ((~((~p(f(Y))) | (~((~p(X)) | (~((~r(Y)) | (~((~r(B!1)) | (~r(C!0)))))))))) | (~q(X)))) | ((~((~p(f(elem!2))) | (~((~p(f(elem!2))) | (~((~r(elem!2)) | (~((~r(B!1)) | (~r(C!0)))))))))) | (~q(f(elem!2))))) <=> ((~![X: $i, Y: $i] : ((~((~p(f(Y))) | (~((~p(X)) | (~((~r(Y)) | (~((~r(B!1)) | (~r(C!0)))))))))) | (~q(X)))) | (~((~p(f(elem!2))) | (~((~p(f(elem!2))) | (~((~r(elem!2)) | (~((~r(B!1)) | (~r(C!0)))))))))) | (~q(f(elem!2))))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(60,plain,
% 0.11/0.38 ((~![X: $i, Y: $i] : ((~((~p(f(Y))) | (~((~p(X)) | (~((~r(Y)) | (~((~r(B!1)) | (~r(C!0)))))))))) | (~q(X)))) | ((~((~p(f(elem!2))) | (~((~p(f(elem!2))) | (~((~r(elem!2)) | (~((~r(B!1)) | (~r(C!0)))))))))) | (~q(f(elem!2))))),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(61,plain,
% 0.11/0.38 ((~![X: $i, Y: $i] : ((~((~p(f(Y))) | (~((~p(X)) | (~((~r(Y)) | (~((~r(B!1)) | (~r(C!0)))))))))) | (~q(X)))) | (~((~p(f(elem!2))) | (~((~p(f(elem!2))) | (~((~r(elem!2)) | (~((~r(B!1)) | (~r(C!0)))))))))) | (~q(f(elem!2)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.11/0.38 tff(62,plain,
% 0.11/0.38 (~q(f(elem!2))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[61, 23, 58])).
% 0.11/0.38 tff(63,plain,
% 0.11/0.38 ($false),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[15, 14, 62])).
% 0.11/0.38 % SZS output end Proof
% 0.11/0.38 % E exiting
%------------------------------------------------------------------------------