TSTP Solution File: SYN940+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN940+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% 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 : Fri Sep 30 00:01:20 EDT 2022
% Result : Theorem 0.14s 0.33s
% Output : Proof 0.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SYN940+1 : TPTP v8.1.0. Released v3.1.0.
% 0.00/0.09 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.09/0.29 % Computer : n007.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 300
% 0.09/0.29 % DateTime : Mon Sep 5 09:21:35 EDT 2022
% 0.09/0.29 % CPUTime :
% 0.09/0.29 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.09/0.29 Usage: tptp [options] [-file:]file
% 0.09/0.29 -h, -? prints this message.
% 0.09/0.29 -smt2 print SMT-LIB2 benchmark.
% 0.09/0.29 -m, -model generate model.
% 0.09/0.29 -p, -proof generate proof.
% 0.09/0.29 -c, -core generate unsat core of named formulas.
% 0.09/0.29 -st, -statistics display statistics.
% 0.09/0.29 -t:timeout set timeout (in second).
% 0.09/0.29 -smt2status display status in smt2 format instead of SZS.
% 0.09/0.29 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.09/0.29 -<param>:<value> configuration parameter and value.
% 0.09/0.29 -o:<output-file> file to place output in.
% 0.14/0.33 % SZS status Theorem
% 0.14/0.33 % SZS output start Proof
% 0.14/0.33 tff(r_type, type, (
% 0.14/0.33 r: $i > $o)).
% 0.14/0.33 tff(tptp_fun_C_0_type, type, (
% 0.14/0.33 tptp_fun_C_0: $i)).
% 0.14/0.33 tff(tptp_fun_B_1_type, type, (
% 0.14/0.33 tptp_fun_B_1: $i)).
% 0.14/0.33 tff(p_type, type, (
% 0.14/0.33 p: $i > $o)).
% 0.14/0.33 tff(f_type, type, (
% 0.14/0.33 f: $i > $i)).
% 0.14/0.33 tff(elem_2_type, type, (
% 0.14/0.33 elem_2: $i)).
% 0.14/0.33 tff(q_type, type, (
% 0.14/0.33 q: $i > $o)).
% 0.14/0.33 tff(1,plain,
% 0.14/0.33 (^[Z: $i] : refl(q(f(Z)) <=> q(f(Z)))),
% 0.14/0.33 inference(bind,[status(th)],[])).
% 0.14/0.33 tff(2,plain,
% 0.14/0.33 (![Z: $i] : q(f(Z)) <=> ![Z: $i] : q(f(Z))),
% 0.14/0.33 inference(quant_intro,[status(thm)],[1])).
% 0.14/0.33 tff(3,plain,
% 0.14/0.33 ((![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))))),
% 0.14/0.33 inference(rewrite,[status(thm)],[])).
% 0.14/0.33 tff(4,plain,
% 0.14/0.33 ((~![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))))),
% 0.14/0.33 inference(rewrite,[status(thm)],[])).
% 0.14/0.33 tff(5,plain,
% 0.14/0.33 ((~![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))))),
% 0.14/0.33 inference(rewrite,[status(thm)],[])).
% 0.14/0.33 tff(6,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')).
% 0.14/0.33 tff(7,plain,
% 0.14/0.33 (~![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)))),
% 0.14/0.33 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.14/0.33 tff(8,plain,
% 0.14/0.33 (~![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)))),
% 0.14/0.33 inference(modus_ponens,[status(thm)],[7, 4])).
% 0.14/0.33 tff(9,plain,
% 0.14/0.33 (~![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)))),
% 0.14/0.33 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.14/0.33 tff(10,plain,
% 0.14/0.33 (~![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)))),
% 0.14/0.33 inference(modus_ponens,[status(thm)],[9, 4])).
% 0.14/0.33 tff(11,plain,
% 0.14/0.33 (~![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)))),
% 0.14/0.33 inference(modus_ponens,[status(thm)],[10, 4])).
% 0.14/0.33 tff(12,plain,
% 0.14/0.33 (~![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)))),
% 0.14/0.33 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.14/0.33 tff(13,plain,
% 0.14/0.33 (~![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)))),
% 0.14/0.33 inference(modus_ponens,[status(thm)],[12, 4])).
% 0.14/0.33 tff(14,plain,
% 0.14/0.33 (![Z: $i] : q(f(Z)) & ![X: $i, Y: $i] : (~(((~p(f(Y))) | (p(X) & ((~r(Y)) | (r(B!1) & r(C!0))))) & q(X)))),
% 0.14/0.33 inference(modus_ponens,[status(thm)],[13, 3])).
% 0.14/0.33 tff(15,plain,
% 0.14/0.33 (![Z: $i] : q(f(Z))),
% 0.14/0.33 inference(and_elim,[status(thm)],[14])).
% 0.14/0.33 tff(16,plain,
% 0.14/0.33 (![Z: $i] : q(f(Z))),
% 0.14/0.33 inference(modus_ponens,[status(thm)],[15, 2])).
% 0.14/0.33 tff(17,plain,
% 0.14/0.33 ((~![Z: $i] : q(f(Z))) | q(f(elem!2))),
% 0.14/0.33 inference(quant_inst,[status(thm)],[])).
% 0.14/0.33 tff(18,plain,
% 0.14/0.33 (q(f(elem!2))),
% 0.14/0.33 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.14/0.33 tff(19,plain,
% 0.14/0.33 (^[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))))),
% 0.14/0.33 inference(bind,[status(th)],[])).
% 0.14/0.33 tff(20,plain,
% 0.14/0.33 (![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)))),
% 0.14/0.33 inference(quant_intro,[status(thm)],[19])).
% 0.14/0.34 tff(21,plain,
% 0.14/0.34 (^[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)))))),
% 0.14/0.34 inference(bind,[status(th)],[])).
% 0.14/0.34 tff(22,plain,
% 0.14/0.34 (![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)))),
% 0.14/0.34 inference(quant_intro,[status(thm)],[21])).
% 0.14/0.34 tff(23,plain,
% 0.14/0.34 (![X: $i, Y: $i] : (~(((~p(f(Y))) | (p(X) & ((~r(Y)) | (r(B!1) & r(C!0))))) & q(X)))),
% 0.14/0.34 inference(and_elim,[status(thm)],[14])).
% 0.14/0.34 tff(24,plain,
% 0.14/0.34 (![X: $i, Y: $i] : ((~((~p(f(Y))) | (~((~p(X)) | (~((~r(Y)) | (~((~r(B!1)) | (~r(C!0)))))))))) | (~q(X)))),
% 0.14/0.34 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.14/0.34 tff(25,plain,
% 0.14/0.34 (![X: $i, Y: $i] : ((~((~p(f(Y))) | (~((~p(X)) | (~((~r(Y)) | (~((~r(B!1)) | (~r(C!0)))))))))) | (~q(X)))),
% 0.14/0.34 inference(modus_ponens,[status(thm)],[24, 20])).
% 0.14/0.34 tff(26,plain,
% 0.14/0.34 (((~![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)))))))))))),
% 0.14/0.34 inference(rewrite,[status(thm)],[])).
% 0.14/0.34 tff(27,plain,
% 0.14/0.34 (((~((~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)))))))))))),
% 0.14/0.34 inference(rewrite,[status(thm)],[])).
% 0.14/0.34 tff(28,plain,
% 0.14/0.34 (((~![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))))))))))))),
% 0.14/0.34 inference(monotonicity,[status(thm)],[27])).
% 0.14/0.34 tff(29,plain,
% 0.14/0.34 (((~![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)))))))))))),
% 0.14/0.34 inference(transitivity,[status(thm)],[28, 26])).
% 0.14/0.34 tff(30,plain,
% 0.14/0.34 ((~![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))))),
% 0.14/0.34 inference(quant_inst,[status(thm)],[])).
% 0.14/0.34 tff(31,plain,
% 0.14/0.34 ((~![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))))))))))),
% 0.14/0.34 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.14/0.34 tff(32,plain,
% 0.14/0.34 (~((~p(f(B!1))) | (~((~p(f(elem!2))) | (~((~r(B!1)) | (~((~r(B!1)) | (~r(C!0)))))))))),
% 0.14/0.34 inference(unit_resolution,[status(thm)],[31, 25, 18])).
% 0.14/0.34 tff(33,plain,
% 0.14/0.34 (((~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)))))))),
% 0.14/0.34 inference(tautology,[status(thm)],[])).
% 0.14/0.34 tff(34,plain,
% 0.14/0.34 ((~p(f(elem!2))) | (~((~r(B!1)) | (~((~r(B!1)) | (~r(C!0))))))),
% 0.14/0.34 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.14/0.34 tff(35,plain,
% 0.14/0.34 (((~![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))))),
% 0.14/0.34 inference(rewrite,[status(thm)],[])).
% 0.14/0.34 tff(36,plain,
% 0.14/0.34 ((~![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))))),
% 0.14/0.34 inference(quant_inst,[status(thm)],[])).
% 0.14/0.34 tff(37,plain,
% 0.14/0.34 ((~![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)))),
% 0.14/0.34 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.14/0.34 tff(38,plain,
% 0.14/0.34 (~((~p(f(elem!2))) | (~((~p(f(elem!2))) | (~((~r(elem!2)) | (~((~r(B!1)) | (~r(C!0)))))))))),
% 0.14/0.34 inference(unit_resolution,[status(thm)],[37, 25, 18])).
% 0.14/0.34 tff(39,plain,
% 0.14/0.34 (((~p(f(elem!2))) | (~((~p(f(elem!2))) | (~((~r(elem!2)) | (~((~r(B!1)) | (~r(C!0))))))))) | p(f(elem!2))),
% 0.14/0.34 inference(tautology,[status(thm)],[])).
% 0.14/0.34 tff(40,plain,
% 0.14/0.34 (p(f(elem!2))),
% 0.14/0.34 inference(unit_resolution,[status(thm)],[39, 38])).
% 0.14/0.34 tff(41,plain,
% 0.14/0.34 ((~((~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))))))),
% 0.14/0.34 inference(tautology,[status(thm)],[])).
% 0.14/0.34 tff(42,plain,
% 0.14/0.34 ((~((~p(f(elem!2))) | (~((~r(B!1)) | (~((~r(B!1)) | (~r(C!0)))))))) | (~((~r(B!1)) | (~((~r(B!1)) | (~r(C!0))))))),
% 0.14/0.34 inference(unit_resolution,[status(thm)],[41, 40])).
% 0.14/0.34 tff(43,plain,
% 0.14/0.34 (~((~r(B!1)) | (~((~r(B!1)) | (~r(C!0)))))),
% 0.14/0.34 inference(unit_resolution,[status(thm)],[42, 34])).
% 0.14/0.34 tff(44,plain,
% 0.14/0.34 (((~r(B!1)) | (~((~r(B!1)) | (~r(C!0))))) | r(B!1)),
% 0.14/0.34 inference(tautology,[status(thm)],[])).
% 0.14/0.34 tff(45,plain,
% 0.14/0.34 (r(B!1)),
% 0.14/0.34 inference(unit_resolution,[status(thm)],[44, 43])).
% 0.14/0.34 tff(46,plain,
% 0.14/0.34 (((~p(f(elem!2))) | (~((~p(f(elem!2))) | (~((~r(elem!2)) | (~((~r(B!1)) | (~r(C!0))))))))) | ((~p(f(elem!2))) | (~((~r(elem!2)) | (~((~r(B!1)) | (~r(C!0)))))))),
% 0.14/0.34 inference(tautology,[status(thm)],[])).
% 0.14/0.34 tff(47,plain,
% 0.14/0.34 ((~p(f(elem!2))) | (~((~r(elem!2)) | (~((~r(B!1)) | (~r(C!0))))))),
% 0.14/0.34 inference(unit_resolution,[status(thm)],[46, 38])).
% 0.14/0.34 tff(48,plain,
% 0.14/0.34 ((~((~p(f(elem!2))) | (~((~r(elem!2)) | (~((~r(B!1)) | (~r(C!0)))))))) | (~p(f(elem!2))) | (~((~r(elem!2)) | (~((~r(B!1)) | (~r(C!0))))))),
% 0.14/0.34 inference(tautology,[status(thm)],[])).
% 0.14/0.34 tff(49,plain,
% 0.14/0.34 (~((~r(elem!2)) | (~((~r(B!1)) | (~r(C!0)))))),
% 0.14/0.34 inference(unit_resolution,[status(thm)],[48, 40, 47])).
% 0.14/0.34 tff(50,plain,
% 0.14/0.34 (((~r(elem!2)) | (~((~r(B!1)) | (~r(C!0))))) | ((~r(B!1)) | (~r(C!0)))),
% 0.14/0.34 inference(tautology,[status(thm)],[])).
% 0.14/0.34 tff(51,plain,
% 0.14/0.34 ((~r(B!1)) | (~r(C!0))),
% 0.14/0.34 inference(unit_resolution,[status(thm)],[50, 49])).
% 0.14/0.34 tff(52,plain,
% 0.14/0.34 ((~((~r(B!1)) | (~r(C!0)))) | (~r(B!1)) | (~r(C!0))),
% 0.14/0.34 inference(tautology,[status(thm)],[])).
% 0.14/0.34 tff(53,plain,
% 0.14/0.34 ((~r(B!1)) | (~r(C!0))),
% 0.14/0.34 inference(unit_resolution,[status(thm)],[52, 51])).
% 0.14/0.34 tff(54,plain,
% 0.14/0.34 (~r(C!0)),
% 0.14/0.34 inference(unit_resolution,[status(thm)],[53, 45])).
% 0.14/0.34 tff(55,plain,
% 0.14/0.34 (((~r(C!0)) | (~((~r(B!1)) | (~r(C!0))))) | r(C!0)),
% 0.14/0.34 inference(tautology,[status(thm)],[])).
% 0.14/0.34 tff(56,plain,
% 0.14/0.34 ((~r(C!0)) | (~((~r(B!1)) | (~r(C!0))))),
% 0.14/0.34 inference(unit_resolution,[status(thm)],[55, 54])).
% 0.14/0.34 tff(57,plain,
% 0.14/0.34 (((~p(f(B!1))) | (~((~p(f(elem!2))) | (~((~r(B!1)) | (~((~r(B!1)) | (~r(C!0))))))))) | p(f(B!1))),
% 0.14/0.34 inference(tautology,[status(thm)],[])).
% 0.14/0.34 tff(58,plain,
% 0.14/0.34 (p(f(B!1))),
% 0.14/0.34 inference(unit_resolution,[status(thm)],[57, 32])).
% 0.14/0.34 tff(59,plain,
% 0.14/0.34 ((~((~p(f(B!1))) | (~((~r(C!0)) | (~((~r(B!1)) | (~r(C!0)))))))) | (~p(f(B!1))) | (~((~r(C!0)) | (~((~r(B!1)) | (~r(C!0))))))),
% 0.14/0.34 inference(tautology,[status(thm)],[])).
% 0.14/0.34 tff(60,plain,
% 0.14/0.34 (~((~p(f(B!1))) | (~((~r(C!0)) | (~((~r(B!1)) | (~r(C!0)))))))),
% 0.14/0.34 inference(unit_resolution,[status(thm)],[59, 58, 56])).
% 0.14/0.35 tff(61,plain,
% 0.14/0.35 (((~p(f(C!0))) | (~((~p(f(B!1))) | (~((~r(C!0)) | (~((~r(B!1)) | (~r(C!0))))))))) | ((~p(f(B!1))) | (~((~r(C!0)) | (~((~r(B!1)) | (~r(C!0)))))))),
% 0.14/0.35 inference(tautology,[status(thm)],[])).
% 0.14/0.35 tff(62,plain,
% 0.14/0.35 ((~p(f(C!0))) | (~((~p(f(B!1))) | (~((~r(C!0)) | (~((~r(B!1)) | (~r(C!0))))))))),
% 0.14/0.35 inference(unit_resolution,[status(thm)],[61, 60])).
% 0.14/0.35 tff(63,plain,
% 0.14/0.35 ((~![Z: $i] : q(f(Z))) | q(f(B!1))),
% 0.14/0.35 inference(quant_inst,[status(thm)],[])).
% 0.14/0.35 tff(64,plain,
% 0.14/0.35 (q(f(B!1))),
% 0.14/0.35 inference(unit_resolution,[status(thm)],[63, 16])).
% 0.14/0.35 tff(65,plain,
% 0.14/0.35 (((~![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(B!1))) | (~((~r(C!0)) | (~((~r(B!1)) | (~r(C!0)))))))))) | (~q(f(B!1))))) <=> ((~![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(B!1))) | (~((~r(C!0)) | (~((~r(B!1)) | (~r(C!0)))))))))) | (~q(f(B!1))))),
% 0.14/0.35 inference(rewrite,[status(thm)],[])).
% 0.14/0.35 tff(66,plain,
% 0.14/0.35 ((~![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(B!1))) | (~((~r(C!0)) | (~((~r(B!1)) | (~r(C!0)))))))))) | (~q(f(B!1))))),
% 0.14/0.35 inference(quant_inst,[status(thm)],[])).
% 0.14/0.35 tff(67,plain,
% 0.14/0.35 ((~![X: $i, Y: $i] : ((~((~p(f(Y))) | (~((~p(X)) | (~((~r(Y)) | (~((~r(B!1)) | (~r(C!0)))))))))) | (~q(X)))) | (~((~p(f(C!0))) | (~((~p(f(B!1))) | (~((~r(C!0)) | (~((~r(B!1)) | (~r(C!0)))))))))) | (~q(f(B!1)))),
% 0.14/0.35 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.14/0.35 tff(68,plain,
% 0.14/0.35 ($false),
% 0.14/0.35 inference(unit_resolution,[status(thm)],[67, 25, 64, 62])).
% 0.14/0.35 % SZS output end Proof
%------------------------------------------------------------------------------