TSTP Solution File: SYN939+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN939+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n015.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 0.13s 0.40s
% Output : Proof 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SYN939+1 : TPTP v8.1.0. Released v3.1.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n015.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Sep 5 09:47:57 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.13/0.40 % SZS status Theorem
% 0.13/0.40 % SZS output start Proof
% 0.13/0.40 tff(q_type, type, (
% 0.13/0.40 q: $i > $o)).
% 0.13/0.40 tff(f_type, type, (
% 0.13/0.40 f: $i > $i)).
% 0.13/0.40 tff(tptp_fun_C_1_type, type, (
% 0.13/0.40 tptp_fun_C_1: $i)).
% 0.13/0.40 tff(r_type, type, (
% 0.13/0.40 r: $i > $o)).
% 0.13/0.40 tff(tptp_fun_B_0_type, type, (
% 0.13/0.40 tptp_fun_B_0: $i)).
% 0.13/0.40 tff(p_type, type, (
% 0.13/0.40 p: $i > $o)).
% 0.13/0.40 tff(elem_2_type, type, (
% 0.13/0.40 elem_2: $i)).
% 0.13/0.40 tff(1,assumption,(~q(f(B!0))), introduced(assumption)).
% 0.13/0.40 tff(2,plain,
% 0.13/0.40 (^[Z: $i] : refl(q(f(Z)) <=> q(f(Z)))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(3,plain,
% 0.13/0.40 (![Z: $i] : q(f(Z)) <=> ![Z: $i] : q(f(Z))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[2])).
% 0.13/0.40 tff(4,plain,
% 0.13/0.40 ((![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))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(5,plain,
% 0.13/0.40 ((~![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))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(6,plain,
% 0.13/0.40 ((~![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))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 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/sandbox/benchmark/theBenchmark.p','prove_this')).
% 0.13/0.40 tff(8,plain,
% 0.13/0.40 (~![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)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.13/0.40 tff(9,plain,
% 0.13/0.40 (~![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)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[8, 5])).
% 0.13/0.40 tff(10,plain,
% 0.13/0.40 (~![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)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.13/0.40 tff(11,plain,
% 0.13/0.40 (~![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)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[10, 5])).
% 0.13/0.40 tff(12,plain,
% 0.13/0.40 (~![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)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[11, 5])).
% 0.13/0.40 tff(13,plain,
% 0.13/0.40 (~![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)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[12, 5])).
% 0.13/0.40 tff(14,plain,
% 0.13/0.40 (~![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)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[13, 5])).
% 0.13/0.40 tff(15,plain,
% 0.13/0.40 (![Z: $i] : q(f(Z)) & ![X: $i, Y: $i] : (~((p(X) | (~p(f(Y)))) & ((~r(Y)) | (r(B!0) & r(C!1))) & q(X)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[14, 4])).
% 0.13/0.40 tff(16,plain,
% 0.13/0.40 (![Z: $i] : q(f(Z))),
% 0.13/0.40 inference(and_elim,[status(thm)],[15])).
% 0.13/0.40 tff(17,plain,
% 0.13/0.40 (![Z: $i] : q(f(Z))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[16, 3])).
% 0.13/0.40 tff(18,plain,
% 0.13/0.40 ((~![Z: $i] : q(f(Z))) | q(f(B!0))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(19,plain,
% 0.13/0.40 ($false),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[18, 17, 1])).
% 0.13/0.40 tff(20,plain,(q(f(B!0))), inference(lemma,lemma(discharge,[]))).
% 0.13/0.40 tff(21,assumption,((~r(B!0)) | (~((~r(B!0)) | (~r(C!1))))), introduced(assumption)).
% 0.13/0.40 tff(22,plain,
% 0.13/0.40 (^[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))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(23,plain,
% 0.13/0.40 (![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)))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[22])).
% 0.13/0.40 tff(24,plain,
% 0.13/0.40 (^[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)))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(25,plain,
% 0.13/0.40 (![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)))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[24])).
% 0.13/0.40 tff(26,plain,
% 0.13/0.40 (![X: $i, Y: $i] : (~((p(X) | (~p(f(Y)))) & ((~r(Y)) | (r(B!0) & r(C!1))) & q(X)))),
% 0.13/0.40 inference(and_elim,[status(thm)],[15])).
% 0.13/0.40 tff(27,plain,
% 0.13/0.40 (![X: $i, Y: $i] : ((~(p(X) | (~p(f(Y))))) | (~((~r(Y)) | (~((~r(B!0)) | (~r(C!1)))))) | (~q(X)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.13/0.40 tff(28,plain,
% 0.13/0.40 (![X: $i, Y: $i] : ((~(p(X) | (~p(f(Y))))) | (~((~r(Y)) | (~((~r(B!0)) | (~r(C!1)))))) | (~q(X)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.13/0.40 tff(29,plain,
% 0.13/0.40 (((~![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: $i] : ((~(p(X) | (~p(f(Y))))) | (~((~r(Y)) | (~((~r(B!0)) | (~r(C!1)))))) | (~q(X)))) | (~((~r(B!0)) | (~((~r(B!0)) | (~r(C!1)))))) | (~q(f(B!0))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(30,plain,
% 0.13/0.40 (($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))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(31,plain,
% 0.13/0.40 ((~$true) <=> $false),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(32,plain,
% 0.13/0.40 ((p(f(B!0)) | (~p(f(B!0)))) <=> $true),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(33,plain,
% 0.13/0.40 ((~(p(f(B!0)) | (~p(f(B!0))))) <=> (~$true)),
% 0.13/0.40 inference(monotonicity,[status(thm)],[32])).
% 0.13/0.40 tff(34,plain,
% 0.13/0.40 ((~(p(f(B!0)) | (~p(f(B!0))))) <=> $false),
% 0.13/0.40 inference(transitivity,[status(thm)],[33, 31])).
% 0.13/0.40 tff(35,plain,
% 0.13/0.40 (((~(p(f(B!0)) | (~p(f(B!0))))) | (~((~r(B!0)) | (~((~r(B!0)) | (~r(C!1)))))) | (~q(f(B!0)))) <=> ($false | (~((~r(B!0)) | (~((~r(B!0)) | (~r(C!1)))))) | (~q(f(B!0))))),
% 0.13/0.40 inference(monotonicity,[status(thm)],[34])).
% 0.13/0.40 tff(36,plain,
% 0.13/0.40 (((~(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))))),
% 0.13/0.40 inference(transitivity,[status(thm)],[35, 30])).
% 0.13/0.40 tff(37,plain,
% 0.13/0.40 (((~![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)))))),
% 0.13/0.40 inference(monotonicity,[status(thm)],[36])).
% 0.13/0.40 tff(38,plain,
% 0.13/0.40 (((~![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))))),
% 0.13/0.40 inference(transitivity,[status(thm)],[37, 29])).
% 0.13/0.40 tff(39,plain,
% 0.13/0.40 ((~![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))))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(40,plain,
% 0.13/0.40 ((~![X: $i, Y: $i] : ((~(p(X) | (~p(f(Y))))) | (~((~r(Y)) | (~((~r(B!0)) | (~r(C!1)))))) | (~q(X)))) | (~((~r(B!0)) | (~((~r(B!0)) | (~r(C!1)))))) | (~q(f(B!0)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.13/0.40 tff(41,plain,
% 0.13/0.40 ($false),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[40, 28, 21, 20])).
% 0.13/0.40 tff(42,plain,(~((~r(B!0)) | (~((~r(B!0)) | (~r(C!1)))))), inference(lemma,lemma(discharge,[]))).
% 0.13/0.40 tff(43,plain,
% 0.13/0.40 (((~r(B!0)) | (~((~r(B!0)) | (~r(C!1))))) | r(B!0)),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(44,plain,
% 0.13/0.40 (r(B!0)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[43, 42])).
% 0.13/0.40 tff(45,plain,
% 0.13/0.40 ((~![Z: $i] : q(f(Z))) | q(f(elem!2))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(46,plain,
% 0.13/0.40 (q(f(elem!2))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[45, 17])).
% 0.13/0.40 tff(47,plain,
% 0.13/0.40 (((~![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: $i] : ((~(p(X) | (~p(f(Y))))) | (~((~r(Y)) | (~((~r(B!0)) | (~r(C!1)))))) | (~q(X)))) | (~((~r(elem!2)) | (~((~r(B!0)) | (~r(C!1)))))) | (~q(f(elem!2))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(48,plain,
% 0.13/0.40 (($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))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(49,plain,
% 0.13/0.40 ((p(f(elem!2)) | (~p(f(elem!2)))) <=> $true),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(50,plain,
% 0.13/0.40 ((~(p(f(elem!2)) | (~p(f(elem!2))))) <=> (~$true)),
% 0.13/0.40 inference(monotonicity,[status(thm)],[49])).
% 0.13/0.40 tff(51,plain,
% 0.13/0.40 ((~(p(f(elem!2)) | (~p(f(elem!2))))) <=> $false),
% 0.13/0.40 inference(transitivity,[status(thm)],[50, 31])).
% 0.13/0.40 tff(52,plain,
% 0.13/0.40 (((~(p(f(elem!2)) | (~p(f(elem!2))))) | (~((~r(elem!2)) | (~((~r(B!0)) | (~r(C!1)))))) | (~q(f(elem!2)))) <=> ($false | (~((~r(elem!2)) | (~((~r(B!0)) | (~r(C!1)))))) | (~q(f(elem!2))))),
% 0.13/0.40 inference(monotonicity,[status(thm)],[51])).
% 0.13/0.40 tff(53,plain,
% 0.13/0.40 (((~(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))))),
% 0.13/0.40 inference(transitivity,[status(thm)],[52, 48])).
% 0.13/0.40 tff(54,plain,
% 0.13/0.40 (((~![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)))))),
% 0.13/0.40 inference(monotonicity,[status(thm)],[53])).
% 0.13/0.40 tff(55,plain,
% 0.13/0.40 (((~![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))))),
% 0.13/0.40 inference(transitivity,[status(thm)],[54, 47])).
% 0.13/0.40 tff(56,plain,
% 0.13/0.40 ((~![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))))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(57,plain,
% 0.13/0.40 ((~![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)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.13/0.41 tff(58,plain,
% 0.13/0.41 (~((~r(elem!2)) | (~((~r(B!0)) | (~r(C!1)))))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[57, 28, 46])).
% 0.13/0.41 tff(59,plain,
% 0.13/0.41 (((~r(elem!2)) | (~((~r(B!0)) | (~r(C!1))))) | ((~r(B!0)) | (~r(C!1)))),
% 0.13/0.41 inference(tautology,[status(thm)],[])).
% 0.13/0.41 tff(60,plain,
% 0.13/0.41 ((~r(B!0)) | (~r(C!1))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[59, 58])).
% 0.13/0.41 tff(61,plain,
% 0.13/0.41 ((~((~r(B!0)) | (~r(C!1)))) | (~r(B!0)) | (~r(C!1))),
% 0.13/0.41 inference(tautology,[status(thm)],[])).
% 0.13/0.41 tff(62,plain,
% 0.13/0.41 ((~r(B!0)) | (~r(C!1))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[61, 60])).
% 0.13/0.41 tff(63,plain,
% 0.13/0.41 (~r(C!1)),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[62, 44])).
% 0.13/0.41 tff(64,plain,
% 0.13/0.41 (((~r(C!1)) | (~((~r(B!0)) | (~r(C!1))))) | r(C!1)),
% 0.13/0.41 inference(tautology,[status(thm)],[])).
% 0.13/0.41 tff(65,plain,
% 0.13/0.41 ((~r(C!1)) | (~((~r(B!0)) | (~r(C!1))))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[64, 63])).
% 0.13/0.41 tff(66,plain,
% 0.13/0.41 (((~![X: $i, Y: $i] : ((~(p(X) | (~p(f(Y))))) | (~((~r(Y)) | (~((~r(B!0)) | (~r(C!1)))))) | (~q(X)))) | ((~q(f(C!1))) | (~((~r(C!1)) | (~((~r(B!0)) | (~r(C!1)))))))) <=> ((~![X: $i, Y: $i] : ((~(p(X) | (~p(f(Y))))) | (~((~r(Y)) | (~((~r(B!0)) | (~r(C!1)))))) | (~q(X)))) | (~q(f(C!1))) | (~((~r(C!1)) | (~((~r(B!0)) | (~r(C!1)))))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(67,plain,
% 0.13/0.41 (($false | (~((~r(C!1)) | (~((~r(B!0)) | (~r(C!1)))))) | (~q(f(C!1)))) <=> ((~q(f(C!1))) | (~((~r(C!1)) | (~((~r(B!0)) | (~r(C!1)))))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(68,plain,
% 0.13/0.41 ((p(f(C!1)) | (~p(f(C!1)))) <=> $true),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(69,plain,
% 0.13/0.41 ((~(p(f(C!1)) | (~p(f(C!1))))) <=> (~$true)),
% 0.13/0.41 inference(monotonicity,[status(thm)],[68])).
% 0.13/0.41 tff(70,plain,
% 0.13/0.41 ((~(p(f(C!1)) | (~p(f(C!1))))) <=> $false),
% 0.13/0.41 inference(transitivity,[status(thm)],[69, 31])).
% 0.13/0.41 tff(71,plain,
% 0.13/0.41 (((~(p(f(C!1)) | (~p(f(C!1))))) | (~((~r(C!1)) | (~((~r(B!0)) | (~r(C!1)))))) | (~q(f(C!1)))) <=> ($false | (~((~r(C!1)) | (~((~r(B!0)) | (~r(C!1)))))) | (~q(f(C!1))))),
% 0.13/0.41 inference(monotonicity,[status(thm)],[70])).
% 0.13/0.41 tff(72,plain,
% 0.13/0.41 (((~(p(f(C!1)) | (~p(f(C!1))))) | (~((~r(C!1)) | (~((~r(B!0)) | (~r(C!1)))))) | (~q(f(C!1)))) <=> ((~q(f(C!1))) | (~((~r(C!1)) | (~((~r(B!0)) | (~r(C!1)))))))),
% 0.13/0.41 inference(transitivity,[status(thm)],[71, 67])).
% 0.13/0.41 tff(73,plain,
% 0.13/0.41 (((~![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)))) | ((~q(f(C!1))) | (~((~r(C!1)) | (~((~r(B!0)) | (~r(C!1))))))))),
% 0.13/0.41 inference(monotonicity,[status(thm)],[72])).
% 0.13/0.41 tff(74,plain,
% 0.13/0.41 (((~![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)))) | (~q(f(C!1))) | (~((~r(C!1)) | (~((~r(B!0)) | (~r(C!1)))))))),
% 0.13/0.41 inference(transitivity,[status(thm)],[73, 66])).
% 0.13/0.41 tff(75,plain,
% 0.13/0.41 ((~![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))))),
% 0.13/0.41 inference(quant_inst,[status(thm)],[])).
% 0.13/0.41 tff(76,plain,
% 0.13/0.41 ((~![X: $i, Y: $i] : ((~(p(X) | (~p(f(Y))))) | (~((~r(Y)) | (~((~r(B!0)) | (~r(C!1)))))) | (~q(X)))) | (~q(f(C!1))) | (~((~r(C!1)) | (~((~r(B!0)) | (~r(C!1))))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.13/0.41 tff(77,plain,
% 0.13/0.41 (~q(f(C!1))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[76, 28, 65])).
% 0.13/0.41 tff(78,plain,
% 0.13/0.41 ((~![Z: $i] : q(f(Z))) | q(f(C!1))),
% 0.13/0.41 inference(quant_inst,[status(thm)],[])).
% 0.13/0.41 tff(79,plain,
% 0.13/0.41 ($false),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[78, 17, 77])).
% 0.13/0.41 % SZS output end Proof
%------------------------------------------------------------------------------