TSTP Solution File: SYN941+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN941+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n006.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 0.20s 0.39s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN941+1 : TPTP v8.1.0. Released v3.1.0.
% 0.03/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n006.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 : Mon Sep 5 09:35:38 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.20/0.39 % SZS status Theorem
% 0.20/0.39 % SZS output start Proof
% 0.20/0.39 tff(r_type, type, (
% 0.20/0.39 r: $i > $o)).
% 0.20/0.39 tff(tptp_fun_C_0_type, type, (
% 0.20/0.39 tptp_fun_C_0: $i)).
% 0.20/0.39 tff(tptp_fun_B_1_type, type, (
% 0.20/0.39 tptp_fun_B_1: $i)).
% 0.20/0.39 tff(p_type, type, (
% 0.20/0.39 p: $i > $o)).
% 0.20/0.39 tff(f_type, type, (
% 0.20/0.39 f: $i > $i)).
% 0.20/0.39 tff(q_type, type, (
% 0.20/0.39 q: $i > $o)).
% 0.20/0.39 tff(1,plain,
% 0.20/0.39 (^[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))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(2,plain,
% 0.20/0.39 (![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)))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.39 tff(3,plain,
% 0.20/0.39 (^[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)))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(4,plain,
% 0.20/0.39 (![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)))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[3])).
% 0.20/0.39 tff(5,plain,
% 0.20/0.39 (((~(~q(f(B!1)))) & ![X: $i, Y: $i] : (~(((~p(f(Y))) | (p(X) & ((~r(Y)) | (r(B!1) & r(C!0))))) & q(X)))) <=> (q(f(B!1)) & ![X: $i, Y: $i] : (~(((~p(f(Y))) | (p(X) & ((~r(Y)) | (r(B!1) & r(C!0))))) & q(X))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(6,plain,
% 0.20/0.39 ((~![B: $i, C: $i] : ((~q(f(B))) | ?[X: $i, Y: $i] : (((~p(f(Y))) | (p(X) & ((~r(Y)) | (r(B) & r(C))))) & q(X)))) <=> (~![B: $i, C: $i] : ((~q(f(B))) | ?[X: $i, Y: $i] : (((~p(f(Y))) | (p(X) & ((~r(Y)) | (r(B) & r(C))))) & q(X))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(7,plain,
% 0.20/0.39 ((~![B: $i, C: $i] : (q(f(B)) => ?[X: $i, Y: $i] : ((p(f(Y)) => (p(X) & (r(Y) => (r(B) & r(C))))) & q(X)))) <=> (~![B: $i, C: $i] : ((~q(f(B))) | ?[X: $i, Y: $i] : (((~p(f(Y))) | (p(X) & ((~r(Y)) | (r(B) & r(C))))) & q(X))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(8,axiom,(~![B: $i, C: $i] : (q(f(B)) => ?[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')).
% 0.20/0.39 tff(9,plain,
% 0.20/0.39 (~![B: $i, C: $i] : ((~q(f(B))) | ?[X: $i, Y: $i] : (((~p(f(Y))) | (p(X) & ((~r(Y)) | (r(B) & r(C))))) & q(X)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.20/0.39 tff(10,plain,
% 0.20/0.39 (~![B: $i, C: $i] : ((~q(f(B))) | ?[X: $i, Y: $i] : (((~p(f(Y))) | (p(X) & ((~r(Y)) | (r(B) & r(C))))) & q(X)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[9, 6])).
% 0.20/0.39 tff(11,plain,
% 0.20/0.39 (~![B: $i, C: $i] : ((~q(f(B))) | ?[X: $i, Y: $i] : (((~p(f(Y))) | (p(X) & ((~r(Y)) | (r(B) & r(C))))) & q(X)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[10, 6])).
% 0.20/0.39 tff(12,plain,
% 0.20/0.39 (~![B: $i, C: $i] : ((~q(f(B))) | ?[X: $i, Y: $i] : (((~p(f(Y))) | (p(X) & ((~r(Y)) | (r(B) & r(C))))) & q(X)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[11, 6])).
% 0.20/0.39 tff(13,plain,
% 0.20/0.39 (~![B: $i, C: $i] : ((~q(f(B))) | ?[X: $i, Y: $i] : (((~p(f(Y))) | (p(X) & ((~r(Y)) | (r(B) & r(C))))) & q(X)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[12, 6])).
% 0.20/0.39 tff(14,plain,
% 0.20/0.39 (~![B: $i, C: $i] : ((~q(f(B))) | ?[X: $i, Y: $i] : (((~p(f(Y))) | (p(X) & ((~r(Y)) | (r(B) & r(C))))) & q(X)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[13, 6])).
% 0.20/0.39 tff(15,plain,
% 0.20/0.39 (~![B: $i, C: $i] : ((~q(f(B))) | ?[X: $i, Y: $i] : (((~p(f(Y))) | (p(X) & ((~r(Y)) | (r(B) & r(C))))) & q(X)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[14, 6])).
% 0.20/0.39 tff(16,plain,
% 0.20/0.39 (q(f(B!1)) & ![X: $i, Y: $i] : (~(((~p(f(Y))) | (p(X) & ((~r(Y)) | (r(B!1) & r(C!0))))) & q(X)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.20/0.39 tff(17,plain,
% 0.20/0.39 (![X: $i, Y: $i] : (~(((~p(f(Y))) | (p(X) & ((~r(Y)) | (r(B!1) & r(C!0))))) & q(X)))),
% 0.20/0.39 inference(and_elim,[status(thm)],[16])).
% 0.20/0.39 tff(18,plain,
% 0.20/0.39 (![X: $i, Y: $i] : ((~((~p(f(Y))) | (~((~p(X)) | (~((~r(Y)) | (~((~r(B!1)) | (~r(C!0)))))))))) | (~q(X)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[17, 4])).
% 0.20/0.39 tff(19,plain,
% 0.20/0.39 (![X: $i, Y: $i] : ((~((~p(f(Y))) | (~((~p(X)) | (~((~r(Y)) | (~((~r(B!1)) | (~r(C!0)))))))))) | (~q(X)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[18, 2])).
% 0.20/0.39 tff(20,plain,
% 0.20/0.39 (q(f(B!1))),
% 0.20/0.39 inference(and_elim,[status(thm)],[16])).
% 0.20/0.39 tff(21,plain,
% 0.20/0.39 (((~![X: $i, Y: $i] : ((~((~p(f(Y))) | (~((~p(X)) | (~((~r(Y)) | (~((~r(B!1)) | (~r(C!0)))))))))) | (~q(X)))) | ((~q(f(B!1))) | (~((~p(f(B!1))) | (~((~p(f(B!1))) | (~((~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(B!1))) | (~((~p(f(B!1))) | (~((~p(f(B!1))) | (~((~r(B!1)) | (~((~r(B!1)) | (~r(C!0)))))))))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(22,plain,
% 0.20/0.39 (((~((~p(f(B!1))) | (~((~p(f(B!1))) | (~((~r(B!1)) | (~((~r(B!1)) | (~r(C!0)))))))))) | (~q(f(B!1)))) <=> ((~q(f(B!1))) | (~((~p(f(B!1))) | (~((~p(f(B!1))) | (~((~r(B!1)) | (~((~r(B!1)) | (~r(C!0)))))))))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(23,plain,
% 0.20/0.39 (((~![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(B!1))) | (~((~r(B!1)) | (~((~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)))) | ((~q(f(B!1))) | (~((~p(f(B!1))) | (~((~p(f(B!1))) | (~((~r(B!1)) | (~((~r(B!1)) | (~r(C!0))))))))))))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[22])).
% 0.20/0.39 tff(24,plain,
% 0.20/0.39 (((~![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(B!1))) | (~((~r(B!1)) | (~((~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)))) | (~q(f(B!1))) | (~((~p(f(B!1))) | (~((~p(f(B!1))) | (~((~r(B!1)) | (~((~r(B!1)) | (~r(C!0)))))))))))),
% 0.20/0.39 inference(transitivity,[status(thm)],[23, 21])).
% 0.20/0.39 tff(25,plain,
% 0.20/0.39 ((~![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(B!1))) | (~((~r(B!1)) | (~((~r(B!1)) | (~r(C!0)))))))))) | (~q(f(B!1))))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(26,plain,
% 0.20/0.39 ((~![X: $i, Y: $i] : ((~((~p(f(Y))) | (~((~p(X)) | (~((~r(Y)) | (~((~r(B!1)) | (~r(C!0)))))))))) | (~q(X)))) | (~q(f(B!1))) | (~((~p(f(B!1))) | (~((~p(f(B!1))) | (~((~r(B!1)) | (~((~r(B!1)) | (~r(C!0))))))))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.20/0.39 tff(27,plain,
% 0.20/0.39 (~((~p(f(B!1))) | (~((~p(f(B!1))) | (~((~r(B!1)) | (~((~r(B!1)) | (~r(C!0)))))))))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[26, 20, 19])).
% 0.20/0.39 tff(28,plain,
% 0.20/0.39 (((~p(f(B!1))) | (~((~p(f(B!1))) | (~((~r(B!1)) | (~((~r(B!1)) | (~r(C!0))))))))) | ((~p(f(B!1))) | (~((~r(B!1)) | (~((~r(B!1)) | (~r(C!0)))))))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(29,plain,
% 0.20/0.39 ((~p(f(B!1))) | (~((~r(B!1)) | (~((~r(B!1)) | (~r(C!0))))))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[28, 27])).
% 0.20/0.40 tff(30,plain,
% 0.20/0.40 (((~p(f(B!1))) | (~((~p(f(B!1))) | (~((~r(B!1)) | (~((~r(B!1)) | (~r(C!0))))))))) | p(f(B!1))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(31,plain,
% 0.20/0.40 (p(f(B!1))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[30, 27])).
% 0.20/0.40 tff(32,plain,
% 0.20/0.40 ((~((~p(f(B!1))) | (~((~r(B!1)) | (~((~r(B!1)) | (~r(C!0)))))))) | (~p(f(B!1))) | (~((~r(B!1)) | (~((~r(B!1)) | (~r(C!0))))))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(33,plain,
% 0.20/0.40 (~((~r(B!1)) | (~((~r(B!1)) | (~r(C!0)))))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[32, 31, 29])).
% 0.20/0.40 tff(34,plain,
% 0.20/0.40 (((~r(B!1)) | (~((~r(B!1)) | (~r(C!0))))) | ((~r(B!1)) | (~r(C!0)))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(35,plain,
% 0.20/0.40 ((~r(B!1)) | (~r(C!0))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[34, 33])).
% 0.20/0.40 tff(36,plain,
% 0.20/0.40 (((~r(B!1)) | (~((~r(B!1)) | (~r(C!0))))) | r(B!1)),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(37,plain,
% 0.20/0.40 (r(B!1)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[36, 33])).
% 0.20/0.40 tff(38,plain,
% 0.20/0.40 ((~((~r(B!1)) | (~r(C!0)))) | (~r(B!1)) | (~r(C!0))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(39,plain,
% 0.20/0.40 (~r(C!0)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[38, 37, 35])).
% 0.20/0.40 tff(40,plain,
% 0.20/0.40 (((~r(C!0)) | (~((~r(B!1)) | (~r(C!0))))) | r(C!0)),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(41,plain,
% 0.20/0.40 ((~r(C!0)) | (~((~r(B!1)) | (~r(C!0))))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[40, 39])).
% 0.20/0.40 tff(42,plain,
% 0.20/0.40 ((~((~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))))))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(43,plain,
% 0.20/0.40 (~((~p(f(B!1))) | (~((~r(C!0)) | (~((~r(B!1)) | (~r(C!0)))))))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[42, 31, 41])).
% 0.20/0.40 tff(44,plain,
% 0.20/0.40 (((~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)))))))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(45,plain,
% 0.20/0.40 ((~p(f(C!0))) | (~((~p(f(B!1))) | (~((~r(C!0)) | (~((~r(B!1)) | (~r(C!0))))))))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[44, 43])).
% 0.20/0.40 tff(46,plain,
% 0.20/0.40 (((~![X: $i, Y: $i] : ((~((~p(f(Y))) | (~((~p(X)) | (~((~r(Y)) | (~((~r(B!1)) | (~r(C!0)))))))))) | (~q(X)))) | ((~q(f(B!1))) | (~((~p(f(C!0))) | (~((~p(f(B!1))) | (~((~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(B!1))) | (~((~p(f(C!0))) | (~((~p(f(B!1))) | (~((~r(C!0)) | (~((~r(B!1)) | (~r(C!0)))))))))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(47,plain,
% 0.20/0.40 (((~((~p(f(C!0))) | (~((~p(f(B!1))) | (~((~r(C!0)) | (~((~r(B!1)) | (~r(C!0)))))))))) | (~q(f(B!1)))) <=> ((~q(f(B!1))) | (~((~p(f(C!0))) | (~((~p(f(B!1))) | (~((~r(C!0)) | (~((~r(B!1)) | (~r(C!0)))))))))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(48,plain,
% 0.20/0.40 (((~![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)))) | ((~q(f(B!1))) | (~((~p(f(C!0))) | (~((~p(f(B!1))) | (~((~r(C!0)) | (~((~r(B!1)) | (~r(C!0))))))))))))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[47])).
% 0.20/0.40 tff(49,plain,
% 0.20/0.40 (((~![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)))) | (~q(f(B!1))) | (~((~p(f(C!0))) | (~((~p(f(B!1))) | (~((~r(C!0)) | (~((~r(B!1)) | (~r(C!0)))))))))))),
% 0.20/0.40 inference(transitivity,[status(thm)],[48, 46])).
% 0.20/0.40 tff(50,plain,
% 0.20/0.40 ((~![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))))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(51,plain,
% 0.20/0.40 ((~![X: $i, Y: $i] : ((~((~p(f(Y))) | (~((~p(X)) | (~((~r(Y)) | (~((~r(B!1)) | (~r(C!0)))))))))) | (~q(X)))) | (~q(f(B!1))) | (~((~p(f(C!0))) | (~((~p(f(B!1))) | (~((~r(C!0)) | (~((~r(B!1)) | (~r(C!0))))))))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.20/0.40 tff(52,plain,
% 0.20/0.40 ($false),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[51, 20, 19, 45])).
% 0.20/0.40 % SZS output end Proof
%------------------------------------------------------------------------------