TSTP Solution File: LCL682+1.001 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LCL682+1.001 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n008.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 : Sun Sep 18 04:57:51 EDT 2022
% Result : Theorem 0.12s 0.39s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL682+1.001 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n008.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 Sep 2 00:16:40 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.
% 0.12/0.39 % SZS status Theorem
% 0.12/0.39 % SZS output start Proof
% 0.12/0.39 tff(r1_type, type, (
% 0.12/0.39 r1: ( $i * $i ) > $o)).
% 0.12/0.39 tff(tptp_fun_Y_5_type, type, (
% 0.12/0.39 tptp_fun_Y_5: $i)).
% 0.12/0.39 tff(p12_type, type, (
% 0.12/0.39 p12: $i > $o)).
% 0.12/0.39 tff(p14_type, type, (
% 0.12/0.39 p14: $i > $o)).
% 0.12/0.39 tff(p16_type, type, (
% 0.12/0.39 p16: $i > $o)).
% 0.12/0.39 tff(tptp_fun_X_0_type, type, (
% 0.12/0.39 tptp_fun_X_0: $i)).
% 0.12/0.39 tff(tptp_fun_X_8_type, type, (
% 0.12/0.39 tptp_fun_X_8: $i)).
% 0.12/0.39 tff(tptp_fun_Y_7_type, type, (
% 0.12/0.39 tptp_fun_Y_7: $i)).
% 0.12/0.39 tff(p11_type, type, (
% 0.12/0.39 p11: $i > $o)).
% 0.12/0.39 tff(tptp_fun_X_6_type, type, (
% 0.12/0.39 tptp_fun_X_6: $i)).
% 0.12/0.39 tff(tptp_fun_X_4_type, type, (
% 0.12/0.39 tptp_fun_X_4: $i)).
% 0.12/0.39 tff(tptp_fun_Y_3_type, type, (
% 0.12/0.39 tptp_fun_Y_3: $i)).
% 0.12/0.39 tff(p13_type, type, (
% 0.12/0.39 p13: $i > $o)).
% 0.12/0.39 tff(tptp_fun_X_2_type, type, (
% 0.12/0.39 tptp_fun_X_2: $i)).
% 0.12/0.39 tff(tptp_fun_Y_1_type, type, (
% 0.12/0.39 tptp_fun_Y_1: $i)).
% 0.12/0.39 tff(p15_type, type, (
% 0.12/0.39 p15: $i > $o)).
% 0.12/0.39 tff(1,plain,
% 0.12/0.39 ((![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p16(X) | (~r1(Y, X))) & ![X: $i] : (p12(X) | (~r1(Y, X))) & ![X: $i] : (p14(X) | (~r1(Y, X))))) & (r1(X!0, Y!1) & (~(p15(X!2) | (~r1(Y!1, X!2))))) & (r1(X!0, Y!3) & (~(p13(X!4) | (~r1(Y!3, X!4))))) & (r1(X!0, Y!5) & (~(p12(X!6) | (~r1(Y!5, X!6))))) & (r1(X!0, Y!7) & (~(p11(X!8) | (~r1(Y!7, X!8)))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p16(X) | (~r1(Y, X))) & ![X: $i] : (p12(X) | (~r1(Y, X))) & ![X: $i] : (p14(X) | (~r1(Y, X))))) & r1(X!0, Y!1) & (~(p15(X!2) | (~r1(Y!1, X!2)))) & r1(X!0, Y!3) & (~(p13(X!4) | (~r1(Y!3, X!4)))) & r1(X!0, Y!5) & (~(p12(X!6) | (~r1(Y!5, X!6)))) & r1(X!0, Y!7) & (~(p11(X!8) | (~r1(Y!7, X!8)))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(2,plain,
% 0.12/0.39 (((~(~r1(X!0, Y!7))) & (~(p11(X!8) | (~r1(Y!7, X!8))))) <=> (r1(X!0, Y!7) & (~(p11(X!8) | (~r1(Y!7, X!8)))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(3,plain,
% 0.12/0.39 (((~(~r1(X!0, Y!5))) & (~(p12(X!6) | (~r1(Y!5, X!6))))) <=> (r1(X!0, Y!5) & (~(p12(X!6) | (~r1(Y!5, X!6)))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(4,plain,
% 0.12/0.39 (((~(~r1(X!0, Y!3))) & (~(p13(X!4) | (~r1(Y!3, X!4))))) <=> (r1(X!0, Y!3) & (~(p13(X!4) | (~r1(Y!3, X!4)))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(5,plain,
% 0.12/0.39 (((~(~r1(X!0, Y!1))) & (~(p15(X!2) | (~r1(Y!1, X!2))))) <=> (r1(X!0, Y!1) & (~(p15(X!2) | (~r1(Y!1, X!2)))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(6,plain,
% 0.12/0.39 ((![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p16(X) | (~r1(Y, X))) & ![X: $i] : (p12(X) | (~r1(Y, X))) & ![X: $i] : (p14(X) | (~r1(Y, X))))) & ((~(~r1(X!0, Y!1))) & (~(p15(X!2) | (~r1(Y!1, X!2))))) & ((~(~r1(X!0, Y!3))) & (~(p13(X!4) | (~r1(Y!3, X!4))))) & ((~(~r1(X!0, Y!5))) & (~(p12(X!6) | (~r1(Y!5, X!6))))) & ((~(~r1(X!0, Y!7))) & (~(p11(X!8) | (~r1(Y!7, X!8)))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p16(X) | (~r1(Y, X))) & ![X: $i] : (p12(X) | (~r1(Y, X))) & ![X: $i] : (p14(X) | (~r1(Y, X))))) & (r1(X!0, Y!1) & (~(p15(X!2) | (~r1(Y!1, X!2))))) & (r1(X!0, Y!3) & (~(p13(X!4) | (~r1(Y!3, X!4))))) & (r1(X!0, Y!5) & (~(p12(X!6) | (~r1(Y!5, X!6))))) & (r1(X!0, Y!7) & (~(p11(X!8) | (~r1(Y!7, X!8))))))),
% 0.12/0.39 inference(monotonicity,[status(thm)],[5, 4, 3, 2])).
% 0.12/0.39 tff(7,plain,
% 0.12/0.39 ((![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p16(X) | (~r1(Y, X))) & ![X: $i] : (p12(X) | (~r1(Y, X))) & ![X: $i] : (p14(X) | (~r1(Y, X))))) & ((~(~r1(X!0, Y!1))) & (~(p15(X!2) | (~r1(Y!1, X!2))))) & ((~(~r1(X!0, Y!3))) & (~(p13(X!4) | (~r1(Y!3, X!4))))) & ((~(~r1(X!0, Y!5))) & (~(p12(X!6) | (~r1(Y!5, X!6))))) & ((~(~r1(X!0, Y!7))) & (~(p11(X!8) | (~r1(Y!7, X!8)))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p16(X) | (~r1(Y, X))) & ![X: $i] : (p12(X) | (~r1(Y, X))) & ![X: $i] : (p14(X) | (~r1(Y, X))))) & r1(X!0, Y!1) & (~(p15(X!2) | (~r1(Y!1, X!2)))) & r1(X!0, Y!3) & (~(p13(X!4) | (~r1(Y!3, X!4)))) & r1(X!0, Y!5) & (~(p12(X!6) | (~r1(Y!5, X!6)))) & r1(X!0, Y!7) & (~(p11(X!8) | (~r1(Y!7, X!8)))))),
% 0.12/0.39 inference(transitivity,[status(thm)],[6, 1])).
% 0.12/0.39 tff(8,plain,
% 0.12/0.39 (?[X: $i] : (~((~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p16(X) | (~r1(Y, X)))) | (~![X: $i] : (p12(X) | (~r1(Y, X)))) | (~![X: $i] : (p14(X) | (~r1(Y, X)))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p15(X) | (~r1(Y, X)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p13(X) | (~r1(Y, X)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p12(X) | (~r1(Y, X)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p11(X) | (~r1(Y, X)))))) <=> ?[X: $i] : (~((~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p16(X) | (~r1(Y, X)))) | (~![X: $i] : (p12(X) | (~r1(Y, X)))) | (~![X: $i] : (p14(X) | (~r1(Y, X)))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p15(X) | (~r1(Y, X)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p13(X) | (~r1(Y, X)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p12(X) | (~r1(Y, X)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p11(X) | (~r1(Y, X))))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(9,plain,
% 0.12/0.39 ((~(~?[X: $i] : (~((~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p16(X) | (~r1(Y, X)))) | (~![X: $i] : (p12(X) | (~r1(Y, X)))) | (~![X: $i] : (p14(X) | (~r1(Y, X)))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p15(X) | (~r1(Y, X)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p13(X) | (~r1(Y, X)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p12(X) | (~r1(Y, X)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p11(X) | (~r1(Y, X)))))))) <=> ?[X: $i] : (~((~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p16(X) | (~r1(Y, X)))) | (~![X: $i] : (p12(X) | (~r1(Y, X)))) | (~![X: $i] : (p14(X) | (~r1(Y, X)))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p15(X) | (~r1(Y, X)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p13(X) | (~r1(Y, X)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p12(X) | (~r1(Y, X)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p11(X) | (~r1(Y, X))))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(10,plain,
% 0.12/0.39 ((~?[X: $i] : (~(((((~![Y: $i] : ((~r1(X, Y)) | (~((((~![X: $i] : ((~r1(Y, X)) | p16(X))) | (~![X: $i] : ((~r1(Y, X)) | p12(X)))) | (~![X: $i] : ((~r1(Y, X)) | p14(X)))) | (~![X: $i] : ((~r1(Y, X)) | p12(X))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p15(X)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p13(X)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p12(X)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p11(X)))))) <=> (~?[X: $i] : (~((~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p16(X) | (~r1(Y, X)))) | (~![X: $i] : (p12(X) | (~r1(Y, X)))) | (~![X: $i] : (p14(X) | (~r1(Y, X)))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p15(X) | (~r1(Y, X)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p13(X) | (~r1(Y, X)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p12(X) | (~r1(Y, X)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p11(X) | (~r1(Y, X)))))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(11,plain,
% 0.12/0.39 ((~(~?[X: $i] : (~(((((~![Y: $i] : ((~r1(X, Y)) | (~((((~![X: $i] : ((~r1(Y, X)) | p16(X))) | (~![X: $i] : ((~r1(Y, X)) | p12(X)))) | (~![X: $i] : ((~r1(Y, X)) | p14(X)))) | (~![X: $i] : ((~r1(Y, X)) | p12(X))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p15(X)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p13(X)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p12(X)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p11(X))))))) <=> (~(~?[X: $i] : (~((~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p16(X) | (~r1(Y, X)))) | (~![X: $i] : (p12(X) | (~r1(Y, X)))) | (~![X: $i] : (p14(X) | (~r1(Y, X)))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p15(X) | (~r1(Y, X)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p13(X) | (~r1(Y, X)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p12(X) | (~r1(Y, X)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p11(X) | (~r1(Y, X))))))))),
% 0.12/0.39 inference(monotonicity,[status(thm)],[10])).
% 0.12/0.39 tff(12,plain,
% 0.12/0.39 ((~(~?[X: $i] : (~(((((~![Y: $i] : ((~r1(X, Y)) | (~((((~![X: $i] : ((~r1(Y, X)) | p16(X))) | (~![X: $i] : ((~r1(Y, X)) | p12(X)))) | (~![X: $i] : ((~r1(Y, X)) | p14(X)))) | (~![X: $i] : ((~r1(Y, X)) | p12(X))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p15(X)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p13(X)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p12(X)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p11(X))))))) <=> ?[X: $i] : (~((~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p16(X) | (~r1(Y, X)))) | (~![X: $i] : (p12(X) | (~r1(Y, X)))) | (~![X: $i] : (p14(X) | (~r1(Y, X)))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p15(X) | (~r1(Y, X)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p13(X) | (~r1(Y, X)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p12(X) | (~r1(Y, X)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p11(X) | (~r1(Y, X))))))),
% 0.21/0.40 inference(transitivity,[status(thm)],[11, 9])).
% 0.21/0.40 tff(13,axiom,(~(~?[X: $i] : (~(((((~![Y: $i] : ((~r1(X, Y)) | (~((((~![X: $i] : ((~r1(Y, X)) | p16(X))) | (~![X: $i] : ((~r1(Y, X)) | p12(X)))) | (~![X: $i] : ((~r1(Y, X)) | p14(X)))) | (~![X: $i] : ((~r1(Y, X)) | p12(X))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p15(X)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p13(X)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p12(X)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p11(X))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','main')).
% 0.21/0.40 tff(14,plain,
% 0.21/0.40 (?[X: $i] : (~((~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p16(X) | (~r1(Y, X)))) | (~![X: $i] : (p12(X) | (~r1(Y, X)))) | (~![X: $i] : (p14(X) | (~r1(Y, X)))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p15(X) | (~r1(Y, X)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p13(X) | (~r1(Y, X)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p12(X) | (~r1(Y, X)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p11(X) | (~r1(Y, X))))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.21/0.40 tff(15,plain,
% 0.21/0.40 (?[X: $i] : (~((~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p16(X) | (~r1(Y, X)))) | (~![X: $i] : (p12(X) | (~r1(Y, X)))) | (~![X: $i] : (p14(X) | (~r1(Y, X)))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p15(X) | (~r1(Y, X)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p13(X) | (~r1(Y, X)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p12(X) | (~r1(Y, X)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p11(X) | (~r1(Y, X))))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[14, 8])).
% 0.21/0.40 tff(16,plain,
% 0.21/0.40 (![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p16(X) | (~r1(Y, X))) & ![X: $i] : (p12(X) | (~r1(Y, X))) & ![X: $i] : (p14(X) | (~r1(Y, X))))) & r1(X!0, Y!1) & (~(p15(X!2) | (~r1(Y!1, X!2)))) & r1(X!0, Y!3) & (~(p13(X!4) | (~r1(Y!3, X!4)))) & r1(X!0, Y!5) & (~(p12(X!6) | (~r1(Y!5, X!6)))) & r1(X!0, Y!7) & (~(p11(X!8) | (~r1(Y!7, X!8))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[15, 7])).
% 0.21/0.40 tff(17,plain,
% 0.21/0.40 (r1(X!0, Y!5)),
% 0.21/0.40 inference(and_elim,[status(thm)],[16])).
% 0.21/0.40 tff(18,plain,
% 0.21/0.40 (^[Y: $i] : refl(((~r1(X!0, Y)) | (~((~![X: $i] : (p16(X) | (~r1(Y, X)))) | (~![X: $i] : (p12(X) | (~r1(Y, X)))) | (~![X: $i] : (p14(X) | (~r1(Y, X))))))) <=> ((~r1(X!0, Y)) | (~((~![X: $i] : (p16(X) | (~r1(Y, X)))) | (~![X: $i] : (p12(X) | (~r1(Y, X)))) | (~![X: $i] : (p14(X) | (~r1(Y, X))))))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(19,plain,
% 0.21/0.40 (![Y: $i] : ((~r1(X!0, Y)) | (~((~![X: $i] : (p16(X) | (~r1(Y, X)))) | (~![X: $i] : (p12(X) | (~r1(Y, X)))) | (~![X: $i] : (p14(X) | (~r1(Y, X))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | (~((~![X: $i] : (p16(X) | (~r1(Y, X)))) | (~![X: $i] : (p12(X) | (~r1(Y, X)))) | (~![X: $i] : (p14(X) | (~r1(Y, X)))))))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[18])).
% 0.21/0.40 tff(20,plain,
% 0.21/0.40 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | (~((~![X: $i] : (p16(X) | (~r1(Y, X)))) | (~![X: $i] : (p12(X) | (~r1(Y, X)))) | (~![X: $i] : (p14(X) | (~r1(Y, X))))))) <=> ((~r1(X!0, Y)) | (~((~![X: $i] : (p16(X) | (~r1(Y, X)))) | (~![X: $i] : (p12(X) | (~r1(Y, X)))) | (~![X: $i] : (p14(X) | (~r1(Y, X))))))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(21,plain,
% 0.21/0.40 (![Y: $i] : ((~r1(X!0, Y)) | (~((~![X: $i] : (p16(X) | (~r1(Y, X)))) | (~![X: $i] : (p12(X) | (~r1(Y, X)))) | (~![X: $i] : (p14(X) | (~r1(Y, X))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | (~((~![X: $i] : (p16(X) | (~r1(Y, X)))) | (~![X: $i] : (p12(X) | (~r1(Y, X)))) | (~![X: $i] : (p14(X) | (~r1(Y, X)))))))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[20])).
% 0.21/0.40 tff(22,plain,
% 0.21/0.40 (![Y: $i] : ((~r1(X!0, Y)) | (~((~![X: $i] : (p16(X) | (~r1(Y, X)))) | (~![X: $i] : (p12(X) | (~r1(Y, X)))) | (~![X: $i] : (p14(X) | (~r1(Y, X))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | (~((~![X: $i] : (p16(X) | (~r1(Y, X)))) | (~![X: $i] : (p12(X) | (~r1(Y, X)))) | (~![X: $i] : (p14(X) | (~r1(Y, X)))))))),
% 0.21/0.40 inference(transitivity,[status(thm)],[21, 19])).
% 0.21/0.40 tff(23,plain,
% 0.21/0.40 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | (![X: $i] : (p16(X) | (~r1(Y, X))) & ![X: $i] : (p12(X) | (~r1(Y, X))) & ![X: $i] : (p14(X) | (~r1(Y, X))))) <=> ((~r1(X!0, Y)) | (~((~![X: $i] : (p16(X) | (~r1(Y, X)))) | (~![X: $i] : (p12(X) | (~r1(Y, X)))) | (~![X: $i] : (p14(X) | (~r1(Y, X))))))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(24,plain,
% 0.21/0.40 (![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p16(X) | (~r1(Y, X))) & ![X: $i] : (p12(X) | (~r1(Y, X))) & ![X: $i] : (p14(X) | (~r1(Y, X))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | (~((~![X: $i] : (p16(X) | (~r1(Y, X)))) | (~![X: $i] : (p12(X) | (~r1(Y, X)))) | (~![X: $i] : (p14(X) | (~r1(Y, X)))))))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[23])).
% 0.21/0.40 tff(25,plain,
% 0.21/0.40 (![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p16(X) | (~r1(Y, X))) & ![X: $i] : (p12(X) | (~r1(Y, X))) & ![X: $i] : (p14(X) | (~r1(Y, X)))))),
% 0.21/0.40 inference(and_elim,[status(thm)],[16])).
% 0.21/0.40 tff(26,plain,
% 0.21/0.40 (![Y: $i] : ((~r1(X!0, Y)) | (~((~![X: $i] : (p16(X) | (~r1(Y, X)))) | (~![X: $i] : (p12(X) | (~r1(Y, X)))) | (~![X: $i] : (p14(X) | (~r1(Y, X)))))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.21/0.40 tff(27,plain,
% 0.21/0.40 (![Y: $i] : ((~r1(X!0, Y)) | (~((~![X: $i] : (p16(X) | (~r1(Y, X)))) | (~![X: $i] : (p12(X) | (~r1(Y, X)))) | (~![X: $i] : (p14(X) | (~r1(Y, X)))))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[26, 22])).
% 0.21/0.40 tff(28,plain,
% 0.21/0.40 (((~![Y: $i] : ((~r1(X!0, Y)) | (~((~![X: $i] : (p16(X) | (~r1(Y, X)))) | (~![X: $i] : (p12(X) | (~r1(Y, X)))) | (~![X: $i] : (p14(X) | (~r1(Y, X)))))))) | ((~r1(X!0, Y!5)) | (~((~![X: $i] : (p16(X) | (~r1(Y!5, X)))) | (~![X: $i] : (p12(X) | (~r1(Y!5, X)))) | (~![X: $i] : (p14(X) | (~r1(Y!5, X)))))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | (~((~![X: $i] : (p16(X) | (~r1(Y, X)))) | (~![X: $i] : (p12(X) | (~r1(Y, X)))) | (~![X: $i] : (p14(X) | (~r1(Y, X)))))))) | (~r1(X!0, Y!5)) | (~((~![X: $i] : (p16(X) | (~r1(Y!5, X)))) | (~![X: $i] : (p12(X) | (~r1(Y!5, X)))) | (~![X: $i] : (p14(X) | (~r1(Y!5, X)))))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(29,plain,
% 0.21/0.40 ((~![Y: $i] : ((~r1(X!0, Y)) | (~((~![X: $i] : (p16(X) | (~r1(Y, X)))) | (~![X: $i] : (p12(X) | (~r1(Y, X)))) | (~![X: $i] : (p14(X) | (~r1(Y, X)))))))) | ((~r1(X!0, Y!5)) | (~((~![X: $i] : (p16(X) | (~r1(Y!5, X)))) | (~![X: $i] : (p12(X) | (~r1(Y!5, X)))) | (~![X: $i] : (p14(X) | (~r1(Y!5, X)))))))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(30,plain,
% 0.21/0.40 ((~![Y: $i] : ((~r1(X!0, Y)) | (~((~![X: $i] : (p16(X) | (~r1(Y, X)))) | (~![X: $i] : (p12(X) | (~r1(Y, X)))) | (~![X: $i] : (p14(X) | (~r1(Y, X)))))))) | (~r1(X!0, Y!5)) | (~((~![X: $i] : (p16(X) | (~r1(Y!5, X)))) | (~![X: $i] : (p12(X) | (~r1(Y!5, X)))) | (~![X: $i] : (p14(X) | (~r1(Y!5, X))))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.21/0.40 tff(31,plain,
% 0.21/0.40 (~((~![X: $i] : (p16(X) | (~r1(Y!5, X)))) | (~![X: $i] : (p12(X) | (~r1(Y!5, X)))) | (~![X: $i] : (p14(X) | (~r1(Y!5, X)))))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[30, 27, 17])).
% 0.21/0.40 tff(32,plain,
% 0.21/0.40 (((~![X: $i] : (p16(X) | (~r1(Y!5, X)))) | (~![X: $i] : (p12(X) | (~r1(Y!5, X)))) | (~![X: $i] : (p14(X) | (~r1(Y!5, X))))) | ![X: $i] : (p12(X) | (~r1(Y!5, X)))),
% 0.21/0.40 inference(tautology,[status(thm)],[])).
% 0.21/0.40 tff(33,plain,
% 0.21/0.40 (![X: $i] : (p12(X) | (~r1(Y!5, X)))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[32, 31])).
% 0.21/0.40 tff(34,plain,
% 0.21/0.40 (~(p12(X!6) | (~r1(Y!5, X!6)))),
% 0.21/0.40 inference(and_elim,[status(thm)],[16])).
% 0.21/0.40 tff(35,plain,
% 0.21/0.40 (r1(Y!5, X!6)),
% 0.21/0.40 inference(or_elim,[status(thm)],[34])).
% 0.21/0.40 tff(36,plain,
% 0.21/0.40 (~p12(X!6)),
% 0.21/0.40 inference(or_elim,[status(thm)],[34])).
% 0.21/0.40 tff(37,plain,
% 0.21/0.40 (((~![X: $i] : (p12(X) | (~r1(Y!5, X)))) | (p12(X!6) | (~r1(Y!5, X!6)))) <=> ((~![X: $i] : (p12(X) | (~r1(Y!5, X)))) | p12(X!6) | (~r1(Y!5, X!6)))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(38,plain,
% 0.21/0.40 ((~![X: $i] : (p12(X) | (~r1(Y!5, X)))) | (p12(X!6) | (~r1(Y!5, X!6)))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(39,plain,
% 0.21/0.40 ((~![X: $i] : (p12(X) | (~r1(Y!5, X)))) | p12(X!6) | (~r1(Y!5, X!6))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.21/0.40 tff(40,plain,
% 0.21/0.40 ($false),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[39, 36, 35, 33])).
% 0.21/0.40 % SZS output end Proof
%------------------------------------------------------------------------------