%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUN073+2 : TPTP v9.0.0. Released v7.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% 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 : Sat Jun 21 05:22:37 AM UTC 2025
% Result : Theorem 0.12s 0.37s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : NUN073+2 : TPTP v9.0.0. Released v7.3.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n007.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 02:13:20 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.37 % SZS status Theorem
% 0.12/0.37 % SZS output start Proof
% 0.12/0.37 tff(r1_type, type, (
% 0.12/0.37 r1: $i > $o)).
% 0.12/0.37 tff(tptp_fun_Y4_15_type, type, (
% 0.12/0.37 tptp_fun_Y4_15: $i)).
% 0.12/0.37 tff(tptp_fun_Y3_16_type, type, (
% 0.12/0.37 tptp_fun_Y3_16: $i)).
% 0.12/0.37 tff(r2_type, type, (
% 0.12/0.37 r2: ( $i * $i ) > $o)).
% 0.12/0.37 tff(tptp_fun_Y1_14_type, type, (
% 0.12/0.37 tptp_fun_Y1_14: $i)).
% 0.12/0.37 tff(tptp_fun_Y5_17_type, type, (
% 0.12/0.37 tptp_fun_Y5_17: $i)).
% 0.12/0.37 tff(1,plain,
% 0.12/0.37 (((~((~r1(Y4!15)) | (~r2(Y4!15, Y1!14)))) & (r2(Y3!16, Y1!14) & (~((~r1(Y5!17)) | (~r2(Y5!17, Y3!16)))))) <=> ((~((~r1(Y4!15)) | (~r2(Y4!15, Y1!14)))) & r2(Y3!16, Y1!14) & (~((~r1(Y5!17)) | (~r2(Y5!17, Y3!16)))))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(2,plain,
% 0.12/0.37 ((~![Y1: $i] : (![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y1))) | ![Y3: $i] : ((~r2(Y3, Y1)) | ![Y5: $i] : ((~r1(Y5)) | (~r2(Y5, Y3)))))) <=> (~![Y1: $i] : (![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y1))) | ![Y3: $i] : ((~r2(Y3, Y1)) | ![Y5: $i] : ((~r1(Y5)) | (~r2(Y5, Y3))))))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(3,plain,
% 0.12/0.37 ((~![Y1: $i] : (![Y2: $i] : (![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y2))) | (~(Y2 = Y1))) | ![Y3: $i] : (![Y5: $i] : ((~r1(Y5)) | (~r2(Y5, Y3))) | (~r2(Y3, Y1))))) <=> (~![Y1: $i] : (![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y1))) | ![Y3: $i] : ((~r2(Y3, Y1)) | ![Y5: $i] : ((~r1(Y5)) | (~r2(Y5, Y3))))))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(4,axiom,(~![Y1: $i] : (![Y2: $i] : (![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y2))) | (~(Y2 = Y1))) | ![Y3: $i] : (![Y5: $i] : ((~r1(Y5)) | (~r2(Y5, Y3))) | (~r2(Y3, Y1))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','oneuneqtwo')).
% 0.12/0.37 tff(5,plain,
% 0.12/0.37 (~![Y1: $i] : (![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y1))) | ![Y3: $i] : ((~r2(Y3, Y1)) | ![Y5: $i] : ((~r1(Y5)) | (~r2(Y5, Y3)))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.12/0.37 tff(6,plain,
% 0.12/0.37 (~![Y1: $i] : (![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y1))) | ![Y3: $i] : ((~r2(Y3, Y1)) | ![Y5: $i] : ((~r1(Y5)) | (~r2(Y5, Y3)))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[5, 2])).
% 0.12/0.37 tff(7,plain,
% 0.12/0.37 (~![Y1: $i] : (![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y1))) | ![Y3: $i] : ((~r2(Y3, Y1)) | ![Y5: $i] : ((~r1(Y5)) | (~r2(Y5, Y3)))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.12/0.37 tff(8,plain,
% 0.12/0.37 (~![Y1: $i] : (![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y1))) | ![Y3: $i] : ((~r2(Y3, Y1)) | ![Y5: $i] : ((~r1(Y5)) | (~r2(Y5, Y3)))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[7, 2])).
% 0.12/0.37 tff(9,plain,
% 0.12/0.37 ((~((~r1(Y4!15)) | (~r2(Y4!15, Y1!14)))) & r2(Y3!16, Y1!14) & (~((~r1(Y5!17)) | (~r2(Y5!17, Y3!16))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[8, 1])).
% 0.12/0.37 tff(10,plain,
% 0.12/0.37 (r2(Y3!16, Y1!14)),
% 0.12/0.37 inference(and_elim,[status(thm)],[9])).
% 0.12/0.37 tff(11,plain,
% 0.12/0.37 (~((~r1(Y4!15)) | (~r2(Y4!15, Y1!14)))),
% 0.12/0.37 inference(and_elim,[status(thm)],[9])).
% 0.12/0.37 tff(12,plain,
% 0.12/0.37 (r2(Y4!15, Y1!14)),
% 0.12/0.37 inference(or_elim,[status(thm)],[11])).
% 0.12/0.37 tff(13,plain,
% 0.12/0.37 (^[X3: $i, X10: $i, Y12: $i] : trans(monotonicity(rewrite(((~r2(X3, Y12)) | (~r2(X10, Y12))) <=> ((~r2(X3, Y12)) | (~r2(X10, Y12)))), (((X3 = X10) | ((~r2(X3, Y12)) | (~r2(X10, Y12)))) <=> ((X3 = X10) | ((~r2(X3, Y12)) | (~r2(X10, Y12)))))), rewrite(((X3 = X10) | ((~r2(X3, Y12)) | (~r2(X10, Y12)))) <=> ((~r2(X3, Y12)) | (~r2(X10, Y12)) | (X3 = X10))), (((X3 = X10) | ((~r2(X3, Y12)) | (~r2(X10, Y12)))) <=> ((~r2(X3, Y12)) | (~r2(X10, Y12)) | (X3 = X10))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(14,plain,
% 0.12/0.37 (![X3: $i, X10: $i, Y12: $i] : ((X3 = X10) | ((~r2(X3, Y12)) | (~r2(X10, Y12)))) <=> ![X3: $i, X10: $i, Y12: $i] : ((~r2(X3, Y12)) | (~r2(X10, Y12)) | (X3 = X10))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[13])).
% 0.12/0.37 tff(15,plain,
% 0.12/0.37 (^[X3: $i, X10: $i, Y12: $i] : refl(((X3 = X10) | ((~r2(X3, Y12)) | (~r2(X10, Y12)))) <=> ((X3 = X10) | ((~r2(X3, Y12)) | (~r2(X10, Y12)))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(16,plain,
% 0.12/0.37 (![X3: $i, X10: $i, Y12: $i] : ((X3 = X10) | ((~r2(X3, Y12)) | (~r2(X10, Y12)))) <=> ![X3: $i, X10: $i, Y12: $i] : ((X3 = X10) | ((~r2(X3, Y12)) | (~r2(X10, Y12))))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[15])).
% 0.12/0.37 tff(17,plain,
% 0.12/0.37 (![X3: $i, X10: $i] : ![Y12: $i] : ((X3 = X10) | ((~r2(X3, Y12)) | (~r2(X10, Y12)))) <=> ![X3: $i, X10: $i, Y12: $i] : ((X3 = X10) | ((~r2(X3, Y12)) | (~r2(X10, Y12))))),
% 0.12/0.37 inference(pull_quant,[status(thm)],[])).
% 0.12/0.37 tff(18,plain,
% 0.12/0.37 (^[X3: $i, X10: $i] : pull_quant(((X3 = X10) | ![Y12: $i] : ((~r2(X3, Y12)) | (~r2(X10, Y12)))) <=> ![Y12: $i] : ((X3 = X10) | ((~r2(X3, Y12)) | (~r2(X10, Y12)))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(19,plain,
% 0.12/0.37 (![X3: $i, X10: $i] : ((X3 = X10) | ![Y12: $i] : ((~r2(X3, Y12)) | (~r2(X10, Y12)))) <=> ![X3: $i, X10: $i] : ![Y12: $i] : ((X3 = X10) | ((~r2(X3, Y12)) | (~r2(X10, Y12))))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[18])).
% 0.12/0.37 tff(20,plain,
% 0.12/0.37 (![X3: $i, X10: $i] : ((X3 = X10) | ![Y12: $i] : ((~r2(X3, Y12)) | (~r2(X10, Y12)))) <=> ![X3: $i, X10: $i, Y12: $i] : ((X3 = X10) | ((~r2(X3, Y12)) | (~r2(X10, Y12))))),
% 0.12/0.37 inference(transitivity,[status(thm)],[19, 17])).
% 0.12/0.37 tff(21,plain,
% 0.12/0.37 (![X3: $i, X10: $i] : ((X3 = X10) | ![Y12: $i] : ((~r2(X3, Y12)) | (~r2(X10, Y12)))) <=> ![X3: $i, X10: $i, Y12: $i] : ((X3 = X10) | ((~r2(X3, Y12)) | (~r2(X10, Y12))))),
% 0.12/0.37 inference(transitivity,[status(thm)],[20, 16])).
% 0.12/0.37 tff(22,plain,
% 0.12/0.37 (^[X3: $i, X10: $i] : rewrite(((X3 = X10) | ![Y12: $i] : ((~r2(X3, Y12)) | (~r2(X10, Y12)))) <=> ((X3 = X10) | ![Y12: $i] : ((~r2(X3, Y12)) | (~r2(X10, Y12)))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(23,plain,
% 0.12/0.37 (![X3: $i, X10: $i] : ((X3 = X10) | ![Y12: $i] : ((~r2(X3, Y12)) | (~r2(X10, Y12)))) <=> ![X3: $i, X10: $i] : ((X3 = X10) | ![Y12: $i] : ((~r2(X3, Y12)) | (~r2(X10, Y12))))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[22])).
% 0.12/0.37 tff(24,plain,
% 0.12/0.37 (![X3: $i, X10: $i] : ((X3 = X10) | ![Y12: $i] : ((~r2(X3, Y12)) | (~r2(X10, Y12)))) <=> ![X3: $i, X10: $i, Y12: $i] : ((X3 = X10) | ((~r2(X3, Y12)) | (~r2(X10, Y12))))),
% 0.12/0.37 inference(transitivity,[status(thm)],[23, 21])).
% 0.12/0.37 tff(25,plain,
% 0.12/0.37 (![X3: $i, X10: $i] : ((X3 = X10) | ![Y12: $i] : ((~r2(X3, Y12)) | (~r2(X10, Y12)))) <=> ![X3: $i, X10: $i] : ((X3 = X10) | ![Y12: $i] : ((~r2(X3, Y12)) | (~r2(X10, Y12))))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(26,plain,
% 0.12/0.37 (^[X3: $i, X10: $i] : trans(monotonicity(quant_intro(proof_bind(^[Y12: $i] : trans(monotonicity(trans(quant_intro(proof_bind(^[Y13: $i] : rewrite(((~r2(X3, Y13)) | (~(Y13 = Y12))) <=> ((~(Y13 = Y12)) | (~r2(X3, Y13))))), (![Y13: $i] : ((~r2(X3, Y13)) | (~(Y13 = Y12))) <=> ![Y13: $i] : ((~(Y13 = Y12)) | (~r2(X3, Y13))))), trans(der(![Y13: $i] : ((~(Y13 = Y12)) | (~r2(X3, Y13))) <=> ![Y13: $i] : (~r2(X3, Y12))), elim_unused(![Y13: $i] : (~r2(X3, Y12)) <=> (~r2(X3, Y12))), (![Y13: $i] : ((~(Y13 = Y12)) | (~r2(X3, Y13))) <=> (~r2(X3, Y12)))), (![Y13: $i] : ((~r2(X3, Y13)) | (~(Y13 = Y12))) <=> (~r2(X3, Y12)))), ((![Y13: $i] : ((~r2(X3, Y13)) | (~(Y13 = Y12))) | (~r2(X10, Y12))) <=> ((~r2(X3, Y12)) | (~r2(X10, Y12))))), rewrite(((~r2(X3, Y12)) | (~r2(X10, Y12))) <=> ((~r2(X3, Y12)) | (~r2(X10, Y12)))), ((![Y13: $i] : ((~r2(X3, Y13)) | (~(Y13 = Y12))) | (~r2(X10, Y12))) <=> ((~r2(X3, Y12)) | (~r2(X10, Y12)))))), (![Y12: $i] : (![Y13: $i] : ((~r2(X3, Y13)) | (~(Y13 = Y12))) | (~r2(X10, Y12))) <=> ![Y12: $i] : ((~r2(X3, Y12)) | (~r2(X10, Y12))))), ((![Y12: $i] : (![Y13: $i] : ((~r2(X3, Y13)) | (~(Y13 = Y12))) | (~r2(X10, Y12))) | (X3 = X10)) <=> (![Y12: $i] : ((~r2(X3, Y12)) | (~r2(X10, Y12))) | (X3 = X10)))), rewrite((![Y12: $i] : ((~r2(X3, Y12)) | (~r2(X10, Y12))) | (X3 = X10)) <=> ((X3 = X10) | ![Y12: $i] : ((~r2(X3, Y12)) | (~r2(X10, Y12))))), ((![Y12: $i] : (![Y13: $i] : ((~r2(X3, Y13)) | (~(Y13 = Y12))) | (~r2(X10, Y12))) | (X3 = X10)) <=> ((X3 = X10) | ![Y12: $i] : ((~r2(X3, Y12)) | (~r2(X10, Y12))))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(27,plain,
% 0.12/0.37 (![X3: $i, X10: $i] : (![Y12: $i] : (![Y13: $i] : ((~r2(X3, Y13)) | (~(Y13 = Y12))) | (~r2(X10, Y12))) | (X3 = X10)) <=> ![X3: $i, X10: $i] : ((X3 = X10) | ![Y12: $i] : ((~r2(X3, Y12)) | (~r2(X10, Y12))))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[26])).
% 0.12/0.37 tff(28,axiom,(![X3: $i, X10: $i] : (![Y12: $i] : (![Y13: $i] : ((~r2(X3, Y13)) | (~(Y13 = Y12))) | (~r2(X10, Y12))) | (X3 = X10))), file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax','axiom_3a')).
% 0.12/0.37 tff(29,plain,
% 0.12/0.37 (![X3: $i, X10: $i] : ((X3 = X10) | ![Y12: $i] : ((~r2(X3, Y12)) | (~r2(X10, Y12))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.12/0.37 tff(30,plain,
% 0.12/0.37 (![X3: $i, X10: $i] : ((X3 = X10) | ![Y12: $i] : ((~r2(X3, Y12)) | (~r2(X10, Y12))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.12/0.37 tff(31,plain,(
% 0.12/0.37 ![X3: $i, X10: $i] : ((X3 = X10) | ![Y12: $i] : ((~r2(X3, Y12)) | (~r2(X10, Y12))))),
% 0.12/0.37 inference(skolemize,[status(sab)],[30])).
% 0.12/0.37 tff(32,plain,
% 0.12/0.37 (![X3: $i, X10: $i, Y12: $i] : ((X3 = X10) | ((~r2(X3, Y12)) | (~r2(X10, Y12))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[31, 24])).
% 0.12/0.37 tff(33,plain,
% 0.12/0.37 (![X3: $i, X10: $i, Y12: $i] : ((~r2(X3, Y12)) | (~r2(X10, Y12)) | (X3 = X10))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[32, 14])).
% 0.12/0.37 tff(34,plain,
% 0.12/0.37 (((~![X3: $i, X10: $i, Y12: $i] : ((~r2(X3, Y12)) | (~r2(X10, Y12)) | (X3 = X10))) | ((~r2(Y4!15, Y1!14)) | (~r2(Y3!16, Y1!14)) | (Y4!15 = Y3!16))) <=> ((~![X3: $i, X10: $i, Y12: $i] : ((~r2(X3, Y12)) | (~r2(X10, Y12)) | (X3 = X10))) | (~r2(Y4!15, Y1!14)) | (~r2(Y3!16, Y1!14)) | (Y4!15 = Y3!16))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(35,plain,
% 0.12/0.37 ((~![X3: $i, X10: $i, Y12: $i] : ((~r2(X3, Y12)) | (~r2(X10, Y12)) | (X3 = X10))) | ((~r2(Y4!15, Y1!14)) | (~r2(Y3!16, Y1!14)) | (Y4!15 = Y3!16))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(36,plain,
% 0.12/0.37 ((~![X3: $i, X10: $i, Y12: $i] : ((~r2(X3, Y12)) | (~r2(X10, Y12)) | (X3 = X10))) | (~r2(Y4!15, Y1!14)) | (~r2(Y3!16, Y1!14)) | (Y4!15 = Y3!16)),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.12/0.37 tff(37,plain,
% 0.12/0.37 (Y4!15 = Y3!16),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[36, 33, 12, 10])).
% 0.12/0.37 tff(38,plain,
% 0.12/0.37 (r1(Y4!15) <=> r1(Y3!16)),
% 0.12/0.37 inference(monotonicity,[status(thm)],[37])).
% 0.12/0.37 tff(39,plain,
% 0.12/0.37 (r1(Y3!16) <=> r1(Y4!15)),
% 0.12/0.37 inference(symmetry,[status(thm)],[38])).
% 0.12/0.37 tff(40,plain,
% 0.12/0.37 ((~r1(Y3!16)) <=> (~r1(Y4!15))),
% 0.12/0.37 inference(monotonicity,[status(thm)],[39])).
% 0.12/0.37 tff(41,plain,
% 0.12/0.37 (~((~r1(Y5!17)) | (~r2(Y5!17, Y3!16)))),
% 0.12/0.37 inference(and_elim,[status(thm)],[9])).
% 0.12/0.37 tff(42,plain,
% 0.12/0.37 (r2(Y5!17, Y3!16)),
% 0.12/0.37 inference(or_elim,[status(thm)],[41])).
% 0.12/0.37 tff(43,plain,
% 0.12/0.37 (^[X7: $i, Y10: $i] : refl(((~r1(Y10)) | (~r2(X7, Y10))) <=> ((~r1(Y10)) | (~r2(X7, Y10))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(44,plain,
% 0.12/0.37 (![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10))) <=> ![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10)))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[43])).
% 0.12/0.37 tff(45,plain,
% 0.12/0.37 (![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10))) <=> ![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10)))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(46,plain,
% 0.12/0.37 (^[X7: $i, Y10: $i] : rewrite((![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10))) | (~r2(X7, Y10))) <=> ((~r1(Y10)) | (~r2(X7, Y10))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(47,plain,
% 0.12/0.37 (![X7: $i, Y10: $i] : (![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10))) | (~r2(X7, Y10))) <=> ![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10)))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[46])).
% 0.12/0.37 tff(48,axiom,(![X7: $i, Y10: $i] : (![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10))) | (~r2(X7, Y10)))), file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax','axiom_7a')).
% 0.12/0.37 tff(49,plain,
% 0.12/0.37 (![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.12/0.37 tff(50,plain,
% 0.12/0.37 (![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[49, 45])).
% 0.12/0.37 tff(51,plain,(
% 0.12/0.37 ![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10)))),
% 0.12/0.37 inference(skolemize,[status(sab)],[50])).
% 0.12/0.37 tff(52,plain,
% 0.12/0.37 (![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[51, 44])).
% 0.12/0.37 tff(53,plain,
% 0.12/0.37 (((~![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10)))) | ((~r1(Y3!16)) | (~r2(Y5!17, Y3!16)))) <=> ((~![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10)))) | (~r1(Y3!16)) | (~r2(Y5!17, Y3!16)))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(54,plain,
% 0.12/0.37 ((~![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10)))) | ((~r1(Y3!16)) | (~r2(Y5!17, Y3!16)))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(55,plain,
% 0.12/0.37 ((~![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10)))) | (~r1(Y3!16)) | (~r2(Y5!17, Y3!16))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.12/0.38 tff(56,plain,
% 0.12/0.38 (~r1(Y3!16)),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[55, 52, 42])).
% 0.12/0.38 tff(57,plain,
% 0.12/0.38 (~r1(Y4!15)),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[56, 40])).
% 0.12/0.38 tff(58,plain,
% 0.12/0.38 (r1(Y4!15)),
% 0.12/0.38 inference(or_elim,[status(thm)],[11])).
% 0.12/0.38 tff(59,plain,
% 0.12/0.38 ($false),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[58, 57])).
% 0.12/0.38 % SZS output end Proof
% 0.12/0.38 % E exiting
%------------------------------------------------------------------------------