TSTP Solution File: SYN690-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN690-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n023.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 : Thu Sep 29 23:56:57 EDT 2022
% Result : Unsatisfiable 0.21s 0.47s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYN690-1 : TPTP v8.1.0. Released v2.5.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n023.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon Sep 5 06:55:32 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 0.21/0.47 % SZS status Unsatisfiable
% 0.21/0.47 % SZS output start Proof
% 0.21/0.47 tff(p2_type, type, (
% 0.21/0.47 p2: ( $i * $i ) > $o)).
% 0.21/0.47 tff(c38_type, type, (
% 0.21/0.47 c38: $i)).
% 0.21/0.47 tff(c40_type, type, (
% 0.21/0.47 c40: $i)).
% 0.21/0.47 tff(p4_type, type, (
% 0.21/0.47 p4: ( $i * $i ) > $o)).
% 0.21/0.47 tff(f5_type, type, (
% 0.21/0.47 f5: ( $i * $i ) > $i)).
% 0.21/0.47 tff(f12_type, type, (
% 0.21/0.47 f12: ( $i * $i ) > $i)).
% 0.21/0.47 tff(f30_type, type, (
% 0.21/0.47 f30: ( $i * $i ) > $i)).
% 0.21/0.47 tff(c39_type, type, (
% 0.21/0.47 c39: $i)).
% 0.21/0.47 tff(f32_type, type, (
% 0.21/0.47 f32: ( $i * $i ) > $i)).
% 0.21/0.47 tff(c37_type, type, (
% 0.21/0.47 c37: $i)).
% 0.21/0.47 tff(c42_type, type, (
% 0.21/0.47 c42: $i)).
% 0.21/0.47 tff(f14_type, type, (
% 0.21/0.47 f14: ( $i * $i ) > $i)).
% 0.21/0.47 tff(f26_type, type, (
% 0.21/0.47 f26: ( $i * $i ) > $i)).
% 0.21/0.47 tff(f28_type, type, (
% 0.21/0.47 f28: ( $i * $i ) > $i)).
% 0.21/0.47 tff(c44_type, type, (
% 0.21/0.47 c44: $i)).
% 0.21/0.47 tff(f16_type, type, (
% 0.21/0.47 f16: ( $i * $i ) > $i)).
% 0.21/0.47 tff(c43_type, type, (
% 0.21/0.47 c43: $i)).
% 0.21/0.47 tff(c41_type, type, (
% 0.21/0.47 c41: $i)).
% 0.21/0.47 tff(f7_type, type, (
% 0.21/0.47 f7: ( $i * $i ) > $i)).
% 0.21/0.47 tff(f18_type, type, (
% 0.21/0.47 f18: ( $i * $i ) > $i)).
% 0.21/0.47 tff(f20_type, type, (
% 0.21/0.47 f20: ( $i * $i ) > $i)).
% 0.21/0.47 tff(f22_type, type, (
% 0.21/0.47 f22: ( $i * $i ) > $i)).
% 0.21/0.47 tff(f24_type, type, (
% 0.21/0.47 f24: ( $i * $i ) > $i)).
% 0.21/0.47 tff(c45_type, type, (
% 0.21/0.47 c45: $i)).
% 0.21/0.47 tff(p34_type, type, (
% 0.21/0.47 p34: ( $i * $i ) > $o)).
% 0.21/0.47 tff(c36_type, type, (
% 0.21/0.47 c36: $i)).
% 0.21/0.47 tff(p35_type, type, (
% 0.21/0.47 p35: ( $i * $i ) > $o)).
% 0.21/0.47 tff(f10_type, type, (
% 0.21/0.47 f10: ( $i * $i ) > $i)).
% 0.21/0.47 tff(1,assumption,(~p2(c40, c38)), introduced(assumption)).
% 0.21/0.47 tff(2,assumption,(~p4(f5(c38, f18(f20(f22(f24(c45, c37), c39), c40), c38)), f5(f7(c39, c38), f18(f20(f22(f24(c45, c37), c39), c40), c38)))), introduced(assumption)).
% 0.21/0.47 tff(3,plain,
% 0.21/0.47 (^[X113: $i] : refl(p4(f5(c38, X113), f5(f7(c39, c38), X113)) <=> p4(f5(c38, X113), f5(f7(c39, c38), X113)))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(4,plain,
% 0.21/0.47 (![X113: $i] : p4(f5(c38, X113), f5(f7(c39, c38), X113)) <=> ![X113: $i] : p4(f5(c38, X113), f5(f7(c39, c38), X113))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[3])).
% 0.21/0.47 tff(5,plain,
% 0.21/0.47 (![X113: $i] : p4(f5(c38, X113), f5(f7(c39, c38), X113)) <=> ![X113: $i] : p4(f5(c38, X113), f5(f7(c39, c38), X113))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(6,axiom,(![X113: $i] : p4(f5(c38, X113), f5(f7(c39, c38), X113))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p4_22')).
% 0.21/0.47 tff(7,plain,
% 0.21/0.47 (![X113: $i] : p4(f5(c38, X113), f5(f7(c39, c38), X113))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.21/0.47 tff(8,plain,(
% 0.21/0.47 ![X113: $i] : p4(f5(c38, X113), f5(f7(c39, c38), X113))),
% 0.21/0.47 inference(skolemize,[status(sab)],[7])).
% 0.21/0.47 tff(9,plain,
% 0.21/0.47 (![X113: $i] : p4(f5(c38, X113), f5(f7(c39, c38), X113))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.21/0.47 tff(10,plain,
% 0.21/0.47 ((~![X113: $i] : p4(f5(c38, X113), f5(f7(c39, c38), X113))) | p4(f5(c38, f18(f20(f22(f24(c45, c37), c39), c40), c38)), f5(f7(c39, c38), f18(f20(f22(f24(c45, c37), c39), c40), c38)))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(11,plain,
% 0.21/0.47 ($false),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[10, 9, 2])).
% 0.21/0.47 tff(12,plain,(p4(f5(c38, f18(f20(f22(f24(c45, c37), c39), c40), c38)), f5(f7(c39, c38), f18(f20(f22(f24(c45, c37), c39), c40), c38)))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.47 tff(13,assumption,(~p4(f5(c40, f18(f20(f22(f24(c45, c37), c39), c40), c38)), f5(f7(c39, c40), f18(f20(f22(f24(c45, c37), c39), c40), c38)))), introduced(assumption)).
% 0.21/0.47 tff(14,plain,
% 0.21/0.47 (^[X114: $i] : refl(p4(f5(c40, X114), f5(f7(c39, c40), X114)) <=> p4(f5(c40, X114), f5(f7(c39, c40), X114)))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(15,plain,
% 0.21/0.47 (![X114: $i] : p4(f5(c40, X114), f5(f7(c39, c40), X114)) <=> ![X114: $i] : p4(f5(c40, X114), f5(f7(c39, c40), X114))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[14])).
% 0.21/0.47 tff(16,plain,
% 0.21/0.47 (![X114: $i] : p4(f5(c40, X114), f5(f7(c39, c40), X114)) <=> ![X114: $i] : p4(f5(c40, X114), f5(f7(c39, c40), X114))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(17,axiom,(![X114: $i] : p4(f5(c40, X114), f5(f7(c39, c40), X114))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p4_21')).
% 0.21/0.47 tff(18,plain,
% 0.21/0.47 (![X114: $i] : p4(f5(c40, X114), f5(f7(c39, c40), X114))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.21/0.47 tff(19,plain,(
% 0.21/0.47 ![X114: $i] : p4(f5(c40, X114), f5(f7(c39, c40), X114))),
% 0.21/0.47 inference(skolemize,[status(sab)],[18])).
% 0.21/0.47 tff(20,plain,
% 0.21/0.47 (![X114: $i] : p4(f5(c40, X114), f5(f7(c39, c40), X114))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.21/0.47 tff(21,plain,
% 0.21/0.47 ((~![X114: $i] : p4(f5(c40, X114), f5(f7(c39, c40), X114))) | p4(f5(c40, f18(f20(f22(f24(c45, c37), c39), c40), c38)), f5(f7(c39, c40), f18(f20(f22(f24(c45, c37), c39), c40), c38)))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(22,plain,
% 0.21/0.47 ($false),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[21, 20, 13])).
% 0.21/0.47 tff(23,plain,(p4(f5(c40, f18(f20(f22(f24(c45, c37), c39), c40), c38)), f5(f7(c39, c40), f18(f20(f22(f24(c45, c37), c39), c40), c38)))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.47 tff(24,plain,
% 0.21/0.47 (^[X31: $i, X32: $i, X34: $i, X33: $i] : refl(((~p34(c36, X33)) | (~p4(f5(f7(X34, f26(f28(c43, X33), X34)), f30(f32(c42, X33), X34)), f5(f7(X34, f26(f28(c44, X33), X34)), f30(f32(c42, X33), X34)))) | (~p4(f5(X32, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X32), f18(f20(f22(f24(c45, X33), X34), X31), X32)))) | (~p4(f5(X31, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X31), f18(f20(f22(f24(c45, X33), X34), X31), X32)))) | p2(X31, X32)) <=> ((~p34(c36, X33)) | (~p4(f5(f7(X34, f26(f28(c43, X33), X34)), f30(f32(c42, X33), X34)), f5(f7(X34, f26(f28(c44, X33), X34)), f30(f32(c42, X33), X34)))) | (~p4(f5(X32, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X32), f18(f20(f22(f24(c45, X33), X34), X31), X32)))) | (~p4(f5(X31, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X31), f18(f20(f22(f24(c45, X33), X34), X31), X32)))) | p2(X31, X32)))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(25,plain,
% 0.21/0.47 (![X31: $i, X32: $i, X34: $i, X33: $i] : ((~p34(c36, X33)) | (~p4(f5(f7(X34, f26(f28(c43, X33), X34)), f30(f32(c42, X33), X34)), f5(f7(X34, f26(f28(c44, X33), X34)), f30(f32(c42, X33), X34)))) | (~p4(f5(X32, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X32), f18(f20(f22(f24(c45, X33), X34), X31), X32)))) | (~p4(f5(X31, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X31), f18(f20(f22(f24(c45, X33), X34), X31), X32)))) | p2(X31, X32)) <=> ![X31: $i, X32: $i, X34: $i, X33: $i] : ((~p34(c36, X33)) | (~p4(f5(f7(X34, f26(f28(c43, X33), X34)), f30(f32(c42, X33), X34)), f5(f7(X34, f26(f28(c44, X33), X34)), f30(f32(c42, X33), X34)))) | (~p4(f5(X32, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X32), f18(f20(f22(f24(c45, X33), X34), X31), X32)))) | (~p4(f5(X31, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X31), f18(f20(f22(f24(c45, X33), X34), X31), X32)))) | p2(X31, X32))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[24])).
% 0.21/0.47 tff(26,plain,
% 0.21/0.47 (![X31: $i, X32: $i, X34: $i, X33: $i] : ((~p34(c36, X33)) | (~p4(f5(f7(X34, f26(f28(c43, X33), X34)), f30(f32(c42, X33), X34)), f5(f7(X34, f26(f28(c44, X33), X34)), f30(f32(c42, X33), X34)))) | (~p4(f5(X32, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X32), f18(f20(f22(f24(c45, X33), X34), X31), X32)))) | (~p4(f5(X31, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X31), f18(f20(f22(f24(c45, X33), X34), X31), X32)))) | p2(X31, X32)) <=> ![X31: $i, X32: $i, X34: $i, X33: $i] : ((~p34(c36, X33)) | (~p4(f5(f7(X34, f26(f28(c43, X33), X34)), f30(f32(c42, X33), X34)), f5(f7(X34, f26(f28(c44, X33), X34)), f30(f32(c42, X33), X34)))) | (~p4(f5(X32, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X32), f18(f20(f22(f24(c45, X33), X34), X31), X32)))) | (~p4(f5(X31, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X31), f18(f20(f22(f24(c45, X33), X34), X31), X32)))) | p2(X31, X32))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(27,plain,
% 0.21/0.47 (^[X31: $i, X32: $i, X34: $i, X33: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((p2(X31, X32) | (~p34(c36, X33))) <=> ((~p34(c36, X33)) | p2(X31, X32))), (((p2(X31, X32) | (~p34(c36, X33))) | (~p4(f5(X31, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X31), f18(f20(f22(f24(c45, X33), X34), X31), X32))))) <=> (((~p34(c36, X33)) | p2(X31, X32)) | (~p4(f5(X31, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X31), f18(f20(f22(f24(c45, X33), X34), X31), X32))))))), rewrite((((~p34(c36, X33)) | p2(X31, X32)) | (~p4(f5(X31, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X31), f18(f20(f22(f24(c45, X33), X34), X31), X32))))) <=> ((~p34(c36, X33)) | (~p4(f5(X31, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X31), f18(f20(f22(f24(c45, X33), X34), X31), X32)))) | p2(X31, X32))), (((p2(X31, X32) | (~p34(c36, X33))) | (~p4(f5(X31, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X31), f18(f20(f22(f24(c45, X33), X34), X31), X32))))) <=> ((~p34(c36, X33)) | (~p4(f5(X31, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X31), f18(f20(f22(f24(c45, X33), X34), X31), X32)))) | p2(X31, X32)))), ((((p2(X31, X32) | (~p34(c36, X33))) | (~p4(f5(X31, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X31), f18(f20(f22(f24(c45, X33), X34), X31), X32))))) | (~p4(f5(X32, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X32), f18(f20(f22(f24(c45, X33), X34), X31), X32))))) <=> (((~p34(c36, X33)) | (~p4(f5(X31, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X31), f18(f20(f22(f24(c45, X33), X34), X31), X32)))) | p2(X31, X32)) | (~p4(f5(X32, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X32), f18(f20(f22(f24(c45, X33), X34), X31), X32))))))), rewrite((((~p34(c36, X33)) | (~p4(f5(X31, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X31), f18(f20(f22(f24(c45, X33), X34), X31), X32)))) | p2(X31, X32)) | (~p4(f5(X32, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X32), f18(f20(f22(f24(c45, X33), X34), X31), X32))))) <=> ((~p34(c36, X33)) | (~p4(f5(X32, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X32), f18(f20(f22(f24(c45, X33), X34), X31), X32)))) | (~p4(f5(X31, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X31), f18(f20(f22(f24(c45, X33), X34), X31), X32)))) | p2(X31, X32))), ((((p2(X31, X32) | (~p34(c36, X33))) | (~p4(f5(X31, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X31), f18(f20(f22(f24(c45, X33), X34), X31), X32))))) | (~p4(f5(X32, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X32), f18(f20(f22(f24(c45, X33), X34), X31), X32))))) <=> ((~p34(c36, X33)) | (~p4(f5(X32, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X32), f18(f20(f22(f24(c45, X33), X34), X31), X32)))) | (~p4(f5(X31, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X31), f18(f20(f22(f24(c45, X33), X34), X31), X32)))) | p2(X31, X32)))), (((((p2(X31, X32) | (~p34(c36, X33))) | (~p4(f5(X31, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X31), f18(f20(f22(f24(c45, X33), X34), X31), X32))))) | (~p4(f5(X32, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X32), f18(f20(f22(f24(c45, X33), X34), X31), X32))))) | (~p4(f5(f7(X34, f26(f28(c43, X33), X34)), f30(f32(c42, X33), X34)), f5(f7(X34, f26(f28(c44, X33), X34)), f30(f32(c42, X33), X34))))) <=> (((~p34(c36, X33)) | (~p4(f5(X32, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X32), f18(f20(f22(f24(c45, X33), X34), X31), X32)))) | (~p4(f5(X31, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X31), f18(f20(f22(f24(c45, X33), X34), X31), X32)))) | p2(X31, X32)) | (~p4(f5(f7(X34, f26(f28(c43, X33), X34)), f30(f32(c42, X33), X34)), f5(f7(X34, f26(f28(c44, X33), X34)), f30(f32(c42, X33), X34))))))), rewrite((((~p34(c36, X33)) | (~p4(f5(X32, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X32), f18(f20(f22(f24(c45, X33), X34), X31), X32)))) | (~p4(f5(X31, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X31), f18(f20(f22(f24(c45, X33), X34), X31), X32)))) | p2(X31, X32)) | (~p4(f5(f7(X34, f26(f28(c43, X33), X34)), f30(f32(c42, X33), X34)), f5(f7(X34, f26(f28(c44, X33), X34)), f30(f32(c42, X33), X34))))) <=> ((~p34(c36, X33)) | (~p4(f5(f7(X34, f26(f28(c43, X33), X34)), f30(f32(c42, X33), X34)), f5(f7(X34, f26(f28(c44, X33), X34)), f30(f32(c42, X33), X34)))) | (~p4(f5(X32, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X32), f18(f20(f22(f24(c45, X33), X34), X31), X32)))) | (~p4(f5(X31, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X31), f18(f20(f22(f24(c45, X33), X34), X31), X32)))) | p2(X31, X32))), (((((p2(X31, X32) | (~p34(c36, X33))) | (~p4(f5(X31, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X31), f18(f20(f22(f24(c45, X33), X34), X31), X32))))) | (~p4(f5(X32, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X32), f18(f20(f22(f24(c45, X33), X34), X31), X32))))) | (~p4(f5(f7(X34, f26(f28(c43, X33), X34)), f30(f32(c42, X33), X34)), f5(f7(X34, f26(f28(c44, X33), X34)), f30(f32(c42, X33), X34))))) <=> ((~p34(c36, X33)) | (~p4(f5(f7(X34, f26(f28(c43, X33), X34)), f30(f32(c42, X33), X34)), f5(f7(X34, f26(f28(c44, X33), X34)), f30(f32(c42, X33), X34)))) | (~p4(f5(X32, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X32), f18(f20(f22(f24(c45, X33), X34), X31), X32)))) | (~p4(f5(X31, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X31), f18(f20(f22(f24(c45, X33), X34), X31), X32)))) | p2(X31, X32))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(28,plain,
% 0.21/0.48 (![X31: $i, X32: $i, X34: $i, X33: $i] : ((((p2(X31, X32) | (~p34(c36, X33))) | (~p4(f5(X31, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X31), f18(f20(f22(f24(c45, X33), X34), X31), X32))))) | (~p4(f5(X32, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X32), f18(f20(f22(f24(c45, X33), X34), X31), X32))))) | (~p4(f5(f7(X34, f26(f28(c43, X33), X34)), f30(f32(c42, X33), X34)), f5(f7(X34, f26(f28(c44, X33), X34)), f30(f32(c42, X33), X34))))) <=> ![X31: $i, X32: $i, X34: $i, X33: $i] : ((~p34(c36, X33)) | (~p4(f5(f7(X34, f26(f28(c43, X33), X34)), f30(f32(c42, X33), X34)), f5(f7(X34, f26(f28(c44, X33), X34)), f30(f32(c42, X33), X34)))) | (~p4(f5(X32, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X32), f18(f20(f22(f24(c45, X33), X34), X31), X32)))) | (~p4(f5(X31, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X31), f18(f20(f22(f24(c45, X33), X34), X31), X32)))) | p2(X31, X32))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[27])).
% 0.21/0.48 tff(29,axiom,(![X31: $i, X32: $i, X34: $i, X33: $i] : ((((p2(X31, X32) | (~p34(c36, X33))) | (~p4(f5(X31, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X31), f18(f20(f22(f24(c45, X33), X34), X31), X32))))) | (~p4(f5(X32, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X32), f18(f20(f22(f24(c45, X33), X34), X31), X32))))) | (~p4(f5(f7(X34, f26(f28(c43, X33), X34)), f30(f32(c42, X33), X34)), f5(f7(X34, f26(f28(c44, X33), X34)), f30(f32(c42, X33), X34)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_62')).
% 0.21/0.48 tff(30,plain,
% 0.21/0.48 (![X31: $i, X32: $i, X34: $i, X33: $i] : ((~p34(c36, X33)) | (~p4(f5(f7(X34, f26(f28(c43, X33), X34)), f30(f32(c42, X33), X34)), f5(f7(X34, f26(f28(c44, X33), X34)), f30(f32(c42, X33), X34)))) | (~p4(f5(X32, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X32), f18(f20(f22(f24(c45, X33), X34), X31), X32)))) | (~p4(f5(X31, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X31), f18(f20(f22(f24(c45, X33), X34), X31), X32)))) | p2(X31, X32))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.21/0.48 tff(31,plain,
% 0.21/0.48 (![X31: $i, X32: $i, X34: $i, X33: $i] : ((~p34(c36, X33)) | (~p4(f5(f7(X34, f26(f28(c43, X33), X34)), f30(f32(c42, X33), X34)), f5(f7(X34, f26(f28(c44, X33), X34)), f30(f32(c42, X33), X34)))) | (~p4(f5(X32, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X32), f18(f20(f22(f24(c45, X33), X34), X31), X32)))) | (~p4(f5(X31, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X31), f18(f20(f22(f24(c45, X33), X34), X31), X32)))) | p2(X31, X32))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.21/0.48 tff(32,plain,(
% 0.21/0.48 ![X31: $i, X32: $i, X34: $i, X33: $i] : ((~p34(c36, X33)) | (~p4(f5(f7(X34, f26(f28(c43, X33), X34)), f30(f32(c42, X33), X34)), f5(f7(X34, f26(f28(c44, X33), X34)), f30(f32(c42, X33), X34)))) | (~p4(f5(X32, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X32), f18(f20(f22(f24(c45, X33), X34), X31), X32)))) | (~p4(f5(X31, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X31), f18(f20(f22(f24(c45, X33), X34), X31), X32)))) | p2(X31, X32))),
% 0.21/0.48 inference(skolemize,[status(sab)],[31])).
% 0.21/0.48 tff(33,plain,
% 0.21/0.48 (![X31: $i, X32: $i, X34: $i, X33: $i] : ((~p34(c36, X33)) | (~p4(f5(f7(X34, f26(f28(c43, X33), X34)), f30(f32(c42, X33), X34)), f5(f7(X34, f26(f28(c44, X33), X34)), f30(f32(c42, X33), X34)))) | (~p4(f5(X32, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X32), f18(f20(f22(f24(c45, X33), X34), X31), X32)))) | (~p4(f5(X31, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X31), f18(f20(f22(f24(c45, X33), X34), X31), X32)))) | p2(X31, X32))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[32, 25])).
% 0.21/0.48 tff(34,plain,
% 0.21/0.48 (p34(c36, c37) <=> p34(c36, c37)),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(35,axiom,(p34(c36, c37)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p34_19')).
% 0.21/0.48 tff(36,plain,
% 0.21/0.48 (p34(c36, c37)),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.21/0.48 tff(37,plain,
% 0.21/0.48 (((~![X31: $i, X32: $i, X34: $i, X33: $i] : ((~p34(c36, X33)) | (~p4(f5(f7(X34, f26(f28(c43, X33), X34)), f30(f32(c42, X33), X34)), f5(f7(X34, f26(f28(c44, X33), X34)), f30(f32(c42, X33), X34)))) | (~p4(f5(X32, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X32), f18(f20(f22(f24(c45, X33), X34), X31), X32)))) | (~p4(f5(X31, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X31), f18(f20(f22(f24(c45, X33), X34), X31), X32)))) | p2(X31, X32))) | ((~p34(c36, c37)) | (~p4(f5(f7(c39, f26(f28(c43, c37), c39)), f30(f32(c42, c37), c39)), f5(f7(c39, f26(f28(c44, c37), c39)), f30(f32(c42, c37), c39)))) | (~p4(f5(c38, f18(f20(f22(f24(c45, c37), c39), c40), c38)), f5(f7(c39, c38), f18(f20(f22(f24(c45, c37), c39), c40), c38)))) | (~p4(f5(c40, f18(f20(f22(f24(c45, c37), c39), c40), c38)), f5(f7(c39, c40), f18(f20(f22(f24(c45, c37), c39), c40), c38)))) | p2(c40, c38))) <=> ((~![X31: $i, X32: $i, X34: $i, X33: $i] : ((~p34(c36, X33)) | (~p4(f5(f7(X34, f26(f28(c43, X33), X34)), f30(f32(c42, X33), X34)), f5(f7(X34, f26(f28(c44, X33), X34)), f30(f32(c42, X33), X34)))) | (~p4(f5(X32, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X32), f18(f20(f22(f24(c45, X33), X34), X31), X32)))) | (~p4(f5(X31, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X31), f18(f20(f22(f24(c45, X33), X34), X31), X32)))) | p2(X31, X32))) | (~p34(c36, c37)) | (~p4(f5(f7(c39, f26(f28(c43, c37), c39)), f30(f32(c42, c37), c39)), f5(f7(c39, f26(f28(c44, c37), c39)), f30(f32(c42, c37), c39)))) | (~p4(f5(c38, f18(f20(f22(f24(c45, c37), c39), c40), c38)), f5(f7(c39, c38), f18(f20(f22(f24(c45, c37), c39), c40), c38)))) | (~p4(f5(c40, f18(f20(f22(f24(c45, c37), c39), c40), c38)), f5(f7(c39, c40), f18(f20(f22(f24(c45, c37), c39), c40), c38)))) | p2(c40, c38))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(38,plain,
% 0.21/0.48 ((~![X31: $i, X32: $i, X34: $i, X33: $i] : ((~p34(c36, X33)) | (~p4(f5(f7(X34, f26(f28(c43, X33), X34)), f30(f32(c42, X33), X34)), f5(f7(X34, f26(f28(c44, X33), X34)), f30(f32(c42, X33), X34)))) | (~p4(f5(X32, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X32), f18(f20(f22(f24(c45, X33), X34), X31), X32)))) | (~p4(f5(X31, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X31), f18(f20(f22(f24(c45, X33), X34), X31), X32)))) | p2(X31, X32))) | ((~p34(c36, c37)) | (~p4(f5(f7(c39, f26(f28(c43, c37), c39)), f30(f32(c42, c37), c39)), f5(f7(c39, f26(f28(c44, c37), c39)), f30(f32(c42, c37), c39)))) | (~p4(f5(c38, f18(f20(f22(f24(c45, c37), c39), c40), c38)), f5(f7(c39, c38), f18(f20(f22(f24(c45, c37), c39), c40), c38)))) | (~p4(f5(c40, f18(f20(f22(f24(c45, c37), c39), c40), c38)), f5(f7(c39, c40), f18(f20(f22(f24(c45, c37), c39), c40), c38)))) | p2(c40, c38))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(39,plain,
% 0.21/0.48 ((~![X31: $i, X32: $i, X34: $i, X33: $i] : ((~p34(c36, X33)) | (~p4(f5(f7(X34, f26(f28(c43, X33), X34)), f30(f32(c42, X33), X34)), f5(f7(X34, f26(f28(c44, X33), X34)), f30(f32(c42, X33), X34)))) | (~p4(f5(X32, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X32), f18(f20(f22(f24(c45, X33), X34), X31), X32)))) | (~p4(f5(X31, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X31), f18(f20(f22(f24(c45, X33), X34), X31), X32)))) | p2(X31, X32))) | (~p34(c36, c37)) | (~p4(f5(f7(c39, f26(f28(c43, c37), c39)), f30(f32(c42, c37), c39)), f5(f7(c39, f26(f28(c44, c37), c39)), f30(f32(c42, c37), c39)))) | (~p4(f5(c38, f18(f20(f22(f24(c45, c37), c39), c40), c38)), f5(f7(c39, c38), f18(f20(f22(f24(c45, c37), c39), c40), c38)))) | (~p4(f5(c40, f18(f20(f22(f24(c45, c37), c39), c40), c38)), f5(f7(c39, c40), f18(f20(f22(f24(c45, c37), c39), c40), c38)))) | p2(c40, c38)),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.21/0.48 tff(40,plain,
% 0.21/0.48 ((~p4(f5(f7(c39, f26(f28(c43, c37), c39)), f30(f32(c42, c37), c39)), f5(f7(c39, f26(f28(c44, c37), c39)), f30(f32(c42, c37), c39)))) | (~p4(f5(c38, f18(f20(f22(f24(c45, c37), c39), c40), c38)), f5(f7(c39, c38), f18(f20(f22(f24(c45, c37), c39), c40), c38)))) | (~p4(f5(c40, f18(f20(f22(f24(c45, c37), c39), c40), c38)), f5(f7(c39, c40), f18(f20(f22(f24(c45, c37), c39), c40), c38)))) | p2(c40, c38)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[39, 36, 33])).
% 0.21/0.48 tff(41,plain,
% 0.21/0.48 ((~p4(f5(f7(c39, f26(f28(c43, c37), c39)), f30(f32(c42, c37), c39)), f5(f7(c39, f26(f28(c44, c37), c39)), f30(f32(c42, c37), c39)))) | (~p4(f5(c38, f18(f20(f22(f24(c45, c37), c39), c40), c38)), f5(f7(c39, c38), f18(f20(f22(f24(c45, c37), c39), c40), c38)))) | p2(c40, c38)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[40, 23])).
% 0.21/0.48 tff(42,plain,
% 0.21/0.48 ((~p4(f5(f7(c39, f26(f28(c43, c37), c39)), f30(f32(c42, c37), c39)), f5(f7(c39, f26(f28(c44, c37), c39)), f30(f32(c42, c37), c39)))) | p2(c40, c38)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[41, 12])).
% 0.21/0.48 tff(43,plain,
% 0.21/0.48 (~p4(f5(f7(c39, f26(f28(c43, c37), c39)), f30(f32(c42, c37), c39)), f5(f7(c39, f26(f28(c44, c37), c39)), f30(f32(c42, c37), c39)))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[42, 1])).
% 0.21/0.48 tff(44,plain,
% 0.21/0.48 (^[X105: $i, X104: $i, X103: $i] : refl((p4(f5(f7(c39, X103), X105), f5(f7(c39, X104), X105)) | (~p4(f5(X103, f12(f14(f16(c41, X103), X104), X105)), f5(X104, f12(f14(f16(c41, X103), X104), X105))))) <=> (p4(f5(f7(c39, X103), X105), f5(f7(c39, X104), X105)) | (~p4(f5(X103, f12(f14(f16(c41, X103), X104), X105)), f5(X104, f12(f14(f16(c41, X103), X104), X105))))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(45,plain,
% 0.21/0.48 (![X105: $i, X104: $i, X103: $i] : (p4(f5(f7(c39, X103), X105), f5(f7(c39, X104), X105)) | (~p4(f5(X103, f12(f14(f16(c41, X103), X104), X105)), f5(X104, f12(f14(f16(c41, X103), X104), X105))))) <=> ![X105: $i, X104: $i, X103: $i] : (p4(f5(f7(c39, X103), X105), f5(f7(c39, X104), X105)) | (~p4(f5(X103, f12(f14(f16(c41, X103), X104), X105)), f5(X104, f12(f14(f16(c41, X103), X104), X105)))))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[44])).
% 0.21/0.48 tff(46,plain,
% 0.21/0.48 (![X105: $i, X104: $i, X103: $i] : (p4(f5(f7(c39, X103), X105), f5(f7(c39, X104), X105)) | (~p4(f5(X103, f12(f14(f16(c41, X103), X104), X105)), f5(X104, f12(f14(f16(c41, X103), X104), X105))))) <=> ![X105: $i, X104: $i, X103: $i] : (p4(f5(f7(c39, X103), X105), f5(f7(c39, X104), X105)) | (~p4(f5(X103, f12(f14(f16(c41, X103), X104), X105)), f5(X104, f12(f14(f16(c41, X103), X104), X105)))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(47,axiom,(![X105: $i, X104: $i, X103: $i] : (p4(f5(f7(c39, X103), X105), f5(f7(c39, X104), X105)) | (~p4(f5(X103, f12(f14(f16(c41, X103), X104), X105)), f5(X104, f12(f14(f16(c41, X103), X104), X105)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p4_58')).
% 0.21/0.48 tff(48,plain,
% 0.21/0.48 (![X105: $i, X104: $i, X103: $i] : (p4(f5(f7(c39, X103), X105), f5(f7(c39, X104), X105)) | (~p4(f5(X103, f12(f14(f16(c41, X103), X104), X105)), f5(X104, f12(f14(f16(c41, X103), X104), X105)))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.21/0.48 tff(49,plain,(
% 0.21/0.48 ![X105: $i, X104: $i, X103: $i] : (p4(f5(f7(c39, X103), X105), f5(f7(c39, X104), X105)) | (~p4(f5(X103, f12(f14(f16(c41, X103), X104), X105)), f5(X104, f12(f14(f16(c41, X103), X104), X105)))))),
% 0.21/0.48 inference(skolemize,[status(sab)],[48])).
% 0.21/0.48 tff(50,plain,
% 0.21/0.48 (![X105: $i, X104: $i, X103: $i] : (p4(f5(f7(c39, X103), X105), f5(f7(c39, X104), X105)) | (~p4(f5(X103, f12(f14(f16(c41, X103), X104), X105)), f5(X104, f12(f14(f16(c41, X103), X104), X105)))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[49, 45])).
% 0.21/0.49 tff(51,plain,
% 0.21/0.49 (((~![X105: $i, X104: $i, X103: $i] : (p4(f5(f7(c39, X103), X105), f5(f7(c39, X104), X105)) | (~p4(f5(X103, f12(f14(f16(c41, X103), X104), X105)), f5(X104, f12(f14(f16(c41, X103), X104), X105)))))) | (p4(f5(f7(c39, f26(f28(c43, c37), c39)), f30(f32(c42, c37), c39)), f5(f7(c39, f26(f28(c44, c37), c39)), f30(f32(c42, c37), c39))) | (~p4(f5(f26(f28(c43, c37), c39), f12(f14(f16(c41, f26(f28(c43, c37), c39)), f26(f28(c44, c37), c39)), f30(f32(c42, c37), c39))), f5(f26(f28(c44, c37), c39), f12(f14(f16(c41, f26(f28(c43, c37), c39)), f26(f28(c44, c37), c39)), f30(f32(c42, c37), c39))))))) <=> ((~![X105: $i, X104: $i, X103: $i] : (p4(f5(f7(c39, X103), X105), f5(f7(c39, X104), X105)) | (~p4(f5(X103, f12(f14(f16(c41, X103), X104), X105)), f5(X104, f12(f14(f16(c41, X103), X104), X105)))))) | p4(f5(f7(c39, f26(f28(c43, c37), c39)), f30(f32(c42, c37), c39)), f5(f7(c39, f26(f28(c44, c37), c39)), f30(f32(c42, c37), c39))) | (~p4(f5(f26(f28(c43, c37), c39), f12(f14(f16(c41, f26(f28(c43, c37), c39)), f26(f28(c44, c37), c39)), f30(f32(c42, c37), c39))), f5(f26(f28(c44, c37), c39), f12(f14(f16(c41, f26(f28(c43, c37), c39)), f26(f28(c44, c37), c39)), f30(f32(c42, c37), c39))))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(52,plain,
% 0.21/0.49 ((~![X105: $i, X104: $i, X103: $i] : (p4(f5(f7(c39, X103), X105), f5(f7(c39, X104), X105)) | (~p4(f5(X103, f12(f14(f16(c41, X103), X104), X105)), f5(X104, f12(f14(f16(c41, X103), X104), X105)))))) | (p4(f5(f7(c39, f26(f28(c43, c37), c39)), f30(f32(c42, c37), c39)), f5(f7(c39, f26(f28(c44, c37), c39)), f30(f32(c42, c37), c39))) | (~p4(f5(f26(f28(c43, c37), c39), f12(f14(f16(c41, f26(f28(c43, c37), c39)), f26(f28(c44, c37), c39)), f30(f32(c42, c37), c39))), f5(f26(f28(c44, c37), c39), f12(f14(f16(c41, f26(f28(c43, c37), c39)), f26(f28(c44, c37), c39)), f30(f32(c42, c37), c39))))))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(53,plain,
% 0.21/0.49 ((~![X105: $i, X104: $i, X103: $i] : (p4(f5(f7(c39, X103), X105), f5(f7(c39, X104), X105)) | (~p4(f5(X103, f12(f14(f16(c41, X103), X104), X105)), f5(X104, f12(f14(f16(c41, X103), X104), X105)))))) | p4(f5(f7(c39, f26(f28(c43, c37), c39)), f30(f32(c42, c37), c39)), f5(f7(c39, f26(f28(c44, c37), c39)), f30(f32(c42, c37), c39))) | (~p4(f5(f26(f28(c43, c37), c39), f12(f14(f16(c41, f26(f28(c43, c37), c39)), f26(f28(c44, c37), c39)), f30(f32(c42, c37), c39))), f5(f26(f28(c44, c37), c39), f12(f14(f16(c41, f26(f28(c43, c37), c39)), f26(f28(c44, c37), c39)), f30(f32(c42, c37), c39)))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.21/0.49 tff(54,plain,
% 0.21/0.49 (~p4(f5(f26(f28(c43, c37), c39), f12(f14(f16(c41, f26(f28(c43, c37), c39)), f26(f28(c44, c37), c39)), f30(f32(c42, c37), c39))), f5(f26(f28(c44, c37), c39), f12(f14(f16(c41, f26(f28(c43, c37), c39)), f26(f28(c44, c37), c39)), f30(f32(c42, c37), c39))))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[53, 50, 43])).
% 0.21/0.49 tff(55,plain,
% 0.21/0.49 (^[X105: $i, X104: $i, X103: $i] : refl((p4(f5(f7(c39, X103), X105), f5(f7(c39, X104), X105)) | p35(f10(c37, f12(f14(f16(c41, X103), X104), X105)), X105)) <=> (p4(f5(f7(c39, X103), X105), f5(f7(c39, X104), X105)) | p35(f10(c37, f12(f14(f16(c41, X103), X104), X105)), X105)))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(56,plain,
% 0.21/0.49 (![X105: $i, X104: $i, X103: $i] : (p4(f5(f7(c39, X103), X105), f5(f7(c39, X104), X105)) | p35(f10(c37, f12(f14(f16(c41, X103), X104), X105)), X105)) <=> ![X105: $i, X104: $i, X103: $i] : (p4(f5(f7(c39, X103), X105), f5(f7(c39, X104), X105)) | p35(f10(c37, f12(f14(f16(c41, X103), X104), X105)), X105))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[55])).
% 0.21/0.49 tff(57,plain,
% 0.21/0.49 (![X105: $i, X104: $i, X103: $i] : (p4(f5(f7(c39, X103), X105), f5(f7(c39, X104), X105)) | p35(f10(c37, f12(f14(f16(c41, X103), X104), X105)), X105)) <=> ![X105: $i, X104: $i, X103: $i] : (p4(f5(f7(c39, X103), X105), f5(f7(c39, X104), X105)) | p35(f10(c37, f12(f14(f16(c41, X103), X104), X105)), X105))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(58,axiom,(![X105: $i, X104: $i, X103: $i] : (p4(f5(f7(c39, X103), X105), f5(f7(c39, X104), X105)) | p35(f10(c37, f12(f14(f16(c41, X103), X104), X105)), X105))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p4_57')).
% 0.21/0.49 tff(59,plain,
% 0.21/0.49 (![X105: $i, X104: $i, X103: $i] : (p4(f5(f7(c39, X103), X105), f5(f7(c39, X104), X105)) | p35(f10(c37, f12(f14(f16(c41, X103), X104), X105)), X105))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.21/0.49 tff(60,plain,(
% 0.21/0.49 ![X105: $i, X104: $i, X103: $i] : (p4(f5(f7(c39, X103), X105), f5(f7(c39, X104), X105)) | p35(f10(c37, f12(f14(f16(c41, X103), X104), X105)), X105))),
% 0.21/0.49 inference(skolemize,[status(sab)],[59])).
% 0.21/0.49 tff(61,plain,
% 0.21/0.49 (![X105: $i, X104: $i, X103: $i] : (p4(f5(f7(c39, X103), X105), f5(f7(c39, X104), X105)) | p35(f10(c37, f12(f14(f16(c41, X103), X104), X105)), X105))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[60, 56])).
% 0.21/0.49 tff(62,plain,
% 0.21/0.49 (((~![X105: $i, X104: $i, X103: $i] : (p4(f5(f7(c39, X103), X105), f5(f7(c39, X104), X105)) | p35(f10(c37, f12(f14(f16(c41, X103), X104), X105)), X105))) | (p4(f5(f7(c39, f26(f28(c43, c37), c39)), f30(f32(c42, c37), c39)), f5(f7(c39, f26(f28(c44, c37), c39)), f30(f32(c42, c37), c39))) | p35(f10(c37, f12(f14(f16(c41, f26(f28(c43, c37), c39)), f26(f28(c44, c37), c39)), f30(f32(c42, c37), c39))), f30(f32(c42, c37), c39)))) <=> ((~![X105: $i, X104: $i, X103: $i] : (p4(f5(f7(c39, X103), X105), f5(f7(c39, X104), X105)) | p35(f10(c37, f12(f14(f16(c41, X103), X104), X105)), X105))) | p4(f5(f7(c39, f26(f28(c43, c37), c39)), f30(f32(c42, c37), c39)), f5(f7(c39, f26(f28(c44, c37), c39)), f30(f32(c42, c37), c39))) | p35(f10(c37, f12(f14(f16(c41, f26(f28(c43, c37), c39)), f26(f28(c44, c37), c39)), f30(f32(c42, c37), c39))), f30(f32(c42, c37), c39)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(63,plain,
% 0.21/0.49 ((~![X105: $i, X104: $i, X103: $i] : (p4(f5(f7(c39, X103), X105), f5(f7(c39, X104), X105)) | p35(f10(c37, f12(f14(f16(c41, X103), X104), X105)), X105))) | (p4(f5(f7(c39, f26(f28(c43, c37), c39)), f30(f32(c42, c37), c39)), f5(f7(c39, f26(f28(c44, c37), c39)), f30(f32(c42, c37), c39))) | p35(f10(c37, f12(f14(f16(c41, f26(f28(c43, c37), c39)), f26(f28(c44, c37), c39)), f30(f32(c42, c37), c39))), f30(f32(c42, c37), c39)))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(64,plain,
% 0.21/0.49 ((~![X105: $i, X104: $i, X103: $i] : (p4(f5(f7(c39, X103), X105), f5(f7(c39, X104), X105)) | p35(f10(c37, f12(f14(f16(c41, X103), X104), X105)), X105))) | p4(f5(f7(c39, f26(f28(c43, c37), c39)), f30(f32(c42, c37), c39)), f5(f7(c39, f26(f28(c44, c37), c39)), f30(f32(c42, c37), c39))) | p35(f10(c37, f12(f14(f16(c41, f26(f28(c43, c37), c39)), f26(f28(c44, c37), c39)), f30(f32(c42, c37), c39))), f30(f32(c42, c37), c39))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.21/0.49 tff(65,plain,
% 0.21/0.49 (p35(f10(c37, f12(f14(f16(c41, f26(f28(c43, c37), c39)), f26(f28(c44, c37), c39)), f30(f32(c42, c37), c39))), f30(f32(c42, c37), c39))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[64, 61, 43])).
% 0.21/0.49 tff(66,plain,
% 0.21/0.49 (^[X31: $i, X32: $i, X35: $i, X34: $i, X33: $i] : refl(((~p34(c36, X33)) | (~p4(f5(X32, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X32), f18(f20(f22(f24(c45, X33), X34), X31), X32)))) | (~p4(f5(X31, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X31), f18(f20(f22(f24(c45, X33), X34), X31), X32)))) | (~p35(f10(X33, X35), f30(f32(c42, X33), X34))) | p4(f5(f26(f28(c43, X33), X34), X35), f5(f26(f28(c44, X33), X34), X35)) | p2(X31, X32)) <=> ((~p34(c36, X33)) | (~p4(f5(X32, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X32), f18(f20(f22(f24(c45, X33), X34), X31), X32)))) | (~p4(f5(X31, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X31), f18(f20(f22(f24(c45, X33), X34), X31), X32)))) | (~p35(f10(X33, X35), f30(f32(c42, X33), X34))) | p4(f5(f26(f28(c43, X33), X34), X35), f5(f26(f28(c44, X33), X34), X35)) | p2(X31, X32)))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(67,plain,
% 0.21/0.49 (![X31: $i, X32: $i, X35: $i, X34: $i, X33: $i] : ((~p34(c36, X33)) | (~p4(f5(X32, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X32), f18(f20(f22(f24(c45, X33), X34), X31), X32)))) | (~p4(f5(X31, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X31), f18(f20(f22(f24(c45, X33), X34), X31), X32)))) | (~p35(f10(X33, X35), f30(f32(c42, X33), X34))) | p4(f5(f26(f28(c43, X33), X34), X35), f5(f26(f28(c44, X33), X34), X35)) | p2(X31, X32)) <=> ![X31: $i, X32: $i, X35: $i, X34: $i, X33: $i] : ((~p34(c36, X33)) | (~p4(f5(X32, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X32), f18(f20(f22(f24(c45, X33), X34), X31), X32)))) | (~p4(f5(X31, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X31), f18(f20(f22(f24(c45, X33), X34), X31), X32)))) | (~p35(f10(X33, X35), f30(f32(c42, X33), X34))) | p4(f5(f26(f28(c43, X33), X34), X35), f5(f26(f28(c44, X33), X34), X35)) | p2(X31, X32))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[66])).
% 0.21/0.49 tff(68,plain,
% 0.21/0.49 (![X31: $i, X32: $i, X35: $i, X34: $i, X33: $i] : ((~p34(c36, X33)) | (~p4(f5(X32, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X32), f18(f20(f22(f24(c45, X33), X34), X31), X32)))) | (~p4(f5(X31, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X31), f18(f20(f22(f24(c45, X33), X34), X31), X32)))) | (~p35(f10(X33, X35), f30(f32(c42, X33), X34))) | p4(f5(f26(f28(c43, X33), X34), X35), f5(f26(f28(c44, X33), X34), X35)) | p2(X31, X32)) <=> ![X31: $i, X32: $i, X35: $i, X34: $i, X33: $i] : ((~p34(c36, X33)) | (~p4(f5(X32, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X32), f18(f20(f22(f24(c45, X33), X34), X31), X32)))) | (~p4(f5(X31, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X31), f18(f20(f22(f24(c45, X33), X34), X31), X32)))) | (~p35(f10(X33, X35), f30(f32(c42, X33), X34))) | p4(f5(f26(f28(c43, X33), X34), X35), f5(f26(f28(c44, X33), X34), X35)) | p2(X31, X32))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(69,plain,
% 0.21/0.49 (^[X31: $i, X32: $i, X35: $i, X34: $i, X33: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((p2(X31, X32) | p4(f5(f26(f28(c43, X33), X34), X35), f5(f26(f28(c44, X33), X34), X35))) | (~p34(c36, X33))) <=> ((~p34(c36, X33)) | p4(f5(f26(f28(c43, X33), X34), X35), f5(f26(f28(c44, X33), X34), X35)) | p2(X31, X32))), ((((p2(X31, X32) | p4(f5(f26(f28(c43, X33), X34), X35), f5(f26(f28(c44, X33), X34), X35))) | (~p34(c36, X33))) | (~p35(f10(X33, X35), f30(f32(c42, X33), X34)))) <=> (((~p34(c36, X33)) | p4(f5(f26(f28(c43, X33), X34), X35), f5(f26(f28(c44, X33), X34), X35)) | p2(X31, X32)) | (~p35(f10(X33, X35), f30(f32(c42, X33), X34)))))), rewrite((((~p34(c36, X33)) | p4(f5(f26(f28(c43, X33), X34), X35), f5(f26(f28(c44, X33), X34), X35)) | p2(X31, X32)) | (~p35(f10(X33, X35), f30(f32(c42, X33), X34)))) <=> ((~p34(c36, X33)) | (~p35(f10(X33, X35), f30(f32(c42, X33), X34))) | p4(f5(f26(f28(c43, X33), X34), X35), f5(f26(f28(c44, X33), X34), X35)) | p2(X31, X32))), ((((p2(X31, X32) | p4(f5(f26(f28(c43, X33), X34), X35), f5(f26(f28(c44, X33), X34), X35))) | (~p34(c36, X33))) | (~p35(f10(X33, X35), f30(f32(c42, X33), X34)))) <=> ((~p34(c36, X33)) | (~p35(f10(X33, X35), f30(f32(c42, X33), X34))) | p4(f5(f26(f28(c43, X33), X34), X35), f5(f26(f28(c44, X33), X34), X35)) | p2(X31, X32)))), (((((p2(X31, X32) | p4(f5(f26(f28(c43, X33), X34), X35), f5(f26(f28(c44, X33), X34), X35))) | (~p34(c36, X33))) | (~p35(f10(X33, X35), f30(f32(c42, X33), X34)))) | (~p4(f5(X31, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X31), f18(f20(f22(f24(c45, X33), X34), X31), X32))))) <=> (((~p34(c36, X33)) | (~p35(f10(X33, X35), f30(f32(c42, X33), X34))) | p4(f5(f26(f28(c43, X33), X34), X35), f5(f26(f28(c44, X33), X34), X35)) | p2(X31, X32)) | (~p4(f5(X31, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X31), f18(f20(f22(f24(c45, X33), X34), X31), X32))))))), rewrite((((~p34(c36, X33)) | (~p35(f10(X33, X35), f30(f32(c42, X33), X34))) | p4(f5(f26(f28(c43, X33), X34), X35), f5(f26(f28(c44, X33), X34), X35)) | p2(X31, X32)) | (~p4(f5(X31, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X31), f18(f20(f22(f24(c45, X33), X34), X31), X32))))) <=> ((~p34(c36, X33)) | (~p4(f5(X31, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X31), f18(f20(f22(f24(c45, X33), X34), X31), X32)))) | (~p35(f10(X33, X35), f30(f32(c42, X33), X34))) | p4(f5(f26(f28(c43, X33), X34), X35), f5(f26(f28(c44, X33), X34), X35)) | p2(X31, X32))), (((((p2(X31, X32) | p4(f5(f26(f28(c43, X33), X34), X35), f5(f26(f28(c44, X33), X34), X35))) | (~p34(c36, X33))) | (~p35(f10(X33, X35), f30(f32(c42, X33), X34)))) | (~p4(f5(X31, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X31), f18(f20(f22(f24(c45, X33), X34), X31), X32))))) <=> ((~p34(c36, X33)) | (~p4(f5(X31, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X31), f18(f20(f22(f24(c45, X33), X34), X31), X32)))) | (~p35(f10(X33, X35), f30(f32(c42, X33), X34))) | p4(f5(f26(f28(c43, X33), X34), X35), f5(f26(f28(c44, X33), X34), X35)) | p2(X31, X32)))), ((((((p2(X31, X32) | p4(f5(f26(f28(c43, X33), X34), X35), f5(f26(f28(c44, X33), X34), X35))) | (~p34(c36, X33))) | (~p35(f10(X33, X35), f30(f32(c42, X33), X34)))) | (~p4(f5(X31, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X31), f18(f20(f22(f24(c45, X33), X34), X31), X32))))) | (~p4(f5(X32, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X32), f18(f20(f22(f24(c45, X33), X34), X31), X32))))) <=> (((~p34(c36, X33)) | (~p4(f5(X31, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X31), f18(f20(f22(f24(c45, X33), X34), X31), X32)))) | (~p35(f10(X33, X35), f30(f32(c42, X33), X34))) | p4(f5(f26(f28(c43, X33), X34), X35), f5(f26(f28(c44, X33), X34), X35)) | p2(X31, X32)) | (~p4(f5(X32, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X32), f18(f20(f22(f24(c45, X33), X34), X31), X32))))))), rewrite((((~p34(c36, X33)) | (~p4(f5(X31, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X31), f18(f20(f22(f24(c45, X33), X34), X31), X32)))) | (~p35(f10(X33, X35), f30(f32(c42, X33), X34))) | p4(f5(f26(f28(c43, X33), X34), X35), f5(f26(f28(c44, X33), X34), X35)) | p2(X31, X32)) | (~p4(f5(X32, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X32), f18(f20(f22(f24(c45, X33), X34), X31), X32))))) <=> ((~p34(c36, X33)) | (~p4(f5(X32, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X32), f18(f20(f22(f24(c45, X33), X34), X31), X32)))) | (~p4(f5(X31, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X31), f18(f20(f22(f24(c45, X33), X34), X31), X32)))) | (~p35(f10(X33, X35), f30(f32(c42, X33), X34))) | p4(f5(f26(f28(c43, X33), X34), X35), f5(f26(f28(c44, X33), X34), X35)) | p2(X31, X32))), ((((((p2(X31, X32) | p4(f5(f26(f28(c43, X33), X34), X35), f5(f26(f28(c44, X33), X34), X35))) | (~p34(c36, X33))) | (~p35(f10(X33, X35), f30(f32(c42, X33), X34)))) | (~p4(f5(X31, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X31), f18(f20(f22(f24(c45, X33), X34), X31), X32))))) | (~p4(f5(X32, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X32), f18(f20(f22(f24(c45, X33), X34), X31), X32))))) <=> ((~p34(c36, X33)) | (~p4(f5(X32, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X32), f18(f20(f22(f24(c45, X33), X34), X31), X32)))) | (~p4(f5(X31, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X31), f18(f20(f22(f24(c45, X33), X34), X31), X32)))) | (~p35(f10(X33, X35), f30(f32(c42, X33), X34))) | p4(f5(f26(f28(c43, X33), X34), X35), f5(f26(f28(c44, X33), X34), X35)) | p2(X31, X32))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(70,plain,
% 0.21/0.49 (![X31: $i, X32: $i, X35: $i, X34: $i, X33: $i] : (((((p2(X31, X32) | p4(f5(f26(f28(c43, X33), X34), X35), f5(f26(f28(c44, X33), X34), X35))) | (~p34(c36, X33))) | (~p35(f10(X33, X35), f30(f32(c42, X33), X34)))) | (~p4(f5(X31, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X31), f18(f20(f22(f24(c45, X33), X34), X31), X32))))) | (~p4(f5(X32, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X32), f18(f20(f22(f24(c45, X33), X34), X31), X32))))) <=> ![X31: $i, X32: $i, X35: $i, X34: $i, X33: $i] : ((~p34(c36, X33)) | (~p4(f5(X32, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X32), f18(f20(f22(f24(c45, X33), X34), X31), X32)))) | (~p4(f5(X31, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X31), f18(f20(f22(f24(c45, X33), X34), X31), X32)))) | (~p35(f10(X33, X35), f30(f32(c42, X33), X34))) | p4(f5(f26(f28(c43, X33), X34), X35), f5(f26(f28(c44, X33), X34), X35)) | p2(X31, X32))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[69])).
% 0.21/0.49 tff(71,axiom,(![X31: $i, X32: $i, X35: $i, X34: $i, X33: $i] : (((((p2(X31, X32) | p4(f5(f26(f28(c43, X33), X34), X35), f5(f26(f28(c44, X33), X34), X35))) | (~p34(c36, X33))) | (~p35(f10(X33, X35), f30(f32(c42, X33), X34)))) | (~p4(f5(X31, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X31), f18(f20(f22(f24(c45, X33), X34), X31), X32))))) | (~p4(f5(X32, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X32), f18(f20(f22(f24(c45, X33), X34), X31), X32)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_61')).
% 0.21/0.49 tff(72,plain,
% 0.21/0.49 (![X31: $i, X32: $i, X35: $i, X34: $i, X33: $i] : ((~p34(c36, X33)) | (~p4(f5(X32, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X32), f18(f20(f22(f24(c45, X33), X34), X31), X32)))) | (~p4(f5(X31, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X31), f18(f20(f22(f24(c45, X33), X34), X31), X32)))) | (~p35(f10(X33, X35), f30(f32(c42, X33), X34))) | p4(f5(f26(f28(c43, X33), X34), X35), f5(f26(f28(c44, X33), X34), X35)) | p2(X31, X32))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.21/0.49 tff(73,plain,
% 0.21/0.49 (![X31: $i, X32: $i, X35: $i, X34: $i, X33: $i] : ((~p34(c36, X33)) | (~p4(f5(X32, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X32), f18(f20(f22(f24(c45, X33), X34), X31), X32)))) | (~p4(f5(X31, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X31), f18(f20(f22(f24(c45, X33), X34), X31), X32)))) | (~p35(f10(X33, X35), f30(f32(c42, X33), X34))) | p4(f5(f26(f28(c43, X33), X34), X35), f5(f26(f28(c44, X33), X34), X35)) | p2(X31, X32))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[72, 68])).
% 0.21/0.49 tff(74,plain,(
% 0.21/0.49 ![X31: $i, X32: $i, X35: $i, X34: $i, X33: $i] : ((~p34(c36, X33)) | (~p4(f5(X32, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X32), f18(f20(f22(f24(c45, X33), X34), X31), X32)))) | (~p4(f5(X31, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X31), f18(f20(f22(f24(c45, X33), X34), X31), X32)))) | (~p35(f10(X33, X35), f30(f32(c42, X33), X34))) | p4(f5(f26(f28(c43, X33), X34), X35), f5(f26(f28(c44, X33), X34), X35)) | p2(X31, X32))),
% 0.21/0.49 inference(skolemize,[status(sab)],[73])).
% 0.21/0.49 tff(75,plain,
% 0.21/0.49 (![X31: $i, X32: $i, X35: $i, X34: $i, X33: $i] : ((~p34(c36, X33)) | (~p4(f5(X32, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X32), f18(f20(f22(f24(c45, X33), X34), X31), X32)))) | (~p4(f5(X31, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X31), f18(f20(f22(f24(c45, X33), X34), X31), X32)))) | (~p35(f10(X33, X35), f30(f32(c42, X33), X34))) | p4(f5(f26(f28(c43, X33), X34), X35), f5(f26(f28(c44, X33), X34), X35)) | p2(X31, X32))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[74, 67])).
% 0.21/0.49 tff(76,plain,
% 0.21/0.49 (((~![X31: $i, X32: $i, X35: $i, X34: $i, X33: $i] : ((~p34(c36, X33)) | (~p4(f5(X32, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X32), f18(f20(f22(f24(c45, X33), X34), X31), X32)))) | (~p4(f5(X31, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X31), f18(f20(f22(f24(c45, X33), X34), X31), X32)))) | (~p35(f10(X33, X35), f30(f32(c42, X33), X34))) | p4(f5(f26(f28(c43, X33), X34), X35), f5(f26(f28(c44, X33), X34), X35)) | p2(X31, X32))) | ((~p34(c36, c37)) | (~p4(f5(c38, f18(f20(f22(f24(c45, c37), c39), c40), c38)), f5(f7(c39, c38), f18(f20(f22(f24(c45, c37), c39), c40), c38)))) | (~p4(f5(c40, f18(f20(f22(f24(c45, c37), c39), c40), c38)), f5(f7(c39, c40), f18(f20(f22(f24(c45, c37), c39), c40), c38)))) | p2(c40, c38) | p4(f5(f26(f28(c43, c37), c39), f12(f14(f16(c41, f26(f28(c43, c37), c39)), f26(f28(c44, c37), c39)), f30(f32(c42, c37), c39))), f5(f26(f28(c44, c37), c39), f12(f14(f16(c41, f26(f28(c43, c37), c39)), f26(f28(c44, c37), c39)), f30(f32(c42, c37), c39)))) | (~p35(f10(c37, f12(f14(f16(c41, f26(f28(c43, c37), c39)), f26(f28(c44, c37), c39)), f30(f32(c42, c37), c39))), f30(f32(c42, c37), c39))))) <=> ((~![X31: $i, X32: $i, X35: $i, X34: $i, X33: $i] : ((~p34(c36, X33)) | (~p4(f5(X32, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X32), f18(f20(f22(f24(c45, X33), X34), X31), X32)))) | (~p4(f5(X31, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X31), f18(f20(f22(f24(c45, X33), X34), X31), X32)))) | (~p35(f10(X33, X35), f30(f32(c42, X33), X34))) | p4(f5(f26(f28(c43, X33), X34), X35), f5(f26(f28(c44, X33), X34), X35)) | p2(X31, X32))) | (~p34(c36, c37)) | (~p4(f5(c38, f18(f20(f22(f24(c45, c37), c39), c40), c38)), f5(f7(c39, c38), f18(f20(f22(f24(c45, c37), c39), c40), c38)))) | (~p4(f5(c40, f18(f20(f22(f24(c45, c37), c39), c40), c38)), f5(f7(c39, c40), f18(f20(f22(f24(c45, c37), c39), c40), c38)))) | p2(c40, c38) | p4(f5(f26(f28(c43, c37), c39), f12(f14(f16(c41, f26(f28(c43, c37), c39)), f26(f28(c44, c37), c39)), f30(f32(c42, c37), c39))), f5(f26(f28(c44, c37), c39), f12(f14(f16(c41, f26(f28(c43, c37), c39)), f26(f28(c44, c37), c39)), f30(f32(c42, c37), c39)))) | (~p35(f10(c37, f12(f14(f16(c41, f26(f28(c43, c37), c39)), f26(f28(c44, c37), c39)), f30(f32(c42, c37), c39))), f30(f32(c42, c37), c39))))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(77,plain,
% 0.21/0.50 (((~p34(c36, c37)) | (~p4(f5(c38, f18(f20(f22(f24(c45, c37), c39), c40), c38)), f5(f7(c39, c38), f18(f20(f22(f24(c45, c37), c39), c40), c38)))) | (~p4(f5(c40, f18(f20(f22(f24(c45, c37), c39), c40), c38)), f5(f7(c39, c40), f18(f20(f22(f24(c45, c37), c39), c40), c38)))) | (~p35(f10(c37, f12(f14(f16(c41, f26(f28(c43, c37), c39)), f26(f28(c44, c37), c39)), f30(f32(c42, c37), c39))), f30(f32(c42, c37), c39))) | p4(f5(f26(f28(c43, c37), c39), f12(f14(f16(c41, f26(f28(c43, c37), c39)), f26(f28(c44, c37), c39)), f30(f32(c42, c37), c39))), f5(f26(f28(c44, c37), c39), f12(f14(f16(c41, f26(f28(c43, c37), c39)), f26(f28(c44, c37), c39)), f30(f32(c42, c37), c39)))) | p2(c40, c38)) <=> ((~p34(c36, c37)) | (~p4(f5(c38, f18(f20(f22(f24(c45, c37), c39), c40), c38)), f5(f7(c39, c38), f18(f20(f22(f24(c45, c37), c39), c40), c38)))) | (~p4(f5(c40, f18(f20(f22(f24(c45, c37), c39), c40), c38)), f5(f7(c39, c40), f18(f20(f22(f24(c45, c37), c39), c40), c38)))) | p2(c40, c38) | p4(f5(f26(f28(c43, c37), c39), f12(f14(f16(c41, f26(f28(c43, c37), c39)), f26(f28(c44, c37), c39)), f30(f32(c42, c37), c39))), f5(f26(f28(c44, c37), c39), f12(f14(f16(c41, f26(f28(c43, c37), c39)), f26(f28(c44, c37), c39)), f30(f32(c42, c37), c39)))) | (~p35(f10(c37, f12(f14(f16(c41, f26(f28(c43, c37), c39)), f26(f28(c44, c37), c39)), f30(f32(c42, c37), c39))), f30(f32(c42, c37), c39))))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(78,plain,
% 0.21/0.50 (((~![X31: $i, X32: $i, X35: $i, X34: $i, X33: $i] : ((~p34(c36, X33)) | (~p4(f5(X32, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X32), f18(f20(f22(f24(c45, X33), X34), X31), X32)))) | (~p4(f5(X31, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X31), f18(f20(f22(f24(c45, X33), X34), X31), X32)))) | (~p35(f10(X33, X35), f30(f32(c42, X33), X34))) | p4(f5(f26(f28(c43, X33), X34), X35), f5(f26(f28(c44, X33), X34), X35)) | p2(X31, X32))) | ((~p34(c36, c37)) | (~p4(f5(c38, f18(f20(f22(f24(c45, c37), c39), c40), c38)), f5(f7(c39, c38), f18(f20(f22(f24(c45, c37), c39), c40), c38)))) | (~p4(f5(c40, f18(f20(f22(f24(c45, c37), c39), c40), c38)), f5(f7(c39, c40), f18(f20(f22(f24(c45, c37), c39), c40), c38)))) | (~p35(f10(c37, f12(f14(f16(c41, f26(f28(c43, c37), c39)), f26(f28(c44, c37), c39)), f30(f32(c42, c37), c39))), f30(f32(c42, c37), c39))) | p4(f5(f26(f28(c43, c37), c39), f12(f14(f16(c41, f26(f28(c43, c37), c39)), f26(f28(c44, c37), c39)), f30(f32(c42, c37), c39))), f5(f26(f28(c44, c37), c39), f12(f14(f16(c41, f26(f28(c43, c37), c39)), f26(f28(c44, c37), c39)), f30(f32(c42, c37), c39)))) | p2(c40, c38))) <=> ((~![X31: $i, X32: $i, X35: $i, X34: $i, X33: $i] : ((~p34(c36, X33)) | (~p4(f5(X32, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X32), f18(f20(f22(f24(c45, X33), X34), X31), X32)))) | (~p4(f5(X31, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X31), f18(f20(f22(f24(c45, X33), X34), X31), X32)))) | (~p35(f10(X33, X35), f30(f32(c42, X33), X34))) | p4(f5(f26(f28(c43, X33), X34), X35), f5(f26(f28(c44, X33), X34), X35)) | p2(X31, X32))) | ((~p34(c36, c37)) | (~p4(f5(c38, f18(f20(f22(f24(c45, c37), c39), c40), c38)), f5(f7(c39, c38), f18(f20(f22(f24(c45, c37), c39), c40), c38)))) | (~p4(f5(c40, f18(f20(f22(f24(c45, c37), c39), c40), c38)), f5(f7(c39, c40), f18(f20(f22(f24(c45, c37), c39), c40), c38)))) | p2(c40, c38) | p4(f5(f26(f28(c43, c37), c39), f12(f14(f16(c41, f26(f28(c43, c37), c39)), f26(f28(c44, c37), c39)), f30(f32(c42, c37), c39))), f5(f26(f28(c44, c37), c39), f12(f14(f16(c41, f26(f28(c43, c37), c39)), f26(f28(c44, c37), c39)), f30(f32(c42, c37), c39)))) | (~p35(f10(c37, f12(f14(f16(c41, f26(f28(c43, c37), c39)), f26(f28(c44, c37), c39)), f30(f32(c42, c37), c39))), f30(f32(c42, c37), c39)))))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[77])).
% 0.21/0.50 tff(79,plain,
% 0.21/0.50 (((~![X31: $i, X32: $i, X35: $i, X34: $i, X33: $i] : ((~p34(c36, X33)) | (~p4(f5(X32, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X32), f18(f20(f22(f24(c45, X33), X34), X31), X32)))) | (~p4(f5(X31, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X31), f18(f20(f22(f24(c45, X33), X34), X31), X32)))) | (~p35(f10(X33, X35), f30(f32(c42, X33), X34))) | p4(f5(f26(f28(c43, X33), X34), X35), f5(f26(f28(c44, X33), X34), X35)) | p2(X31, X32))) | ((~p34(c36, c37)) | (~p4(f5(c38, f18(f20(f22(f24(c45, c37), c39), c40), c38)), f5(f7(c39, c38), f18(f20(f22(f24(c45, c37), c39), c40), c38)))) | (~p4(f5(c40, f18(f20(f22(f24(c45, c37), c39), c40), c38)), f5(f7(c39, c40), f18(f20(f22(f24(c45, c37), c39), c40), c38)))) | (~p35(f10(c37, f12(f14(f16(c41, f26(f28(c43, c37), c39)), f26(f28(c44, c37), c39)), f30(f32(c42, c37), c39))), f30(f32(c42, c37), c39))) | p4(f5(f26(f28(c43, c37), c39), f12(f14(f16(c41, f26(f28(c43, c37), c39)), f26(f28(c44, c37), c39)), f30(f32(c42, c37), c39))), f5(f26(f28(c44, c37), c39), f12(f14(f16(c41, f26(f28(c43, c37), c39)), f26(f28(c44, c37), c39)), f30(f32(c42, c37), c39)))) | p2(c40, c38))) <=> ((~![X31: $i, X32: $i, X35: $i, X34: $i, X33: $i] : ((~p34(c36, X33)) | (~p4(f5(X32, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X32), f18(f20(f22(f24(c45, X33), X34), X31), X32)))) | (~p4(f5(X31, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X31), f18(f20(f22(f24(c45, X33), X34), X31), X32)))) | (~p35(f10(X33, X35), f30(f32(c42, X33), X34))) | p4(f5(f26(f28(c43, X33), X34), X35), f5(f26(f28(c44, X33), X34), X35)) | p2(X31, X32))) | (~p34(c36, c37)) | (~p4(f5(c38, f18(f20(f22(f24(c45, c37), c39), c40), c38)), f5(f7(c39, c38), f18(f20(f22(f24(c45, c37), c39), c40), c38)))) | (~p4(f5(c40, f18(f20(f22(f24(c45, c37), c39), c40), c38)), f5(f7(c39, c40), f18(f20(f22(f24(c45, c37), c39), c40), c38)))) | p2(c40, c38) | p4(f5(f26(f28(c43, c37), c39), f12(f14(f16(c41, f26(f28(c43, c37), c39)), f26(f28(c44, c37), c39)), f30(f32(c42, c37), c39))), f5(f26(f28(c44, c37), c39), f12(f14(f16(c41, f26(f28(c43, c37), c39)), f26(f28(c44, c37), c39)), f30(f32(c42, c37), c39)))) | (~p35(f10(c37, f12(f14(f16(c41, f26(f28(c43, c37), c39)), f26(f28(c44, c37), c39)), f30(f32(c42, c37), c39))), f30(f32(c42, c37), c39))))),
% 0.21/0.50 inference(transitivity,[status(thm)],[78, 76])).
% 0.21/0.50 tff(80,plain,
% 0.21/0.50 ((~![X31: $i, X32: $i, X35: $i, X34: $i, X33: $i] : ((~p34(c36, X33)) | (~p4(f5(X32, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X32), f18(f20(f22(f24(c45, X33), X34), X31), X32)))) | (~p4(f5(X31, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X31), f18(f20(f22(f24(c45, X33), X34), X31), X32)))) | (~p35(f10(X33, X35), f30(f32(c42, X33), X34))) | p4(f5(f26(f28(c43, X33), X34), X35), f5(f26(f28(c44, X33), X34), X35)) | p2(X31, X32))) | ((~p34(c36, c37)) | (~p4(f5(c38, f18(f20(f22(f24(c45, c37), c39), c40), c38)), f5(f7(c39, c38), f18(f20(f22(f24(c45, c37), c39), c40), c38)))) | (~p4(f5(c40, f18(f20(f22(f24(c45, c37), c39), c40), c38)), f5(f7(c39, c40), f18(f20(f22(f24(c45, c37), c39), c40), c38)))) | (~p35(f10(c37, f12(f14(f16(c41, f26(f28(c43, c37), c39)), f26(f28(c44, c37), c39)), f30(f32(c42, c37), c39))), f30(f32(c42, c37), c39))) | p4(f5(f26(f28(c43, c37), c39), f12(f14(f16(c41, f26(f28(c43, c37), c39)), f26(f28(c44, c37), c39)), f30(f32(c42, c37), c39))), f5(f26(f28(c44, c37), c39), f12(f14(f16(c41, f26(f28(c43, c37), c39)), f26(f28(c44, c37), c39)), f30(f32(c42, c37), c39)))) | p2(c40, c38))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(81,plain,
% 0.21/0.50 ((~![X31: $i, X32: $i, X35: $i, X34: $i, X33: $i] : ((~p34(c36, X33)) | (~p4(f5(X32, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X32), f18(f20(f22(f24(c45, X33), X34), X31), X32)))) | (~p4(f5(X31, f18(f20(f22(f24(c45, X33), X34), X31), X32)), f5(f7(X34, X31), f18(f20(f22(f24(c45, X33), X34), X31), X32)))) | (~p35(f10(X33, X35), f30(f32(c42, X33), X34))) | p4(f5(f26(f28(c43, X33), X34), X35), f5(f26(f28(c44, X33), X34), X35)) | p2(X31, X32))) | (~p34(c36, c37)) | (~p4(f5(c38, f18(f20(f22(f24(c45, c37), c39), c40), c38)), f5(f7(c39, c38), f18(f20(f22(f24(c45, c37), c39), c40), c38)))) | (~p4(f5(c40, f18(f20(f22(f24(c45, c37), c39), c40), c38)), f5(f7(c39, c40), f18(f20(f22(f24(c45, c37), c39), c40), c38)))) | p2(c40, c38) | p4(f5(f26(f28(c43, c37), c39), f12(f14(f16(c41, f26(f28(c43, c37), c39)), f26(f28(c44, c37), c39)), f30(f32(c42, c37), c39))), f5(f26(f28(c44, c37), c39), f12(f14(f16(c41, f26(f28(c43, c37), c39)), f26(f28(c44, c37), c39)), f30(f32(c42, c37), c39)))) | (~p35(f10(c37, f12(f14(f16(c41, f26(f28(c43, c37), c39)), f26(f28(c44, c37), c39)), f30(f32(c42, c37), c39))), f30(f32(c42, c37), c39)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.21/0.50 tff(82,plain,
% 0.21/0.50 ($false),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[81, 36, 75, 12, 23, 1, 65, 54])).
% 0.21/0.50 tff(83,plain,(p2(c40, c38)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.50 tff(84,plain,
% 0.21/0.50 (^[X36: $i] : refl(p2(X36, X36) <=> p2(X36, X36))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(85,plain,
% 0.21/0.50 (![X36: $i] : p2(X36, X36) <=> ![X36: $i] : p2(X36, X36)),
% 0.21/0.50 inference(quant_intro,[status(thm)],[84])).
% 0.21/0.50 tff(86,plain,
% 0.21/0.50 (![X36: $i] : p2(X36, X36) <=> ![X36: $i] : p2(X36, X36)),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(87,axiom,(![X36: $i] : p2(X36, X36)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_14')).
% 0.21/0.50 tff(88,plain,
% 0.21/0.50 (![X36: $i] : p2(X36, X36)),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.21/0.50 tff(89,plain,(
% 0.21/0.50 ![X36: $i] : p2(X36, X36)),
% 0.21/0.50 inference(skolemize,[status(sab)],[88])).
% 0.21/0.50 tff(90,plain,
% 0.21/0.50 (![X36: $i] : p2(X36, X36)),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[89, 85])).
% 0.21/0.50 tff(91,plain,
% 0.21/0.50 ((~![X36: $i] : p2(X36, X36)) | p2(c40, c40)),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(92,plain,
% 0.21/0.50 (p2(c40, c40)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[91, 90])).
% 0.21/0.50 tff(93,plain,
% 0.21/0.50 (^[X38: $i, X37: $i, X36: $i] : refl(((~p2(X36, X38)) | (~p2(X36, X37)) | p2(X37, X38)) <=> ((~p2(X36, X38)) | (~p2(X36, X37)) | p2(X37, X38)))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(94,plain,
% 0.21/0.50 (![X38: $i, X37: $i, X36: $i] : ((~p2(X36, X38)) | (~p2(X36, X37)) | p2(X37, X38)) <=> ![X38: $i, X37: $i, X36: $i] : ((~p2(X36, X38)) | (~p2(X36, X37)) | p2(X37, X38))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[93])).
% 0.21/0.50 tff(95,plain,
% 0.21/0.50 (![X38: $i, X37: $i, X36: $i] : ((~p2(X36, X38)) | (~p2(X36, X37)) | p2(X37, X38)) <=> ![X38: $i, X37: $i, X36: $i] : ((~p2(X36, X38)) | (~p2(X36, X37)) | p2(X37, X38))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(96,plain,
% 0.21/0.50 (^[X38: $i, X37: $i, X36: $i] : trans(monotonicity(rewrite((p2(X37, X38) | (~p2(X36, X37))) <=> ((~p2(X36, X37)) | p2(X37, X38))), (((p2(X37, X38) | (~p2(X36, X37))) | (~p2(X36, X38))) <=> (((~p2(X36, X37)) | p2(X37, X38)) | (~p2(X36, X38))))), rewrite((((~p2(X36, X37)) | p2(X37, X38)) | (~p2(X36, X38))) <=> ((~p2(X36, X38)) | (~p2(X36, X37)) | p2(X37, X38))), (((p2(X37, X38) | (~p2(X36, X37))) | (~p2(X36, X38))) <=> ((~p2(X36, X38)) | (~p2(X36, X37)) | p2(X37, X38))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(97,plain,
% 0.21/0.50 (![X38: $i, X37: $i, X36: $i] : ((p2(X37, X38) | (~p2(X36, X37))) | (~p2(X36, X38))) <=> ![X38: $i, X37: $i, X36: $i] : ((~p2(X36, X38)) | (~p2(X36, X37)) | p2(X37, X38))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[96])).
% 0.21/0.50 tff(98,axiom,(![X38: $i, X37: $i, X36: $i] : ((p2(X37, X38) | (~p2(X36, X37))) | (~p2(X36, X38)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_36')).
% 0.21/0.50 tff(99,plain,
% 0.21/0.50 (![X38: $i, X37: $i, X36: $i] : ((~p2(X36, X38)) | (~p2(X36, X37)) | p2(X37, X38))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.21/0.51 tff(100,plain,
% 0.21/0.51 (![X38: $i, X37: $i, X36: $i] : ((~p2(X36, X38)) | (~p2(X36, X37)) | p2(X37, X38))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[99, 95])).
% 0.21/0.51 tff(101,plain,(
% 0.21/0.51 ![X38: $i, X37: $i, X36: $i] : ((~p2(X36, X38)) | (~p2(X36, X37)) | p2(X37, X38))),
% 0.21/0.51 inference(skolemize,[status(sab)],[100])).
% 0.21/0.51 tff(102,plain,
% 0.21/0.51 (![X38: $i, X37: $i, X36: $i] : ((~p2(X36, X38)) | (~p2(X36, X37)) | p2(X37, X38))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[101, 94])).
% 0.21/0.51 tff(103,plain,
% 0.21/0.51 ((~p2(c38, c40)) <=> (~p2(c38, c40))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(104,axiom,(~p2(c38, c40)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','not_p2_20')).
% 0.21/0.51 tff(105,plain,
% 0.21/0.51 (~p2(c38, c40)),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.21/0.51 tff(106,plain,
% 0.21/0.51 (((~![X38: $i, X37: $i, X36: $i] : ((~p2(X36, X38)) | (~p2(X36, X37)) | p2(X37, X38))) | (p2(c38, c40) | (~p2(c40, c38)) | (~p2(c40, c40)))) <=> ((~![X38: $i, X37: $i, X36: $i] : ((~p2(X36, X38)) | (~p2(X36, X37)) | p2(X37, X38))) | p2(c38, c40) | (~p2(c40, c38)) | (~p2(c40, c40)))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(107,plain,
% 0.21/0.51 (((~p2(c40, c40)) | (~p2(c40, c38)) | p2(c38, c40)) <=> (p2(c38, c40) | (~p2(c40, c38)) | (~p2(c40, c40)))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(108,plain,
% 0.21/0.51 (((~![X38: $i, X37: $i, X36: $i] : ((~p2(X36, X38)) | (~p2(X36, X37)) | p2(X37, X38))) | ((~p2(c40, c40)) | (~p2(c40, c38)) | p2(c38, c40))) <=> ((~![X38: $i, X37: $i, X36: $i] : ((~p2(X36, X38)) | (~p2(X36, X37)) | p2(X37, X38))) | (p2(c38, c40) | (~p2(c40, c38)) | (~p2(c40, c40))))),
% 0.21/0.51 inference(monotonicity,[status(thm)],[107])).
% 0.21/0.51 tff(109,plain,
% 0.21/0.51 (((~![X38: $i, X37: $i, X36: $i] : ((~p2(X36, X38)) | (~p2(X36, X37)) | p2(X37, X38))) | ((~p2(c40, c40)) | (~p2(c40, c38)) | p2(c38, c40))) <=> ((~![X38: $i, X37: $i, X36: $i] : ((~p2(X36, X38)) | (~p2(X36, X37)) | p2(X37, X38))) | p2(c38, c40) | (~p2(c40, c38)) | (~p2(c40, c40)))),
% 0.21/0.51 inference(transitivity,[status(thm)],[108, 106])).
% 0.21/0.51 tff(110,plain,
% 0.21/0.51 ((~![X38: $i, X37: $i, X36: $i] : ((~p2(X36, X38)) | (~p2(X36, X37)) | p2(X37, X38))) | ((~p2(c40, c40)) | (~p2(c40, c38)) | p2(c38, c40))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(111,plain,
% 0.21/0.51 ((~![X38: $i, X37: $i, X36: $i] : ((~p2(X36, X38)) | (~p2(X36, X37)) | p2(X37, X38))) | p2(c38, c40) | (~p2(c40, c38)) | (~p2(c40, c40))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.21/0.51 tff(112,plain,
% 0.21/0.51 ($false),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[111, 105, 102, 92, 83])).
% 0.21/0.51 % SZS output end Proof
%------------------------------------------------------------------------------