TSTP Solution File: TOP052-1 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : TOP052-1 : TPTP v8.1.2. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 12:39:01 EDT 2023
% Result : Unsatisfiable 14.80s 4.13s
% Output : Refutation 14.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 288
% Syntax : Number of formulae : 434 ( 291 unt; 143 typ; 0 def)
% Number of atoms : 291 ( 290 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 1158 ( 2 ~; 0 |; 0 &;1156 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 142 ( 142 >; 0 *; 0 +; 0 <<)
% Number of symbols : 145 ( 143 usr; 142 con; 0-140 aty)
% Number of variables : 12 ( 0 ^; 12 !; 0 ?; 12 :)
% Comments :
%------------------------------------------------------------------------------
thf(tuple_type,type,
tuple: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i ).
thf(a1_type,type,
a1: $i ).
thf(a2_type,type,
a2: $i ).
thf(a41_type,type,
a41: $i ).
thf(a42_type,type,
a42: $i ).
thf(a3_type,type,
a3: $i ).
thf(a40_type,type,
a40: $i ).
thf(a4_type,type,
a4: $i ).
thf(a13_type,type,
a13: $i ).
thf(a14_type,type,
a14: $i ).
thf(a5_type,type,
a5: $i ).
thf(a38_type,type,
a38: $i ).
thf(a39_type,type,
a39: $i ).
thf(a6_type,type,
a6: $i ).
thf(a135_type,type,
a135: $i ).
thf(a136_type,type,
a136: $i ).
thf(a7_type,type,
a7: $i ).
thf(a52_type,type,
a52: $i ).
thf(a51_type,type,
a51: $i ).
thf(a8_type,type,
a8: $i ).
thf(a16_type,type,
a16: $i ).
thf(a17_type,type,
a17: $i ).
thf(a9_type,type,
a9: $i ).
thf(a55_type,type,
a55: $i ).
thf(a56_type,type,
a56: $i ).
thf(a10_type,type,
a10: $i ).
thf(a133_type,type,
a133: $i ).
thf(a134_type,type,
a134: $i ).
thf(a11_type,type,
a11: $i ).
thf(a36_type,type,
a36: $i ).
thf(a37_type,type,
a37: $i ).
thf(a12_type,type,
a12: $i ).
thf(a21_type,type,
a21: $i ).
thf(a20_type,type,
a20: $i ).
thf(a23_type,type,
a23: $i ).
thf(a31_type,type,
a31: $i ).
thf(a32_type,type,
a32: $i ).
thf(a15_type,type,
a15: $i ).
thf(a53_type,type,
a53: $i ).
thf(a28_type,type,
a28: $i ).
thf(a29_type,type,
a29: $i ).
thf(a18_type,type,
a18: $i ).
thf(a132_type,type,
a132: $i ).
thf(a19_type,type,
a19: $i ).
thf(a58_type,type,
a58: $i ).
thf(a57_type,type,
a57: $i ).
thf(a25_type,type,
a25: $i ).
thf(a26_type,type,
a26: $i ).
thf(a34_type,type,
a34: $i ).
thf(a35_type,type,
a35: $i ).
thf(a140_type,type,
a140: $i ).
thf(a44_type,type,
a44: $i ).
thf(a45_type,type,
a45: $i ).
thf(a24_type,type,
a24: $i ).
thf(a48_type,type,
a48: $i ).
thf(a49_type,type,
a49: $i ).
thf(a138_type,type,
a138: $i ).
thf(a137_type,type,
a137: $i ).
thf(a27_type,type,
a27: $i ).
thf(a30_type,type,
a30: $i ).
thf(a33_type,type,
a33: $i ).
thf(a130_type,type,
a130: $i ).
thf(a131_type,type,
a131: $i ).
thf(a59_type,type,
a59: $i ).
thf(a60_type,type,
a60: $i ).
thf(a139_type,type,
a139: $i ).
thf(a46_type,type,
a46: $i ).
thf(a47_type,type,
a47: $i ).
thf(a43_type,type,
a43: $i ).
thf(a61_type,type,
a61: $i ).
thf(a62_type,type,
a62: $i ).
thf(a127_type,type,
a127: $i ).
thf(a128_type,type,
a128: $i ).
thf(a50_type,type,
a50: $i ).
thf(a54_type,type,
a54: $i ).
thf(a63_type,type,
a63: $i ).
thf(a95_type,type,
a95: $i ).
thf(a96_type,type,
a96: $i ).
thf(a64_type,type,
a64: $i ).
thf(a126_type,type,
a126: $i ).
thf(a65_type,type,
a65: $i ).
thf(a66_type,type,
a66: $i ).
thf(a67_type,type,
a67: $i ).
thf(a91_type,type,
a91: $i ).
thf(a92_type,type,
a92: $i ).
thf(a68_type,type,
a68: $i ).
thf(a97_type,type,
a97: $i ).
thf(a98_type,type,
a98: $i ).
thf(a69_type,type,
a69: $i ).
thf(a70_type,type,
a70: $i ).
thf(a71_type,type,
a71: $i ).
thf(a118_type,type,
a118: $i ).
thf(a117_type,type,
a117: $i ).
thf(a72_type,type,
a72: $i ).
thf(a108_type,type,
a108: $i ).
thf(a109_type,type,
a109: $i ).
thf(a73_type,type,
a73: $i ).
thf(a81_type,type,
a81: $i ).
thf(a82_type,type,
a82: $i ).
thf(a74_type,type,
a74: $i ).
thf(a75_type,type,
a75: $i ).
thf(a76_type,type,
a76: $i ).
thf(a77_type,type,
a77: $i ).
thf(a113_type,type,
a113: $i ).
thf(a114_type,type,
a114: $i ).
thf(a78_type,type,
a78: $i ).
thf(a79_type,type,
a79: $i ).
thf(a80_type,type,
a80: $i ).
thf(a119_type,type,
a119: $i ).
thf(a83_type,type,
a83: $i ).
thf(a84_type,type,
a84: $i ).
thf(a85_type,type,
a85: $i ).
thf(a86_type,type,
a86: $i ).
thf(a87_type,type,
a87: $i ).
thf(a103_type,type,
a103: $i ).
thf(a104_type,type,
a104: $i ).
thf(a88_type,type,
a88: $i ).
thf(a89_type,type,
a89: $i ).
thf(a90_type,type,
a90: $i ).
thf(a99_type,type,
a99: $i ).
thf(a100_type,type,
a100: $i ).
thf(a123_type,type,
a123: $i ).
thf(a124_type,type,
a124: $i ).
thf(a93_type,type,
a93: $i ).
thf(a94_type,type,
a94: $i ).
thf(a101_type,type,
a101: $i ).
thf(a102_type,type,
a102: $i ).
thf(a105_type,type,
a105: $i ).
thf(a106_type,type,
a106: $i ).
thf(a107_type,type,
a107: $i ).
thf(a110_type,type,
a110: $i ).
thf(a111_type,type,
a111: $i ).
thf(a112_type,type,
a112: $i ).
thf(a115_type,type,
a115: $i ).
thf(a116_type,type,
a116: $i ).
thf(a120_type,type,
a120: $i ).
thf(a121_type,type,
a121: $i ).
thf(a122_type,type,
a122: $i ).
thf(a125_type,type,
a125: $i ).
thf(a129_type,type,
a129: $i ).
thf(a22_type,type,
a22: $i ).
thf(a141_type,type,
a141: $i ).
thf(product_type,type,
product: $i > $i > $i ).
thf(15,axiom,
( a79
= ( product @ a78 @ a33 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_79) ).
thf(175,plain,
( a79
= ( product @ a78 @ a33 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(110,axiom,
( a80
= ( product @ a79 @ a119 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_80) ).
thf(365,plain,
( a80
= ( product @ a79 @ a119 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(101,axiom,
( a138
= ( product @ a137 @ a51 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_138) ).
thf(347,plain,
( a138
= ( product @ a137 @ a51 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(94,axiom,
( a119
= ( product @ a118 @ a70 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_119) ).
thf(333,plain,
( a119
= ( product @ a118 @ a70 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(52,axiom,
( a104
= ( product @ a103 @ a87 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_104) ).
thf(249,plain,
( a104
= ( product @ a103 @ a87 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(36,axiom,
( a15
= ( product @ a14 @ a53 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_15) ).
thf(217,plain,
( a15
= ( product @ a14 @ a53 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(51,axiom,
( a137
= ( product @ a136 @ a39 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_137) ).
thf(247,plain,
( a137
= ( product @ a136 @ a39 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(117,axiom,
( a28
= ( product @ a27 @ a37 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_28) ).
thf(379,plain,
( a28
= ( product @ a27 @ a37 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(62,axiom,
( a120
= ( product @ a119 @ a13 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_120) ).
thf(269,plain,
( a120
= ( product @ a119 @ a13 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(120,axiom,
( a77
= ( product @ a76 @ a114 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_77) ).
thf(385,plain,
( a77
= ( product @ a76 @ a114 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( product @ ( product @ A @ B ) @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutory_quandle_01) ).
thf(153,plain,
! [B: $i,A: $i] :
( ( product @ ( product @ A @ B ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(20,axiom,
( a44
= ( product @ a43 @ a128 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_44) ).
thf(185,plain,
( a44
= ( product @ a43 @ a128 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(136,axiom,
( a111
= ( product @ a110 @ a119 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_111) ).
thf(417,plain,
( a111
= ( product @ a110 @ a119 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(78,axiom,
( a36
= ( product @ a35 @ a139 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_36) ).
thf(301,plain,
( a36
= ( product @ a35 @ a139 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(56,axiom,
( a59
= ( product @ a58 @ a138 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_59) ).
thf(257,plain,
( a59
= ( product @ a58 @ a138 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(122,axiom,
( a64
= ( product @ a63 @ a127 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_64) ).
thf(389,plain,
( a64
= ( product @ a63 @ a127 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(106,axiom,
( a17
= ( product @ a16 @ a29 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_17) ).
thf(357,plain,
( a17
= ( product @ a16 @ a29 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(6,axiom,
( a117
= ( product @ a116 @ a74 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_117) ).
thf(157,plain,
( a117
= ( product @ a116 @ a74 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(22,axiom,
( a134
= ( product @ a133 @ a26 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_134) ).
thf(189,plain,
( a134
= ( product @ a133 @ a26 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(138,axiom,
( a4
= ( product @ a3 @ a14 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_04) ).
thf(421,plain,
( a4
= ( product @ a3 @ a14 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(90,axiom,
( a114
= ( product @ a113 @ a13 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_114) ).
thf(325,plain,
( a114
= ( product @ a113 @ a13 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(72,axiom,
( a99
= ( product @ a98 @ a92 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_99) ).
thf(289,plain,
( a99
= ( product @ a98 @ a92 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(58,axiom,
( a66
= ( product @ a65 @ a2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_66) ).
thf(261,plain,
( a66
= ( product @ a65 @ a2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(17,axiom,
( a60
= ( product @ a59 @ a131 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_60) ).
thf(179,plain,
( a60
= ( product @ a59 @ a131 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(88,axiom,
( a139
= ( product @ a138 @ a20 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_139) ).
thf(321,plain,
( a139
= ( product @ a138 @ a20 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(104,axiom,
( a55
= ( product @ a54 @ a135 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_55) ).
thf(353,plain,
( a55
= ( product @ a54 @ a135 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(33,axiom,
( a96
= ( product @ a95 @ a64 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_96) ).
thf(211,plain,
( a96
= ( product @ a95 @ a64 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(54,axiom,
( a5
= ( product @ a4 @ a39 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_05) ).
thf(253,plain,
( a5
= ( product @ a4 @ a39 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(126,axiom,
( a32
= ( product @ a31 @ a39 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_32) ).
thf(397,plain,
( a32
= ( product @ a31 @ a39 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(38,axiom,
( a8
= ( product @ a7 @ a17 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_08) ).
thf(221,plain,
( a8
= ( product @ a7 @ a17 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(74,axiom,
( a127
= ( product @ a126 @ a41 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_127) ).
thf(293,plain,
( a127
= ( product @ a126 @ a41 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(133,axiom,
( a26
= ( product @ a25 @ a138 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_26) ).
thf(411,plain,
( a26
= ( product @ a25 @ a138 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(49,axiom,
( a73
= ( product @ a72 @ a82 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_73) ).
thf(243,plain,
( a73
= ( product @ a72 @ a82 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(60,axiom,
( a92
= ( product @ a91 @ a124 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_92) ).
thf(265,plain,
( a92
= ( product @ a91 @ a124 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(81,axiom,
( a100
= ( product @ a99 @ a124 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_100) ).
thf(307,plain,
( a100
= ( product @ a99 @ a124 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(44,axiom,
( a3
= ( product @ a2 @ a41 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_03) ).
thf(233,plain,
( a3
= ( product @ a2 @ a41 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(28,axiom,
( a50
= ( product @ a49 @ a131 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_50) ).
thf(201,plain,
( a50
= ( product @ a49 @ a131 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(118,axiom,
( a87
= ( product @ a86 @ a104 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_87) ).
thf(381,plain,
( a87
= ( product @ a86 @ a104 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(102,axiom,
( a41
= ( product @ a40 @ a14 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_41) ).
thf(349,plain,
( a41
= ( product @ a40 @ a14 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(76,axiom,
( a95
= ( product @ a94 @ a127 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_95) ).
thf(297,plain,
( a95
= ( product @ a94 @ a127 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(131,axiom,
( a22
= ( product @ a21 @ a141 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_22) ).
thf(407,plain,
( a22
= ( product @ a21 @ a141 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(142,axiom,
( a69
= ( product @ a68 @ a32 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_69) ).
thf(429,plain,
( a69
= ( product @ a68 @ a32 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(65,axiom,
( a109
= ( product @ a108 @ a118 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_109) ).
thf(275,plain,
( a109
= ( product @ a108 @ a118 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(10,axiom,
( a65
= ( product @ a64 @ a41 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_65) ).
thf(165,plain,
( a65
= ( product @ a64 @ a41 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(42,axiom,
( a121
= ( product @ a120 @ a32 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_121) ).
thf(229,plain,
( a121
= ( product @ a120 @ a32 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(26,axiom,
( a75
= ( product @ a74 @ a14 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_75) ).
thf(197,plain,
( a75
= ( product @ a74 @ a14 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(108,axiom,
( a33
= ( product @ a32 @ a13 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_33) ).
thf(361,plain,
( a33
= ( product @ a32 @ a13 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(145,axiom,
( a56
= ( product @ a55 @ a37 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_56) ).
thf(435,plain,
( a56
= ( product @ a55 @ a37 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(92,axiom,
( a42
= ( product @ a41 @ a2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_42) ).
thf(329,plain,
( a42
= ( product @ a41 @ a2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(70,axiom,
( a31
= ( product @ a30 @ a5 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_31) ).
thf(285,plain,
( a31
= ( product @ a30 @ a5 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(86,axiom,
( a35
= ( product @ a34 @ a60 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_35) ).
thf(317,plain,
( a35
= ( product @ a34 @ a60 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(129,axiom,
( a85
= ( product @ a84 @ a5 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_85) ).
thf(403,plain,
( a85
= ( product @ a84 @ a5 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(12,axiom,
( a49
= ( product @ a48 @ a138 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_49) ).
thf(169,plain,
( a49
= ( product @ a48 @ a138 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(40,axiom,
( a16
= ( product @ a15 @ a136 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_16) ).
thf(225,plain,
( a16
= ( product @ a15 @ a136 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(97,axiom,
( a7
= ( product @ a6 @ a52 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_07) ).
thf(339,plain,
( a7
= ( product @ a6 @ a52 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(24,axiom,
( a12
= ( product @ a11 @ a21 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_12) ).
thf(193,plain,
( a12
= ( product @ a11 @ a21 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(124,axiom,
( a29
= ( product @ a28 @ a17 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_29) ).
thf(393,plain,
( a29
= ( product @ a28 @ a17 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(14,axiom,
( a118
= ( product @ a117 @ a32 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_118) ).
thf(173,plain,
( a118
= ( product @ a117 @ a32 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(113,axiom,
( a25
= ( product @ a24 @ a49 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_25) ).
thf(371,plain,
( a25
= ( product @ a24 @ a49 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(30,axiom,
( a140
= ( product @ a139 @ a47 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_140) ).
thf(205,plain,
( a140
= ( product @ a139 @ a47 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(83,axiom,
( a129
= ( product @ a128 @ a62 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_129) ).
thf(311,plain,
( a129
= ( product @ a128 @ a62 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(99,axiom,
( a21
= ( product @ a20 @ a35 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_21) ).
thf(343,plain,
( a21
= ( product @ a20 @ a35 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(46,axiom,
( a9
= ( product @ a8 @ a56 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_09) ).
thf(237,plain,
( a9
= ( product @ a8 @ a56 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(140,axiom,
( a10
= ( product @ a9 @ a134 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_10) ).
thf(425,plain,
( a10
= ( product @ a9 @ a134 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(8,axiom,
( a68
= ( product @ a67 @ a98 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_68) ).
thf(161,plain,
( a68
= ( product @ a67 @ a98 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(67,axiom,
( a18
= ( product @ a17 @ a133 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_18) ).
thf(279,plain,
( a18
= ( product @ a17 @ a133 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(2,axiom,
! [A: $i] :
( ( product @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutory_quandle) ).
thf(149,plain,
! [A: $i] :
( ( product @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(115,axiom,
( a86
= ( product @ a85 @ a30 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_86) ).
thf(375,plain,
( a86
= ( product @ a85 @ a30 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(139,axiom,
( a2
= ( product @ a1 @ a42 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot) ).
thf(423,plain,
( a2
= ( product @ a1 @ a42 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(23,axiom,
( a115
= ( product @ a114 @ a68 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_115) ).
thf(191,plain,
( a115
= ( product @ a114 @ a68 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(73,axiom,
( a110
= ( product @ a109 @ a70 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_110) ).
thf(291,plain,
( a110
= ( product @ a109 @ a70 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(68,axiom,
( a84
= ( product @ a83 @ a39 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_84) ).
thf(281,plain,
( a84
= ( product @ a83 @ a39 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(57,axiom,
( a43
= ( product @ a42 @ a62 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_43) ).
thf(259,plain,
( a43
= ( product @ a42 @ a62 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(134,axiom,
( a67
= ( product @ a66 @ a92 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_67) ).
thf(413,plain,
( a67
= ( product @ a66 @ a92 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(123,axiom,
( a89
= ( product @ a88 @ a14 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_89) ).
thf(391,plain,
( a89
= ( product @ a88 @ a14 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(84,axiom,
( a81
= ( product @ a80 @ a70 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_81) ).
thf(313,plain,
( a81
= ( product @ a80 @ a70 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(95,axiom,
( a47
= ( product @ a46 @ a11 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_47) ).
thf(335,plain,
( a47
= ( product @ a46 @ a11 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(18,axiom,
( a48
= ( product @ a47 @ a20 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_48) ).
thf(181,plain,
( a48
= ( product @ a47 @ a20 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(7,axiom,
( a106
= ( product @ a105 @ a5 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_106) ).
thf(159,plain,
( a106
= ( product @ a105 @ a5 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(21,axiom,
( a135
= ( product @ a134 @ a37 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_135) ).
thf(187,plain,
( a135
= ( product @ a134 @ a37 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(37,axiom,
( a14
= ( product @ a13 @ a32 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_14) ).
thf(219,plain,
( a14
= ( product @ a13 @ a32 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(137,axiom,
( a74
= ( product @ a73 @ a32 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_74) ).
thf(419,plain,
( a74
= ( product @ a73 @ a32 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(116,axiom,
( a101
= ( product @ a100 @ a14 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_101) ).
thf(377,plain,
( a101
= ( product @ a100 @ a14 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(50,axiom,
( a107
= ( product @ a106 @ a84 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_107) ).
thf(245,plain,
( a107
= ( product @ a106 @ a84 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(79,axiom,
( a72
= ( product @ a71 @ a109 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_72) ).
thf(303,plain,
( a72
= ( product @ a71 @ a109 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(63,axiom,
( a45
= ( product @ a44 @ a23 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_45) ).
thf(271,plain,
( a45
= ( product @ a44 @ a23 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(121,axiom,
( a78
= ( product @ a77 @ a13 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_78) ).
thf(387,plain,
( a78
= ( product @ a77 @ a13 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(89,axiom,
( a6
= ( product @ a5 @ a136 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_06) ).
thf(323,plain,
( a6
= ( product @ a5 @ a136 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(34,axiom,
( a98
= ( product @ a97 @ a1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_98) ).
thf(213,plain,
( a98
= ( product @ a97 @ a1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(53,axiom,
( a39
= ( product @ a38 @ a7 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_39) ).
thf(251,plain,
( a39
= ( product @ a38 @ a7 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(5,axiom,
( a54
= ( product @ a53 @ a29 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_54) ).
thf(155,plain,
( a54
= ( product @ a53 @ a29 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(100,axiom,
( a51
= ( product @ a50 @ a59 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_51) ).
thf(345,plain,
( a51
= ( product @ a50 @ a59 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(111,axiom,
( a34
= ( product @ a33 @ a131 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_34) ).
thf(367,plain,
( a34
= ( product @ a33 @ a131 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(127,axiom,
( a27
= ( product @ a26 @ a8 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_27) ).
thf(399,plain,
( a27
= ( product @ a26 @ a8 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(39,axiom,
( a102
= ( product @ a101 @ a40 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_102) ).
thf(223,plain,
( a102
= ( product @ a101 @ a40 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(77,axiom,
( a108
= ( product @ a107 @ a39 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_108) ).
thf(299,plain,
( a108
= ( product @ a107 @ a39 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(61,axiom,
( a136
= ( product @ a135 @ a29 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_136) ).
thf(267,plain,
( a136
= ( product @ a135 @ a29 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(143,axiom,
( a113
= ( product @ a112 @ a33 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_113) ).
thf(431,plain,
( a113
= ( product @ a112 @ a33 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(48,axiom,
( a123
= ( product @ a122 @ a115 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_123) ).
thf(241,plain,
( a123
= ( product @ a122 @ a115 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(11,axiom,
( a125
= ( product @ a124 @ a2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_125) ).
thf(167,plain,
( a125
= ( product @ a124 @ a2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(55,axiom,
( a82
= ( product @ a81 @ a109 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_82) ).
thf(255,plain,
( a82
= ( product @ a81 @ a109 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(32,axiom,
( a131
= ( product @ a130 @ a13 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_131) ).
thf(209,plain,
( a131
= ( product @ a130 @ a13 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(105,axiom,
( a97
= ( product @ a96 @ a42 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_97) ).
thf(355,plain,
( a97
= ( product @ a96 @ a42 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(75,axiom,
( a46
= ( product @ a45 @ a141 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_46) ).
thf(295,plain,
( a46
= ( product @ a45 @ a141 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(91,axiom,
( a76
= ( product @ a75 @ a68 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_76) ).
thf(327,plain,
( a76
= ( product @ a75 @ a68 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(132,axiom,
( a13
= ( product @ a12 @ a23 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_13) ).
thf(409,plain,
( a13
= ( product @ a12 @ a23 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(59,axiom,
( a83
= ( product @ a82 @ a118 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_83) ).
thf(263,plain,
( a83
= ( product @ a82 @ a118 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(27,axiom,
( a24
= ( product @ a23 @ a35 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_24) ).
thf(199,plain,
( a24
= ( product @ a23 @ a35 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(16,axiom,
( a88
= ( product @ a87 @ a4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_88) ).
thf(177,plain,
( a88
= ( product @ a87 @ a4 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(93,axiom,
( a141
= ( product @ a140 @ a11 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_141) ).
thf(331,plain,
( a141
= ( product @ a140 @ a11 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(107,axiom,
( a105
= ( product @ a104 @ a30 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_105) ).
thf(359,plain,
( a105
= ( product @ a104 @ a30 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(43,axiom,
( a30
= ( product @ a29 @ a14 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_30) ).
thf(231,plain,
( a30
= ( product @ a29 @ a14 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(109,axiom,
( a61
= ( product @ a60 @ a13 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_61) ).
thf(363,plain,
( a61
= ( product @ a60 @ a13 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(29,axiom,
( a126
= ( product @ a125 @ a65 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_126) ).
thf(203,plain,
( a126
= ( product @ a125 @ a65 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(87,axiom,
( a116
= ( product @ a115 @ a14 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_116) ).
thf(319,plain,
( a116
= ( product @ a115 @ a14 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(103,axiom,
( a122
= ( product @ a121 @ a68 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_122) ).
thf(351,plain,
( a122
= ( product @ a121 @ a68 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(128,axiom,
( a57
= ( product @ a56 @ a134 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_57) ).
thf(401,plain,
( a57
= ( product @ a56 @ a134 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(13,axiom,
( a93
= ( product @ a92 @ a2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_93) ).
thf(171,plain,
( a93
= ( product @ a92 @ a2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(45,axiom,
( a133
= ( product @ a132 @ a58 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_133) ).
thf(235,plain,
( a133
= ( product @ a132 @ a58 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(144,axiom,
( a11
= ( product @ a10 @ a37 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_11) ).
thf(433,plain,
( a11
= ( product @ a10 @ a37 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(31,axiom,
( a19
= ( product @ a18 @ a58 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_19) ).
thf(207,plain,
( a19
= ( product @ a18 @ a58 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(119,axiom,
( a103
= ( product @ a102 @ a4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_103) ).
thf(383,plain,
( a103
= ( product @ a102 @ a4 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(71,axiom,
( a40
= ( product @ a39 @ a4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_40) ).
thf(287,plain,
( a40
= ( product @ a39 @ a4 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(3,axiom,
! [C: $i,B: $i,A: $i] :
( ( product @ ( product @ A @ B ) @ C )
= ( product @ ( product @ A @ C ) @ ( product @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutory_quandle_02) ).
thf(151,plain,
! [C: $i,B: $i,A: $i] :
( ( product @ ( product @ A @ B ) @ C )
= ( product @ ( product @ A @ C ) @ ( product @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(85,axiom,
( a71
= ( product @ a70 @ a118 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_71) ).
thf(315,plain,
( a71
= ( product @ a70 @ a118 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(1,negated_conjecture,
( ( tuple @ a1 @ a2 @ a41 @ a42 @ a3 @ a40 @ a4 @ a13 @ a14 @ a5 @ a38 @ a39 @ a6 @ a135 @ a136 @ a7 @ a52 @ a51 @ a8 @ a16 @ a17 @ a9 @ a55 @ a56 @ a10 @ a133 @ a134 @ a11 @ a36 @ a37 @ a12 @ a21 @ a20 @ a23 @ a31 @ a32 @ a15 @ a53 @ a28 @ a29 @ a18 @ a132 @ a19 @ a58 @ a57 @ a20 @ a25 @ a26 @ a34 @ a35 @ a140 @ a44 @ a45 @ a24 @ a48 @ a49 @ a138 @ a137 @ a27 @ a30 @ a33 @ a130 @ a131 @ a59 @ a60 @ a139 @ a46 @ a47 @ a43 @ a61 @ a62 @ a127 @ a128 @ a50 @ a54 @ a63 @ a95 @ a96 @ a64 @ a126 @ a65 @ a66 @ a67 @ a91 @ a92 @ a68 @ a97 @ a98 @ a69 @ a70 @ a71 @ a118 @ a117 @ a72 @ a108 @ a109 @ a73 @ a81 @ a82 @ a74 @ a75 @ a76 @ a77 @ a113 @ a114 @ a78 @ a79 @ a80 @ a119 @ a83 @ a84 @ a85 @ a86 @ a87 @ a103 @ a104 @ a88 @ a89 @ a90 @ a99 @ a100 @ a123 @ a124 @ a93 @ a94 @ a101 @ a102 @ a105 @ a106 @ a107 @ a110 @ a111 @ a112 @ a115 @ a116 @ a120 @ a121 @ a122 @ a125 @ a129 )
!= ( tuple @ a2 @ a3 @ a42 @ a43 @ a4 @ a41 @ a5 @ a14 @ a15 @ a6 @ a39 @ a40 @ a7 @ a136 @ a137 @ a8 @ a53 @ a52 @ a9 @ a17 @ a18 @ a10 @ a56 @ a57 @ a11 @ a134 @ a135 @ a12 @ a37 @ a38 @ a13 @ a23 @ a21 @ a24 @ a32 @ a33 @ a16 @ a54 @ a29 @ a30 @ a19 @ a133 @ a20 @ a59 @ a58 @ a22 @ a26 @ a27 @ a35 @ a36 @ a141 @ a45 @ a46 @ a25 @ a49 @ a50 @ a139 @ a138 @ a28 @ a31 @ a34 @ a131 @ a132 @ a60 @ a61 @ a140 @ a47 @ a48 @ a44 @ a62 @ a63 @ a128 @ a129 @ a51 @ a55 @ a64 @ a96 @ a97 @ a65 @ a127 @ a66 @ a67 @ a68 @ a92 @ a93 @ a69 @ a98 @ a99 @ a70 @ a71 @ a72 @ a119 @ a118 @ a73 @ a109 @ a110 @ a74 @ a82 @ a83 @ a75 @ a76 @ a77 @ a78 @ a114 @ a115 @ a79 @ a80 @ a81 @ a120 @ a84 @ a85 @ a86 @ a87 @ a88 @ a104 @ a105 @ a89 @ a90 @ a91 @ a100 @ a101 @ a124 @ a125 @ a94 @ a95 @ a102 @ a103 @ a106 @ a107 @ a108 @ a111 @ a112 @ a113 @ a116 @ a117 @ a121 @ a122 @ a123 @ a126 @ a130 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal) ).
thf(146,plain,
( ( tuple @ a1 @ a2 @ a41 @ a42 @ a3 @ a40 @ a4 @ a13 @ a14 @ a5 @ a38 @ a39 @ a6 @ a135 @ a136 @ a7 @ a52 @ a51 @ a8 @ a16 @ a17 @ a9 @ a55 @ a56 @ a10 @ a133 @ a134 @ a11 @ a36 @ a37 @ a12 @ a21 @ a20 @ a23 @ a31 @ a32 @ a15 @ a53 @ a28 @ a29 @ a18 @ a132 @ a19 @ a58 @ a57 @ a20 @ a25 @ a26 @ a34 @ a35 @ a140 @ a44 @ a45 @ a24 @ a48 @ a49 @ a138 @ a137 @ a27 @ a30 @ a33 @ a130 @ a131 @ a59 @ a60 @ a139 @ a46 @ a47 @ a43 @ a61 @ a62 @ a127 @ a128 @ a50 @ a54 @ a63 @ a95 @ a96 @ a64 @ a126 @ a65 @ a66 @ a67 @ a91 @ a92 @ a68 @ a97 @ a98 @ a69 @ a70 @ a71 @ a118 @ a117 @ a72 @ a108 @ a109 @ a73 @ a81 @ a82 @ a74 @ a75 @ a76 @ a77 @ a113 @ a114 @ a78 @ a79 @ a80 @ a119 @ a83 @ a84 @ a85 @ a86 @ a87 @ a103 @ a104 @ a88 @ a89 @ a90 @ a99 @ a100 @ a123 @ a124 @ a93 @ a94 @ a101 @ a102 @ a105 @ a106 @ a107 @ a110 @ a111 @ a112 @ a115 @ a116 @ a120 @ a121 @ a122 @ a125 @ a129 )
!= ( tuple @ a2 @ a3 @ a42 @ a43 @ a4 @ a41 @ a5 @ a14 @ a15 @ a6 @ a39 @ a40 @ a7 @ a136 @ a137 @ a8 @ a53 @ a52 @ a9 @ a17 @ a18 @ a10 @ a56 @ a57 @ a11 @ a134 @ a135 @ a12 @ a37 @ a38 @ a13 @ a23 @ a21 @ a24 @ a32 @ a33 @ a16 @ a54 @ a29 @ a30 @ a19 @ a133 @ a20 @ a59 @ a58 @ a22 @ a26 @ a27 @ a35 @ a36 @ a141 @ a45 @ a46 @ a25 @ a49 @ a50 @ a139 @ a138 @ a28 @ a31 @ a34 @ a131 @ a132 @ a60 @ a61 @ a140 @ a47 @ a48 @ a44 @ a62 @ a63 @ a128 @ a129 @ a51 @ a55 @ a64 @ a96 @ a97 @ a65 @ a127 @ a66 @ a67 @ a68 @ a92 @ a93 @ a69 @ a98 @ a99 @ a70 @ a71 @ a72 @ a119 @ a118 @ a73 @ a109 @ a110 @ a74 @ a82 @ a83 @ a75 @ a76 @ a77 @ a78 @ a114 @ a115 @ a79 @ a80 @ a81 @ a120 @ a84 @ a85 @ a86 @ a87 @ a88 @ a104 @ a105 @ a89 @ a90 @ a91 @ a100 @ a101 @ a124 @ a125 @ a94 @ a95 @ a102 @ a103 @ a106 @ a107 @ a108 @ a111 @ a112 @ a113 @ a116 @ a117 @ a121 @ a122 @ a123 @ a126 @ a130 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(130,axiom,
( a94
= ( product @ a93 @ a41 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_94) ).
thf(405,plain,
( a94
= ( product @ a93 @ a41 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(19,axiom,
( a23
= ( product @ a22 @ a45 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_23) ).
thf(183,plain,
( a23
= ( product @ a22 @ a45 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(64,axiom,
( a1
= ( product @ a141 @ a23 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_142) ).
thf(273,plain,
( a1
= ( product @ a141 @ a23 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(114,axiom,
( a128
= ( product @ a127 @ a96 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_128) ).
thf(373,plain,
( a128
= ( product @ a127 @ a96 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(80,axiom,
( a38
= ( product @ a37 @ a17 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_38) ).
thf(305,plain,
( a38
= ( product @ a37 @ a17 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(47,axiom,
( a91
= ( product @ a90 @ a100 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_91) ).
thf(239,plain,
( a91
= ( product @ a90 @ a100 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(98,axiom,
( a130
= ( product @ a129 @ a1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_130) ).
thf(341,plain,
( a130
= ( product @ a129 @ a1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(25,axiom,
( a52
= ( product @ a51 @ a39 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_52) ).
thf(195,plain,
( a52
= ( product @ a51 @ a39 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(69,axiom,
( a124
= ( product @ a123 @ a75 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_124) ).
thf(283,plain,
( a124
= ( product @ a123 @ a75 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(135,axiom,
( a90
= ( product @ a89 @ a41 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_90) ).
thf(415,plain,
( a90
= ( product @ a89 @ a41 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(125,axiom,
( a37
= ( product @ a36 @ a47 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_37) ).
thf(395,plain,
( a37
= ( product @ a36 @ a47 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(141,axiom,
( a20
= ( product @ a19 @ a26 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_20) ).
thf(427,plain,
( a20
= ( product @ a19 @ a26 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(9,axiom,
( a112
= ( product @ a111 @ a79 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_112) ).
thf(163,plain,
( a112
= ( product @ a111 @ a79 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(66,axiom,
( a63
= ( product @ a62 @ a96 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_63) ).
thf(277,plain,
( a63
= ( product @ a62 @ a96 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(112,axiom,
( a62
= ( product @ a61 @ a1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_62) ).
thf(369,plain,
( a62
= ( product @ a61 @ a1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(41,axiom,
( a53
= ( product @ a52 @ a136 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_53) ).
thf(227,plain,
( a53
= ( product @ a52 @ a136 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(96,axiom,
( a70
= ( product @ a69 @ a13 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_70) ).
thf(337,plain,
( a70
= ( product @ a69 @ a13 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(82,axiom,
( a132
= ( product @ a131 @ a138 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_132) ).
thf(309,plain,
( a132
= ( product @ a131 @ a138 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(35,axiom,
( a58
= ( product @ a57 @ a26 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_58) ).
thf(215,plain,
( a58
= ( product @ a57 @ a26 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(1176,plain,
$false,
inference(e,[status(thm)],[175,365,347,333,249,217,247,379,269,385,153,185,417,301,257,389,357,157,189,421,325,289,261,179,321,353,211,253,397,221,293,411,243,265,307,233,201,381,349,297,407,429,275,165,229,197,361,435,329,285,317,403,169,225,339,193,393,173,371,205,311,343,237,425,161,279,149,375,423,191,291,281,259,413,391,313,335,181,159,187,219,419,377,245,303,271,387,323,213,251,155,345,367,399,223,299,267,431,241,167,255,209,355,295,327,409,263,199,177,331,359,231,363,203,319,351,401,171,235,433,207,383,287,151,315,146,405,183,273,373,305,239,341,195,283,415,395,427,163,277,369,227,337,309,215]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : TOP052-1 : TPTP v8.1.2. Released v8.1.0.
% 0.11/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n017.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu May 18 19:30:31 EDT 2023
% 0.15/0.37 % CPUTime :
% 1.02/0.91 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.26/1.08 % [INFO] Parsing done (167ms).
% 1.56/1.09 % [INFO] Running in sequential loop mode.
% 1.84/1.28 % [INFO] eprover registered as external prover.
% 1.84/1.29 % [INFO] cvc4 registered as external prover.
% 1.84/1.29 % [INFO] Scanning for conjecture ...
% 2.30/1.40 % [INFO] Found a conjecture and 144 axioms. Running axiom selection ...
% 2.63/1.49 % [INFO] Axiom selection finished. Selected 144 axioms (removed 0 axioms).
% 2.84/1.53 % [INFO] Problem is propositional (TPTP CNF).
% 2.84/1.54 % [INFO] Type checking passed.
% 2.84/1.54 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 14.80/4.13 % External prover 'e' found a proof!
% 14.80/4.13 % [INFO] Killing All external provers ...
% 14.80/4.13 % Time passed: 3602ms (effective reasoning time: 3040ms)
% 14.80/4.13 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 14.80/4.13 % Axioms used in derivation (144): knot_104, knot_64, knot_142, knot_59, knot_19, knot_43, knot_83, knot_131, knot_50, knot_118, knot_124, knot_99, knot_103, knot_86, knot_132, involutory_quandle_01, knot_04, knot_92, knot_26, knot_123, knot_72, knot_58, knot_54, knot_18, knot_37, knot_98, knot_117, knot_32, knot_47, knot_65, knot_07, knot_15, knot_137, knot_10, knot_76, knot_128, knot_61, knot_21, knot_113, knot_95, knot_69, knot_29, knot_110, knot_116, knot_87, knot_44, knot_84, knot_127, knot_119, knot_81, knot_97, knot_77, knot_62, knot_06, knot_40, knot_17, knot_51, knot_70, knot_14, knot_46, knot_22, knot_11, knot_57, knot_129, involutory_quandle, knot_25, knot_28, knot_73, knot_36, knot_68, knot_33, knot_135, knot_122, knot_109, knot_66, knot_136, knot_55, knot_94, knot_03, knot_39, knot_126, knot_12, knot_52, knot_74, knot_63, knot_79, knot_115, knot_90, knot_88, knot_34, knot_111, knot_27, knot_85, knot_120, knot_100, knot_30, knot_105, knot_05, knot_16, knot_23, knot_140, knot, knot_49, knot_09, knot_80, knot_121, knot_108, knot_35, knot_93, knot_41, knot_24, knot_134, knot_13, knot_78, knot_139, knot_89, knot_106, knot_82, knot_42, knot_130, knot_60, knot_101, knot_67, knot_141, knot_56, knot_45, knot_112, knot_133, knot_91, knot_71, knot_31, knot_96, knot_20, knot_102, knot_125, knot_138, knot_107, knot_48, knot_53, knot_08, knot_114, knot_38, involutory_quandle_02, knot_75
% 14.80/4.13 % No. of inferences in proof: 291
% 14.80/4.13 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3602 ms resp. 3040 ms w/o parsing
% 14.80/4.18 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 14.80/4.18 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------