TSTP Solution File: GRP258-1 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : GRP258-1 : TPTP v8.1.2. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n010.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 11:13:34 EDT 2023
% Result : Unsatisfiable 5.52s 2.25s
% Output : Refutation 5.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 89
% Syntax : Number of formulae : 164 ( 7 unt; 15 typ; 0 def)
% Number of atoms : 321 ( 320 equ; 0 cnn)
% Maximal formula atoms : 17 ( 2 avg)
% Number of connectives : 714 ( 34 ~; 172 |; 0 &; 508 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 15 usr; 14 con; 0-2 aty)
% Number of variables : 28 ( 0 ^; 28 !; 0 ?; 28 :)
% Comments :
%------------------------------------------------------------------------------
thf(multiply_type,type,
multiply: $i > $i > $i ).
thf(sk_c1_type,type,
sk_c1: $i ).
thf(sk_c12_type,type,
sk_c12: $i ).
thf(sk_c11_type,type,
sk_c11: $i ).
thf(sk_c4_type,type,
sk_c4: $i ).
thf(inverse_type,type,
inverse: $i > $i ).
thf(sk_c5_type,type,
sk_c5: $i ).
thf(sk_c10_type,type,
sk_c10: $i ).
thf(sk_c6_type,type,
sk_c6: $i ).
thf(sk_c9_type,type,
sk_c9: $i ).
thf(sk_c8_type,type,
sk_c8: $i ).
thf(sk_c7_type,type,
sk_c7: $i ).
thf(sk_c2_type,type,
sk_c2: $i ).
thf(sk_c3_type,type,
sk_c3: $i ).
thf(identity_type,type,
identity: $i ).
thf(47,negated_conjecture,
( ( ( multiply @ sk_c10 @ sk_c12 )
= sk_c11 )
| ( ( multiply @ sk_c9 @ sk_c11 )
= sk_c12 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_47) ).
thf(142,plain,
( ( ( multiply @ sk_c10 @ sk_c12 )
= sk_c11 )
| ( ( multiply @ sk_c9 @ sk_c11 )
= sk_c12 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(58,negated_conjecture,
( ( ( multiply @ sk_c3 @ sk_c10 )
= sk_c12 )
| ( ( inverse @ sk_c8 )
= sk_c7 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_58) ).
thf(137,plain,
( ( ( multiply @ sk_c3 @ sk_c10 )
= sk_c12 )
| ( ( inverse @ sk_c8 )
= sk_c7 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(19,negated_conjecture,
( ( ( inverse @ sk_c1 )
= sk_c12 )
| ( ( inverse @ sk_c7 )
= sk_c9 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_19) ).
thf(141,plain,
( ( ( inverse @ sk_c1 )
= sk_c12 )
| ( ( inverse @ sk_c7 )
= sk_c9 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(31,negated_conjecture,
( ( ( inverse @ sk_c2 )
= sk_c11 )
| ( ( multiply @ sk_c4 @ sk_c12 )
= sk_c11 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_31) ).
thf(129,plain,
( ( ( inverse @ sk_c2 )
= sk_c11 )
| ( ( multiply @ sk_c4 @ sk_c12 )
= sk_c11 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(6,negated_conjecture,
( ( ( multiply @ sk_c1 @ sk_c12 )
= sk_c11 )
| ( ( inverse @ sk_c6 )
= sk_c9 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
thf(95,plain,
( ( ( multiply @ sk_c1 @ sk_c12 )
= sk_c11 )
| ( ( inverse @ sk_c6 )
= sk_c9 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(67,negated_conjecture,
( ( ( inverse @ sk_c3 )
= sk_c10 )
| ( ( multiply @ sk_c9 @ sk_c11 )
= sk_c12 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_67) ).
thf(127,plain,
( ( ( inverse @ sk_c3 )
= sk_c10 )
| ( ( multiply @ sk_c9 @ sk_c11 )
= sk_c12 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(15,negated_conjecture,
( ( ( inverse @ sk_c1 )
= sk_c12 )
| ( ( multiply @ sk_c6 @ sk_c9 )
= sk_c12 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
thf(143,plain,
( ( ( inverse @ sk_c1 )
= sk_c12 )
| ( ( multiply @ sk_c6 @ sk_c9 )
= sk_c12 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(43,negated_conjecture,
( ( ( multiply @ sk_c10 @ sk_c12 )
= sk_c11 )
| ( ( multiply @ sk_c5 @ sk_c11 )
= sk_c10 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_43) ).
thf(131,plain,
( ( ( multiply @ sk_c10 @ sk_c12 )
= sk_c11 )
| ( ( multiply @ sk_c5 @ sk_c11 )
= sk_c10 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(36,negated_conjecture,
( ( ( inverse @ sk_c2 )
= sk_c11 )
| ( ( inverse @ sk_c6 )
= sk_c9 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_36) ).
thf(138,plain,
( ( ( inverse @ sk_c2 )
= sk_c11 )
| ( ( inverse @ sk_c6 )
= sk_c9 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(38,negated_conjecture,
( ( ( inverse @ sk_c2 )
= sk_c11 )
| ( ( inverse @ sk_c8 )
= sk_c7 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_38) ).
thf(101,plain,
( ( ( inverse @ sk_c2 )
= sk_c11 )
| ( ( inverse @ sk_c8 )
= sk_c7 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(14,negated_conjecture,
( ( ( inverse @ sk_c1 )
= sk_c12 )
| ( ( inverse @ sk_c5 )
= sk_c11 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
thf(88,plain,
( ( ( inverse @ sk_c1 )
= sk_c12 )
| ( ( inverse @ sk_c5 )
= sk_c11 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(71,negated_conjecture,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( multiply @ A @ sk_c12 )
!= sk_c11 )
| ( ( inverse @ A )
!= sk_c12 )
| ( ( multiply @ B @ sk_c11 )
!= sk_c10 )
| ( ( inverse @ B )
!= sk_c11 )
| ( ( multiply @ sk_c10 @ sk_c12 )
!= sk_c11 )
| ( ( multiply @ C @ sk_c10 )
!= sk_c12 )
| ( ( inverse @ C )
!= sk_c10 )
| ( ( multiply @ D @ sk_c12 )
!= sk_c11 )
| ( ( inverse @ D )
!= sk_c12 )
| ( ( multiply @ E @ sk_c11 )
!= sk_c10 )
| ( ( inverse @ E )
!= sk_c11 )
| ( ( multiply @ F @ G )
!= sk_c12 )
| ( ( inverse @ F )
!= G )
| ( ( multiply @ G @ sk_c11 )
!= sk_c12 )
| ( ( inverse @ H )
!= I )
| ( ( inverse @ I )
!= G )
| ( ( multiply @ H @ G )
!= I ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_71) ).
thf(115,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( multiply @ A @ sk_c12 )
!= sk_c11 )
| ( ( inverse @ A )
!= sk_c12 )
| ( ( multiply @ B @ sk_c11 )
!= sk_c10 )
| ( ( inverse @ B )
!= sk_c11 )
| ( ( multiply @ sk_c10 @ sk_c12 )
!= sk_c11 )
| ( ( multiply @ C @ sk_c10 )
!= sk_c12 )
| ( ( inverse @ C )
!= sk_c10 )
| ( ( multiply @ D @ sk_c12 )
!= sk_c11 )
| ( ( inverse @ D )
!= sk_c12 )
| ( ( multiply @ E @ sk_c11 )
!= sk_c10 )
| ( ( inverse @ E )
!= sk_c11 )
| ( ( multiply @ F @ G )
!= sk_c12 )
| ( ( inverse @ F )
!= G )
| ( ( multiply @ G @ sk_c11 )
!= sk_c12 )
| ( ( inverse @ H )
!= I )
| ( ( inverse @ I )
!= G )
| ( ( multiply @ H @ G )
!= I ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(39,negated_conjecture,
( ( ( inverse @ sk_c2 )
= sk_c11 )
| ( ( inverse @ sk_c7 )
= sk_c9 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_39) ).
thf(120,plain,
( ( ( inverse @ sk_c2 )
= sk_c11 )
| ( ( inverse @ sk_c7 )
= sk_c9 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(34,negated_conjecture,
( ( ( inverse @ sk_c2 )
= sk_c11 )
| ( ( inverse @ sk_c5 )
= sk_c11 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_34) ).
thf(110,plain,
( ( ( inverse @ sk_c2 )
= sk_c11 )
| ( ( inverse @ sk_c5 )
= sk_c11 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(18,negated_conjecture,
( ( ( inverse @ sk_c1 )
= sk_c12 )
| ( ( inverse @ sk_c8 )
= sk_c7 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).
thf(125,plain,
( ( ( inverse @ sk_c1 )
= sk_c12 )
| ( ( inverse @ sk_c8 )
= sk_c7 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(61,negated_conjecture,
( ( ( inverse @ sk_c3 )
= sk_c10 )
| ( ( multiply @ sk_c4 @ sk_c12 )
= sk_c11 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_61) ).
thf(93,plain,
( ( ( inverse @ sk_c3 )
= sk_c10 )
| ( ( multiply @ sk_c4 @ sk_c12 )
= sk_c11 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(72,axiom,
! [A: $i] :
( ( multiply @ identity @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
thf(289,plain,
! [A: $i] :
( ( multiply @ identity @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(2,negated_conjecture,
( ( ( multiply @ sk_c1 @ sk_c12 )
= sk_c11 )
| ( ( inverse @ sk_c4 )
= sk_c12 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
thf(78,plain,
( ( ( multiply @ sk_c1 @ sk_c12 )
= sk_c11 )
| ( ( inverse @ sk_c4 )
= sk_c12 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(45,negated_conjecture,
( ( ( multiply @ sk_c10 @ sk_c12 )
= sk_c11 )
| ( ( multiply @ sk_c6 @ sk_c9 )
= sk_c12 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_45) ).
thf(106,plain,
( ( ( multiply @ sk_c10 @ sk_c12 )
= sk_c11 )
| ( ( multiply @ sk_c6 @ sk_c9 )
= sk_c12 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(3,negated_conjecture,
( ( ( multiply @ sk_c1 @ sk_c12 )
= sk_c11 )
| ( ( multiply @ sk_c5 @ sk_c11 )
= sk_c10 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
thf(121,plain,
( ( ( multiply @ sk_c1 @ sk_c12 )
= sk_c11 )
| ( ( multiply @ sk_c5 @ sk_c11 )
= sk_c10 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(24,negated_conjecture,
( ( ( multiply @ sk_c2 @ sk_c11 )
= sk_c10 )
| ( ( inverse @ sk_c5 )
= sk_c11 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_24) ).
thf(84,plain,
( ( ( multiply @ sk_c2 @ sk_c11 )
= sk_c10 )
| ( ( inverse @ sk_c5 )
= sk_c11 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(74,axiom,
! [C: $i,B: $i,A: $i] :
( ( multiply @ ( multiply @ A @ B ) @ C )
= ( multiply @ A @ ( multiply @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity) ).
thf(293,plain,
! [C: $i,B: $i,A: $i] :
( ( multiply @ ( multiply @ A @ B ) @ C )
= ( multiply @ A @ ( multiply @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(40,negated_conjecture,
( ( ( inverse @ sk_c2 )
= sk_c11 )
| ( ( multiply @ sk_c8 @ sk_c9 )
= sk_c7 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_40) ).
thf(132,plain,
( ( ( inverse @ sk_c2 )
= sk_c11 )
| ( ( multiply @ sk_c8 @ sk_c9 )
= sk_c7 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(12,negated_conjecture,
( ( ( inverse @ sk_c1 )
= sk_c12 )
| ( ( inverse @ sk_c4 )
= sk_c12 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_12) ).
thf(116,plain,
( ( ( inverse @ sk_c1 )
= sk_c12 )
| ( ( inverse @ sk_c4 )
= sk_c12 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(20,negated_conjecture,
( ( ( inverse @ sk_c1 )
= sk_c12 )
| ( ( multiply @ sk_c8 @ sk_c9 )
= sk_c7 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_20) ).
thf(89,plain,
( ( ( inverse @ sk_c1 )
= sk_c12 )
| ( ( multiply @ sk_c8 @ sk_c9 )
= sk_c7 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(26,negated_conjecture,
( ( ( multiply @ sk_c2 @ sk_c11 )
= sk_c10 )
| ( ( inverse @ sk_c6 )
= sk_c9 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_26) ).
thf(133,plain,
( ( ( multiply @ sk_c2 @ sk_c11 )
= sk_c10 )
| ( ( inverse @ sk_c6 )
= sk_c9 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(54,negated_conjecture,
( ( ( multiply @ sk_c3 @ sk_c10 )
= sk_c12 )
| ( ( inverse @ sk_c5 )
= sk_c11 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_54) ).
thf(117,plain,
( ( ( multiply @ sk_c3 @ sk_c10 )
= sk_c12 )
| ( ( inverse @ sk_c5 )
= sk_c11 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(37,negated_conjecture,
( ( ( inverse @ sk_c2 )
= sk_c11 )
| ( ( multiply @ sk_c9 @ sk_c11 )
= sk_c12 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_37) ).
thf(85,plain,
( ( ( inverse @ sk_c2 )
= sk_c11 )
| ( ( multiply @ sk_c9 @ sk_c11 )
= sk_c12 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(9,negated_conjecture,
( ( ( multiply @ sk_c1 @ sk_c12 )
= sk_c11 )
| ( ( inverse @ sk_c7 )
= sk_c9 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).
thf(102,plain,
( ( ( multiply @ sk_c1 @ sk_c12 )
= sk_c11 )
| ( ( inverse @ sk_c7 )
= sk_c9 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(29,negated_conjecture,
( ( ( multiply @ sk_c2 @ sk_c11 )
= sk_c10 )
| ( ( inverse @ sk_c7 )
= sk_c9 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_29) ).
thf(92,plain,
( ( ( multiply @ sk_c2 @ sk_c11 )
= sk_c10 )
| ( ( inverse @ sk_c7 )
= sk_c9 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(70,negated_conjecture,
( ( ( inverse @ sk_c3 )
= sk_c10 )
| ( ( multiply @ sk_c8 @ sk_c9 )
= sk_c7 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_70) ).
thf(97,plain,
( ( ( inverse @ sk_c3 )
= sk_c10 )
| ( ( multiply @ sk_c8 @ sk_c9 )
= sk_c7 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(32,negated_conjecture,
( ( ( inverse @ sk_c2 )
= sk_c11 )
| ( ( inverse @ sk_c4 )
= sk_c12 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_32) ).
thf(109,plain,
( ( ( inverse @ sk_c2 )
= sk_c11 )
| ( ( inverse @ sk_c4 )
= sk_c12 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(63,negated_conjecture,
( ( ( inverse @ sk_c3 )
= sk_c10 )
| ( ( multiply @ sk_c5 @ sk_c11 )
= sk_c10 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_63) ).
thf(124,plain,
( ( ( inverse @ sk_c3 )
= sk_c10 )
| ( ( multiply @ sk_c5 @ sk_c11 )
= sk_c10 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(65,negated_conjecture,
( ( ( inverse @ sk_c3 )
= sk_c10 )
| ( ( multiply @ sk_c6 @ sk_c9 )
= sk_c12 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_65) ).
thf(77,plain,
( ( ( inverse @ sk_c3 )
= sk_c10 )
| ( ( multiply @ sk_c6 @ sk_c9 )
= sk_c12 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(60,negated_conjecture,
( ( ( multiply @ sk_c3 @ sk_c10 )
= sk_c12 )
| ( ( multiply @ sk_c8 @ sk_c9 )
= sk_c7 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_60) ).
thf(96,plain,
( ( ( multiply @ sk_c3 @ sk_c10 )
= sk_c12 )
| ( ( multiply @ sk_c8 @ sk_c9 )
= sk_c7 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(55,negated_conjecture,
( ( ( multiply @ sk_c3 @ sk_c10 )
= sk_c12 )
| ( ( multiply @ sk_c6 @ sk_c9 )
= sk_c12 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_55) ).
thf(134,plain,
( ( ( multiply @ sk_c3 @ sk_c10 )
= sk_c12 )
| ( ( multiply @ sk_c6 @ sk_c9 )
= sk_c12 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(16,negated_conjecture,
( ( ( inverse @ sk_c1 )
= sk_c12 )
| ( ( inverse @ sk_c6 )
= sk_c9 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_16) ).
thf(128,plain,
( ( ( inverse @ sk_c1 )
= sk_c12 )
| ( ( inverse @ sk_c6 )
= sk_c9 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(41,negated_conjecture,
( ( ( multiply @ sk_c10 @ sk_c12 )
= sk_c11 )
| ( ( multiply @ sk_c4 @ sk_c12 )
= sk_c11 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_41) ).
thf(105,plain,
( ( ( multiply @ sk_c10 @ sk_c12 )
= sk_c11 )
| ( ( multiply @ sk_c4 @ sk_c12 )
= sk_c11 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(73,axiom,
! [A: $i] :
( ( multiply @ ( inverse @ A ) @ A )
= identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).
thf(291,plain,
! [A: $i] :
( ( multiply @ ( inverse @ A ) @ A )
= identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(49,negated_conjecture,
( ( ( multiply @ sk_c10 @ sk_c12 )
= sk_c11 )
| ( ( inverse @ sk_c7 )
= sk_c9 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_49) ).
thf(118,plain,
( ( ( multiply @ sk_c10 @ sk_c12 )
= sk_c11 )
| ( ( inverse @ sk_c7 )
= sk_c9 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(68,negated_conjecture,
( ( ( inverse @ sk_c3 )
= sk_c10 )
| ( ( inverse @ sk_c8 )
= sk_c7 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_68) ).
thf(144,plain,
( ( ( inverse @ sk_c3 )
= sk_c10 )
| ( ( inverse @ sk_c8 )
= sk_c7 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(25,negated_conjecture,
( ( ( multiply @ sk_c2 @ sk_c11 )
= sk_c10 )
| ( ( multiply @ sk_c6 @ sk_c9 )
= sk_c12 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_25) ).
thf(86,plain,
( ( ( multiply @ sk_c2 @ sk_c11 )
= sk_c10 )
| ( ( multiply @ sk_c6 @ sk_c9 )
= sk_c12 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(59,negated_conjecture,
( ( ( multiply @ sk_c3 @ sk_c10 )
= sk_c12 )
| ( ( inverse @ sk_c7 )
= sk_c9 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_59) ).
thf(113,plain,
( ( ( multiply @ sk_c3 @ sk_c10 )
= sk_c12 )
| ( ( inverse @ sk_c7 )
= sk_c9 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(10,negated_conjecture,
( ( ( multiply @ sk_c1 @ sk_c12 )
= sk_c11 )
| ( ( multiply @ sk_c8 @ sk_c9 )
= sk_c7 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).
thf(81,plain,
( ( ( multiply @ sk_c1 @ sk_c12 )
= sk_c11 )
| ( ( multiply @ sk_c8 @ sk_c9 )
= sk_c7 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(5,negated_conjecture,
( ( ( multiply @ sk_c1 @ sk_c12 )
= sk_c11 )
| ( ( multiply @ sk_c6 @ sk_c9 )
= sk_c12 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
thf(76,plain,
( ( ( multiply @ sk_c1 @ sk_c12 )
= sk_c11 )
| ( ( multiply @ sk_c6 @ sk_c9 )
= sk_c12 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(21,negated_conjecture,
( ( ( multiply @ sk_c2 @ sk_c11 )
= sk_c10 )
| ( ( multiply @ sk_c4 @ sk_c12 )
= sk_c11 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
thf(98,plain,
( ( ( multiply @ sk_c2 @ sk_c11 )
= sk_c10 )
| ( ( multiply @ sk_c4 @ sk_c12 )
= sk_c11 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(53,negated_conjecture,
( ( ( multiply @ sk_c3 @ sk_c10 )
= sk_c12 )
| ( ( multiply @ sk_c5 @ sk_c11 )
= sk_c10 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_53) ).
thf(103,plain,
( ( ( multiply @ sk_c3 @ sk_c10 )
= sk_c12 )
| ( ( multiply @ sk_c5 @ sk_c11 )
= sk_c10 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(51,negated_conjecture,
( ( ( multiply @ sk_c3 @ sk_c10 )
= sk_c12 )
| ( ( multiply @ sk_c4 @ sk_c12 )
= sk_c11 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_51) ).
thf(140,plain,
( ( ( multiply @ sk_c3 @ sk_c10 )
= sk_c12 )
| ( ( multiply @ sk_c4 @ sk_c12 )
= sk_c11 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(57,negated_conjecture,
( ( ( multiply @ sk_c3 @ sk_c10 )
= sk_c12 )
| ( ( multiply @ sk_c9 @ sk_c11 )
= sk_c12 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_57) ).
thf(91,plain,
( ( ( multiply @ sk_c3 @ sk_c10 )
= sk_c12 )
| ( ( multiply @ sk_c9 @ sk_c11 )
= sk_c12 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(17,negated_conjecture,
( ( ( inverse @ sk_c1 )
= sk_c12 )
| ( ( multiply @ sk_c9 @ sk_c11 )
= sk_c12 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_17) ).
thf(108,plain,
( ( ( inverse @ sk_c1 )
= sk_c12 )
| ( ( multiply @ sk_c9 @ sk_c11 )
= sk_c12 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(11,negated_conjecture,
( ( ( inverse @ sk_c1 )
= sk_c12 )
| ( ( multiply @ sk_c4 @ sk_c12 )
= sk_c11 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
thf(130,plain,
( ( ( inverse @ sk_c1 )
= sk_c12 )
| ( ( multiply @ sk_c4 @ sk_c12 )
= sk_c11 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(23,negated_conjecture,
( ( ( multiply @ sk_c2 @ sk_c11 )
= sk_c10 )
| ( ( multiply @ sk_c5 @ sk_c11 )
= sk_c10 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_23) ).
thf(135,plain,
( ( ( multiply @ sk_c2 @ sk_c11 )
= sk_c10 )
| ( ( multiply @ sk_c5 @ sk_c11 )
= sk_c10 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(4,negated_conjecture,
( ( ( multiply @ sk_c1 @ sk_c12 )
= sk_c11 )
| ( ( inverse @ sk_c5 )
= sk_c11 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
thf(80,plain,
( ( ( multiply @ sk_c1 @ sk_c12 )
= sk_c11 )
| ( ( inverse @ sk_c5 )
= sk_c11 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(44,negated_conjecture,
( ( ( multiply @ sk_c10 @ sk_c12 )
= sk_c11 )
| ( ( inverse @ sk_c5 )
= sk_c11 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_44) ).
thf(112,plain,
( ( ( multiply @ sk_c10 @ sk_c12 )
= sk_c11 )
| ( ( inverse @ sk_c5 )
= sk_c11 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(48,negated_conjecture,
( ( ( multiply @ sk_c10 @ sk_c12 )
= sk_c11 )
| ( ( inverse @ sk_c8 )
= sk_c7 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_48) ).
thf(123,plain,
( ( ( multiply @ sk_c10 @ sk_c12 )
= sk_c11 )
| ( ( inverse @ sk_c8 )
= sk_c7 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(62,negated_conjecture,
( ( ( inverse @ sk_c3 )
= sk_c10 )
| ( ( inverse @ sk_c4 )
= sk_c12 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_62) ).
thf(145,plain,
( ( ( inverse @ sk_c3 )
= sk_c10 )
| ( ( inverse @ sk_c4 )
= sk_c12 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(33,negated_conjecture,
( ( ( inverse @ sk_c2 )
= sk_c11 )
| ( ( multiply @ sk_c5 @ sk_c11 )
= sk_c10 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_33) ).
thf(99,plain,
( ( ( inverse @ sk_c2 )
= sk_c11 )
| ( ( multiply @ sk_c5 @ sk_c11 )
= sk_c10 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(52,negated_conjecture,
( ( ( multiply @ sk_c3 @ sk_c10 )
= sk_c12 )
| ( ( inverse @ sk_c4 )
= sk_c12 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_52) ).
thf(87,plain,
( ( ( multiply @ sk_c3 @ sk_c10 )
= sk_c12 )
| ( ( inverse @ sk_c4 )
= sk_c12 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(13,negated_conjecture,
( ( ( inverse @ sk_c1 )
= sk_c12 )
| ( ( multiply @ sk_c5 @ sk_c11 )
= sk_c10 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_13) ).
thf(104,plain,
( ( ( inverse @ sk_c1 )
= sk_c12 )
| ( ( multiply @ sk_c5 @ sk_c11 )
= sk_c10 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(27,negated_conjecture,
( ( ( multiply @ sk_c2 @ sk_c11 )
= sk_c10 )
| ( ( multiply @ sk_c9 @ sk_c11 )
= sk_c12 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_27) ).
thf(114,plain,
( ( ( multiply @ sk_c2 @ sk_c11 )
= sk_c10 )
| ( ( multiply @ sk_c9 @ sk_c11 )
= sk_c12 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(30,negated_conjecture,
( ( ( multiply @ sk_c2 @ sk_c11 )
= sk_c10 )
| ( ( multiply @ sk_c8 @ sk_c9 )
= sk_c7 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_30) ).
thf(139,plain,
( ( ( multiply @ sk_c2 @ sk_c11 )
= sk_c10 )
| ( ( multiply @ sk_c8 @ sk_c9 )
= sk_c7 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(69,negated_conjecture,
( ( ( inverse @ sk_c3 )
= sk_c10 )
| ( ( inverse @ sk_c7 )
= sk_c9 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_69) ).
thf(75,plain,
( ( ( inverse @ sk_c3 )
= sk_c10 )
| ( ( inverse @ sk_c7 )
= sk_c9 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(7,negated_conjecture,
( ( ( multiply @ sk_c1 @ sk_c12 )
= sk_c11 )
| ( ( multiply @ sk_c9 @ sk_c11 )
= sk_c12 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_7) ).
thf(119,plain,
( ( ( multiply @ sk_c1 @ sk_c12 )
= sk_c11 )
| ( ( multiply @ sk_c9 @ sk_c11 )
= sk_c12 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(56,negated_conjecture,
( ( ( multiply @ sk_c3 @ sk_c10 )
= sk_c12 )
| ( ( inverse @ sk_c6 )
= sk_c9 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_56) ).
thf(82,plain,
( ( ( multiply @ sk_c3 @ sk_c10 )
= sk_c12 )
| ( ( inverse @ sk_c6 )
= sk_c9 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(64,negated_conjecture,
( ( ( inverse @ sk_c3 )
= sk_c10 )
| ( ( inverse @ sk_c5 )
= sk_c11 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_64) ).
thf(107,plain,
( ( ( inverse @ sk_c3 )
= sk_c10 )
| ( ( inverse @ sk_c5 )
= sk_c11 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(66,negated_conjecture,
( ( ( inverse @ sk_c3 )
= sk_c10 )
| ( ( inverse @ sk_c6 )
= sk_c9 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_66) ).
thf(79,plain,
( ( ( inverse @ sk_c3 )
= sk_c10 )
| ( ( inverse @ sk_c6 )
= sk_c9 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(1,negated_conjecture,
( ( ( multiply @ sk_c1 @ sk_c12 )
= sk_c11 )
| ( ( multiply @ sk_c4 @ sk_c12 )
= sk_c11 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
thf(94,plain,
( ( ( multiply @ sk_c1 @ sk_c12 )
= sk_c11 )
| ( ( multiply @ sk_c4 @ sk_c12 )
= sk_c11 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(50,negated_conjecture,
( ( ( multiply @ sk_c10 @ sk_c12 )
= sk_c11 )
| ( ( multiply @ sk_c8 @ sk_c9 )
= sk_c7 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_50) ).
thf(126,plain,
( ( ( multiply @ sk_c10 @ sk_c12 )
= sk_c11 )
| ( ( multiply @ sk_c8 @ sk_c9 )
= sk_c7 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(8,negated_conjecture,
( ( ( multiply @ sk_c1 @ sk_c12 )
= sk_c11 )
| ( ( inverse @ sk_c8 )
= sk_c7 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_8) ).
thf(136,plain,
( ( ( multiply @ sk_c1 @ sk_c12 )
= sk_c11 )
| ( ( inverse @ sk_c8 )
= sk_c7 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(35,negated_conjecture,
( ( ( inverse @ sk_c2 )
= sk_c11 )
| ( ( multiply @ sk_c6 @ sk_c9 )
= sk_c12 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_35) ).
thf(122,plain,
( ( ( inverse @ sk_c2 )
= sk_c11 )
| ( ( multiply @ sk_c6 @ sk_c9 )
= sk_c12 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(42,negated_conjecture,
( ( ( multiply @ sk_c10 @ sk_c12 )
= sk_c11 )
| ( ( inverse @ sk_c4 )
= sk_c12 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_42) ).
thf(83,plain,
( ( ( multiply @ sk_c10 @ sk_c12 )
= sk_c11 )
| ( ( inverse @ sk_c4 )
= sk_c12 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(28,negated_conjecture,
( ( ( multiply @ sk_c2 @ sk_c11 )
= sk_c10 )
| ( ( inverse @ sk_c8 )
= sk_c7 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_28) ).
thf(100,plain,
( ( ( multiply @ sk_c2 @ sk_c11 )
= sk_c10 )
| ( ( inverse @ sk_c8 )
= sk_c7 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(46,negated_conjecture,
( ( ( multiply @ sk_c10 @ sk_c12 )
= sk_c11 )
| ( ( inverse @ sk_c6 )
= sk_c9 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_46) ).
thf(90,plain,
( ( ( multiply @ sk_c10 @ sk_c12 )
= sk_c11 )
| ( ( inverse @ sk_c6 )
= sk_c9 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(22,negated_conjecture,
( ( ( multiply @ sk_c2 @ sk_c11 )
= sk_c10 )
| ( ( inverse @ sk_c4 )
= sk_c12 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_22) ).
thf(111,plain,
( ( ( multiply @ sk_c2 @ sk_c11 )
= sk_c10 )
| ( ( inverse @ sk_c4 )
= sk_c12 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(470,plain,
$false,
inference(e,[status(thm)],[142,137,141,129,95,127,143,131,138,101,88,115,120,110,125,93,289,78,106,121,84,293,132,116,89,133,117,85,102,92,97,109,124,77,96,134,128,105,291,118,144,86,113,81,76,98,103,140,91,108,130,135,80,112,123,145,99,87,104,114,139,75,119,82,107,79,94,126,136,122,83,100,90,111]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : GRP258-1 : TPTP v8.1.2. Released v2.5.0.
% 0.10/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n010.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 : Fri May 19 01:41:29 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.86/0.84 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.19/0.99 % [INFO] Parsing done (147ms).
% 1.19/1.00 % [INFO] Running in sequential loop mode.
% 1.79/1.20 % [INFO] eprover registered as external prover.
% 1.79/1.20 % [INFO] cvc4 registered as external prover.
% 1.79/1.20 % [INFO] Scanning for conjecture ...
% 1.97/1.32 % [INFO] Found a conjecture and 3 axioms. Running axiom selection ...
% 2.25/1.37 % [INFO] Axiom selection finished. Selected 3 axioms (removed 0 axioms).
% 2.25/1.37 % [INFO] Problem is propositional (TPTP CNF).
% 2.25/1.38 % [INFO] Type checking passed.
% 2.25/1.38 % [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 ...
% 5.52/2.25 % External prover 'e' found a proof!
% 5.52/2.25 % [INFO] Killing All external provers ...
% 5.52/2.25 % Time passed: 1734ms (effective reasoning time: 1247ms)
% 5.52/2.25 % 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)>
% 5.52/2.25 % Axioms used in derivation (3): left_identity, associativity, left_inverse
% 5.52/2.25 % No. of inferences in proof: 149
% 5.52/2.25 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1734 ms resp. 1247 ms w/o parsing
% 5.82/2.30 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.82/2.30 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------