%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : GRP220-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:20:29 AM UTC 2026
% Result : Unsatisfiable 42.45s 10.76s
% Output : Refutation 35.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 76
% Syntax : Number of formulae : 239 ( 22 unt; 0 typ; 0 def)
% Number of atoms : 788 ( 787 equ; 0 cnn)
% Maximal formula atoms : 17 ( 3 avg)
% Number of connectives : 2276 ( 411 ~; 549 |; 0 &;1316 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 4 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 15 usr; 14 con; 0-2 aty)
% Number of variables : 155 ( 0 ^; 155 !; 0 ?; 155 :)
% Comments :
%------------------------------------------------------------------------------
thf(inverse_decl,type,
inverse: $i > $i ).
thf(sk_c1_decl,type,
sk_c1: $i ).
thf(sk_c12_decl,type,
sk_c12: $i ).
thf(sk_c11_decl,type,
sk_c11: $i ).
thf(sk_c6_decl,type,
sk_c6: $i ).
thf(multiply_decl,type,
multiply: $i > $i > $i ).
thf(sk_c7_decl,type,
sk_c7: $i ).
thf(sk_c10_decl,type,
sk_c10: $i ).
thf(sk_c9_decl,type,
sk_c9: $i ).
thf(sk_c8_decl,type,
sk_c8: $i ).
thf(sk_c2_decl,type,
sk_c2: $i ).
thf(sk_c3_decl,type,
sk_c3: $i ).
thf(sk_c5_decl,type,
sk_c5: $i ).
thf(sk_c4_decl,type,
sk_c4: $i ).
thf(identity_decl,type,
identity: $i ).
thf(71,negated_conjecture,
( ( ( sk_c8 @ inverse )
= sk_c10 )
| ( ( sk_c4 @ inverse )
= sk_c12 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_71) ).
thf(118,plain,
( ( ( sk_c8 @ inverse )
= sk_c10 )
| ( ( sk_c4 @ inverse )
= sk_c12 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(1,negated_conjecture,
( ( ( sk_c12 @ inverse )
= sk_c11 )
| ( ( sk_c1 @ inverse )
= sk_c12 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
thf(95,plain,
( ( ( sk_c12 @ inverse )
= sk_c11 )
| ( ( sk_c1 @ inverse )
= sk_c12 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(63,negated_conjecture,
( ( ( sk_c10 @ ( sk_c9 @ multiply ) )
= sk_c8 )
| ( ( sk_c12 @ ( sk_c4 @ multiply ) )
= sk_c5 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_63) ).
thf(127,plain,
( ( ( sk_c10 @ ( sk_c9 @ multiply ) )
= sk_c8 )
| ( ( sk_c12 @ ( sk_c4 @ multiply ) )
= sk_c5 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(30,negated_conjecture,
( ( ( sk_c11 @ ( sk_c6 @ multiply ) )
= sk_c12 )
| ( ( sk_c2 @ inverse )
= sk_c3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_30) ).
thf(143,plain,
( ( ( sk_c11 @ ( sk_c6 @ multiply ) )
= sk_c12 )
| ( ( sk_c2 @ inverse )
= sk_c3 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(16,negated_conjecture,
( ( ( sk_c9 @ inverse )
= sk_c8 )
| ( ( sk_c11 @ ( sk_c1 @ multiply ) )
= sk_c12 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
thf(131,plain,
( ( ( sk_c9 @ inverse )
= sk_c8 )
| ( ( sk_c11 @ ( sk_c1 @ multiply ) )
= sk_c12 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(55,negated_conjecture,
( ( ( sk_c12 @ inverse )
= sk_c11 )
| ( ( sk_c12 @ ( sk_c4 @ multiply ) )
= sk_c5 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_55) ).
thf(138,plain,
( ( ( sk_c12 @ inverse )
= sk_c11 )
| ( ( sk_c12 @ ( sk_c4 @ multiply ) )
= sk_c5 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(28,negated_conjecture,
( ( ( sk_c12 @ inverse )
= sk_c11 )
| ( ( sk_c2 @ inverse )
= sk_c3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_28) ).
thf(101,plain,
( ( ( sk_c12 @ inverse )
= sk_c11 )
| ( ( sk_c2 @ inverse )
= sk_c3 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(52,negated_conjecture,
( ( ( sk_c9 @ inverse )
= sk_c8 )
| ( ( sk_c5 @ ( sk_c12 @ multiply ) )
= sk_c11 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_52) ).
thf(88,plain,
( ( ( sk_c9 @ inverse )
= sk_c8 )
| ( ( sk_c5 @ ( sk_c12 @ multiply ) )
= sk_c11 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(44,negated_conjecture,
( ( ( sk_c8 @ inverse )
= sk_c10 )
| ( ( sk_c12 @ ( sk_c3 @ multiply ) )
= sk_c11 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_44) ).
thf(115,plain,
( ( ( sk_c8 @ inverse )
= sk_c10 )
| ( ( sk_c12 @ ( sk_c3 @ multiply ) )
= sk_c11 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(54,negated_conjecture,
( ( ( sk_c10 @ ( sk_c9 @ multiply ) )
= sk_c8 )
| ( ( sk_c5 @ ( sk_c12 @ multiply ) )
= sk_c11 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_54) ).
thf(120,plain,
( ( ( sk_c10 @ ( sk_c9 @ multiply ) )
= sk_c8 )
| ( ( sk_c5 @ ( sk_c12 @ multiply ) )
= sk_c11 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(36,negated_conjecture,
( ( ( sk_c10 @ ( sk_c9 @ multiply ) )
= sk_c8 )
| ( ( sk_c2 @ inverse )
= sk_c3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_36) ).
thf(142,plain,
( ( ( sk_c10 @ ( sk_c9 @ multiply ) )
= sk_c8 )
| ( ( sk_c2 @ inverse )
= sk_c3 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(26,negated_conjecture,
( ( ( sk_c8 @ inverse )
= sk_c10 )
| ( ( sk_c3 @ ( sk_c2 @ multiply ) )
= sk_c11 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_26) ).
thf(137,plain,
( ( ( sk_c8 @ inverse )
= sk_c10 )
| ( ( sk_c3 @ ( sk_c2 @ multiply ) )
= sk_c11 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(152,plain,
( ( ( sk_c8 @ inverse )
= sk_c10 )
| ( ( sk_c3 @ ( sk_c2 @ multiply ) )
= sk_c11 ) ),
inference(cnf,[status(esa)],[137]) ).
thf(153,plain,
( ( ( sk_c8 @ inverse )
= sk_c10 )
| ( ( sk_c3 @ ( sk_c2 @ multiply ) )
= sk_c11 ) ),
inference(lifteq,[status(thm)],[152]) ).
thf(29,negated_conjecture,
( ( ( sk_c6 @ inverse )
= sk_c12 )
| ( ( sk_c2 @ inverse )
= sk_c3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_29) ).
thf(93,plain,
( ( ( sk_c6 @ inverse )
= sk_c12 )
| ( ( sk_c2 @ inverse )
= sk_c3 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(184,plain,
( ( ( sk_c6 @ inverse )
= sk_c12 )
| ( ( sk_c2 @ inverse )
= sk_c3 ) ),
inference(cnf,[status(esa)],[93]) ).
thf(185,plain,
( ( ( sk_c6 @ inverse )
= sk_c12 )
| ( ( sk_c2 @ inverse )
= sk_c3 ) ),
inference(lifteq,[status(thm)],[184]) ).
thf(76,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ multiply ) @ multiply ) )
= ( C @ ( B @ multiply ) @ ( A @ multiply ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity) ).
thf(301,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ multiply ) @ multiply ) )
= ( C @ ( B @ multiply ) @ ( A @ multiply ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(64,negated_conjecture,
( ( ( sk_c12 @ inverse )
= sk_c11 )
| ( ( sk_c4 @ inverse )
= sk_c12 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_64) ).
thf(110,plain,
( ( ( sk_c12 @ inverse )
= sk_c11 )
| ( ( sk_c4 @ inverse )
= sk_c12 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(35,negated_conjecture,
( ( ( sk_c8 @ inverse )
= sk_c10 )
| ( ( sk_c2 @ inverse )
= sk_c3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_35) ).
thf(125,plain,
( ( ( sk_c8 @ inverse )
= sk_c10 )
| ( ( sk_c2 @ inverse )
= sk_c3 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(50,negated_conjecture,
( ( ( sk_c7 @ inverse )
= sk_c10 )
| ( ( sk_c5 @ ( sk_c12 @ multiply ) )
= sk_c11 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_50) ).
thf(129,plain,
( ( ( sk_c7 @ inverse )
= sk_c10 )
| ( ( sk_c5 @ ( sk_c12 @ multiply ) )
= sk_c11 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(156,plain,
( ( ( sk_c7 @ inverse )
= sk_c10 )
| ( ( sk_c5 @ ( sk_c12 @ multiply ) )
= sk_c11 ) ),
inference(cnf,[status(esa)],[129]) ).
thf(157,plain,
( ( ( sk_c7 @ inverse )
= sk_c10 )
| ( ( sk_c5 @ ( sk_c12 @ multiply ) )
= sk_c11 ) ),
inference(lifteq,[status(thm)],[156]) ).
thf(5,negated_conjecture,
( ( ( sk_c7 @ inverse )
= sk_c10 )
| ( ( sk_c1 @ inverse )
= sk_c12 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
thf(78,plain,
( ( ( sk_c7 @ inverse )
= sk_c10 )
| ( ( sk_c1 @ inverse )
= sk_c12 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(41,negated_conjecture,
( ( ( sk_c7 @ inverse )
= sk_c10 )
| ( ( sk_c12 @ ( sk_c3 @ multiply ) )
= sk_c11 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_41) ).
thf(106,plain,
( ( ( sk_c7 @ inverse )
= sk_c10 )
| ( ( sk_c12 @ ( sk_c3 @ multiply ) )
= sk_c11 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(49,negated_conjecture,
( ( ( sk_c10 @ ( sk_c7 @ multiply ) )
= sk_c12 )
| ( ( sk_c5 @ ( sk_c12 @ multiply ) )
= sk_c11 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_49) ).
thf(121,plain,
( ( ( sk_c10 @ ( sk_c7 @ multiply ) )
= sk_c12 )
| ( ( sk_c5 @ ( sk_c12 @ multiply ) )
= sk_c11 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(42,negated_conjecture,
( ( ( sk_c11 @ ( sk_c10 @ multiply ) )
= sk_c12 )
| ( ( sk_c12 @ ( sk_c3 @ multiply ) )
= sk_c11 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_42) ).
thf(84,plain,
( ( ( sk_c11 @ ( sk_c10 @ multiply ) )
= sk_c12 )
| ( ( sk_c12 @ ( sk_c3 @ multiply ) )
= sk_c11 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(15,negated_conjecture,
( ( ( sk_c11 @ ( sk_c10 @ multiply ) )
= sk_c12 )
| ( ( sk_c11 @ ( sk_c1 @ multiply ) )
= sk_c12 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
thf(147,plain,
( ( ( sk_c11 @ ( sk_c10 @ multiply ) )
= sk_c12 )
| ( ( sk_c11 @ ( sk_c1 @ multiply ) )
= sk_c12 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(31,negated_conjecture,
( ( ( sk_c10 @ ( sk_c7 @ multiply ) )
= sk_c12 )
| ( ( sk_c2 @ inverse )
= sk_c3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_31) ).
thf(132,plain,
( ( ( sk_c10 @ ( sk_c7 @ multiply ) )
= sk_c12 )
| ( ( sk_c2 @ inverse )
= sk_c3 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(59,negated_conjecture,
( ( ( sk_c7 @ inverse )
= sk_c10 )
| ( ( sk_c12 @ ( sk_c4 @ multiply ) )
= sk_c5 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_59) ).
thf(116,plain,
( ( ( sk_c7 @ inverse )
= sk_c10 )
| ( ( sk_c12 @ ( sk_c4 @ multiply ) )
= sk_c5 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(14,negated_conjecture,
( ( ( sk_c7 @ inverse )
= sk_c10 )
| ( ( sk_c11 @ ( sk_c1 @ multiply ) )
= sk_c12 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
thf(89,plain,
( ( ( sk_c7 @ inverse )
= sk_c10 )
| ( ( sk_c11 @ ( sk_c1 @ multiply ) )
= sk_c12 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(11,negated_conjecture,
( ( ( sk_c6 @ inverse )
= sk_c12 )
| ( ( sk_c11 @ ( sk_c1 @ multiply ) )
= sk_c12 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
thf(133,plain,
( ( ( sk_c6 @ inverse )
= sk_c12 )
| ( ( sk_c11 @ ( sk_c1 @ multiply ) )
= sk_c12 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(27,negated_conjecture,
( ( ( sk_c10 @ ( sk_c9 @ multiply ) )
= sk_c8 )
| ( ( sk_c3 @ ( sk_c2 @ multiply ) )
= sk_c11 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_27) ).
thf(117,plain,
( ( ( sk_c10 @ ( sk_c9 @ multiply ) )
= sk_c8 )
| ( ( sk_c3 @ ( sk_c2 @ multiply ) )
= sk_c11 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(24,negated_conjecture,
( ( ( sk_c11 @ ( sk_c10 @ multiply ) )
= sk_c12 )
| ( ( sk_c3 @ ( sk_c2 @ multiply ) )
= sk_c11 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).
thf(85,plain,
( ( ( sk_c11 @ ( sk_c10 @ multiply ) )
= sk_c12 )
| ( ( sk_c3 @ ( sk_c2 @ multiply ) )
= sk_c11 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(38,negated_conjecture,
( ( ( sk_c6 @ inverse )
= sk_c12 )
| ( ( sk_c12 @ ( sk_c3 @ multiply ) )
= sk_c11 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_38) ).
thf(102,plain,
( ( ( sk_c6 @ inverse )
= sk_c12 )
| ( ( sk_c12 @ ( sk_c3 @ multiply ) )
= sk_c11 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(302,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ multiply ) @ multiply ) )
= ( C @ ( B @ multiply ) @ ( A @ multiply ) ) ),
inference(lifteq,[status(thm)],[301]) ).
thf(74,axiom,
! [A: $i] :
( ( A @ ( identity @ multiply ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_identity) ).
thf(297,plain,
! [A: $i] :
( ( A @ ( identity @ multiply ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(57,negated_conjecture,
( ( ( sk_c11 @ ( sk_c6 @ multiply ) )
= sk_c12 )
| ( ( sk_c12 @ ( sk_c4 @ multiply ) )
= sk_c5 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_57) ).
thf(92,plain,
( ( ( sk_c11 @ ( sk_c6 @ multiply ) )
= sk_c12 )
| ( ( sk_c12 @ ( sk_c4 @ multiply ) )
= sk_c5 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(68,negated_conjecture,
( ( ( sk_c7 @ inverse )
= sk_c10 )
| ( ( sk_c4 @ inverse )
= sk_c12 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_68) ).
thf(148,plain,
( ( ( sk_c7 @ inverse )
= sk_c10 )
| ( ( sk_c4 @ inverse )
= sk_c12 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(228,plain,
( ( ( sk_c7 @ inverse )
= sk_c10 )
| ( ( sk_c4 @ inverse )
= sk_c12 ) ),
inference(cnf,[status(esa)],[148]) ).
thf(229,plain,
( ( ( sk_c7 @ inverse )
= sk_c10 )
| ( ( sk_c4 @ inverse )
= sk_c12 ) ),
inference(lifteq,[status(thm)],[228]) ).
thf(60,negated_conjecture,
( ( ( sk_c11 @ ( sk_c10 @ multiply ) )
= sk_c12 )
| ( ( sk_c12 @ ( sk_c4 @ multiply ) )
= sk_c5 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_60) ).
thf(97,plain,
( ( ( sk_c11 @ ( sk_c10 @ multiply ) )
= sk_c12 )
| ( ( sk_c12 @ ( sk_c4 @ multiply ) )
= sk_c5 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(298,plain,
! [A: $i] :
( ( A @ ( identity @ multiply ) )
= A ),
inference(lifteq,[status(thm)],[297]) ).
thf(75,axiom,
! [A: $i] :
( ( A @ ( A @ inverse @ multiply ) )
= identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_inverse) ).
thf(299,plain,
! [A: $i] :
( ( A @ ( A @ inverse @ multiply ) )
= identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(300,plain,
! [A: $i] :
( ( A @ ( A @ inverse @ multiply ) )
= identity ),
inference(lifteq,[status(thm)],[299]) ).
thf(315,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ inverse @ multiply ) )
!= ( C @ ( B @ multiply ) ) )
| ( ( D @ ( identity @ multiply ) )
= ( D @ ( C @ multiply ) @ ( B @ multiply ) ) ) ),
inference(paramod_ordered,[status(thm)],[300,302]) ).
thf(316,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ multiply ) @ ( B @ inverse @ multiply ) )
= ( A @ ( identity @ multiply ) ) ),
inference(pattern_uni,[status(thm)],[315:[bind(A,$thf( E )),bind(B,$thf( E @ inverse )),bind(C,$thf( E ))]]) ).
thf(327,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ multiply ) @ ( B @ inverse @ multiply ) )
= ( A @ ( identity @ multiply ) ) ),
inference(simp,[status(thm)],[316]) ).
thf(983,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ multiply ) @ ( B @ inverse @ multiply ) )
= A ),
inference(rewrite,[status(thm)],[327,298]) ).
thf(1004,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( identity @ multiply ) )
!= ( B @ ( C @ multiply ) ) )
| ( ( A @ ( C @ inverse @ multiply ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[298,983]) ).
thf(1005,plain,
! [A: $i] :
( ( A @ ( identity @ inverse @ multiply ) )
= A ),
inference(pattern_uni,[status(thm)],[1004:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( identity ))]]) ).
thf(1201,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( identity @ inverse @ multiply ) )
!= ( B @ ( C @ multiply ) ) )
| ( ( A @ ( C @ inverse @ multiply ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[1005,983]) ).
thf(1202,plain,
! [A: $i] :
( ( A @ ( identity @ inverse @ inverse @ multiply ) )
= A ),
inference(pattern_uni,[status(thm)],[1201:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( identity @ inverse ))]]) ).
thf(1539,plain,
! [B: $i,A: $i] :
( ( ( A @ ( identity @ inverse @ inverse @ multiply ) )
!= ( B @ ( B @ inverse @ multiply ) ) )
| ( A = identity ) ),
inference(paramod_ordered,[status(thm)],[1202,300]) ).
thf(1540,plain,
( ( identity @ inverse )
= identity ),
inference(pattern_uni,[status(thm)],[1539:[bind(A,$thf( identity @ inverse )),bind(B,$thf( identity @ inverse ))]]) ).
thf(58,negated_conjecture,
( ( ( sk_c10 @ ( sk_c7 @ multiply ) )
= sk_c12 )
| ( ( sk_c12 @ ( sk_c4 @ multiply ) )
= sk_c5 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_58) ).
thf(141,plain,
( ( ( sk_c10 @ ( sk_c7 @ multiply ) )
= sk_c12 )
| ( ( sk_c12 @ ( sk_c4 @ multiply ) )
= sk_c5 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(45,negated_conjecture,
( ( ( sk_c10 @ ( sk_c9 @ multiply ) )
= sk_c8 )
| ( ( sk_c12 @ ( sk_c3 @ multiply ) )
= sk_c11 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_45) ).
thf(109,plain,
( ( ( sk_c10 @ ( sk_c9 @ multiply ) )
= sk_c8 )
| ( ( sk_c12 @ ( sk_c3 @ multiply ) )
= sk_c11 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(3,negated_conjecture,
( ( ( sk_c11 @ ( sk_c6 @ multiply ) )
= sk_c12 )
| ( ( sk_c1 @ inverse )
= sk_c12 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
thf(124,plain,
( ( ( sk_c11 @ ( sk_c6 @ multiply ) )
= sk_c12 )
| ( ( sk_c1 @ inverse )
= sk_c12 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(69,negated_conjecture,
( ( ( sk_c11 @ ( sk_c10 @ multiply ) )
= sk_c12 )
| ( ( sk_c4 @ inverse )
= sk_c12 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_69) ).
thf(77,plain,
( ( ( sk_c11 @ ( sk_c10 @ multiply ) )
= sk_c12 )
| ( ( sk_c4 @ inverse )
= sk_c12 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(6,negated_conjecture,
( ( ( sk_c11 @ ( sk_c10 @ multiply ) )
= sk_c12 )
| ( ( sk_c1 @ inverse )
= sk_c12 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
thf(96,plain,
( ( ( sk_c11 @ ( sk_c10 @ multiply ) )
= sk_c12 )
| ( ( sk_c1 @ inverse )
= sk_c12 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(172,plain,
( ( ( sk_c12 @ inverse )
= sk_c11 )
| ( ( sk_c2 @ inverse )
= sk_c3 ) ),
inference(cnf,[status(esa)],[101]) ).
thf(173,plain,
( ( ( sk_c12 @ inverse )
= sk_c11 )
| ( ( sk_c2 @ inverse )
= sk_c3 ) ),
inference(lifteq,[status(thm)],[172]) ).
thf(73,negated_conjecture,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( H @ ( I @ multiply ) )
!= J )
| ( ( J @ inverse )
!= H )
| ( ( I @ inverse )
!= J )
| ( ( sk_c11 @ ( H @ multiply ) )
!= sk_c12 )
| ( ( G @ inverse )
!= H )
| ( ( H @ ( G @ multiply ) )
!= sk_c12 )
| ( ( sk_c11 @ ( F @ multiply ) )
!= sk_c12 )
| ( ( F @ inverse )
!= sk_c12 )
| ( ( sk_c12 @ inverse )
!= sk_c11 )
| ( ( E @ inverse )
!= sk_c12 )
| ( ( sk_c12 @ ( E @ multiply ) )
!= D )
| ( ( D @ ( sk_c12 @ multiply ) )
!= sk_c11 )
| ( ( sk_c12 @ ( C @ multiply ) )
!= sk_c11 )
| ( ( B @ inverse )
!= C )
| ( ( C @ ( B @ multiply ) )
!= sk_c11 )
| ( ( sk_c11 @ ( A @ multiply ) )
!= sk_c12 )
| ( ( A @ inverse )
!= sk_c12 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_73) ).
thf(107,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( H @ ( I @ multiply ) )
!= J )
| ( ( J @ inverse )
!= H )
| ( ( I @ inverse )
!= J )
| ( ( sk_c11 @ ( H @ multiply ) )
!= sk_c12 )
| ( ( G @ inverse )
!= H )
| ( ( H @ ( G @ multiply ) )
!= sk_c12 )
| ( ( sk_c11 @ ( F @ multiply ) )
!= sk_c12 )
| ( ( F @ inverse )
!= sk_c12 )
| ( ( sk_c12 @ inverse )
!= sk_c11 )
| ( ( E @ inverse )
!= sk_c12 )
| ( ( sk_c12 @ ( E @ multiply ) )
!= D )
| ( ( D @ ( sk_c12 @ multiply ) )
!= sk_c11 )
| ( ( sk_c12 @ ( C @ multiply ) )
!= sk_c11 )
| ( ( B @ inverse )
!= C )
| ( ( C @ ( B @ multiply ) )
!= sk_c11 )
| ( ( sk_c11 @ ( A @ multiply ) )
!= sk_c12 )
| ( ( A @ inverse )
!= sk_c12 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(276,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( H @ ( I @ multiply ) )
!= J )
| ( ( J @ inverse )
!= H )
| ( ( I @ inverse )
!= J )
| ( ( sk_c11 @ ( H @ multiply ) )
!= sk_c12 )
| ( ( G @ inverse )
!= H )
| ( ( H @ ( G @ multiply ) )
!= sk_c12 )
| ( ( sk_c11 @ ( F @ multiply ) )
!= sk_c12 )
| ( ( F @ inverse )
!= sk_c12 )
| ( ( sk_c12 @ inverse )
!= sk_c11 )
| ( ( E @ inverse )
!= sk_c12 )
| ( ( sk_c12 @ ( E @ multiply ) )
!= D )
| ( ( D @ ( sk_c12 @ multiply ) )
!= sk_c11 )
| ( ( sk_c12 @ ( C @ multiply ) )
!= sk_c11 )
| ( ( B @ inverse )
!= C )
| ( ( C @ ( B @ multiply ) )
!= sk_c11 )
| ( ( sk_c11 @ ( A @ multiply ) )
!= sk_c12 )
| ( ( A @ inverse )
!= sk_c12 ) ),
inference(cnf,[status(esa)],[107]) ).
thf(277,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( H @ ( I @ multiply ) )
!= J )
| ( ( J @ inverse )
!= H )
| ( ( I @ inverse )
!= J )
| ( ( sk_c11 @ ( H @ multiply ) )
!= sk_c12 )
| ( ( G @ inverse )
!= H )
| ( ( H @ ( G @ multiply ) )
!= sk_c12 )
| ( ( sk_c11 @ ( F @ multiply ) )
!= sk_c12 )
| ( ( F @ inverse )
!= sk_c12 )
| ( ( sk_c12 @ inverse )
!= sk_c11 )
| ( ( E @ inverse )
!= sk_c12 )
| ( ( sk_c12 @ ( E @ multiply ) )
!= D )
| ( ( D @ ( sk_c12 @ multiply ) )
!= sk_c11 )
| ( ( sk_c12 @ ( C @ multiply ) )
!= sk_c11 )
| ( ( B @ inverse )
!= C )
| ( ( C @ ( B @ multiply ) )
!= sk_c11 )
| ( ( sk_c11 @ ( A @ multiply ) )
!= sk_c12 )
| ( ( A @ inverse )
!= sk_c12 ) ),
inference(lifteq,[status(thm)],[276]) ).
thf(278,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ inverse @ ( F @ multiply ) )
!= ( F @ inverse ) )
| ( ( F @ inverse @ inverse )
!= ( E @ inverse ) )
| ( ( sk_c11 @ ( E @ inverse @ multiply ) )
!= sk_c12 )
| ( ( E @ inverse @ ( E @ multiply ) )
!= sk_c12 )
| ( ( sk_c11 @ ( D @ multiply ) )
!= sk_c12 )
| ( ( D @ inverse )
!= sk_c12 )
| ( ( sk_c12 @ inverse )
!= sk_c11 )
| ( ( C @ inverse )
!= sk_c12 )
| ( ( sk_c12 @ ( C @ multiply ) @ ( sk_c12 @ multiply ) )
!= sk_c11 )
| ( ( sk_c12 @ ( B @ inverse @ multiply ) )
!= sk_c11 )
| ( ( B @ inverse @ ( B @ multiply ) )
!= sk_c11 )
| ( ( sk_c11 @ ( A @ multiply ) )
!= sk_c12 )
| ( ( A @ inverse )
!= sk_c12 ) ),
inference(simp,[status(thm)],[277]) ).
thf(359,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ inverse @ multiply ) )
!= ( sk_c11 @ ( F @ inverse @ multiply ) ) )
| ( ( F @ inverse @ ( G @ multiply ) )
!= ( G @ inverse ) )
| ( ( G @ inverse @ inverse )
!= ( F @ inverse ) )
| ( identity != sk_c12 )
| ( ( F @ inverse @ ( F @ multiply ) )
!= sk_c12 )
| ( ( sk_c11 @ ( E @ multiply ) )
!= sk_c12 )
| ( ( E @ inverse )
!= sk_c12 )
| ( ( sk_c12 @ inverse )
!= sk_c11 )
| ( ( D @ inverse )
!= sk_c12 )
| ( ( sk_c12 @ ( D @ multiply ) @ ( sk_c12 @ multiply ) )
!= sk_c11 )
| ( ( sk_c12 @ ( C @ inverse @ multiply ) )
!= sk_c11 )
| ( ( C @ inverse @ ( C @ multiply ) )
!= sk_c11 )
| ( ( sk_c11 @ ( B @ multiply ) )
!= sk_c12 )
| ( ( B @ inverse )
!= sk_c12 ) ),
inference(paramod_ordered,[status(thm)],[300,278]) ).
thf(360,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( sk_c11 @ inverse @ ( E @ multiply ) )
!= ( E @ inverse ) )
| ( ( E @ inverse @ inverse )
!= ( sk_c11 @ inverse ) )
| ( identity != sk_c12 )
| ( ( sk_c11 @ inverse @ ( sk_c11 @ multiply ) )
!= sk_c12 )
| ( ( sk_c11 @ ( D @ multiply ) )
!= sk_c12 )
| ( ( D @ inverse )
!= sk_c12 )
| ( ( sk_c12 @ inverse )
!= sk_c11 )
| ( ( C @ inverse )
!= sk_c12 )
| ( ( sk_c12 @ ( C @ multiply ) @ ( sk_c12 @ multiply ) )
!= sk_c11 )
| ( ( sk_c12 @ ( B @ inverse @ multiply ) )
!= sk_c11 )
| ( ( B @ inverse @ ( B @ multiply ) )
!= sk_c11 )
| ( ( sk_c11 @ ( A @ multiply ) )
!= sk_c12 )
| ( ( A @ inverse )
!= sk_c12 ) ),
inference(pattern_uni,[status(thm)],[359:[bind(A,$thf( sk_c11 )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( sk_c11 ))]]) ).
thf(503,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( sk_c11 @ inverse @ ( E @ multiply ) )
!= ( E @ inverse ) )
| ( ( E @ inverse @ inverse )
!= ( sk_c11 @ inverse ) )
| ( identity != sk_c12 )
| ( ( sk_c11 @ inverse @ ( sk_c11 @ multiply ) )
!= sk_c12 )
| ( ( sk_c11 @ ( D @ multiply ) )
!= sk_c12 )
| ( ( D @ inverse )
!= sk_c12 )
| ( ( sk_c12 @ inverse )
!= sk_c11 )
| ( ( C @ inverse )
!= sk_c12 )
| ( ( sk_c12 @ ( C @ multiply ) @ ( sk_c12 @ multiply ) )
!= sk_c11 )
| ( ( sk_c12 @ ( B @ inverse @ multiply ) )
!= sk_c11 )
| ( ( B @ inverse @ ( B @ multiply ) )
!= sk_c11 )
| ( ( sk_c11 @ ( A @ multiply ) )
!= sk_c12 )
| ( ( A @ inverse )
!= sk_c12 ) ),
inference(simp,[status(thm)],[360]) ).
thf(542,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ inverse @ multiply ) )
!= ( sk_c12 @ ( C @ inverse @ multiply ) ) )
| ( ( sk_c11 @ inverse @ ( F @ multiply ) )
!= ( F @ inverse ) )
| ( ( F @ inverse @ inverse )
!= ( sk_c11 @ inverse ) )
| ( identity != sk_c12 )
| ( ( sk_c11 @ inverse @ ( sk_c11 @ multiply ) )
!= sk_c12 )
| ( ( sk_c11 @ ( E @ multiply ) )
!= sk_c12 )
| ( ( E @ inverse )
!= sk_c12 )
| ( ( sk_c12 @ inverse )
!= sk_c11 )
| ( ( D @ inverse )
!= sk_c12 )
| ( ( sk_c12 @ ( D @ multiply ) @ ( sk_c12 @ multiply ) )
!= sk_c11 )
| ( identity != sk_c11 )
| ( ( C @ inverse @ ( C @ multiply ) )
!= sk_c11 )
| ( ( sk_c11 @ ( B @ multiply ) )
!= sk_c12 )
| ( ( B @ inverse )
!= sk_c12 ) ),
inference(paramod_ordered,[status(thm)],[300,503]) ).
thf(543,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( sk_c11 @ inverse @ ( D @ multiply ) )
!= ( D @ inverse ) )
| ( ( D @ inverse @ inverse )
!= ( sk_c11 @ inverse ) )
| ( identity != sk_c12 )
| ( ( sk_c11 @ inverse @ ( sk_c11 @ multiply ) )
!= sk_c12 )
| ( ( sk_c11 @ ( C @ multiply ) )
!= sk_c12 )
| ( ( C @ inverse )
!= sk_c12 )
| ( ( sk_c12 @ inverse )
!= sk_c11 )
| ( ( B @ inverse )
!= sk_c12 )
| ( ( sk_c12 @ ( B @ multiply ) @ ( sk_c12 @ multiply ) )
!= sk_c11 )
| ( identity != sk_c11 )
| ( ( sk_c12 @ inverse @ ( sk_c12 @ multiply ) )
!= sk_c11 )
| ( ( sk_c11 @ ( A @ multiply ) )
!= sk_c12 )
| ( ( A @ inverse )
!= sk_c12 ) ),
inference(pattern_uni,[status(thm)],[542:[bind(A,$thf( sk_c12 )),bind(B,$thf( B )),bind(C,$thf( sk_c12 ))]]) ).
thf(622,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( sk_c11 @ inverse @ ( D @ multiply ) )
!= ( D @ inverse ) )
| ( ( D @ inverse @ inverse )
!= ( sk_c11 @ inverse ) )
| ( identity != sk_c12 )
| ( ( sk_c11 @ inverse @ ( sk_c11 @ multiply ) )
!= sk_c12 )
| ( ( sk_c11 @ ( C @ multiply ) )
!= sk_c12 )
| ( ( C @ inverse )
!= sk_c12 )
| ( ( sk_c12 @ inverse )
!= sk_c11 )
| ( ( B @ inverse )
!= sk_c12 )
| ( ( sk_c12 @ ( B @ multiply ) @ ( sk_c12 @ multiply ) )
!= sk_c11 )
| ( identity != sk_c11 )
| ( ( sk_c12 @ inverse @ ( sk_c12 @ multiply ) )
!= sk_c11 )
| ( ( sk_c11 @ ( A @ multiply ) )
!= sk_c12 )
| ( ( A @ inverse )
!= sk_c12 ) ),
inference(simp,[status(thm)],[543]) ).
thf(1735,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( sk_c12 != sk_c12 )
| ( ( sk_c11 @ ( C @ multiply ) )
!= ( sk_c11 @ ( A @ multiply ) ) )
| ( ( sk_c11 @ inverse @ ( D @ multiply ) )
!= ( D @ inverse ) )
| ( ( D @ inverse @ inverse )
!= ( sk_c11 @ inverse ) )
| ( identity != sk_c12 )
| ( ( sk_c11 @ inverse @ ( sk_c11 @ multiply ) )
!= sk_c12 )
| ( ( C @ inverse )
!= sk_c12 )
| ( ( sk_c12 @ inverse )
!= sk_c11 )
| ( ( B @ inverse )
!= sk_c12 )
| ( ( sk_c12 @ ( B @ multiply ) @ ( sk_c12 @ multiply ) )
!= sk_c11 )
| ( identity != sk_c11 )
| ( ( sk_c12 @ inverse @ ( sk_c12 @ multiply ) )
!= sk_c11 )
| ( ( sk_c11 @ ( A @ multiply ) )
!= sk_c12 )
| ( ( A @ inverse )
!= sk_c12 ) ),
inference(eqfactor_ordered,[status(thm)],[622]) ).
thf(1748,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk_c11 @ inverse @ ( C @ multiply ) )
!= ( C @ inverse ) )
| ( ( C @ inverse @ inverse )
!= ( sk_c11 @ inverse ) )
| ( identity != sk_c12 )
| ( ( sk_c11 @ inverse @ ( sk_c11 @ multiply ) )
!= sk_c12 )
| ( ( B @ inverse )
!= sk_c12 )
| ( ( sk_c12 @ inverse )
!= sk_c11 )
| ( ( A @ inverse )
!= sk_c12 )
| ( ( sk_c12 @ ( A @ multiply ) @ ( sk_c12 @ multiply ) )
!= sk_c11 )
| ( identity != sk_c11 )
| ( ( sk_c12 @ inverse @ ( sk_c12 @ multiply ) )
!= sk_c11 )
| ( ( sk_c11 @ ( B @ multiply ) )
!= sk_c12 )
| ( ( B @ inverse )
!= sk_c12 ) ),
inference(pattern_uni,[status(thm)],[1735:[bind(A,$thf( C ))]]) ).
thf(1933,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk_c11 @ inverse @ ( C @ multiply ) )
!= ( C @ inverse ) )
| ( ( C @ inverse @ inverse )
!= ( sk_c11 @ inverse ) )
| ( identity != sk_c12 )
| ( ( sk_c11 @ inverse @ ( sk_c11 @ multiply ) )
!= sk_c12 )
| ( ( sk_c12 @ inverse )
!= sk_c11 )
| ( ( A @ inverse )
!= sk_c12 )
| ( ( sk_c12 @ ( A @ multiply ) @ ( sk_c12 @ multiply ) )
!= sk_c11 )
| ( identity != sk_c11 )
| ( ( sk_c12 @ inverse @ ( sk_c12 @ multiply ) )
!= sk_c11 )
| ( ( sk_c11 @ ( B @ multiply ) )
!= sk_c12 )
| ( ( B @ inverse )
!= sk_c12 ) ),
inference(simp,[status(thm)],[1748]) ).
thf(2109,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( identity @ multiply ) )
!= ( sk_c11 @ inverse @ ( D @ multiply ) ) )
| ( A
!= ( D @ inverse ) )
| ( ( D @ inverse @ inverse )
!= ( sk_c11 @ inverse ) )
| ( identity != sk_c12 )
| ( ( sk_c11 @ inverse @ ( sk_c11 @ multiply ) )
!= sk_c12 )
| ( ( sk_c12 @ inverse )
!= sk_c11 )
| ( ( B @ inverse )
!= sk_c12 )
| ( ( sk_c12 @ ( B @ multiply ) @ ( sk_c12 @ multiply ) )
!= sk_c11 )
| ( identity != sk_c11 )
| ( ( sk_c12 @ inverse @ ( sk_c12 @ multiply ) )
!= sk_c11 )
| ( ( sk_c11 @ ( C @ multiply ) )
!= sk_c12 )
| ( ( C @ inverse )
!= sk_c12 ) ),
inference(paramod_ordered,[status(thm)],[298,1933]) ).
thf(2110,plain,
! [B: $i,A: $i] :
( ( ( identity @ inverse )
!= ( sk_c11 @ inverse ) )
| ( ( identity @ inverse @ inverse )
!= ( sk_c11 @ inverse ) )
| ( identity != sk_c12 )
| ( ( sk_c11 @ inverse @ ( sk_c11 @ multiply ) )
!= sk_c12 )
| ( ( sk_c12 @ inverse )
!= sk_c11 )
| ( ( A @ inverse )
!= sk_c12 )
| ( ( sk_c12 @ ( A @ multiply ) @ ( sk_c12 @ multiply ) )
!= sk_c11 )
| ( identity != sk_c11 )
| ( ( sk_c12 @ inverse @ ( sk_c12 @ multiply ) )
!= sk_c11 )
| ( ( sk_c11 @ ( B @ multiply ) )
!= sk_c12 )
| ( ( B @ inverse )
!= sk_c12 ) ),
inference(pattern_uni,[status(thm)],[2109:[bind(A,$thf( sk_c11 @ inverse )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( identity ))]]) ).
thf(2314,plain,
! [B: $i,A: $i] :
( ( ( identity @ inverse )
!= ( sk_c11 @ inverse ) )
| ( ( identity @ inverse @ inverse )
!= ( sk_c11 @ inverse ) )
| ( identity != sk_c12 )
| ( ( sk_c11 @ inverse @ ( sk_c11 @ multiply ) )
!= sk_c12 )
| ( ( sk_c12 @ inverse )
!= sk_c11 )
| ( ( A @ inverse )
!= sk_c12 )
| ( ( sk_c12 @ ( A @ multiply ) @ ( sk_c12 @ multiply ) )
!= sk_c11 )
| ( identity != sk_c11 )
| ( ( sk_c12 @ inverse @ ( sk_c12 @ multiply ) )
!= sk_c11 )
| ( ( sk_c11 @ ( B @ multiply ) )
!= sk_c12 )
| ( ( B @ inverse )
!= sk_c12 ) ),
inference(simp,[status(thm)],[2110]) ).
thf(2961,plain,
! [B: $i,A: $i] :
( ( ( sk_c11 @ inverse )
!= identity )
| ( ( identity @ inverse )
!= ( sk_c11 @ inverse ) )
| ( identity != sk_c12 )
| ( ( sk_c11 @ inverse @ ( sk_c11 @ multiply ) )
!= sk_c12 )
| ( ( sk_c12 @ inverse )
!= sk_c11 )
| ( ( A @ inverse )
!= sk_c12 )
| ( ( sk_c12 @ ( A @ multiply ) @ ( sk_c12 @ multiply ) )
!= sk_c11 )
| ( identity != sk_c11 )
| ( ( sk_c12 @ inverse @ ( sk_c12 @ multiply ) )
!= sk_c11 )
| ( ( sk_c11 @ ( B @ multiply ) )
!= sk_c12 )
| ( ( B @ inverse )
!= sk_c12 ) ),
inference(rewrite,[status(thm)],[2314,1540]) ).
thf(3081,plain,
! [B: $i,A: $i] :
( ( sk_c12 != sk_c12 )
| ( ( sk_c11 @ inverse @ ( sk_c11 @ multiply ) )
!= ( sk_c11 @ ( B @ multiply ) ) )
| ( ( sk_c11 @ inverse )
!= identity )
| ( ( identity @ inverse )
!= ( sk_c11 @ inverse ) )
| ( identity != sk_c12 )
| ( ( sk_c12 @ inverse )
!= sk_c11 )
| ( ( A @ inverse )
!= sk_c12 )
| ( ( sk_c12 @ ( A @ multiply ) @ ( sk_c12 @ multiply ) )
!= sk_c11 )
| ( identity != sk_c11 )
| ( ( sk_c12 @ inverse @ ( sk_c12 @ multiply ) )
!= sk_c11 )
| ( ( sk_c11 @ ( B @ multiply ) )
!= sk_c12 )
| ( ( B @ inverse )
!= sk_c12 ) ),
inference(eqfactor_ordered,[status(thm)],[2961]) ).
thf(3175,plain,
! [B: $i,A: $i] :
( ( ( sk_c11 @ inverse )
!= sk_c11 )
| ( sk_c11 != B )
| ( ( sk_c11 @ inverse )
!= identity )
| ( identity != sk_c11 )
| ( identity != sk_c12 )
| ( ( sk_c12 @ inverse )
!= sk_c11 )
| ( ( A @ inverse )
!= sk_c12 )
| ( ( sk_c12 @ ( A @ multiply ) @ ( sk_c12 @ multiply ) )
!= sk_c11 )
| ( identity != sk_c11 )
| ( ( sk_c12 @ inverse @ ( sk_c12 @ multiply ) )
!= sk_c11 )
| ( ( sk_c11 @ ( B @ multiply ) )
!= sk_c12 )
| ( ( B @ inverse )
!= sk_c12 ) ),
inference(simp,[status(thm)],[3081]) ).
thf(3321,plain,
! [A: $i] :
( ( ( sk_c11 @ inverse )
!= sk_c11 )
| ( ( sk_c11 @ inverse )
!= identity )
| ( identity != sk_c12 )
| ( ( sk_c12 @ inverse )
!= sk_c11 )
| ( ( A @ inverse )
!= sk_c12 )
| ( ( sk_c12 @ ( A @ multiply ) @ ( sk_c12 @ multiply ) )
!= sk_c11 )
| ( identity != sk_c11 )
| ( ( sk_c12 @ inverse @ ( sk_c12 @ multiply ) )
!= sk_c11 )
| ( ( sk_c11 @ ( sk_c11 @ multiply ) )
!= sk_c12 )
| ( ( sk_c11 @ inverse )
!= sk_c12 ) ),
inference(simp,[status(thm)],[3175]) ).
thf(3399,plain,
! [A: $i] :
( ( ( identity @ inverse )
!= ( A @ inverse ) )
| ( ( sk_c11 @ inverse )
!= sk_c11 )
| ( ( sk_c11 @ inverse )
!= identity )
| ( identity != sk_c12 )
| ( ( sk_c12 @ inverse )
!= sk_c11 )
| ( identity != sk_c12 )
| ( ( sk_c12 @ ( A @ multiply ) @ ( sk_c12 @ multiply ) )
!= sk_c11 )
| ( identity != sk_c11 )
| ( ( sk_c12 @ inverse @ ( sk_c12 @ multiply ) )
!= sk_c11 )
| ( ( sk_c11 @ ( sk_c11 @ multiply ) )
!= sk_c12 )
| ( ( sk_c11 @ inverse )
!= sk_c12 ) ),
inference(paramod_ordered,[status(thm)],[1540,3321]) ).
thf(3400,plain,
! [A: $i] :
( ( ( identity @ inverse )
!= ( A @ inverse ) )
| ( ( sk_c11 @ inverse )
!= sk_c11 )
| ( ( sk_c11 @ inverse )
!= identity )
| ( ( sk_c12 @ inverse )
!= sk_c11 )
| ( identity != sk_c12 )
| ( ( sk_c12 @ ( A @ multiply ) @ ( sk_c12 @ multiply ) )
!= sk_c11 )
| ( identity != sk_c11 )
| ( ( sk_c12 @ inverse @ ( sk_c12 @ multiply ) )
!= sk_c11 )
| ( ( sk_c11 @ ( sk_c11 @ multiply ) )
!= sk_c12 )
| ( ( sk_c11 @ inverse )
!= sk_c12 ) ),
inference(simp,[status(thm)],[3399]) ).
thf(3401,plain,
( ( ( sk_c11 @ inverse )
!= sk_c11 )
| ( ( sk_c11 @ inverse )
!= identity )
| ( ( sk_c12 @ inverse )
!= sk_c11 )
| ( identity != sk_c12 )
| ( ( sk_c12 @ ( identity @ multiply ) @ ( sk_c12 @ multiply ) )
!= sk_c11 )
| ( identity != sk_c11 )
| ( ( sk_c12 @ inverse @ ( sk_c12 @ multiply ) )
!= sk_c11 )
| ( ( sk_c11 @ ( sk_c11 @ multiply ) )
!= sk_c12 )
| ( ( sk_c11 @ inverse )
!= sk_c12 ) ),
inference(pattern_uni,[status(thm)],[3400:[bind(A,$thf( identity ))]]) ).
thf(4820,plain,
( ( ( sk_c11 @ inverse )
!= sk_c11 )
| ( ( sk_c11 @ inverse )
!= identity )
| ( ( sk_c12 @ inverse )
!= sk_c11 )
| ( identity != sk_c12 )
| ( ( sk_c12 @ ( sk_c12 @ multiply ) )
!= sk_c11 )
| ( identity != sk_c11 )
| ( ( sk_c12 @ inverse @ ( sk_c12 @ multiply ) )
!= sk_c11 )
| ( ( sk_c11 @ ( sk_c11 @ multiply ) )
!= sk_c12 )
| ( ( sk_c11 @ inverse )
!= sk_c12 ) ),
inference(rewrite,[status(thm)],[3401,298]) ).
thf(4863,plain,
! [A: $i] :
( ( ( A @ ( identity @ multiply ) )
!= ( sk_c12 @ inverse @ ( sk_c12 @ multiply ) ) )
| ( ( sk_c11 @ inverse )
!= sk_c11 )
| ( ( sk_c11 @ inverse )
!= identity )
| ( ( sk_c12 @ inverse )
!= sk_c11 )
| ( identity != sk_c12 )
| ( ( sk_c12 @ ( sk_c12 @ multiply ) )
!= sk_c11 )
| ( identity != sk_c11 )
| ( A != sk_c11 )
| ( ( sk_c11 @ ( sk_c11 @ multiply ) )
!= sk_c12 )
| ( ( sk_c11 @ inverse )
!= sk_c12 ) ),
inference(paramod_ordered,[status(thm)],[298,4820]) ).
thf(4998,plain,
( ( ( sk_c12 @ inverse )
!= sk_c11 )
| ( identity != sk_c12 )
| ( ( sk_c11 @ inverse )
!= sk_c11 )
| ( ( sk_c11 @ inverse )
!= identity )
| ( ( sk_c12 @ inverse )
!= sk_c11 )
| ( identity != sk_c12 )
| ( ( sk_c12 @ ( sk_c12 @ multiply ) )
!= sk_c11 )
| ( identity != sk_c11 )
| ( ( sk_c11 @ ( sk_c11 @ multiply ) )
!= sk_c12 )
| ( ( sk_c11 @ inverse )
!= sk_c12 ) ),
inference(simp,[status(thm)],[4863]) ).
thf(5001,plain,
( ( ( sk_c11 @ inverse )
!= sk_c11 )
| ( ( sk_c11 @ inverse )
!= identity )
| ( ( sk_c12 @ inverse )
!= sk_c11 )
| ( identity != sk_c12 )
| ( ( sk_c12 @ ( sk_c12 @ multiply ) )
!= sk_c11 )
| ( identity != sk_c11 )
| ( ( sk_c11 @ ( sk_c11 @ multiply ) )
!= sk_c12 )
| ( ( sk_c11 @ inverse )
!= sk_c12 ) ),
inference(simp,[status(thm)],[4998]) ).
thf(5044,plain,
( ( ( identity @ inverse )
!= ( sk_c12 @ inverse ) )
| ( ( sk_c11 @ inverse )
!= sk_c11 )
| ( ( sk_c11 @ inverse )
!= identity )
| ( identity != sk_c11 )
| ( identity != sk_c12 )
| ( ( sk_c12 @ ( sk_c12 @ multiply ) )
!= sk_c11 )
| ( identity != sk_c11 )
| ( ( sk_c11 @ ( sk_c11 @ multiply ) )
!= sk_c12 )
| ( ( sk_c11 @ inverse )
!= sk_c12 ) ),
inference(paramod_ordered,[status(thm)],[1540,5001]) ).
thf(5045,plain,
( ( ( identity @ inverse )
!= ( sk_c12 @ inverse ) )
| ( ( sk_c11 @ inverse )
!= sk_c11 )
| ( ( sk_c11 @ inverse )
!= identity )
| ( identity != sk_c12 )
| ( ( sk_c12 @ ( sk_c12 @ multiply ) )
!= sk_c11 )
| ( identity != sk_c11 )
| ( ( sk_c11 @ ( sk_c11 @ multiply ) )
!= sk_c12 )
| ( ( sk_c11 @ inverse )
!= sk_c12 ) ),
inference(simp,[status(thm)],[5044]) ).
thf(5128,plain,
( ( identity != sk_c12 )
| ( ( sk_c11 @ inverse )
!= sk_c11 )
| ( ( sk_c11 @ inverse )
!= identity )
| ( identity != sk_c12 )
| ( ( sk_c12 @ ( sk_c12 @ multiply ) )
!= sk_c11 )
| ( identity != sk_c11 )
| ( ( sk_c11 @ ( sk_c11 @ multiply ) )
!= sk_c12 )
| ( ( sk_c11 @ inverse )
!= sk_c12 ) ),
inference(simp,[status(thm)],[5045]) ).
thf(5162,plain,
( ( ( sk_c11 @ inverse )
!= sk_c11 )
| ( ( sk_c11 @ inverse )
!= identity )
| ( identity != sk_c12 )
| ( ( sk_c12 @ ( sk_c12 @ multiply ) )
!= sk_c11 )
| ( identity != sk_c11 )
| ( ( sk_c11 @ ( sk_c11 @ multiply ) )
!= sk_c12 )
| ( ( sk_c11 @ inverse )
!= sk_c12 ) ),
inference(simp,[status(thm)],[5128]) ).
thf(6106,plain,
( ( ( identity @ inverse )
!= ( sk_c11 @ inverse ) )
| ( ( sk_c11 @ inverse )
!= sk_c11 )
| ( ( sk_c11 @ inverse )
!= identity )
| ( identity != sk_c12 )
| ( ( sk_c12 @ ( sk_c12 @ multiply ) )
!= sk_c11 )
| ( identity != sk_c11 )
| ( ( sk_c11 @ ( sk_c11 @ multiply ) )
!= sk_c12 )
| ( identity != sk_c12 ) ),
inference(paramod_ordered,[status(thm)],[1540,5162]) ).
thf(6107,plain,
( ( ( identity @ inverse )
!= ( sk_c11 @ inverse ) )
| ( ( sk_c11 @ inverse )
!= sk_c11 )
| ( ( sk_c11 @ inverse )
!= identity )
| ( ( sk_c12 @ ( sk_c12 @ multiply ) )
!= sk_c11 )
| ( identity != sk_c11 )
| ( ( sk_c11 @ ( sk_c11 @ multiply ) )
!= sk_c12 )
| ( identity != sk_c12 ) ),
inference(simp,[status(thm)],[6106]) ).
thf(6194,plain,
( ( identity != sk_c11 )
| ( ( sk_c11 @ inverse )
!= sk_c11 )
| ( ( sk_c11 @ inverse )
!= identity )
| ( ( sk_c12 @ ( sk_c12 @ multiply ) )
!= sk_c11 )
| ( identity != sk_c11 )
| ( ( sk_c11 @ ( sk_c11 @ multiply ) )
!= sk_c12 )
| ( identity != sk_c12 ) ),
inference(simp,[status(thm)],[6107]) ).
thf(6239,plain,
( ( ( sk_c11 @ inverse )
!= sk_c11 )
| ( ( sk_c11 @ inverse )
!= identity )
| ( ( sk_c12 @ ( sk_c12 @ multiply ) )
!= sk_c11 )
| ( identity != sk_c11 )
| ( ( sk_c11 @ ( sk_c11 @ multiply ) )
!= sk_c12 )
| ( identity != sk_c12 ) ),
inference(simp,[status(thm)],[6194]) ).
thf(72,negated_conjecture,
( ( ( sk_c10 @ ( sk_c9 @ multiply ) )
= sk_c8 )
| ( ( sk_c4 @ inverse )
= sk_c12 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_72) ).
thf(134,plain,
( ( ( sk_c10 @ ( sk_c9 @ multiply ) )
= sk_c8 )
| ( ( sk_c4 @ inverse )
= sk_c12 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(13,negated_conjecture,
( ( ( sk_c10 @ ( sk_c7 @ multiply ) )
= sk_c12 )
| ( ( sk_c11 @ ( sk_c1 @ multiply ) )
= sk_c12 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
thf(105,plain,
( ( ( sk_c10 @ ( sk_c7 @ multiply ) )
= sk_c12 )
| ( ( sk_c11 @ ( sk_c1 @ multiply ) )
= sk_c12 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(18,negated_conjecture,
( ( ( sk_c10 @ ( sk_c9 @ multiply ) )
= sk_c8 )
| ( ( sk_c11 @ ( sk_c1 @ multiply ) )
= sk_c12 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
thf(128,plain,
( ( ( sk_c10 @ ( sk_c9 @ multiply ) )
= sk_c8 )
| ( ( sk_c11 @ ( sk_c1 @ multiply ) )
= sk_c12 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(34,negated_conjecture,
( ( ( sk_c9 @ inverse )
= sk_c8 )
| ( ( sk_c2 @ inverse )
= sk_c3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_34) ).
thf(113,plain,
( ( ( sk_c9 @ inverse )
= sk_c8 )
| ( ( sk_c2 @ inverse )
= sk_c3 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(236,plain,
( ( ( sk_c9 @ inverse )
= sk_c8 )
| ( ( sk_c2 @ inverse )
= sk_c3 ) ),
inference(cnf,[status(esa)],[113]) ).
thf(237,plain,
( ( ( sk_c9 @ inverse )
= sk_c8 )
| ( ( sk_c2 @ inverse )
= sk_c3 ) ),
inference(lifteq,[status(thm)],[236]) ).
thf(160,plain,
( ( ( sk_c12 @ inverse )
= sk_c11 )
| ( ( sk_c1 @ inverse )
= sk_c12 ) ),
inference(cnf,[status(esa)],[95]) ).
thf(161,plain,
( ( ( sk_c12 @ inverse )
= sk_c11 )
| ( ( sk_c1 @ inverse )
= sk_c12 ) ),
inference(lifteq,[status(thm)],[160]) ).
thf(62,negated_conjecture,
( ( ( sk_c8 @ inverse )
= sk_c10 )
| ( ( sk_c12 @ ( sk_c4 @ multiply ) )
= sk_c5 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_62) ).
thf(149,plain,
( ( ( sk_c8 @ inverse )
= sk_c10 )
| ( ( sk_c12 @ ( sk_c4 @ multiply ) )
= sk_c5 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(51,negated_conjecture,
( ( ( sk_c11 @ ( sk_c10 @ multiply ) )
= sk_c12 )
| ( ( sk_c5 @ ( sk_c12 @ multiply ) )
= sk_c11 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_51) ).
thf(144,plain,
( ( ( sk_c11 @ ( sk_c10 @ multiply ) )
= sk_c12 )
| ( ( sk_c5 @ ( sk_c12 @ multiply ) )
= sk_c11 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(1516,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( identity @ inverse @ inverse @ multiply ) )
!= ( B @ ( C @ multiply ) ) )
| ( ( A @ ( C @ inverse @ multiply ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[1202,983]) ).
thf(1517,plain,
! [A: $i] :
( ( A @ ( identity @ inverse @ inverse @ inverse @ multiply ) )
= A ),
inference(pattern_uni,[status(thm)],[1516:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( identity @ inverse @ inverse ))]]) ).
thf(4573,plain,
! [A: $i] :
( ( A @ ( identity @ inverse @ inverse @ multiply ) )
= A ),
inference(rewrite,[status(thm)],[1517,1540]) ).
thf(180,plain,
( ( ( sk_c12 @ inverse )
= sk_c11 )
| ( ( sk_c4 @ inverse )
= sk_c12 ) ),
inference(cnf,[status(esa)],[110]) ).
thf(181,plain,
( ( ( sk_c12 @ inverse )
= sk_c11 )
| ( ( sk_c4 @ inverse )
= sk_c12 ) ),
inference(lifteq,[status(thm)],[180]) ).
thf(37,negated_conjecture,
( ( ( sk_c12 @ inverse )
= sk_c11 )
| ( ( sk_c12 @ ( sk_c3 @ multiply ) )
= sk_c11 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_37) ).
thf(86,plain,
( ( ( sk_c12 @ inverse )
= sk_c11 )
| ( ( sk_c12 @ ( sk_c3 @ multiply ) )
= sk_c11 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(158,plain,
( ( ( sk_c8 @ inverse )
= sk_c10 )
| ( ( sk_c4 @ inverse )
= sk_c12 ) ),
inference(cnf,[status(esa)],[118]) ).
thf(159,plain,
( ( ( sk_c8 @ inverse )
= sk_c10 )
| ( ( sk_c4 @ inverse )
= sk_c12 ) ),
inference(lifteq,[status(thm)],[158]) ).
thf(186,plain,
( ( ( sk_c7 @ inverse )
= sk_c10 )
| ( ( sk_c1 @ inverse )
= sk_c12 ) ),
inference(cnf,[status(esa)],[78]) ).
thf(187,plain,
( ( ( sk_c7 @ inverse )
= sk_c10 )
| ( ( sk_c1 @ inverse )
= sk_c12 ) ),
inference(lifteq,[status(thm)],[186]) ).
thf(4,negated_conjecture,
( ( ( sk_c10 @ ( sk_c7 @ multiply ) )
= sk_c12 )
| ( ( sk_c1 @ inverse )
= sk_c12 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
thf(81,plain,
( ( ( sk_c10 @ ( sk_c7 @ multiply ) )
= sk_c12 )
| ( ( sk_c1 @ inverse )
= sk_c12 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(8,negated_conjecture,
( ( ( sk_c8 @ inverse )
= sk_c10 )
| ( ( sk_c1 @ inverse )
= sk_c12 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
thf(140,plain,
( ( ( sk_c8 @ inverse )
= sk_c10 )
| ( ( sk_c1 @ inverse )
= sk_c12 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(244,plain,
( ( ( sk_c8 @ inverse )
= sk_c10 )
| ( ( sk_c1 @ inverse )
= sk_c12 ) ),
inference(cnf,[status(esa)],[140]) ).
thf(245,plain,
( ( ( sk_c8 @ inverse )
= sk_c10 )
| ( ( sk_c1 @ inverse )
= sk_c12 ) ),
inference(lifteq,[status(thm)],[244]) ).
thf(70,negated_conjecture,
( ( ( sk_c9 @ inverse )
= sk_c8 )
| ( ( sk_c4 @ inverse )
= sk_c12 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_70) ).
thf(98,plain,
( ( ( sk_c9 @ inverse )
= sk_c8 )
| ( ( sk_c4 @ inverse )
= sk_c12 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(1025,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ inverse @ multiply ) )
!= ( B @ ( C @ multiply ) ) )
| ( ( identity @ ( C @ inverse @ multiply ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[300,983]) ).
thf(1026,plain,
! [A: $i] :
( ( identity @ ( A @ inverse @ inverse @ multiply ) )
= A ),
inference(pattern_uni,[status(thm)],[1025:[bind(A,$thf( D )),bind(B,$thf( D )),bind(C,$thf( D @ inverse ))]]) ).
thf(1101,plain,
! [A: $i] :
( ( identity @ ( A @ inverse @ inverse @ multiply ) )
= A ),
inference(simp,[status(thm)],[1026]) ).
thf(1310,plain,
! [C: $i,B: $i,A: $i] :
( ( ( identity @ ( A @ inverse @ inverse @ multiply ) )
!= ( B @ ( C @ multiply ) ) )
| ( ( A @ ( C @ inverse @ multiply ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[1101,983]) ).
thf(1311,plain,
! [A: $i] :
( ( A @ ( A @ inverse @ inverse @ inverse @ multiply ) )
= identity ),
inference(pattern_uni,[status(thm)],[1310:[bind(A,$thf( E )),bind(B,$thf( identity )),bind(C,$thf( E @ inverse @ inverse ))]]) ).
thf(1408,plain,
! [A: $i] :
( ( A @ ( A @ inverse @ inverse @ inverse @ multiply ) )
= identity ),
inference(simp,[status(thm)],[1311]) ).
thf(9,negated_conjecture,
( ( ( sk_c10 @ ( sk_c9 @ multiply ) )
= sk_c8 )
| ( ( sk_c1 @ inverse )
= sk_c12 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
thf(103,plain,
( ( ( sk_c10 @ ( sk_c9 @ multiply ) )
= sk_c8 )
| ( ( sk_c1 @ inverse )
= sk_c12 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(46,negated_conjecture,
( ( ( sk_c12 @ inverse )
= sk_c11 )
| ( ( sk_c5 @ ( sk_c12 @ multiply ) )
= sk_c11 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_46) ).
thf(91,plain,
( ( ( sk_c12 @ inverse )
= sk_c11 )
| ( ( sk_c5 @ ( sk_c12 @ multiply ) )
= sk_c11 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(154,plain,
( ( ( sk_c10 @ ( sk_c7 @ multiply ) )
= sk_c12 )
| ( ( sk_c12 @ ( sk_c4 @ multiply ) )
= sk_c5 ) ),
inference(cnf,[status(esa)],[141]) ).
thf(155,plain,
( ( ( sk_c10 @ ( sk_c7 @ multiply ) )
= sk_c12 )
| ( ( sk_c12 @ ( sk_c4 @ multiply ) )
= sk_c5 ) ),
inference(lifteq,[status(thm)],[154]) ).
thf(2,negated_conjecture,
( ( ( sk_c6 @ inverse )
= sk_c12 )
| ( ( sk_c1 @ inverse )
= sk_c12 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
thf(108,plain,
( ( ( sk_c6 @ inverse )
= sk_c12 )
| ( ( sk_c1 @ inverse )
= sk_c12 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(67,negated_conjecture,
( ( ( sk_c10 @ ( sk_c7 @ multiply ) )
= sk_c12 )
| ( ( sk_c4 @ inverse )
= sk_c12 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_67) ).
thf(130,plain,
( ( ( sk_c10 @ ( sk_c7 @ multiply ) )
= sk_c12 )
| ( ( sk_c4 @ inverse )
= sk_c12 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(43,negated_conjecture,
( ( ( sk_c9 @ inverse )
= sk_c8 )
| ( ( sk_c12 @ ( sk_c3 @ multiply ) )
= sk_c11 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_43) ).
thf(135,plain,
( ( ( sk_c9 @ inverse )
= sk_c8 )
| ( ( sk_c12 @ ( sk_c3 @ multiply ) )
= sk_c11 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(240,plain,
( ( ( sk_c9 @ inverse )
= sk_c8 )
| ( ( sk_c4 @ inverse )
= sk_c12 ) ),
inference(cnf,[status(esa)],[98]) ).
thf(241,plain,
( ( ( sk_c9 @ inverse )
= sk_c8 )
| ( ( sk_c4 @ inverse )
= sk_c12 ) ),
inference(lifteq,[status(thm)],[240]) ).
thf(66,negated_conjecture,
( ( ( sk_c11 @ ( sk_c6 @ multiply ) )
= sk_c12 )
| ( ( sk_c4 @ inverse )
= sk_c12 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_66) ).
thf(80,plain,
( ( ( sk_c11 @ ( sk_c6 @ multiply ) )
= sk_c12 )
| ( ( sk_c4 @ inverse )
= sk_c12 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(32,negated_conjecture,
( ( ( sk_c7 @ inverse )
= sk_c10 )
| ( ( sk_c2 @ inverse )
= sk_c3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_32) ).
thf(112,plain,
( ( ( sk_c7 @ inverse )
= sk_c10 )
| ( ( sk_c2 @ inverse )
= sk_c3 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(39,negated_conjecture,
( ( ( sk_c11 @ ( sk_c6 @ multiply ) )
= sk_c12 )
| ( ( sk_c12 @ ( sk_c3 @ multiply ) )
= sk_c11 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_39) ).
thf(123,plain,
( ( ( sk_c11 @ ( sk_c6 @ multiply ) )
= sk_c12 )
| ( ( sk_c12 @ ( sk_c3 @ multiply ) )
= sk_c11 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(19,negated_conjecture,
( ( ( sk_c12 @ inverse )
= sk_c11 )
| ( ( sk_c3 @ ( sk_c2 @ multiply ) )
= sk_c11 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
thf(145,plain,
( ( ( sk_c12 @ inverse )
= sk_c11 )
| ( ( sk_c3 @ ( sk_c2 @ multiply ) )
= sk_c11 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(21,negated_conjecture,
( ( ( sk_c11 @ ( sk_c6 @ multiply ) )
= sk_c12 )
| ( ( sk_c3 @ ( sk_c2 @ multiply ) )
= sk_c11 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
thf(99,plain,
( ( ( sk_c11 @ ( sk_c6 @ multiply ) )
= sk_c12 )
| ( ( sk_c3 @ ( sk_c2 @ multiply ) )
= sk_c11 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(25,negated_conjecture,
( ( ( sk_c9 @ inverse )
= sk_c8 )
| ( ( sk_c3 @ ( sk_c2 @ multiply ) )
= sk_c11 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
thf(87,plain,
( ( ( sk_c9 @ inverse )
= sk_c8 )
| ( ( sk_c3 @ ( sk_c2 @ multiply ) )
= sk_c11 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(53,negated_conjecture,
( ( ( sk_c8 @ inverse )
= sk_c10 )
| ( ( sk_c5 @ ( sk_c12 @ multiply ) )
= sk_c11 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_53) ).
thf(104,plain,
( ( ( sk_c8 @ inverse )
= sk_c10 )
| ( ( sk_c5 @ ( sk_c12 @ multiply ) )
= sk_c11 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(22,negated_conjecture,
( ( ( sk_c10 @ ( sk_c7 @ multiply ) )
= sk_c12 )
| ( ( sk_c3 @ ( sk_c2 @ multiply ) )
= sk_c11 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
thf(114,plain,
( ( ( sk_c10 @ ( sk_c7 @ multiply ) )
= sk_c12 )
| ( ( sk_c3 @ ( sk_c2 @ multiply ) )
= sk_c11 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(23,negated_conjecture,
( ( ( sk_c7 @ inverse )
= sk_c10 )
| ( ( sk_c3 @ ( sk_c2 @ multiply ) )
= sk_c11 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
thf(139,plain,
( ( ( sk_c7 @ inverse )
= sk_c10 )
| ( ( sk_c3 @ ( sk_c2 @ multiply ) )
= sk_c11 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(12,negated_conjecture,
( ( ( sk_c11 @ ( sk_c6 @ multiply ) )
= sk_c12 )
| ( ( sk_c11 @ ( sk_c1 @ multiply ) )
= sk_c12 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
thf(119,plain,
( ( ( sk_c11 @ ( sk_c6 @ multiply ) )
= sk_c12 )
| ( ( sk_c11 @ ( sk_c1 @ multiply ) )
= sk_c12 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(10,negated_conjecture,
( ( ( sk_c12 @ inverse )
= sk_c11 )
| ( ( sk_c11 @ ( sk_c1 @ multiply ) )
= sk_c12 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
thf(82,plain,
( ( ( sk_c12 @ inverse )
= sk_c11 )
| ( ( sk_c11 @ ( sk_c1 @ multiply ) )
= sk_c12 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(150,plain,
( ( ( sk_c10 @ ( sk_c9 @ multiply ) )
= sk_c8 )
| ( ( sk_c2 @ inverse )
= sk_c3 ) ),
inference(cnf,[status(esa)],[142]) ).
thf(151,plain,
( ( ( sk_c10 @ ( sk_c9 @ multiply ) )
= sk_c8 )
| ( ( sk_c2 @ inverse )
= sk_c3 ) ),
inference(lifteq,[status(thm)],[150]) ).
thf(47,negated_conjecture,
( ( ( sk_c6 @ inverse )
= sk_c12 )
| ( ( sk_c5 @ ( sk_c12 @ multiply ) )
= sk_c11 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_47) ).
thf(146,plain,
( ( ( sk_c6 @ inverse )
= sk_c12 )
| ( ( sk_c5 @ ( sk_c12 @ multiply ) )
= sk_c11 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(182,plain,
( ( ( sk_c8 @ inverse )
= sk_c10 )
| ( ( sk_c2 @ inverse )
= sk_c3 ) ),
inference(cnf,[status(esa)],[125]) ).
thf(183,plain,
( ( ( sk_c8 @ inverse )
= sk_c10 )
| ( ( sk_c2 @ inverse )
= sk_c3 ) ),
inference(lifteq,[status(thm)],[182]) ).
thf(65,negated_conjecture,
( ( ( sk_c6 @ inverse )
= sk_c12 )
| ( ( sk_c4 @ inverse )
= sk_c12 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_65) ).
thf(79,plain,
( ( ( sk_c6 @ inverse )
= sk_c12 )
| ( ( sk_c4 @ inverse )
= sk_c12 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(61,negated_conjecture,
( ( ( sk_c9 @ inverse )
= sk_c8 )
| ( ( sk_c12 @ ( sk_c4 @ multiply ) )
= sk_c5 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_61) ).
thf(94,plain,
( ( ( sk_c9 @ inverse )
= sk_c8 )
| ( ( sk_c12 @ ( sk_c4 @ multiply ) )
= sk_c5 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(48,negated_conjecture,
( ( ( sk_c11 @ ( sk_c6 @ multiply ) )
= sk_c12 )
| ( ( sk_c5 @ ( sk_c12 @ multiply ) )
= sk_c11 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_48) ).
thf(126,plain,
( ( ( sk_c11 @ ( sk_c6 @ multiply ) )
= sk_c12 )
| ( ( sk_c5 @ ( sk_c12 @ multiply ) )
= sk_c11 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(40,negated_conjecture,
( ( ( sk_c10 @ ( sk_c7 @ multiply ) )
= sk_c12 )
| ( ( sk_c12 @ ( sk_c3 @ multiply ) )
= sk_c11 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_40) ).
thf(136,plain,
( ( ( sk_c10 @ ( sk_c7 @ multiply ) )
= sk_c12 )
| ( ( sk_c12 @ ( sk_c3 @ multiply ) )
= sk_c11 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(7,negated_conjecture,
( ( ( sk_c9 @ inverse )
= sk_c8 )
| ( ( sk_c1 @ inverse )
= sk_c12 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
thf(122,plain,
( ( ( sk_c9 @ inverse )
= sk_c8 )
| ( ( sk_c1 @ inverse )
= sk_c12 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(56,negated_conjecture,
( ( ( sk_c6 @ inverse )
= sk_c12 )
| ( ( sk_c12 @ ( sk_c4 @ multiply ) )
= sk_c5 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_56) ).
thf(83,plain,
( ( ( sk_c6 @ inverse )
= sk_c12 )
| ( ( sk_c12 @ ( sk_c4 @ multiply ) )
= sk_c5 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(33,negated_conjecture,
( ( ( sk_c11 @ ( sk_c10 @ multiply ) )
= sk_c12 )
| ( ( sk_c2 @ inverse )
= sk_c3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_33) ).
thf(100,plain,
( ( ( sk_c11 @ ( sk_c10 @ multiply ) )
= sk_c12 )
| ( ( sk_c2 @ inverse )
= sk_c3 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(20,negated_conjecture,
( ( ( sk_c6 @ inverse )
= sk_c12 )
| ( ( sk_c3 @ ( sk_c2 @ multiply ) )
= sk_c11 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
thf(90,plain,
( ( ( sk_c6 @ inverse )
= sk_c12 )
| ( ( sk_c3 @ ( sk_c2 @ multiply ) )
= sk_c11 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(17,negated_conjecture,
( ( ( sk_c8 @ inverse )
= sk_c10 )
| ( ( sk_c11 @ ( sk_c1 @ multiply ) )
= sk_c12 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_17) ).
thf(111,plain,
( ( ( sk_c8 @ inverse )
= sk_c10 )
| ( ( sk_c11 @ ( sk_c1 @ multiply ) )
= sk_c12 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(7826,plain,
$false,
inference(e,[status(thm)],[118,95,127,143,131,138,101,88,115,120,142,153,185,301,110,125,157,93,78,106,121,84,147,132,116,89,133,117,85,102,302,297,137,92,229,97,1540,141,109,124,77,96,173,6239,129,503,134,105,3321,128,237,298,148,161,149,144,4573,181,86,159,187,81,1933,245,98,113,1408,103,140,91,155,108,983,130,278,135,299,241,80,112,123,145,99,87,104,1101,114,139,119,82,151,300,146,183,107,79,2961,94,126,136,122,83,100,90,111]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP220-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.14 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.26/0.71 % Computer : n019.cluster.edu
% 0.26/0.71 % Model : x86_64 x86_64
% 0.26/0.71 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.26/0.71 % Memory : 8046.5625MB
% 0.26/0.71 % OS : Linux 6.8.0-71-generic
% 0.26/0.71 % CPULimit : 300
% 0.26/0.71 % WCLimit : 300
% 0.26/0.71 % DateTime : Fri Sep 25 14:38:49 UTC 2026
% 0.26/0.72 % CPUTime :
% 0.26/0.72 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 1.28/1.44 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.98/1.72 % [INFO] Parsing done (276ms).
% 1.98/1.74 % [INFO] Running in sequential loop mode.
% 3.23/2.20 % [INFO] eprover registered as external prover.
% 3.23/2.21 % [INFO] Scanning for conjecture ...
% 3.72/2.41 % [INFO] Found a conjecture (or negated_conjecture) and 3 axioms. Running axiom selection ...
% 3.72/2.48 % [INFO] Axiom selection finished. Selected 3 axioms (removed 0 axioms).
% 3.72/2.48 % [INFO] Problem is propositional (TPTP CNF).
% 3.72/2.49 % [INFO] Type checking passed.
% 3.72/2.50 % [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 ...
% 42.45/10.75 % External prover 'e' found a proof!
% 42.45/10.75 % [INFO] Killing All external provers ...
% 42.45/10.75 % Time passed: 9846ms (effective reasoning time: 8998ms)
% 42.45/10.76 % Axioms used in derivation (3): associativity, left_identity, left_inverse
% 42.45/10.76 % No. of inferences in proof: 239
% 42.45/10.76 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 9846 ms resp. 8998 ms w/o parsing
% 35.53/10.87 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 35.53/10.87 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------