%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : GRP313-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n016.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 07:20:43 AM UTC 2026
% Result : Unsatisfiable 10.68s 4.80s
% Output : Refutation 11.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 53
% Syntax : Number of formulae : 107 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 231 ( 230 equ; 0 cnn)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 530 ( 28 ~; 124 |; 0 &; 378 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 12 usr; 11 con; 0-2 aty)
% Number of variables : 22 ( 0 ^; 22 !; 0 ?; 22 :)
% Comments :
%------------------------------------------------------------------------------
thf(multiply_decl,type,
multiply: $i > $i > $i ).
thf(sk_c8_decl,type,
sk_c8: $i ).
thf(sk_c9_decl,type,
sk_c9: $i ).
thf(sk_c7_decl,type,
sk_c7: $i ).
thf(sk_c4_decl,type,
sk_c4: $i ).
thf(inverse_decl,type,
inverse: $i > $i ).
thf(sk_c5_decl,type,
sk_c5: $i ).
thf(sk_c6_decl,type,
sk_c6: $i ).
thf(sk_c1_decl,type,
sk_c1: $i ).
thf(sk_c2_decl,type,
sk_c2: $i ).
thf(sk_c3_decl,type,
sk_c3: $i ).
thf(identity_decl,type,
identity: $i ).
thf(14,negated_conjecture,
( ( ( sk_c6 @ inverse )
= sk_c7 )
| ( ( sk_c9 @ ( sk_c1 @ multiply ) )
= sk_c8 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
thf(56,plain,
( ( ( sk_c6 @ inverse )
= sk_c7 )
| ( ( sk_c9 @ ( sk_c1 @ multiply ) )
= sk_c8 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(49,negated_conjecture,
( ( ( sk_c6 @ inverse )
= sk_c7 )
| ( ( sk_c3 @ inverse )
= sk_c8 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_49) ).
thf(84,plain,
( ( ( sk_c6 @ inverse )
= sk_c7 )
| ( ( sk_c3 @ inverse )
= sk_c8 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(21,negated_conjecture,
( ( ( sk_c6 @ inverse )
= sk_c7 )
| ( ( sk_c1 @ inverse )
= sk_c9 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
thf(70,plain,
( ( ( sk_c6 @ inverse )
= sk_c7 )
| ( ( sk_c1 @ inverse )
= sk_c9 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(38,negated_conjecture,
( ( ( sk_c8 @ ( sk_c5 @ multiply ) )
= sk_c7 )
| ( ( sk_c8 @ ( sk_c3 @ multiply ) )
= sk_c9 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_38) ).
thf(73,plain,
( ( ( sk_c8 @ ( sk_c5 @ multiply ) )
= sk_c7 )
| ( ( sk_c8 @ ( sk_c3 @ multiply ) )
= sk_c9 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(24,negated_conjecture,
( ( ( sk_c8 @ ( sk_c5 @ multiply ) )
= sk_c7 )
| ( ( sk_c8 @ ( sk_c2 @ multiply ) )
= sk_c7 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_24) ).
thf(64,plain,
( ( ( sk_c8 @ ( sk_c5 @ multiply ) )
= sk_c7 )
| ( ( sk_c8 @ ( sk_c2 @ multiply ) )
= sk_c7 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(22,negated_conjecture,
( ( ( sk_c9 @ ( sk_c4 @ multiply ) )
= sk_c8 )
| ( ( sk_c8 @ ( sk_c2 @ multiply ) )
= sk_c7 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_22) ).
thf(80,plain,
( ( ( sk_c9 @ ( sk_c4 @ multiply ) )
= sk_c8 )
| ( ( sk_c8 @ ( sk_c2 @ multiply ) )
= sk_c7 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(20,negated_conjecture,
( ( ( sk_c7 @ ( sk_c6 @ multiply ) )
= sk_c9 )
| ( ( sk_c1 @ inverse )
= sk_c9 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_20) ).
thf(67,plain,
( ( ( sk_c7 @ ( sk_c6 @ multiply ) )
= sk_c9 )
| ( ( sk_c1 @ inverse )
= sk_c9 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(28,negated_conjecture,
( ( ( sk_c6 @ inverse )
= sk_c7 )
| ( ( sk_c8 @ ( sk_c2 @ multiply ) )
= sk_c7 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_28) ).
thf(72,plain,
( ( ( sk_c6 @ inverse )
= sk_c7 )
| ( ( sk_c8 @ ( sk_c2 @ multiply ) )
= sk_c7 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(10,negated_conjecture,
( ( ( sk_c8 @ ( sk_c5 @ multiply ) )
= sk_c7 )
| ( ( sk_c9 @ ( sk_c1 @ multiply ) )
= sk_c8 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).
thf(55,plain,
( ( ( sk_c8 @ ( sk_c5 @ multiply ) )
= sk_c7 )
| ( ( sk_c9 @ ( sk_c1 @ multiply ) )
= sk_c8 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(29,negated_conjecture,
( ( ( sk_c9 @ ( sk_c4 @ multiply ) )
= sk_c8 )
| ( ( sk_c2 @ inverse )
= sk_c8 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_29) ).
thf(69,plain,
( ( ( sk_c9 @ ( sk_c4 @ multiply ) )
= sk_c8 )
| ( ( sk_c2 @ inverse )
= sk_c8 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(19,negated_conjecture,
( ( ( sk_c9 @ ( sk_c7 @ multiply ) )
= sk_c8 )
| ( ( sk_c1 @ inverse )
= sk_c9 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_19) ).
thf(101,plain,
( ( ( sk_c9 @ ( sk_c7 @ multiply ) )
= sk_c8 )
| ( ( sk_c1 @ inverse )
= sk_c9 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(35,negated_conjecture,
( ( ( sk_c6 @ inverse )
= sk_c7 )
| ( ( sk_c2 @ inverse )
= sk_c8 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_35) ).
thf(88,plain,
( ( ( sk_c6 @ inverse )
= sk_c7 )
| ( ( sk_c2 @ inverse )
= sk_c8 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(31,negated_conjecture,
( ( ( sk_c8 @ ( sk_c5 @ multiply ) )
= sk_c7 )
| ( ( sk_c2 @ inverse )
= sk_c8 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_31) ).
thf(93,plain,
( ( ( sk_c8 @ ( sk_c5 @ multiply ) )
= sk_c7 )
| ( ( sk_c2 @ inverse )
= sk_c8 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(1,negated_conjecture,
( ( ( sk_c9 @ ( sk_c4 @ multiply ) )
= sk_c8 )
| ( ( sk_c9 @ ( sk_c8 @ multiply ) )
= sk_c7 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
thf(57,plain,
( ( ( sk_c9 @ ( sk_c4 @ multiply ) )
= sk_c8 )
| ( ( sk_c9 @ ( sk_c8 @ multiply ) )
= sk_c7 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(32,negated_conjecture,
( ( ( sk_c5 @ inverse )
= sk_c8 )
| ( ( sk_c2 @ inverse )
= sk_c8 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_32) ).
thf(78,plain,
( ( ( sk_c5 @ inverse )
= sk_c8 )
| ( ( sk_c2 @ inverse )
= sk_c8 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(8,negated_conjecture,
( ( ( sk_c9 @ ( sk_c4 @ multiply ) )
= sk_c8 )
| ( ( sk_c9 @ ( sk_c1 @ multiply ) )
= sk_c8 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_8) ).
thf(61,plain,
( ( ( sk_c9 @ ( sk_c4 @ multiply ) )
= sk_c8 )
| ( ( sk_c9 @ ( sk_c1 @ multiply ) )
= sk_c8 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(48,negated_conjecture,
( ( ( sk_c7 @ ( sk_c6 @ multiply ) )
= sk_c9 )
| ( ( sk_c3 @ inverse )
= sk_c8 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_48) ).
thf(89,plain,
( ( ( sk_c7 @ ( sk_c6 @ multiply ) )
= sk_c9 )
| ( ( sk_c3 @ inverse )
= sk_c8 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(13,negated_conjecture,
( ( ( sk_c7 @ ( sk_c6 @ multiply ) )
= sk_c9 )
| ( ( sk_c9 @ ( sk_c1 @ multiply ) )
= sk_c8 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_13) ).
thf(74,plain,
( ( ( sk_c7 @ ( sk_c6 @ multiply ) )
= sk_c9 )
| ( ( sk_c9 @ ( sk_c1 @ multiply ) )
= sk_c8 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(52,axiom,
! [A: $i] :
( ( A @ ( A @ inverse @ multiply ) )
= identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).
thf(206,plain,
! [A: $i] :
( ( A @ ( A @ inverse @ multiply ) )
= identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(2,negated_conjecture,
( ( ( sk_c4 @ inverse )
= sk_c9 )
| ( ( sk_c9 @ ( sk_c8 @ multiply ) )
= sk_c7 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
thf(60,plain,
( ( ( sk_c4 @ inverse )
= sk_c9 )
| ( ( sk_c9 @ ( sk_c8 @ multiply ) )
= sk_c7 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(7,negated_conjecture,
( ( ( sk_c6 @ inverse )
= sk_c7 )
| ( ( sk_c9 @ ( sk_c8 @ multiply ) )
= sk_c7 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_7) ).
thf(85,plain,
( ( ( sk_c6 @ inverse )
= sk_c7 )
| ( ( sk_c9 @ ( sk_c8 @ multiply ) )
= sk_c7 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(47,negated_conjecture,
( ( ( sk_c9 @ ( sk_c7 @ multiply ) )
= sk_c8 )
| ( ( sk_c3 @ inverse )
= sk_c8 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_47) ).
thf(102,plain,
( ( ( sk_c9 @ ( sk_c7 @ multiply ) )
= sk_c8 )
| ( ( sk_c3 @ inverse )
= sk_c8 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(16,negated_conjecture,
( ( ( sk_c4 @ inverse )
= sk_c9 )
| ( ( sk_c1 @ inverse )
= sk_c9 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_16) ).
thf(92,plain,
( ( ( sk_c4 @ inverse )
= sk_c9 )
| ( ( sk_c1 @ inverse )
= sk_c9 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(37,negated_conjecture,
( ( ( sk_c4 @ inverse )
= sk_c9 )
| ( ( sk_c8 @ ( sk_c3 @ multiply ) )
= sk_c9 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_37) ).
thf(65,plain,
( ( ( sk_c4 @ inverse )
= sk_c9 )
| ( ( sk_c8 @ ( sk_c3 @ multiply ) )
= sk_c9 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(26,negated_conjecture,
( ( ( sk_c9 @ ( sk_c7 @ multiply ) )
= sk_c8 )
| ( ( sk_c8 @ ( sk_c2 @ multiply ) )
= sk_c7 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_26) ).
thf(97,plain,
( ( ( sk_c9 @ ( sk_c7 @ multiply ) )
= sk_c8 )
| ( ( sk_c8 @ ( sk_c2 @ multiply ) )
= sk_c7 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(17,negated_conjecture,
( ( ( sk_c8 @ ( sk_c5 @ multiply ) )
= sk_c7 )
| ( ( sk_c1 @ inverse )
= sk_c9 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_17) ).
thf(77,plain,
( ( ( sk_c8 @ ( sk_c5 @ multiply ) )
= sk_c7 )
| ( ( sk_c1 @ inverse )
= sk_c9 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(40,negated_conjecture,
( ( ( sk_c9 @ ( sk_c7 @ multiply ) )
= sk_c8 )
| ( ( sk_c8 @ ( sk_c3 @ multiply ) )
= sk_c9 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_40) ).
thf(96,plain,
( ( ( sk_c9 @ ( sk_c7 @ multiply ) )
= sk_c8 )
| ( ( sk_c8 @ ( sk_c3 @ multiply ) )
= sk_c9 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(9,negated_conjecture,
( ( ( sk_c4 @ inverse )
= sk_c9 )
| ( ( sk_c9 @ ( sk_c1 @ multiply ) )
= sk_c8 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).
thf(59,plain,
( ( ( sk_c4 @ inverse )
= sk_c9 )
| ( ( sk_c9 @ ( sk_c1 @ multiply ) )
= sk_c8 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(51,axiom,
! [A: $i] :
( ( A @ ( identity @ multiply ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
thf(204,plain,
! [A: $i] :
( ( A @ ( identity @ multiply ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(33,negated_conjecture,
( ( ( sk_c9 @ ( sk_c7 @ multiply ) )
= sk_c8 )
| ( ( sk_c2 @ inverse )
= sk_c8 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_33) ).
thf(71,plain,
( ( ( sk_c9 @ ( sk_c7 @ multiply ) )
= sk_c8 )
| ( ( sk_c2 @ inverse )
= sk_c8 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(5,negated_conjecture,
( ( ( sk_c9 @ ( sk_c7 @ multiply ) )
= sk_c8 )
| ( ( sk_c9 @ ( sk_c8 @ multiply ) )
= sk_c7 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
thf(54,plain,
( ( ( sk_c9 @ ( sk_c7 @ multiply ) )
= sk_c8 )
| ( ( sk_c9 @ ( sk_c8 @ multiply ) )
= sk_c7 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(39,negated_conjecture,
( ( ( sk_c5 @ inverse )
= sk_c8 )
| ( ( sk_c8 @ ( sk_c3 @ multiply ) )
= sk_c9 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_39) ).
thf(86,plain,
( ( ( sk_c5 @ inverse )
= sk_c8 )
| ( ( sk_c8 @ ( sk_c3 @ multiply ) )
= sk_c9 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(44,negated_conjecture,
( ( ( sk_c4 @ inverse )
= sk_c9 )
| ( ( sk_c3 @ inverse )
= sk_c8 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_44) ).
thf(81,plain,
( ( ( sk_c4 @ inverse )
= sk_c9 )
| ( ( sk_c3 @ inverse )
= sk_c8 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(45,negated_conjecture,
( ( ( sk_c8 @ ( sk_c5 @ multiply ) )
= sk_c7 )
| ( ( sk_c3 @ inverse )
= sk_c8 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_45) ).
thf(76,plain,
( ( ( sk_c8 @ ( sk_c5 @ multiply ) )
= sk_c7 )
| ( ( sk_c3 @ inverse )
= sk_c8 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(23,negated_conjecture,
( ( ( sk_c4 @ inverse )
= sk_c9 )
| ( ( sk_c8 @ ( sk_c2 @ multiply ) )
= sk_c7 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_23) ).
thf(98,plain,
( ( ( sk_c4 @ inverse )
= sk_c9 )
| ( ( sk_c8 @ ( sk_c2 @ multiply ) )
= sk_c7 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(53,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ multiply ) @ multiply ) )
= ( C @ ( B @ multiply ) @ ( A @ multiply ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity) ).
thf(208,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)],[53]) ).
thf(15,negated_conjecture,
( ( ( sk_c9 @ ( sk_c4 @ multiply ) )
= sk_c8 )
| ( ( sk_c1 @ inverse )
= sk_c9 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
thf(103,plain,
( ( ( sk_c9 @ ( sk_c4 @ multiply ) )
= sk_c8 )
| ( ( sk_c1 @ inverse )
= sk_c9 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(50,negated_conjecture,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( F @ inverse )
!= sk_c7 )
| ( ( sk_c7 @ ( F @ multiply ) )
!= sk_c9 )
| ( ( sk_c9 @ ( sk_c7 @ multiply ) )
!= sk_c8 )
| ( ( E @ inverse )
!= sk_c8 )
| ( ( sk_c8 @ ( E @ multiply ) )
!= sk_c7 )
| ( ( D @ inverse )
!= sk_c9 )
| ( ( sk_c9 @ ( D @ multiply ) )
!= sk_c8 )
| ( ( C @ inverse )
!= sk_c8 )
| ( ( sk_c8 @ ( C @ multiply ) )
!= sk_c9 )
| ( ( B @ inverse )
!= sk_c8 )
| ( ( sk_c8 @ ( B @ multiply ) )
!= sk_c7 )
| ( ( A @ inverse )
!= sk_c9 )
| ( ( sk_c9 @ ( A @ multiply ) )
!= sk_c8 )
| ( ( sk_c9 @ ( sk_c8 @ multiply ) )
!= sk_c7 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_50) ).
thf(91,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( F @ inverse )
!= sk_c7 )
| ( ( sk_c7 @ ( F @ multiply ) )
!= sk_c9 )
| ( ( sk_c9 @ ( sk_c7 @ multiply ) )
!= sk_c8 )
| ( ( E @ inverse )
!= sk_c8 )
| ( ( sk_c8 @ ( E @ multiply ) )
!= sk_c7 )
| ( ( D @ inverse )
!= sk_c9 )
| ( ( sk_c9 @ ( D @ multiply ) )
!= sk_c8 )
| ( ( C @ inverse )
!= sk_c8 )
| ( ( sk_c8 @ ( C @ multiply ) )
!= sk_c9 )
| ( ( B @ inverse )
!= sk_c8 )
| ( ( sk_c8 @ ( B @ multiply ) )
!= sk_c7 )
| ( ( A @ inverse )
!= sk_c9 )
| ( ( sk_c9 @ ( A @ multiply ) )
!= sk_c8 )
| ( ( sk_c9 @ ( sk_c8 @ multiply ) )
!= sk_c7 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(25,negated_conjecture,
( ( ( sk_c5 @ inverse )
= sk_c8 )
| ( ( sk_c8 @ ( sk_c2 @ multiply ) )
= sk_c7 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_25) ).
thf(66,plain,
( ( ( sk_c5 @ inverse )
= sk_c8 )
| ( ( sk_c8 @ ( sk_c2 @ multiply ) )
= sk_c7 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(42,negated_conjecture,
( ( ( sk_c6 @ inverse )
= sk_c7 )
| ( ( sk_c8 @ ( sk_c3 @ multiply ) )
= sk_c9 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_42) ).
thf(63,plain,
( ( ( sk_c6 @ inverse )
= sk_c7 )
| ( ( sk_c8 @ ( sk_c3 @ multiply ) )
= sk_c9 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(43,negated_conjecture,
( ( ( sk_c9 @ ( sk_c4 @ multiply ) )
= sk_c8 )
| ( ( sk_c3 @ inverse )
= sk_c8 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_43) ).
thf(95,plain,
( ( ( sk_c9 @ ( sk_c4 @ multiply ) )
= sk_c8 )
| ( ( sk_c3 @ inverse )
= sk_c8 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(36,negated_conjecture,
( ( ( sk_c9 @ ( sk_c4 @ multiply ) )
= sk_c8 )
| ( ( sk_c8 @ ( sk_c3 @ multiply ) )
= sk_c9 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_36) ).
thf(99,plain,
( ( ( sk_c9 @ ( sk_c4 @ multiply ) )
= sk_c8 )
| ( ( sk_c8 @ ( sk_c3 @ multiply ) )
= sk_c9 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(3,negated_conjecture,
( ( ( sk_c8 @ ( sk_c5 @ multiply ) )
= sk_c7 )
| ( ( sk_c9 @ ( sk_c8 @ multiply ) )
= sk_c7 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
thf(87,plain,
( ( ( sk_c8 @ ( sk_c5 @ multiply ) )
= sk_c7 )
| ( ( sk_c9 @ ( sk_c8 @ multiply ) )
= sk_c7 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(41,negated_conjecture,
( ( ( sk_c7 @ ( sk_c6 @ multiply ) )
= sk_c9 )
| ( ( sk_c8 @ ( sk_c3 @ multiply ) )
= sk_c9 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_41) ).
thf(75,plain,
( ( ( sk_c7 @ ( sk_c6 @ multiply ) )
= sk_c9 )
| ( ( sk_c8 @ ( sk_c3 @ multiply ) )
= sk_c9 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(6,negated_conjecture,
( ( ( sk_c7 @ ( sk_c6 @ multiply ) )
= sk_c9 )
| ( ( sk_c9 @ ( sk_c8 @ multiply ) )
= sk_c7 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
thf(58,plain,
( ( ( sk_c7 @ ( sk_c6 @ multiply ) )
= sk_c9 )
| ( ( sk_c9 @ ( sk_c8 @ multiply ) )
= sk_c7 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(27,negated_conjecture,
( ( ( sk_c7 @ ( sk_c6 @ multiply ) )
= sk_c9 )
| ( ( sk_c8 @ ( sk_c2 @ multiply ) )
= sk_c7 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_27) ).
thf(82,plain,
( ( ( sk_c7 @ ( sk_c6 @ multiply ) )
= sk_c9 )
| ( ( sk_c8 @ ( sk_c2 @ multiply ) )
= sk_c7 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(34,negated_conjecture,
( ( ( sk_c7 @ ( sk_c6 @ multiply ) )
= sk_c9 )
| ( ( sk_c2 @ inverse )
= sk_c8 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_34) ).
thf(79,plain,
( ( ( sk_c7 @ ( sk_c6 @ multiply ) )
= sk_c9 )
| ( ( sk_c2 @ inverse )
= sk_c8 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(11,negated_conjecture,
( ( ( sk_c5 @ inverse )
= sk_c8 )
| ( ( sk_c9 @ ( sk_c1 @ multiply ) )
= sk_c8 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
thf(94,plain,
( ( ( sk_c5 @ inverse )
= sk_c8 )
| ( ( sk_c9 @ ( sk_c1 @ multiply ) )
= sk_c8 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(46,negated_conjecture,
( ( ( sk_c5 @ inverse )
= sk_c8 )
| ( ( sk_c3 @ inverse )
= sk_c8 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_46) ).
thf(68,plain,
( ( ( sk_c5 @ inverse )
= sk_c8 )
| ( ( sk_c3 @ inverse )
= sk_c8 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(4,negated_conjecture,
( ( ( sk_c5 @ inverse )
= sk_c8 )
| ( ( sk_c9 @ ( sk_c8 @ multiply ) )
= sk_c7 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
thf(62,plain,
( ( ( sk_c5 @ inverse )
= sk_c8 )
| ( ( sk_c9 @ ( sk_c8 @ multiply ) )
= sk_c7 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(18,negated_conjecture,
( ( ( sk_c5 @ inverse )
= sk_c8 )
| ( ( sk_c1 @ inverse )
= sk_c9 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).
thf(90,plain,
( ( ( sk_c5 @ inverse )
= sk_c8 )
| ( ( sk_c1 @ inverse )
= sk_c9 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(12,negated_conjecture,
( ( ( sk_c9 @ ( sk_c7 @ multiply ) )
= sk_c8 )
| ( ( sk_c9 @ ( sk_c1 @ multiply ) )
= sk_c8 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_12) ).
thf(83,plain,
( ( ( sk_c9 @ ( sk_c7 @ multiply ) )
= sk_c8 )
| ( ( sk_c9 @ ( sk_c1 @ multiply ) )
= sk_c8 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(30,negated_conjecture,
( ( ( sk_c4 @ inverse )
= sk_c9 )
| ( ( sk_c2 @ inverse )
= sk_c8 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_30) ).
thf(100,plain,
( ( ( sk_c4 @ inverse )
= sk_c9 )
| ( ( sk_c2 @ inverse )
= sk_c8 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(339,plain,
$false,
inference(e,[status(thm)],[56,84,70,73,64,80,67,72,55,69,101,88,93,57,78,61,89,74,206,60,85,102,92,65,97,77,96,59,204,71,54,86,81,76,98,208,103,91,66,63,95,99,87,75,58,82,79,94,68,62,90,83,100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP313-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.13 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.23/0.50 % Computer : n016.cluster.edu
% 0.23/0.50 % Model : x86_64 x86_64
% 0.23/0.50 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.23/0.50 % Memory : 8046.5625MB
% 0.23/0.50 % OS : Linux 6.8.0-71-generic
% 0.23/0.50 % CPULimit : 300
% 0.23/0.50 % WCLimit : 300
% 0.23/0.50 % DateTime : Fri Sep 25 14:49:13 UTC 2026
% 0.23/0.50 % CPUTime :
% 0.23/0.50 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 1.41/1.39 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.17/1.73 % [INFO] Parsing done (339ms).
% 2.17/1.75 % [INFO] Running in sequential loop mode.
% 3.24/2.39 % [INFO] eprover registered as external prover.
% 3.47/2.40 % [INFO] Scanning for conjecture ...
% 3.86/2.68 % [INFO] Found a conjecture (or negated_conjecture) and 3 axioms. Running axiom selection ...
% 4.11/2.79 % [INFO] Axiom selection finished. Selected 3 axioms (removed 0 axioms).
% 4.40/2.80 % [INFO] Problem is propositional (TPTP CNF).
% 4.40/2.81 % [INFO] Type checking passed.
% 4.40/2.82 % [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 ...
% 10.23/4.79 % External prover 'e' found a proof!
% 10.23/4.79 % [INFO] Killing All external provers ...
% 10.23/4.79 % Time passed: 4078ms (effective reasoning time: 3031ms)
% 10.68/4.80 % Axioms used in derivation (3): left_inverse, left_identity, associativity
% 10.68/4.80 % No. of inferences in proof: 107
% 10.68/4.80 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 4078 ms resp. 3031 ms w/o parsing
% 11.13/4.90 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 11.13/4.90 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------