%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : GRP705-1 : TPTP v9.3.1. Released v4.0.0.
% 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 : n011.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 07:21:49 AM UTC 2026
% Result : Unsatisfiable 30.18s 7.60s
% Output : Refutation 30.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of formulae : 99 ( 54 unt; 0 typ; 0 def)
% Number of atoms : 168 ( 167 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 821 ( 104 ~; 69 |; 0 &; 648 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 116 ( 0 ^; 116 !; 0 ?; 116 :)
% Comments :
%------------------------------------------------------------------------------
thf(mult_decl,type,
mult: $i > $i > $i ).
thf(op_a_decl,type,
op_a: $i ).
thf(op_b_decl,type,
op_b: $i ).
thf(a_decl,type,
a: $i ).
thf(ld_decl,type,
ld: $i > $i > $i ).
thf(rd_decl,type,
rd: $i > $i > $i ).
thf(unit_decl,type,
unit: $i ).
thf(6,axiom,
! [A: $i] :
( ( unit @ ( A @ mult ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c05) ).
thf(22,plain,
! [A: $i] :
( ( unit @ ( A @ mult ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(23,plain,
! [A: $i] :
( ( unit @ ( A @ mult ) )
= A ),
inference(lifteq,[status(thm)],[22]) ).
thf(7,axiom,
! [A: $i] :
( ( A @ ( unit @ mult ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c06) ).
thf(24,plain,
! [A: $i] :
( ( A @ ( unit @ mult ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(25,plain,
! [A: $i] :
( ( A @ ( unit @ mult ) )
= A ),
inference(lifteq,[status(thm)],[24]) ).
thf(1,negated_conjecture,
( ( a @ ( op_b @ mult ) @ ( op_a @ mult ) )
!= ( a @ ( op_b @ ( op_a @ mult ) @ mult ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
thf(11,plain,
( ( a @ ( op_b @ mult ) @ ( op_a @ mult ) )
!= ( a @ ( op_b @ ( op_a @ mult ) @ mult ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(12,plain,
( ( a @ ( op_b @ mult ) @ ( op_a @ mult ) )
!= ( a @ ( op_b @ ( op_a @ mult ) @ mult ) ) ),
inference(polarity_switch,[status(thm)],[11]) ).
thf(13,plain,
( ( a @ ( op_b @ ( op_a @ mult ) @ mult ) )
!= ( a @ ( op_b @ mult ) @ ( op_a @ mult ) ) ),
inference(lifteq,[status(thm)],[12]) ).
thf(70,plain,
! [A: $i] :
( ( ( A @ ( unit @ mult ) )
!= ( op_b @ ( op_a @ mult ) ) )
| ( ( a @ ( A @ mult ) )
!= ( a @ ( op_b @ mult ) @ ( op_a @ mult ) ) ) ),
inference(paramod_ordered,[status(thm)],[25,13]) ).
thf(77,plain,
! [A: $i] :
( ( A != op_b )
| ( unit != op_a )
| ( ( a @ ( op_b @ mult ) )
!= a )
| ( A != op_a ) ),
inference(simp,[status(thm)],[70]) ).
thf(89,plain,
( ( op_b != op_a )
| ( unit != op_a )
| ( ( a @ ( op_b @ mult ) )
!= a ) ),
inference(simp,[status(thm)],[77]) ).
thf(376,plain,
! [A: $i] :
( ( ( unit @ ( A @ mult ) )
!= ( a @ ( op_b @ mult ) ) )
| ( op_b != op_a )
| ( unit != op_a )
| ( A != a ) ),
inference(paramod_ordered,[status(thm)],[23,89]) ).
thf(379,plain,
( ( unit != a )
| ( a != op_b )
| ( op_b != op_a )
| ( unit != op_a ) ),
inference(simp,[status(thm)],[376]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ rd ) @ mult ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c03) ).
thf(18,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ rd ) @ mult ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(19,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ rd ) @ mult ) )
= A ),
inference(lifteq,[status(thm)],[18]) ).
thf(397,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ rd ) @ mult ) )
!= ( a @ ( op_b @ ( op_a @ mult ) @ mult ) ) )
| ( A
!= ( a @ ( op_b @ mult ) @ ( op_a @ mult ) ) ) ),
inference(paramod_ordered,[status(thm)],[19,13]) ).
thf(434,plain,
! [A: $i] :
( ( A != a )
| ( ( A @ ( a @ ( op_b @ mult ) @ ( op_a @ mult ) @ rd ) )
!= ( op_b @ ( op_a @ mult ) ) ) ),
inference(simp,[status(thm)],[397]) ).
thf(472,plain,
( ( a @ ( a @ ( op_b @ mult ) @ ( op_a @ mult ) @ rd ) )
!= ( op_b @ ( op_a @ mult ) ) ),
inference(simp,[status(thm)],[434]) ).
thf(2,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ld ) @ ( A @ mult ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c01) ).
thf(14,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ld ) @ ( A @ mult ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(15,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ld ) @ ( A @ mult ) )
= B ),
inference(lifteq,[status(thm)],[14]) ).
thf(377,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ld ) @ ( A @ mult ) )
!= ( a @ ( op_b @ mult ) ) )
| ( op_b != op_a )
| ( unit != op_a )
| ( B != a ) ),
inference(paramod_ordered,[status(thm)],[15,89]) ).
thf(382,plain,
! [A: $i] :
( ( ( a @ ( A @ ld ) )
!= a )
| ( A != op_b )
| ( op_b != op_a )
| ( unit != op_a ) ),
inference(simp,[status(thm)],[377]) ).
thf(388,plain,
( ( ( a @ ( op_b @ ld ) )
!= a )
| ( op_b != op_a )
| ( unit != op_a ) ),
inference(simp,[status(thm)],[382]) ).
thf(433,plain,
! [A: $i] :
( ( A @ ( A @ ( a @ ( op_b @ mult ) @ ( op_a @ mult ) @ rd ) @ mult ) )
!= ( a @ ( op_b @ ( op_a @ mult ) @ mult ) ) ),
inference(simp,[status(thm)],[397]) ).
thf(471,plain,
! [A: $i] :
( ( A @ ( A @ ( a @ ( op_b @ mult ) @ ( op_a @ mult ) @ rd ) @ mult ) )
!= ( a @ ( op_b @ ( op_a @ mult ) @ mult ) ) ),
inference(simp,[status(thm)],[433]) ).
thf(8,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ mult ) @ ( B @ mult ) @ ( A @ mult ) )
= ( C @ ( B @ ( B @ ( A @ mult ) @ mult ) @ mult ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c07) ).
thf(26,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ mult ) @ ( B @ mult ) @ ( A @ mult ) )
= ( C @ ( B @ ( B @ ( A @ mult ) @ mult ) @ mult ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(27,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( B @ ( A @ mult ) @ mult ) @ mult ) )
= ( C @ ( B @ mult ) @ ( B @ mult ) @ ( A @ mult ) ) ),
inference(lifteq,[status(thm)],[26]) ).
thf(933,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( unit @ ( A @ mult ) )
!= ( C @ ( C @ ( B @ mult ) @ mult ) ) )
| ( ( D @ ( A @ mult ) )
= ( D @ ( C @ mult ) @ ( C @ mult ) @ ( B @ mult ) ) ) ),
inference(paramod_ordered,[status(thm)],[23,27]) ).
thf(934,plain,
! [B: $i,A: $i] :
( ( A @ ( unit @ ( B @ mult ) @ mult ) )
= ( A @ ( unit @ mult ) @ ( unit @ mult ) @ ( B @ mult ) ) ),
inference(pattern_uni,[status(thm)],[933:[bind(A,$thf( unit @ ( E @ mult ) )),bind(B,$thf( E )),bind(C,$thf( unit )),bind(D,$thf( D ))]]) ).
thf(1023,plain,
! [B: $i,A: $i] :
( ( A @ ( unit @ ( B @ mult ) @ mult ) )
= ( A @ ( unit @ mult ) @ ( unit @ mult ) @ ( B @ mult ) ) ),
inference(simp,[status(thm)],[934]) ).
thf(1187,plain,
! [B: $i,A: $i] :
( ( A @ ( unit @ mult ) @ ( B @ mult ) )
= ( A @ ( B @ mult ) ) ),
inference(rewrite,[status(thm)],[1023,23,25]) ).
thf(3,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ mult ) @ ( A @ ld ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c02) ).
thf(16,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ mult ) @ ( A @ ld ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(17,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ mult ) @ ( A @ ld ) )
= B ),
inference(lifteq,[status(thm)],[16]) ).
thf(9,axiom,
( ( op_a @ ( op_a @ mult ) @ ( op_a @ mult ) @ ( op_a @ mult ) )
= unit ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c08) ).
thf(28,plain,
( ( op_a @ ( op_a @ mult ) @ ( op_a @ mult ) @ ( op_a @ mult ) )
= unit ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(29,plain,
( ( op_a @ ( op_a @ mult ) @ ( op_a @ mult ) @ ( op_a @ mult ) )
= unit ),
inference(lifteq,[status(thm)],[28]) ).
thf(353,plain,
! [B: $i,A: $i] :
( ( ( op_a @ ( op_a @ mult ) @ ( op_a @ mult ) @ ( op_a @ mult ) )
!= ( B @ ( A @ mult ) ) )
| ( ( unit @ ( A @ ld ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[29,17]) ).
thf(354,plain,
( ( unit @ ( op_a @ ld ) )
= ( op_a @ ( op_a @ mult ) @ ( op_a @ mult ) ) ),
inference(pattern_uni,[status(thm)],[353:[bind(A,$thf( op_a )),bind(B,$thf( op_a @ ( op_a @ mult ) @ ( op_a @ mult ) ))]]) ).
thf(32,plain,
( ( ( op_a @ ( op_a @ mult ) @ ( op_a @ mult ) @ ( op_a @ mult ) )
!= ( op_a @ ( op_a @ mult ) @ ( op_a @ mult ) ) )
| ( ( unit @ ( op_a @ mult ) )
= unit ) ),
inference(paramod_ordered,[status(thm)],[29,29]) ).
thf(34,plain,
( ( ( op_a @ ( op_a @ mult ) @ ( op_a @ mult ) )
!= ( op_a @ ( op_a @ mult ) ) )
| ( op_a != op_a )
| ( ( unit @ ( op_a @ mult ) )
= unit ) ),
inference(simp,[status(thm)],[32]) ).
thf(36,plain,
( ( ( op_a @ ( op_a @ mult ) @ ( op_a @ mult ) )
!= ( op_a @ ( op_a @ mult ) ) )
| ( ( unit @ ( op_a @ mult ) )
= unit ) ),
inference(simp,[status(thm)],[34]) ).
thf(1379,plain,
( ( ( op_a @ ( op_a @ mult ) @ ( op_a @ mult ) )
!= ( op_a @ ( op_a @ mult ) ) )
| ( unit = op_a ) ),
inference(rewrite,[status(thm)],[36,23]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ mult ) @ rd ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c04) ).
thf(20,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ mult ) @ rd ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(21,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ mult ) @ rd ) )
= A ),
inference(lifteq,[status(thm)],[20]) ).
thf(590,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ld ) @ ( A @ mult ) )
!= ( D @ ( C @ mult ) ) )
| ( ( D @ ( B @ rd ) )
= C ) ),
inference(paramod_ordered,[status(thm)],[15,21]) ).
thf(591,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ld ) @ ( B @ rd ) )
= A ),
inference(pattern_uni,[status(thm)],[590:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( E )),bind(D,$thf( F @ ( E @ ld ) ))]]) ).
thf(598,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ld ) @ ( B @ rd ) )
= A ),
inference(simp,[status(thm)],[591]) ).
thf(231,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ld ) @ ( A @ mult ) )
!= ( C @ ( unit @ mult ) ) )
| ( B = C ) ),
inference(paramod_ordered,[status(thm)],[15,25]) ).
thf(232,plain,
! [A: $i] :
( ( A @ ( unit @ ld ) )
= A ),
inference(pattern_uni,[status(thm)],[231:[bind(A,$thf( unit )),bind(B,$thf( E )),bind(C,$thf( E @ ( unit @ ld ) ))]]) ).
thf(297,plain,
! [A: $i] :
( ( A @ ( unit @ ld ) )
= A ),
inference(simp,[status(thm)],[232]) ).
thf(10,axiom,
( ( op_b @ ( op_b @ mult ) @ ( op_b @ mult ) @ ( op_b @ mult ) @ ( op_b @ mult ) @ ( op_b @ mult ) @ ( op_b @ mult ) @ ( op_b @ mult ) @ ( op_b @ mult ) )
= unit ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c09) ).
thf(30,plain,
( ( op_b @ ( op_b @ mult ) @ ( op_b @ mult ) @ ( op_b @ mult ) @ ( op_b @ mult ) @ ( op_b @ mult ) @ ( op_b @ mult ) @ ( op_b @ mult ) @ ( op_b @ mult ) )
= unit ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(31,plain,
( ( op_b @ ( op_b @ mult ) @ ( op_b @ mult ) @ ( op_b @ mult ) @ ( op_b @ mult ) @ ( op_b @ mult ) @ ( op_b @ mult ) @ ( op_b @ mult ) @ ( op_b @ mult ) )
= unit ),
inference(lifteq,[status(thm)],[30]) ).
thf(360,plain,
! [B: $i,A: $i] :
( ( ( op_b @ ( op_b @ mult ) @ ( op_b @ mult ) @ ( op_b @ mult ) @ ( op_b @ mult ) @ ( op_b @ mult ) @ ( op_b @ mult ) @ ( op_b @ mult ) @ ( op_b @ mult ) )
!= ( B @ ( A @ mult ) ) )
| ( ( unit @ ( A @ ld ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[31,17]) ).
thf(361,plain,
( ( unit @ ( op_b @ ld ) )
= ( op_b @ ( op_b @ mult ) @ ( op_b @ mult ) @ ( op_b @ mult ) @ ( op_b @ mult ) @ ( op_b @ mult ) @ ( op_b @ mult ) @ ( op_b @ mult ) ) ),
inference(pattern_uni,[status(thm)],[360:[bind(A,$thf( op_b )),bind(B,$thf( op_b @ ( op_b @ mult ) @ ( op_b @ mult ) @ ( op_b @ mult ) @ ( op_b @ mult ) @ ( op_b @ mult ) @ ( op_b @ mult ) @ ( op_b @ mult ) ))]]) ).
thf(582,plain,
! [B: $i,A: $i] :
( ( ( op_b @ ( op_b @ mult ) @ ( op_b @ mult ) @ ( op_b @ mult ) @ ( op_b @ mult ) @ ( op_b @ mult ) @ ( op_b @ mult ) @ ( op_b @ mult ) @ ( op_b @ mult ) )
!= ( B @ ( A @ mult ) ) )
| ( ( B @ ( unit @ rd ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[31,21]) ).
thf(583,plain,
( ( op_b @ ( op_b @ mult ) @ ( op_b @ mult ) @ ( op_b @ mult ) @ ( op_b @ mult ) @ ( op_b @ mult ) @ ( op_b @ mult ) @ ( op_b @ mult ) @ ( unit @ rd ) )
= op_b ),
inference(pattern_uni,[status(thm)],[582:[bind(A,$thf( op_b )),bind(B,$thf( op_b @ ( op_b @ mult ) @ ( op_b @ mult ) @ ( op_b @ mult ) @ ( op_b @ mult ) @ ( op_b @ mult ) @ ( op_b @ mult ) @ ( op_b @ mult ) ))]]) ).
thf(399,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ rd ) @ mult ) )
!= ( D @ ( C @ mult ) ) )
| ( ( A @ ( C @ ld ) )
= D ) ),
inference(paramod_ordered,[status(thm)],[19,17]) ).
thf(400,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ rd ) @ ld ) )
= B ),
inference(pattern_uni,[status(thm)],[399:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( F @ ( E @ rd ) )),bind(D,$thf( F ))]]) ).
thf(456,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ rd ) @ ld ) )
= B ),
inference(simp,[status(thm)],[400]) ).
thf(66,plain,
( ( ( a @ ( op_b @ mult ) )
!= a )
| ( ( op_b @ ( op_a @ mult ) )
!= op_a ) ),
inference(simp,[status(thm)],[13]) ).
thf(253,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ld ) @ ( A @ mult ) )
!= ( a @ ( op_b @ mult ) ) )
| ( B != a )
| ( ( op_b @ ( op_a @ mult ) )
!= op_a ) ),
inference(paramod_ordered,[status(thm)],[15,66]) ).
thf(265,plain,
! [A: $i] :
( ( ( a @ ( A @ ld ) )
!= a )
| ( A != op_b )
| ( ( op_b @ ( op_a @ mult ) )
!= op_a ) ),
inference(simp,[status(thm)],[253]) ).
thf(285,plain,
( ( ( a @ ( op_b @ ld ) )
!= a )
| ( ( op_b @ ( op_a @ mult ) )
!= op_a ) ),
inference(simp,[status(thm)],[265]) ).
thf(413,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ rd ) @ mult ) )
!= ( unit @ ( C @ mult ) ) )
| ( A = C ) ),
inference(paramod_ordered,[status(thm)],[19,23]) ).
thf(414,plain,
! [A: $i] :
( ( unit @ ( A @ rd ) )
= A ),
inference(pattern_uni,[status(thm)],[413:[bind(A,$thf( D )),bind(B,$thf( unit )),bind(C,$thf( unit @ ( D @ rd ) ))]]) ).
thf(457,plain,
! [A: $i] :
( ( unit @ ( A @ rd ) )
= A ),
inference(simp,[status(thm)],[414]) ).
thf(578,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( unit @ mult ) )
!= ( C @ ( B @ mult ) ) )
| ( ( C @ ( A @ rd ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[25,21]) ).
thf(579,plain,
! [A: $i] :
( ( A @ ( A @ rd ) )
= unit ),
inference(pattern_uni,[status(thm)],[578:[bind(A,$thf( A )),bind(B,$thf( unit )),bind(C,$thf( A ))]]) ).
thf(68,plain,
! [A: $i] :
( ( ( unit @ ( A @ mult ) )
!= ( op_b @ ( op_a @ mult ) ) )
| ( ( a @ ( A @ mult ) )
!= ( a @ ( op_b @ mult ) @ ( op_a @ mult ) ) ) ),
inference(paramod_ordered,[status(thm)],[23,13]) ).
thf(86,plain,
! [A: $i] :
( ( unit != op_b )
| ( A != op_a )
| ( ( a @ ( op_b @ mult ) )
!= a )
| ( A != op_a ) ),
inference(simp,[status(thm)],[68]) ).
thf(94,plain,
( ( unit != op_b )
| ( ( a @ ( op_b @ mult ) )
!= a ) ),
inference(simp,[status(thm)],[86]) ).
thf(95,plain,
! [A: $i] :
( ( ( A @ ( unit @ mult ) )
!= ( a @ ( op_b @ mult ) ) )
| ( unit != op_b )
| ( A != a ) ),
inference(paramod_ordered,[status(thm)],[25,94]) ).
thf(99,plain,
( ( a != a )
| ( unit != op_b )
| ( unit != op_b ) ),
inference(simp,[status(thm)],[95]) ).
thf(103,plain,
unit != op_b,
inference(simp,[status(thm)],[99]) ).
thf(33,plain,
( ( ( op_a @ ( op_a @ mult ) @ ( op_a @ mult ) @ ( op_a @ mult ) )
!= ( op_a @ ( op_a @ mult ) ) )
| ( ( unit @ ( op_a @ mult ) @ ( op_a @ mult ) )
= unit ) ),
inference(paramod_ordered,[status(thm)],[29,29]) ).
thf(35,plain,
( ( ( op_a @ ( op_a @ mult ) @ ( op_a @ mult ) )
!= op_a )
| ( op_a != op_a )
| ( ( unit @ ( op_a @ mult ) @ ( op_a @ mult ) )
= unit ) ),
inference(simp,[status(thm)],[33]) ).
thf(37,plain,
( ( ( op_a @ ( op_a @ mult ) @ ( op_a @ mult ) )
!= op_a )
| ( ( unit @ ( op_a @ mult ) @ ( op_a @ mult ) )
= unit ) ),
inference(simp,[status(thm)],[35]) ).
thf(1528,plain,
( ( ( op_a @ ( op_a @ mult ) @ ( op_a @ mult ) )
!= op_a )
| ( ( op_a @ ( op_a @ mult ) )
= unit ) ),
inference(rewrite,[status(thm)],[37,23]) ).
thf(214,plain,
! [A: $i] :
( ( ( unit @ ( A @ mult ) )
!= ( a @ ( op_b @ mult ) ) )
| ( A != a )
| ( ( op_b @ ( op_a @ mult ) )
!= op_a ) ),
inference(paramod_ordered,[status(thm)],[23,66]) ).
thf(226,plain,
( ( unit != a )
| ( a != op_b )
| ( ( op_b @ ( op_a @ mult ) )
!= op_a ) ),
inference(simp,[status(thm)],[214]) ).
thf(239,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ld ) @ ( A @ mult ) )
!= ( a @ ( op_b @ ( op_a @ mult ) @ mult ) ) )
| ( B
!= ( a @ ( op_b @ mult ) @ ( op_a @ mult ) ) ) ),
inference(paramod_ordered,[status(thm)],[15,13]) ).
thf(276,plain,
! [A: $i] :
( ( ( a @ ( op_b @ mult ) @ ( op_a @ mult ) @ ( A @ ld ) )
!= a )
| ( A
!= ( op_b @ ( op_a @ mult ) ) ) ),
inference(simp,[status(thm)],[239]) ).
thf(295,plain,
( ( a @ ( op_b @ mult ) @ ( op_a @ mult ) @ ( op_b @ ( op_a @ mult ) @ ld ) )
!= a ),
inference(simp,[status(thm)],[276]) ).
thf(398,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ rd ) @ mult ) )
!= ( op_b @ ( op_a @ mult ) ) )
| ( ( a @ ( A @ mult ) )
!= ( a @ ( op_b @ mult ) @ ( op_a @ mult ) ) ) ),
inference(paramod_ordered,[status(thm)],[19,13]) ).
thf(425,plain,
! [B: $i,A: $i] :
( ( B != op_b )
| ( ( B @ ( A @ rd ) )
!= op_a )
| ( ( a @ ( op_b @ mult ) )
!= a )
| ( A != op_a ) ),
inference(simp,[status(thm)],[398]) ).
thf(463,plain,
( ( ( op_b @ ( op_a @ rd ) )
!= op_a )
| ( ( a @ ( op_b @ mult ) )
!= a ) ),
inference(simp,[status(thm)],[425]) ).
thf(362,plain,
! [C: $i,B: $i,A: $i] :
( ( ( unit @ ( A @ mult ) )
!= ( C @ ( B @ mult ) ) )
| ( ( A @ ( B @ ld ) )
= C ) ),
inference(paramod_ordered,[status(thm)],[23,17]) ).
thf(363,plain,
! [A: $i] :
( ( A @ ( A @ ld ) )
= unit ),
inference(pattern_uni,[status(thm)],[362:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( unit ))]]) ).
thf(580,plain,
! [B: $i,A: $i] :
( ( ( op_a @ ( op_a @ mult ) @ ( op_a @ mult ) @ ( op_a @ mult ) )
!= ( B @ ( A @ mult ) ) )
| ( ( B @ ( unit @ rd ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[29,21]) ).
thf(581,plain,
( ( op_a @ ( op_a @ mult ) @ ( op_a @ mult ) @ ( unit @ rd ) )
= op_a ),
inference(pattern_uni,[status(thm)],[580:[bind(A,$thf( op_a )),bind(B,$thf( op_a @ ( op_a @ mult ) @ ( op_a @ mult ) ))]]) ).
thf(8073,plain,
$false,
inference(e,[status(thm)],[379,472,14,89,388,471,1187,17,11,15,354,24,25,1379,20,29,28,598,297,21,361,583,456,285,457,13,22,579,27,103,66,1528,226,295,18,16,463,31,363,581,26,23,30,19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP705-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % 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
% 0.12/0.39 % Computer : n011.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Fri Sep 25 15:39:14 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.40 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
% 1.28/1.26 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.77/1.54 % [INFO] Parsing done (276ms).
% 1.77/1.56 % [INFO] Running in sequential loop mode.
% 2.58/2.13 % [INFO] eprover registered as external prover.
% 2.58/2.13 % [INFO] Scanning for conjecture ...
% 2.87/2.22 % [INFO] Found a conjecture (or negated_conjecture) and 9 axioms. Running axiom selection ...
% 2.87/2.26 % [INFO] Axiom selection finished. Selected 9 axioms (removed 0 axioms).
% 2.87/2.27 % [INFO] Problem is propositional (TPTP CNF).
% 2.87/2.28 % [INFO] Type checking passed.
% 2.87/2.29 % [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 ...
% 30.18/7.60 % External prover 'e' found a proof!
% 30.18/7.60 % [INFO] Killing All external provers ...
% 30.18/7.60 % Time passed: 6995ms (effective reasoning time: 6030ms)
% 30.18/7.60 % Axioms used in derivation (9): c05, c08, c01, c03, c06, c02, c07, c09, c04
% 30.18/7.60 % No. of inferences in proof: 99
% 30.18/7.60 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 6995 ms resp. 6030 ms w/o parsing
% 30.18/7.64 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 30.18/7.64 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------