%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL894+1 : TPTP v9.3.1. Released v5.5.0.
% 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 : n017.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 07:53:19 AM UTC 2026
% Result : Theorem 41.59s 9.24s
% Output : Refutation 41.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 13
% Syntax : Number of formulae : 118 ( 30 unt; 0 typ; 0 def)
% Number of atoms : 348 ( 116 equ; 0 cnn)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 1002 ( 166 ~; 143 |; 16 &; 658 @)
% ( 3 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 7 con; 0-2 aty)
% Number of variables : 169 ( 0 ^; 169 !; 0 ?; 169 :)
% Comments :
%------------------------------------------------------------------------------
thf('>=_decl',type,
'>=': $i > $i > $o ).
thf(c_decl,type,
c: $i ).
thf(a_decl,type,
a: $i ).
thf(b_decl,type,
b: $i ).
thf('+_decl',type,
'+': $i > $i > $i ).
thf('==>_decl',type,
'==>': $i > $i > $i ).
thf('0_decl',type,
'0': $i ).
thf(sk1_decl,type,
sk1: $o ).
thf(13,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ '>=' ) )
=> ( B @ ( C @ '==>' ) @ ( A @ ( C @ '==>' ) @ '>=' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_11) ).
thf(52,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ '>=' ) )
=> ( B @ ( C @ '==>' ) @ ( A @ ( C @ '==>' ) @ '>=' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(10,axiom,
! [A: $i] : ( '0' @ ( A @ '>=' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_08) ).
thf(44,plain,
! [A: $i] : ( '0' @ ( A @ '>=' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(45,plain,
! [A: $i] : ( '0' @ ( A @ '>=' ) ),
inference(cnf,[status(esa)],[44]) ).
thf(1,conjecture,
( ( ( b @ ( c @ '>=' ) )
& ( a @ ( c @ '>=' ) ) )
<=> ( b @ ( a @ '==>' ) @ ( a @ '+' ) @ ( c @ '>=' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals_13) ).
thf(2,negated_conjecture,
~ ( ( ( b @ ( c @ '>=' ) )
& ( a @ ( c @ '>=' ) ) )
<=> ( b @ ( a @ '==>' ) @ ( a @ '+' ) @ ( c @ '>=' ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(15,plain,
~ ( ( ( b @ ( a @ '==>' ) @ ( a @ '+' ) @ ( c @ '>=' ) )
=> ( ( b @ ( c @ '>=' ) )
& ( a @ ( c @ '>=' ) ) ) )
& ( ( ( b @ ( c @ '>=' ) )
& ( a @ ( c @ '>=' ) ) )
=> ( b @ ( a @ '==>' ) @ ( a @ '+' ) @ ( c @ '>=' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(16,plain,
( ( ~ ( b @ ( c @ '>=' ) )
| ~ ( a @ ( c @ '>=' ) )
| sk1 )
& ( ( b @ ( a @ '==>' ) @ ( a @ '+' ) @ ( c @ '>=' ) )
| sk1 )
& ( ~ sk1
| ~ ( b @ ( a @ '==>' ) @ ( a @ '+' ) @ ( c @ '>=' ) ) )
& ( ~ sk1
| ( b @ ( c @ '>=' ) ) )
& ( ~ sk1
| ( a @ ( c @ '>=' ) ) ) ),
inference(cnf,[status(esa)],[15]) ).
thf(18,plain,
( ~ ( b @ ( c @ '>=' ) )
| ~ ( a @ ( c @ '>=' ) )
| sk1 ),
inference(cnfConj,[status(thm)],[16]) ).
thf(116,plain,
! [A: $i] :
( ( ( '0' @ ( A @ '>=' ) )
!= ( b @ ( c @ '>=' ) ) )
| ~ $true
| ~ ( a @ ( c @ '>=' ) )
| sk1 ),
inference(paramod_ordered,[status(thm)],[45,18]) ).
thf(117,plain,
! [A: $i] :
( ( ( '0' @ ( A @ '>=' ) )
!= ( b @ ( c @ '>=' ) ) )
| ~ ( a @ ( c @ '>=' ) )
| sk1 ),
inference(simp,[status(thm)],[116]) ).
thf(130,plain,
! [A: $i] :
( ( '0' != b )
| ( A != c )
| ~ ( a @ ( c @ '>=' ) )
| sk1 ),
inference(simp,[status(thm)],[117]) ).
thf(134,plain,
( ( '0' != b )
| ~ ( a @ ( c @ '>=' ) )
| sk1 ),
inference(simp,[status(thm)],[130]) ).
thf(1089,plain,
! [A: $i] :
( ( ( '0' @ ( A @ '>=' ) )
!= ( a @ ( c @ '>=' ) ) )
| ( '0' != b )
| ~ $true
| sk1 ),
inference(paramod_ordered,[status(thm)],[45,134]) ).
thf(1090,plain,
! [A: $i] :
( ( ( '0' @ ( A @ '>=' ) )
!= ( a @ ( c @ '>=' ) ) )
| ( '0' != b )
| sk1 ),
inference(simp,[status(thm)],[1089]) ).
thf(1101,plain,
! [A: $i] :
( ( '0' != a )
| ( A != c )
| ( '0' != b )
| sk1 ),
inference(simp,[status(thm)],[1090]) ).
thf(1109,plain,
( ( '0' != a )
| ( '0' != b )
| sk1 ),
inference(simp,[status(thm)],[1101]) ).
thf(6,axiom,
! [A: $i] : ( A @ ( A @ '>=' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_04) ).
thf(31,plain,
! [A: $i] : ( A @ ( A @ '>=' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(32,plain,
! [A: $i] : ( A @ ( A @ '>=' ) ),
inference(cnf,[status(esa)],[31]) ).
thf(110,plain,
! [A: $i] :
( ( ( A @ ( A @ '>=' ) )
!= ( a @ ( c @ '>=' ) ) )
| ~ ( b @ ( c @ '>=' ) )
| ~ $true
| sk1 ),
inference(paramod_ordered,[status(thm)],[32,18]) ).
thf(111,plain,
! [A: $i] :
( ( ( A @ ( A @ '>=' ) )
!= ( a @ ( c @ '>=' ) ) )
| ~ ( b @ ( c @ '>=' ) )
| sk1 ),
inference(simp,[status(thm)],[110]) ).
thf(129,plain,
! [A: $i] :
( ( A != a )
| ( A != c )
| ~ ( b @ ( c @ '>=' ) )
| sk1 ),
inference(simp,[status(thm)],[111]) ).
thf(133,plain,
( ( a != c )
| ~ ( b @ ( c @ '>=' ) )
| sk1 ),
inference(simp,[status(thm)],[129]) ).
thf(5,axiom,
! [A: $i] :
( ( '0' @ ( A @ '+' ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_03) ).
thf(28,plain,
! [A: $i] :
( ( '0' @ ( A @ '+' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(29,plain,
! [A: $i] :
( ( '0' @ ( A @ '+' ) )
= A ),
inference(cnf,[status(esa)],[28]) ).
thf(30,plain,
! [A: $i] :
( ( '0' @ ( A @ '+' ) )
= A ),
inference(lifteq,[status(thm)],[29]) ).
thf(21,plain,
( ~ sk1
| ( a @ ( c @ '>=' ) ) ),
inference(cnfConj,[status(thm)],[16]) ).
thf(19,plain,
( ~ sk1
| ~ ( b @ ( a @ '==>' ) @ ( a @ '+' ) @ ( c @ '>=' ) ) ),
inference(cnfConj,[status(thm)],[16]) ).
thf(97,plain,
( ( ( b @ ( a @ '==>' ) @ ( a @ '+' ) @ ( c @ '>=' ) )
!= ( a @ ( c @ '>=' ) ) )
| ~ sk1
| ~ $true
| ~ sk1 ),
inference(paramod_ordered,[status(thm)],[21,19]) ).
thf(98,plain,
( ( ( b @ ( a @ '==>' ) @ ( a @ '+' ) @ ( c @ '>=' ) )
!= ( a @ ( c @ '>=' ) ) )
| ~ sk1 ),
inference(simp,[status(thm)],[97]) ).
thf(99,plain,
( ( ( b @ ( a @ '==>' ) @ ( a @ '+' ) )
!= a )
| ( c != c )
| ~ sk1 ),
inference(simp,[status(thm)],[98]) ).
thf(100,plain,
( ( ( b @ ( a @ '==>' ) @ ( a @ '+' ) )
!= a )
| ~ sk1 ),
inference(simp,[status(thm)],[99]) ).
thf(350,plain,
! [A: $i] :
( ( ( '0' @ ( A @ '+' ) )
!= ( b @ ( a @ '==>' ) @ ( a @ '+' ) ) )
| ( A != a )
| ~ sk1 ),
inference(paramod_ordered,[status(thm)],[30,100]) ).
thf(355,plain,
( ( ( b @ ( a @ '==>' ) )
!= '0' )
| ( a != a )
| ~ sk1 ),
inference(simp,[status(thm)],[350]) ).
thf(356,plain,
( ( ( b @ ( a @ '==>' ) )
!= '0' )
| ~ sk1 ),
inference(simp,[status(thm)],[355]) ).
thf(12,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ '>=' ) )
=> ( C @ ( A @ '==>' ) @ ( C @ ( B @ '==>' ) @ '>=' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_10) ).
thf(49,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ '>=' ) )
=> ( C @ ( A @ '==>' ) @ ( C @ ( B @ '==>' ) @ '>=' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ '+' ) @ '>=' ) )
<=> ( C @ ( A @ '==>' ) @ ( B @ '>=' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_07) ).
thf(38,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ '==>' ) @ ( B @ '>=' ) )
=> ( C @ ( B @ ( A @ '+' ) @ '>=' ) ) )
& ( ( C @ ( B @ ( A @ '+' ) @ '>=' ) )
=> ( C @ ( A @ '==>' ) @ ( B @ '>=' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(39,plain,
( ! [A: $i,B: $i,C: $i] :
( ( C @ ( A @ '==>' ) @ ( B @ '>=' ) )
=> ( C @ ( B @ ( A @ '+' ) @ '>=' ) ) )
& ! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ '+' ) @ '>=' ) )
=> ( C @ ( A @ '==>' ) @ ( B @ '>=' ) ) ) ),
inference(miniscope,[status(thm)],[38]) ).
thf(40,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( F @ ( E @ ( D @ '+' ) @ '>=' ) )
| ~ ( F @ ( D @ '==>' ) @ ( E @ '>=' ) ) )
& ( ( C @ ( A @ '==>' ) @ ( B @ '>=' ) )
| ~ ( C @ ( B @ ( A @ '+' ) @ '>=' ) ) ) ),
inference(cnf,[status(esa)],[39]) ).
thf(41,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ '==>' ) @ ( B @ '>=' ) )
| ~ ( C @ ( B @ ( A @ '+' ) @ '>=' ) ) ),
inference(cnfConj,[status(thm)],[40]) ).
thf(1187,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( '0' @ ( A @ '>=' ) )
!= ( D @ ( C @ ( B @ '+' ) @ '>=' ) ) )
| ( D @ ( B @ '==>' ) @ ( C @ '>=' ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[45,41]) ).
thf(1188,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( '0' @ ( A @ '>=' ) )
!= ( D @ ( C @ ( B @ '+' ) @ '>=' ) ) )
| ( D @ ( B @ '==>' ) @ ( C @ '>=' ) ) ),
inference(simp,[status(thm)],[1187]) ).
thf(1189,plain,
! [B: $i,A: $i] : ( '0' @ ( A @ '==>' ) @ ( B @ '>=' ) ),
inference(pattern_uni,[status(thm)],[1188:[bind(A,$thf( F @ ( E @ '+' ) )),bind(B,$thf( E )),bind(C,$thf( F )),bind(D,$thf( '0' ))]]) ).
thf(1250,plain,
! [B: $i,A: $i] : ( '0' @ ( A @ '==>' ) @ ( B @ '>=' ) ),
inference(simp,[status(thm)],[1189]) ).
thf(1261,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( '0' @ ( A @ '==>' ) @ ( B @ '>=' ) )
!= ( E @ ( D @ ( C @ '+' ) @ '>=' ) ) )
| ( E @ ( C @ '==>' ) @ ( D @ '>=' ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1250,41]) ).
thf(1262,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( '0' @ ( A @ '==>' ) @ ( B @ '>=' ) )
!= ( E @ ( D @ ( C @ '+' ) @ '>=' ) ) )
| ( E @ ( C @ '==>' ) @ ( D @ '>=' ) ) ),
inference(simp,[status(thm)],[1261]) ).
thf(1263,plain,
! [C: $i,B: $i,A: $i] : ( '0' @ ( C @ '==>' ) @ ( A @ '==>' ) @ ( B @ '>=' ) ),
inference(pattern_uni,[status(thm)],[1262:[bind(A,$thf( H )),bind(B,$thf( G @ ( F @ '+' ) )),bind(C,$thf( F )),bind(D,$thf( G )),bind(E,$thf( '0' @ ( H @ '==>' ) ))]]) ).
thf(1304,plain,
! [C: $i,B: $i,A: $i] : ( '0' @ ( C @ '==>' ) @ ( A @ '==>' ) @ ( B @ '>=' ) ),
inference(simp,[status(thm)],[1263]) ).
thf(42,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ '+' ) @ '>=' ) )
| ~ ( C @ ( A @ '==>' ) @ ( B @ '>=' ) ) ),
inference(cnfConj,[status(thm)],[40]) ).
thf(43,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ '+' ) @ '>=' ) )
| ~ ( C @ ( A @ '==>' ) @ ( B @ '>=' ) ) ),
inference(simp,[status(thm)],[42]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ '==>' ) @ ( A @ '+' ) )
= ( A @ ( B @ '==>' ) @ ( B @ '+' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_12) ).
thf(55,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ '==>' ) @ ( A @ '+' ) )
= ( A @ ( B @ '==>' ) @ ( B @ '+' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(3,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ '+' ) @ '+' ) )
= ( C @ ( B @ '+' ) @ ( A @ '+' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_01) ).
thf(22,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ '+' ) @ '+' ) )
= ( C @ ( B @ '+' ) @ ( A @ '+' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(23,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ '+' ) @ '+' ) )
= ( C @ ( B @ '+' ) @ ( A @ '+' ) ) ),
inference(cnf,[status(esa)],[22]) ).
thf(24,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ '+' ) @ '+' ) )
= ( C @ ( B @ '+' ) @ ( A @ '+' ) ) ),
inference(lifteq,[status(thm)],[23]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ '>=' ) )
& ( B @ ( A @ '>=' ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_06) ).
thf(35,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ '>=' ) )
& ( B @ ( A @ '>=' ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(36,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( A @ ( B @ '>=' ) )
| ~ ( B @ ( A @ '>=' ) ) ),
inference(cnf,[status(esa)],[35]) ).
thf(37,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ '>=' ) )
| ~ ( B @ ( A @ '>=' ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[36]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ '+' ) )
= ( A @ ( B @ '+' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_02) ).
thf(25,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ '+' ) )
= ( A @ ( B @ '+' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(20,plain,
( ( b @ ( a @ '==>' ) @ ( a @ '+' ) @ ( c @ '>=' ) )
| sk1 ),
inference(cnfConj,[status(thm)],[16]) ).
thf(11,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ '>=' ) )
=> ( C @ ( B @ '+' ) @ ( C @ ( A @ '+' ) @ '>=' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_09) ).
thf(46,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ '>=' ) )
=> ( C @ ( B @ '+' ) @ ( C @ ( A @ '+' ) @ '>=' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(56,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ '==>' ) @ ( A @ '+' ) )
= ( A @ ( B @ '==>' ) @ ( B @ '+' ) ) ),
inference(cnf,[status(esa)],[55]) ).
thf(57,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ '==>' ) @ ( A @ '+' ) )
= ( A @ ( B @ '==>' ) @ ( B @ '+' ) ) ),
inference(lifteq,[status(thm)],[56]) ).
thf(71,plain,
! [A: $i] :
( ( ( '0' @ ( A @ '>=' ) )
!= ( b @ ( a @ '==>' ) @ ( a @ '+' ) @ ( c @ '>=' ) ) )
| ~ sk1
| ~ $true ),
inference(paramod_ordered,[status(thm)],[45,19]) ).
thf(72,plain,
! [A: $i] :
( ( ( '0' @ ( A @ '>=' ) )
!= ( b @ ( a @ '==>' ) @ ( a @ '+' ) @ ( c @ '>=' ) ) )
| ~ sk1 ),
inference(simp,[status(thm)],[71]) ).
thf(75,plain,
! [A: $i] :
( ( ( b @ ( a @ '==>' ) @ ( a @ '+' ) )
!= '0' )
| ( A != c )
| ~ sk1 ),
inference(simp,[status(thm)],[72]) ).
thf(78,plain,
( ( ( b @ ( a @ '==>' ) @ ( a @ '+' ) )
!= '0' )
| ~ sk1 ),
inference(simp,[status(thm)],[75]) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ '>=' ) )
& ( B @ ( A @ '>=' ) ) )
=> ( C @ ( A @ '>=' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_05) ).
thf(33,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ '>=' ) )
& ( B @ ( A @ '>=' ) ) )
=> ( C @ ( A @ '>=' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(26,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ '+' ) )
= ( A @ ( B @ '+' ) ) ),
inference(cnf,[status(esa)],[25]) ).
thf(27,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ '+' ) )
= ( A @ ( B @ '+' ) ) ),
inference(lifteq,[status(thm)],[26]) ).
thf(58,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ '+' ) )
!= ( '0' @ ( C @ '+' ) ) )
| ( ( A @ ( B @ '+' ) )
= C ) ),
inference(paramod_ordered,[status(thm)],[27,30]) ).
thf(59,plain,
! [A: $i] :
( ( A @ ( '0' @ '+' ) )
= A ),
inference(pattern_uni,[status(thm)],[58:[bind(A,$thf( A )),bind(B,$thf( '0' )),bind(C,$thf( A ))]]) ).
thf(17,plain,
( ~ sk1
| ( b @ ( c @ '>=' ) ) ),
inference(cnfConj,[status(thm)],[16]) ).
thf(93,plain,
( ( ( b @ ( a @ '==>' ) @ ( a @ '+' ) @ ( c @ '>=' ) )
!= ( b @ ( c @ '>=' ) ) )
| ~ sk1
| ~ $true
| ~ sk1 ),
inference(paramod_ordered,[status(thm)],[17,19]) ).
thf(94,plain,
( ( ( b @ ( a @ '==>' ) @ ( a @ '+' ) @ ( c @ '>=' ) )
!= ( b @ ( c @ '>=' ) ) )
| ~ sk1 ),
inference(simp,[status(thm)],[93]) ).
thf(95,plain,
( ( ( b @ ( a @ '==>' ) @ ( a @ '+' ) )
!= b )
| ( c != c )
| ~ sk1 ),
inference(simp,[status(thm)],[94]) ).
thf(96,plain,
( ( ( b @ ( a @ '==>' ) @ ( a @ '+' ) )
!= b )
| ~ sk1 ),
inference(simp,[status(thm)],[95]) ).
thf(333,plain,
! [A: $i] :
( ( ( A @ ( '0' @ '+' ) )
!= ( b @ ( a @ '==>' ) @ ( a @ '+' ) ) )
| ( A != b )
| ~ sk1 ),
inference(paramod_ordered,[status(thm)],[59,96]) ).
thf(339,plain,
( ( ( b @ ( a @ '==>' ) )
!= b )
| ( '0' != a )
| ~ sk1 ),
inference(simp,[status(thm)],[333]) ).
thf(69,plain,
! [A: $i] :
( ( ( A @ ( A @ '>=' ) )
!= ( b @ ( a @ '==>' ) @ ( a @ '+' ) @ ( c @ '>=' ) ) )
| ~ sk1
| ~ $true ),
inference(paramod_ordered,[status(thm)],[32,19]) ).
thf(70,plain,
! [A: $i] :
( ( ( A @ ( A @ '>=' ) )
!= ( b @ ( a @ '==>' ) @ ( a @ '+' ) @ ( c @ '>=' ) ) )
| ~ sk1 ),
inference(simp,[status(thm)],[69]) ).
thf(74,plain,
! [A: $i] :
( ( A
!= ( b @ ( a @ '==>' ) @ ( a @ '+' ) ) )
| ( A != c )
| ~ sk1 ),
inference(simp,[status(thm)],[70]) ).
thf(77,plain,
( ( ( b @ ( a @ '==>' ) @ ( a @ '+' ) )
!= c )
| ~ sk1 ),
inference(simp,[status(thm)],[74]) ).
thf(114,plain,
! [A: $i] :
( ( ( '0' @ ( A @ '>=' ) )
!= ( a @ ( c @ '>=' ) ) )
| ~ ( b @ ( c @ '>=' ) )
| ~ $true
| sk1 ),
inference(paramod_ordered,[status(thm)],[45,18]) ).
thf(115,plain,
! [A: $i] :
( ( ( '0' @ ( A @ '>=' ) )
!= ( a @ ( c @ '>=' ) ) )
| ~ ( b @ ( c @ '>=' ) )
| sk1 ),
inference(simp,[status(thm)],[114]) ).
thf(124,plain,
! [A: $i] :
( ( '0' != a )
| ( A != c )
| ~ ( b @ ( c @ '>=' ) )
| sk1 ),
inference(simp,[status(thm)],[115]) ).
thf(136,plain,
( ( '0' != a )
| ~ ( b @ ( c @ '>=' ) )
| sk1 ),
inference(simp,[status(thm)],[124]) ).
thf(1439,plain,
! [A: $i] :
( ( ( A @ ( A @ '>=' ) )
!= ( b @ ( c @ '>=' ) ) )
| ( '0' != a )
| ~ $true
| sk1 ),
inference(paramod_ordered,[status(thm)],[32,136]) ).
thf(1440,plain,
! [A: $i] :
( ( ( A @ ( A @ '>=' ) )
!= ( b @ ( c @ '>=' ) ) )
| ( '0' != a )
| sk1 ),
inference(simp,[status(thm)],[1439]) ).
thf(1448,plain,
! [A: $i] :
( ( A != b )
| ( A != c )
| ( '0' != a )
| sk1 ),
inference(simp,[status(thm)],[1440]) ).
thf(1456,plain,
( ( b != c )
| ( '0' != a )
| sk1 ),
inference(simp,[status(thm)],[1448]) ).
thf(374,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ '==>' ) @ ( A @ '+' ) )
!= ( b @ ( a @ '==>' ) @ ( a @ '+' ) ) )
| ( A @ ( B @ '==>' ) @ ( B @ '+' ) @ ( c @ '>=' ) )
| sk1 ),
inference(paramod_ordered,[status(thm)],[57,20]) ).
thf(375,plain,
( ( a @ ( b @ '==>' ) @ ( b @ '+' ) @ ( c @ '>=' ) )
| sk1 ),
inference(pattern_uni,[status(thm)],[374:[bind(A,$thf( a )),bind(B,$thf( b ))]]) ).
thf(34,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ '>=' ) )
| ~ ( C @ ( B @ '>=' ) )
| ~ ( B @ ( A @ '>=' ) ) ),
inference(cnf,[status(esa)],[33]) ).
thf(232,plain,
! [A: $i] :
( ( ( '0' @ ( A @ '>=' ) )
!= ( b @ ( c @ '>=' ) ) )
| ( a != c )
| ~ $true
| sk1 ),
inference(paramod_ordered,[status(thm)],[45,133]) ).
thf(233,plain,
! [A: $i] :
( ( ( '0' @ ( A @ '>=' ) )
!= ( b @ ( c @ '>=' ) ) )
| ( a != c )
| sk1 ),
inference(simp,[status(thm)],[232]) ).
thf(237,plain,
! [A: $i] :
( ( '0' != b )
| ( A != c )
| ( a != c )
| sk1 ),
inference(simp,[status(thm)],[233]) ).
thf(240,plain,
( ( '0' != b )
| ( a != c )
| sk1 ),
inference(simp,[status(thm)],[237]) ).
thf(140,plain,
! [A: $i] :
( ( ( A @ ( '0' @ '+' ) )
!= ( b @ ( a @ '==>' ) @ ( a @ '+' ) ) )
| ( A != c )
| ~ sk1 ),
inference(paramod_ordered,[status(thm)],[59,77]) ).
thf(155,plain,
( ( ( b @ ( a @ '==>' ) )
!= c )
| ( '0' != a )
| ~ sk1 ),
inference(simp,[status(thm)],[140]) ).
thf(390,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ '==>' ) @ ( A @ '+' ) )
!= ( C @ ( '0' @ '+' ) ) )
| ( ( A @ ( B @ '==>' ) @ ( B @ '+' ) )
= C ) ),
inference(paramod_ordered,[status(thm)],[57,59]) ).
thf(391,plain,
! [A: $i] :
( ( '0' @ ( A @ '==>' ) @ ( A @ '+' ) )
= ( A @ ( '0' @ '==>' ) ) ),
inference(pattern_uni,[status(thm)],[390:[bind(A,$thf( '0' )),bind(B,$thf( E )),bind(C,$thf( E @ ( '0' @ '==>' ) ))]]) ).
thf(422,plain,
! [A: $i] :
( ( '0' @ ( A @ '==>' ) @ ( A @ '+' ) )
= ( A @ ( '0' @ '==>' ) ) ),
inference(simp,[status(thm)],[391]) ).
thf(230,plain,
! [A: $i] :
( ( ( A @ ( A @ '>=' ) )
!= ( b @ ( c @ '>=' ) ) )
| ( a != c )
| ~ $true
| sk1 ),
inference(paramod_ordered,[status(thm)],[32,133]) ).
thf(231,plain,
! [A: $i] :
( ( ( A @ ( A @ '>=' ) )
!= ( b @ ( c @ '>=' ) ) )
| ( a != c )
| sk1 ),
inference(simp,[status(thm)],[230]) ).
thf(239,plain,
! [A: $i] :
( ( A != b )
| ( A != c )
| ( a != c )
| sk1 ),
inference(simp,[status(thm)],[231]) ).
thf(242,plain,
( ( b != c )
| ( a != c )
| sk1 ),
inference(simp,[status(thm)],[239]) ).
thf(12813,plain,
$false,
inference(e,[status(thm)],[52,1109,133,356,134,49,1304,18,31,43,55,15,100,24,37,25,20,46,57,78,21,33,28,38,339,77,96,1456,41,45,17,375,32,34,22,44,59,27,240,155,1250,35,30,19,422,242,136]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL894+1 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.08 % 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
% 0.14/0.41 % Computer : n017.cluster.edu
% 0.14/0.41 % Model : x86_64 x86_64
% 0.14/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.41 % Memory : 8046.5625MB
% 0.14/0.41 % OS : Linux 6.8.0-71-generic
% 0.14/0.41 % CPULimit : 300
% 0.14/0.41 % WCLimit : 300
% 0.14/0.41 % DateTime : Fri Sep 25 23:42:18 UTC 2026
% 0.14/0.41 % CPUTime :
% 0.14/0.41 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
% 1.01/0.90 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.37/1.09 % [INFO] Parsing done (189ms).
% 1.37/1.11 % [INFO] Running in sequential loop mode.
% 2.23/1.69 % [INFO] eprover registered as external prover.
% 2.46/1.70 % [INFO] Scanning for conjecture ...
% 2.62/1.84 % [INFO] Found a conjecture (or negated_conjecture) and 12 axioms. Running axiom selection ...
% 2.62/1.89 % [INFO] Axiom selection finished. Selected 12 axioms (removed 0 axioms).
% 2.79/1.94 % [INFO] Problem is first-order (TPTP FOF).
% 2.79/1.95 % [INFO] Type checking passed.
% 2.79/1.96 % [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 ...
% 41.59/9.23 % External prover 'e' found a proof!
% 41.59/9.23 % [INFO] Killing All external provers ...
% 41.59/9.23 % Time passed: 8684ms (effective reasoning time: 8112ms)
% 41.59/9.23 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 41.59/9.24 % Axioms used in derivation (12): sos_01, sos_05, sos_02, sos_11, sos_07, sos_08, sos_12, sos_06, sos_09, sos_03, sos_04, sos_10
% 41.59/9.24 % No. of inferences in proof: 118
% 41.59/9.24 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 8684 ms resp. 8112 ms w/o parsing
% 41.59/9.29 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 41.59/9.29 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------