%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL080-2 : TPTP v9.3.1. Released v1.0.0.
% 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 07:50:46 AM UTC 2026
% Result : Unsatisfiable 9.43s 5.10s
% Output : Refutation 8.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 6
% Syntax : Number of formulae : 89 ( 47 unt; 0 typ; 0 def)
% Number of atoms : 218 ( 79 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 915 ( 124 ~; 57 |; 0 &; 734 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 6 con; 0-2 aty)
% Number of variables : 136 ( 0 ^; 136 !; 0 ?; 136 :)
% Comments :
%------------------------------------------------------------------------------
thf(is_a_theorem_decl,type,
is_a_theorem: $i > $o ).
thf(implies_decl,type,
implies: $i > $i > $i ).
thf(a_decl,type,
a: $i ).
thf(b_decl,type,
b: $i ).
thf(c_decl,type,
c: $i ).
thf(e_decl,type,
e: $i ).
thf(6,axiom,
! [C: $i,B: $i,A: $i] : ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ic_4) ).
thf(14,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(3,axiom,
! [A: $i] : ( A @ ( A @ implies ) @ is_a_theorem ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ic_1) ).
thf(11,plain,
! [A: $i] : ( A @ ( A @ implies ) @ is_a_theorem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(4,axiom,
! [B: $i,A: $i] : ( A @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ic_2) ).
thf(12,plain,
! [B: $i,A: $i] : ( A @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(2,axiom,
! [B: $i,A: $i] :
( ( B @ is_a_theorem )
| ~ ( A @ is_a_theorem )
| ~ ( B @ ( A @ implies ) @ is_a_theorem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',condensed_detachment) ).
thf(9,plain,
! [B: $i,A: $i] :
( ( B @ is_a_theorem )
| ~ ( A @ is_a_theorem )
| ~ ( B @ ( A @ implies ) @ is_a_theorem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(10,plain,
! [B: $i,A: $i] :
( ( B @ is_a_theorem )
| ~ ( A @ is_a_theorem )
| ~ ( B @ ( A @ implies ) @ is_a_theorem ) ),
inference(cnf,[status(esa)],[9]) ).
thf(43,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ ( C @ implies ) @ is_a_theorem ) )
| ( D @ is_a_theorem )
| ~ ( C @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12,10]) ).
thf(44,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ ( C @ implies ) @ is_a_theorem ) )
| ( D @ is_a_theorem )
| ~ ( C @ is_a_theorem ) ),
inference(simp,[status(thm)],[43]) ).
thf(45,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ is_a_theorem )
| ~ ( B @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[44:[bind(A,$thf( F )),bind(B,$thf( E )),bind(C,$thf( F )),bind(D,$thf( F @ ( E @ implies ) ))]]) ).
thf(64,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ is_a_theorem )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[45]) ).
thf(1,negated_conjecture,
~ ( a @ ( e @ implies ) @ ( a @ ( c @ implies ) @ implies ) @ ( c @ ( b @ ( a @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_ic_JLukasiewicz) ).
thf(7,plain,
~ ( a @ ( e @ implies ) @ ( a @ ( c @ implies ) @ implies ) @ ( c @ ( b @ ( a @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(8,plain,
~ ( a @ ( e @ implies ) @ ( a @ ( c @ implies ) @ implies ) @ ( c @ ( b @ ( a @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
inference(polarity_switch,[status(thm)],[7]) ).
thf(91,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( e @ implies ) @ ( a @ ( c @ implies ) @ implies ) @ ( c @ ( b @ ( a @ implies ) @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[64,8]) ).
thf(92,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( e @ implies ) @ ( a @ ( c @ implies ) @ implies ) @ ( c @ ( b @ ( a @ implies ) @ implies ) @ implies ) @ is_a_theorem ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[91]) ).
thf(93,plain,
~ ( a @ ( e @ implies ) @ ( a @ ( c @ implies ) @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[92:[bind(A,$thf( c @ ( b @ ( a @ implies ) @ implies ) )),bind(B,$thf( a @ ( e @ implies ) @ ( a @ ( c @ implies ) @ implies ) ))]]) ).
thf(110,plain,
! [A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( e @ implies ) @ ( a @ ( c @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11,93]) ).
thf(111,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( e @ implies ) @ ( a @ ( c @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[110]) ).
thf(117,plain,
! [A: $i] :
( ( A @ ( A @ implies ) )
!= ( a @ ( e @ implies ) @ ( a @ ( c @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[111]) ).
thf(5,axiom,
! [B: $i,A: $i] : ( A @ ( A @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ic_3) ).
thf(13,plain,
! [B: $i,A: $i] : ( A @ ( A @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(17,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( e @ implies ) @ ( a @ ( c @ implies ) @ implies ) @ ( c @ ( b @ ( a @ implies ) @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12,8]) ).
thf(18,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( e @ implies ) @ ( a @ ( c @ implies ) @ implies ) @ ( c @ ( b @ ( a @ implies ) @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[17]) ).
thf(20,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ implies ) @ ( A @ implies ) )
!= ( a @ ( e @ implies ) @ ( a @ ( c @ implies ) @ implies ) @ ( c @ ( b @ ( a @ implies ) @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[18]) ).
thf(65,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ implies ) )
!= ( a @ ( e @ implies ) @ ( a @ ( c @ implies ) @ implies ) ) )
| ( A
!= ( c @ ( b @ ( a @ implies ) @ implies ) ) ) ),
inference(simp,[status(thm)],[20]) ).
thf(66,plain,
! [A: $i] :
( ( c @ ( b @ ( a @ implies ) @ implies ) @ ( A @ implies ) )
!= ( a @ ( e @ implies ) @ ( a @ ( c @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[65]) ).
thf(107,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( e @ implies ) @ ( a @ ( c @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[64,93]) ).
thf(108,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( e @ implies ) @ ( a @ ( c @ implies ) @ implies ) @ is_a_theorem ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[107]) ).
thf(109,plain,
~ ( a @ ( e @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[108:[bind(A,$thf( a @ ( c @ implies ) )),bind(B,$thf( a @ ( e @ implies ) ))]]) ).
thf(127,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( e @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12,109]) ).
thf(128,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( e @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[127]) ).
thf(130,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ implies ) @ ( A @ implies ) )
!= ( a @ ( e @ implies ) ) ),
inference(simp,[status(thm)],[128]) ).
thf(122,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( e @ implies ) @ is_a_theorem ) )
| ~ $true
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[64,109]) ).
thf(123,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( e @ implies ) @ is_a_theorem ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[122]) ).
thf(124,plain,
~ ( a @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[123:[bind(A,$thf( e )),bind(B,$thf( a ))]]) ).
thf(140,plain,
! [A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11,124]) ).
thf(141,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) ),
inference(simp,[status(thm)],[140]) ).
thf(145,plain,
! [A: $i] :
( ( A @ ( A @ implies ) )
!= a ),
inference(simp,[status(thm)],[141]) ).
thf(125,plain,
! [A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( e @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11,109]) ).
thf(126,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( e @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[125]) ).
thf(132,plain,
! [A: $i] :
( ( A @ ( A @ implies ) )
!= ( a @ ( e @ implies ) ) ),
inference(simp,[status(thm)],[126]) ).
thf(149,plain,
! [A: $i] :
( ( A != a )
| ( A != e ) ),
inference(simp,[status(thm)],[132]) ).
thf(150,plain,
e != a,
inference(simp,[status(thm)],[149]) ).
thf(67,plain,
! [A: $i] :
( ( ( c @ ( b @ ( a @ implies ) @ implies ) )
!= ( a @ ( e @ implies ) ) )
| ( A
!= ( a @ ( c @ implies ) ) ) ),
inference(simp,[status(thm)],[66]) ).
thf(68,plain,
( ( c @ ( b @ ( a @ implies ) @ implies ) )
!= ( a @ ( e @ implies ) ) ),
inference(simp,[status(thm)],[67]) ).
thf(69,plain,
( ( c != a )
| ( ( b @ ( a @ implies ) )
!= e ) ),
inference(simp,[status(thm)],[68]) ).
thf(88,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( C @ ( B @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11,64]) ).
thf(89,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( C @ ( B @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[88]) ).
thf(90,plain,
! [B: $i,A: $i] : ( B @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[89:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( E @ ( E @ implies ) ))]]) ).
thf(101,plain,
! [B: $i,A: $i] : ( B @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[90]) ).
thf(55,plain,
! [B: $i,A: $i] :
( ~ $true
| ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( A @ is_a_theorem ) )
| ( B @ is_a_theorem )
| ~ ( A @ is_a_theorem ) ),
inference(eqfactor_ordered,[status(thm)],[10]) ).
thf(56,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( A @ is_a_theorem ) )
| ~ ( A @ is_a_theorem )
| ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[55]) ).
thf(170,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[101,124]) ).
thf(171,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) ),
inference(simp,[status(thm)],[170]) ).
thf(174,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( A @ implies ) )
!= a ),
inference(simp,[status(thm)],[171]) ).
thf(15,plain,
! [A: $i] :
( ( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( e @ implies ) @ ( a @ ( c @ implies ) @ implies ) @ ( c @ ( b @ ( a @ implies ) @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11,8]) ).
thf(16,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( e @ implies ) @ ( a @ ( c @ implies ) @ implies ) @ ( c @ ( b @ ( a @ implies ) @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[15]) ).
thf(19,plain,
! [A: $i] :
( ( A @ ( A @ implies ) )
!= ( a @ ( e @ implies ) @ ( a @ ( c @ implies ) @ implies ) @ ( c @ ( b @ ( a @ implies ) @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[16]) ).
thf(24,plain,
! [A: $i] :
( ( A
!= ( a @ ( e @ implies ) @ ( a @ ( c @ implies ) @ implies ) ) )
| ( A
!= ( c @ ( b @ ( a @ implies ) @ implies ) ) ) ),
inference(simp,[status(thm)],[19]) ).
thf(25,plain,
( ( a @ ( e @ implies ) @ ( a @ ( c @ implies ) @ implies ) )
!= ( c @ ( b @ ( a @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[24]) ).
thf(151,plain,
! [A: $i] :
( ( A
!= ( a @ ( e @ implies ) ) )
| ( A
!= ( a @ ( c @ implies ) ) ) ),
inference(simp,[status(thm)],[117]) ).
thf(152,plain,
( ( a @ ( e @ implies ) )
!= ( a @ ( c @ implies ) ) ),
inference(simp,[status(thm)],[151]) ).
thf(27,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ ( e @ implies ) @ ( a @ ( c @ implies ) @ implies ) @ ( c @ ( b @ ( a @ implies ) @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[14,8]) ).
thf(28,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ ( e @ implies ) @ ( a @ ( c @ implies ) @ implies ) @ ( c @ ( b @ ( a @ implies ) @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[27]) ).
thf(29,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) )
!= ( a @ ( e @ implies ) @ ( a @ ( c @ implies ) @ implies ) @ ( c @ ( b @ ( a @ implies ) @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[28]) ).
thf(142,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12,124]) ).
thf(143,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) ),
inference(simp,[status(thm)],[142]) ).
thf(147,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ implies ) @ ( A @ implies ) )
!= a ),
inference(simp,[status(thm)],[143]) ).
thf(138,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) )
| ~ $true
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[64,124]) ).
thf(139,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[138]) ).
thf(148,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
!= a )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[139]) ).
thf(21,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ ( e @ implies ) @ ( a @ ( c @ implies ) @ implies ) @ ( c @ ( b @ ( a @ implies ) @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13,8]) ).
thf(22,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ ( e @ implies ) @ ( a @ ( c @ implies ) @ implies ) @ ( c @ ( b @ ( a @ implies ) @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[21]) ).
thf(23,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( A @ implies ) @ implies ) @ implies ) )
!= ( a @ ( e @ implies ) @ ( a @ ( c @ implies ) @ implies ) @ ( c @ ( b @ ( a @ implies ) @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[22]) ).
thf(70,plain,
! [B: $i,A: $i] :
( ( A
!= ( a @ ( e @ implies ) @ ( a @ ( c @ implies ) @ implies ) ) )
| ( ( A @ ( B @ ( A @ implies ) @ implies ) )
!= ( c @ ( b @ ( a @ implies ) @ implies ) ) ) ),
inference(simp,[status(thm)],[23]) ).
thf(71,plain,
! [A: $i] :
( ( a @ ( e @ implies ) @ ( a @ ( c @ implies ) @ implies ) @ ( A @ ( a @ ( e @ implies ) @ ( a @ ( c @ implies ) @ implies ) @ implies ) @ implies ) )
!= ( c @ ( b @ ( a @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[70]) ).
thf(168,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( e @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[101,109]) ).
thf(169,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( e @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[168]) ).
thf(172,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ implies ) @ ( A @ implies ) )
!= ( a @ ( e @ implies ) ) ),
inference(simp,[status(thm)],[169]) ).
thf(229,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ implies ) )
!= a )
| ( A != e ) ),
inference(simp,[status(thm)],[130]) ).
thf(230,plain,
! [A: $i] :
( ( e @ ( A @ implies ) )
!= a ),
inference(simp,[status(thm)],[229]) ).
thf(153,plain,
( ( a != a )
| ( e != c ) ),
inference(simp,[status(thm)],[152]) ).
thf(154,plain,
e != c,
inference(simp,[status(thm)],[153]) ).
thf(26,plain,
( ( ( a @ ( e @ implies ) )
!= c )
| ( ( a @ ( c @ implies ) )
!= ( b @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[25]) ).
thf(30,plain,
( ( ( a @ ( e @ implies ) )
!= c )
| ( b != a )
| ( c != a ) ),
inference(simp,[status(thm)],[26]) ).
thf(443,plain,
$false,
inference(e,[status(thm)],[14,117,9,13,66,130,145,150,8,68,69,101,10,56,174,25,20,93,152,29,147,132,109,124,148,64,71,12,172,230,7,154,11,26,23,30,19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LCL080-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.11 % 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
% 0.16/0.47 % Computer : n019.cluster.edu
% 0.16/0.47 % Model : x86_64 x86_64
% 0.16/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.47 % Memory : 8046.5625MB
% 0.16/0.47 % OS : Linux 6.8.0-71-generic
% 0.16/0.47 % CPULimit : 300
% 0.16/0.47 % WCLimit : 300
% 0.16/0.47 % DateTime : Fri Sep 25 21:50:18 UTC 2026
% 0.18/0.48 % CPUTime :
% 0.18/0.48 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
% 0.97/1.32 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.25/1.53 % [INFO] Parsing done (197ms).
% 1.25/1.54 % [INFO] Running in sequential loop mode.
% 1.71/2.01 % [INFO] eprover registered as external prover.
% 1.71/2.02 % [INFO] Scanning for conjecture ...
% 1.98/2.11 % [INFO] Found a conjecture (or negated_conjecture) and 5 axioms. Running axiom selection ...
% 1.98/2.13 % [INFO] Axiom selection finished. Selected 5 axioms (removed 0 axioms).
% 1.98/2.14 % [INFO] Problem is propositional (TPTP CNF).
% 1.98/2.15 % [INFO] Type checking passed.
% 1.98/2.15 % [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 ...
% 9.43/5.09 % External prover 'e' found a proof!
% 9.43/5.09 % [INFO] Killing All external provers ...
% 9.43/5.09 % Time passed: 4334ms (effective reasoning time: 3541ms)
% 9.43/5.10 % Axioms used in derivation (5): ic_1, condensed_detachment, ic_2, ic_3, ic_4
% 9.43/5.10 % No. of inferences in proof: 89
% 9.43/5.10 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 4334 ms resp. 3541 ms w/o parsing
% 8.35/5.22 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 8.35/5.22 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------