%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL113-1 : TPTP v9.3.1. Released v1.0.0.
% 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 : n008.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 07:50:53 AM UTC 2026
% Result : Unsatisfiable 8.62s 8.47s
% Output : Refutation 9.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 6
% Syntax : Number of formulae : 90 ( 41 unt; 0 typ; 0 def)
% Number of atoms : 238 ( 113 equ; 0 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 1023 ( 150 ~; 88 |; 0 &; 785 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 181 ( 0 ^; 181 !; 0 ?; 181 :)
% Comments :
%------------------------------------------------------------------------------
thf(is_a_theorem_decl,type,
is_a_theorem: $i > $o ).
thf(implies_decl,type,
implies: $i > $i > $i ).
thf(not_decl,type,
not: $i > $i ).
thf(a_decl,type,
a: $i ).
thf(b_decl,type,
b: $i ).
thf(3,axiom,
! [B: $i,A: $i] : ( A @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mv_1) ).
thf(11,plain,
! [B: $i,A: $i] : ( A @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(2,axiom,
! [B: $i,A: $i] :
( ( B @ is_a_theorem )
| ~ ( A @ is_a_theorem )
| ~ ( B @ ( A @ implies ) @ is_a_theorem ) ),
file('/export/starexec/sandbox2/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(70,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)],[11,10]) ).
thf(71,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)],[70]) ).
thf(72,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ is_a_theorem )
| ~ ( B @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[71:[bind(A,$thf( F )),bind(B,$thf( E )),bind(C,$thf( F )),bind(D,$thf( F @ ( E @ implies ) ))]]) ).
thf(81,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ is_a_theorem )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[72]) ).
thf(1,negated_conjecture,
~ ( a @ ( b @ not @ implies ) @ ( b @ ( a @ not @ implies ) @ implies ) @ is_a_theorem ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_mv_33) ).
thf(7,plain,
~ ( a @ ( b @ not @ implies ) @ ( b @ ( a @ not @ implies ) @ implies ) @ is_a_theorem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(8,plain,
~ ( a @ ( b @ not @ implies ) @ ( b @ ( a @ not @ implies ) @ implies ) @ is_a_theorem ),
inference(polarity_switch,[status(thm)],[7]) ).
thf(113,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ ( b @ ( a @ not @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[81,8]) ).
thf(114,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ ( b @ ( a @ not @ implies ) @ implies ) @ is_a_theorem ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[113]) ).
thf(115,plain,
~ ( a @ ( b @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[114:[bind(A,$thf( b @ ( a @ not @ implies ) )),bind(B,$thf( a @ ( b @ not @ implies ) ))]]) ).
thf(15,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ ( b @ ( a @ not @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11,8]) ).
thf(16,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ ( b @ ( a @ not @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[15]) ).
thf(17,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ implies ) @ ( A @ implies ) )
!= ( a @ ( b @ not @ implies ) @ ( b @ ( a @ not @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[16]) ).
thf(21,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ implies ) )
!= ( a @ ( b @ not @ implies ) ) )
| ( A
!= ( b @ ( a @ not @ implies ) ) ) ),
inference(simp,[status(thm)],[17]) ).
thf(22,plain,
! [A: $i] :
( ( b @ ( a @ not @ implies ) @ ( A @ implies ) )
!= ( a @ ( b @ not @ implies ) ) ),
inference(simp,[status(thm)],[21]) ).
thf(23,plain,
! [A: $i] :
( ( ( b @ ( a @ not @ implies ) )
!= a )
| ( A
!= ( b @ not ) ) ),
inference(simp,[status(thm)],[22]) ).
thf(24,plain,
( ( b @ ( a @ not @ implies ) )
!= a ),
inference(simp,[status(thm)],[23]) ).
thf(5,axiom,
! [B: $i,A: $i] : ( A @ ( A @ ( B @ implies ) @ implies ) @ ( B @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mv_3) ).
thf(13,plain,
! [B: $i,A: $i] : ( A @ ( A @ ( B @ implies ) @ implies ) @ ( B @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(138,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11,115]) ).
thf(139,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[138]) ).
thf(145,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ implies ) @ ( A @ implies ) )
!= ( a @ ( b @ not @ implies ) ) ),
inference(simp,[status(thm)],[139]) ).
thf(6,axiom,
! [B: $i,A: $i] : ( A @ ( B @ implies ) @ ( B @ not @ ( A @ not @ implies ) @ implies ) @ is_a_theorem ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mv_5) ).
thf(14,plain,
! [B: $i,A: $i] : ( A @ ( B @ implies ) @ ( B @ not @ ( A @ not @ implies ) @ implies ) @ is_a_theorem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(18,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( B @ not @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ ( b @ ( a @ not @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[14,8]) ).
thf(19,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ implies ) @ ( B @ not @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ ( b @ ( a @ not @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[18]) ).
thf(20,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ implies ) @ ( B @ not @ ( A @ not @ implies ) @ implies ) )
!= ( a @ ( b @ not @ implies ) @ ( b @ ( a @ not @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[19]) ).
thf(28,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ implies ) )
!= ( a @ ( b @ not @ implies ) ) )
| ( ( B @ not @ ( A @ not @ implies ) )
!= ( b @ ( a @ not @ implies ) ) ) ),
inference(simp,[status(thm)],[20]) ).
thf(33,plain,
! [B: $i,A: $i] :
( ( ( a @ ( b @ not @ implies ) )
!= ( B @ not @ ( A @ not @ implies ) ) )
| ( ( A @ ( B @ implies ) )
!= ( b @ ( a @ not @ implies ) ) )
| ( ( B @ not @ ( A @ not @ implies ) )
!= ( b @ ( a @ not @ implies ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[28]) ).
thf(39,plain,
! [B: $i,A: $i] :
( ( ( B @ not )
!= a )
| ( ( b @ not )
!= ( A @ not ) )
| ( A != b )
| ( B
!= ( a @ not ) )
| ( ( B @ not @ ( A @ not @ implies ) )
!= ( b @ ( a @ not @ implies ) ) ) ),
inference(simp,[status(thm)],[33]) ).
thf(50,plain,
( ( ( a @ not @ not )
!= a )
| ( ( a @ not @ not @ ( b @ not @ implies ) )
!= ( b @ ( a @ not @ implies ) ) ) ),
inference(simp,[status(thm)],[39]) ).
thf(110,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( D @ ( C @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11,81]) ).
thf(111,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( D @ ( C @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[110]) ).
thf(112,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[111:[bind(A,$thf( H )),bind(B,$thf( G )),bind(C,$thf( C )),bind(D,$thf( H @ ( G @ implies ) @ ( H @ implies ) ))]]) ).
thf(125,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[112]) ).
thf(135,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ is_a_theorem ) )
| ~ $true
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[81,115]) ).
thf(136,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ is_a_theorem ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[135]) ).
thf(137,plain,
~ ( a @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[136:[bind(A,$thf( b @ not )),bind(B,$thf( a ))]]) ).
thf(182,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[125,137]) ).
thf(183,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) ),
inference(simp,[status(thm)],[182]) ).
thf(186,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) )
!= a ),
inference(simp,[status(thm)],[183]) ).
thf(101,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( B @ not @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( D @ ( C @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[14,81]) ).
thf(102,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( B @ not @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( D @ ( C @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[101]) ).
thf(103,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ implies ) @ ( B @ not @ ( C @ not @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[102:[bind(A,$thf( L )),bind(B,$thf( K )),bind(C,$thf( C )),bind(D,$thf( L @ ( K @ implies ) @ ( K @ not @ ( L @ not @ implies ) @ implies ) ))]]) ).
thf(126,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ implies ) @ ( B @ not @ ( C @ not @ implies ) @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[103]) ).
thf(30,plain,
! [B: $i,A: $i] :
( ( A != a )
| ( B
!= ( b @ not ) )
| ( ( B @ not @ ( A @ not @ implies ) )
!= ( b @ ( a @ not @ implies ) ) ) ),
inference(simp,[status(thm)],[28]) ).
thf(56,plain,
( ( b @ not @ not @ ( a @ not @ implies ) )
!= ( b @ ( a @ not @ implies ) ) ),
inference(simp,[status(thm)],[30]) ).
thf(169,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[125,115]) ).
thf(170,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[169]) ).
thf(184,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) )
!= ( a @ ( b @ not @ implies ) ) ),
inference(simp,[status(thm)],[170]) ).
thf(146,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( B @ not @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[14,137]) ).
thf(147,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ implies ) @ ( B @ not @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) ),
inference(simp,[status(thm)],[146]) ).
thf(157,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ implies ) @ ( B @ not @ ( A @ not @ implies ) @ implies ) )
!= a ),
inference(simp,[status(thm)],[147]) ).
thf(171,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( E @ ( D @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[125,81]) ).
thf(172,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( E @ ( D @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[171]) ).
thf(173,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ implies ) @ ( D @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[172:[bind(A,$thf( F )),bind(B,$thf( J )),bind(C,$thf( K )),bind(D,$thf( D )),bind(E,$thf( K @ ( J @ implies ) @ ( K @ implies ) @ ( F @ implies ) ))]]) ).
thf(189,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ implies ) @ ( D @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[173]) ).
thf(29,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ implies ) )
!= ( a @ ( b @ not @ implies ) ) )
| ( ( B @ not )
!= b )
| ( ( A @ not )
!= ( a @ not ) ) ),
inference(simp,[status(thm)],[28]) ).
thf(161,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ implies ) )
!= ( a @ ( b @ not @ implies ) ) )
| ( ( B @ not )
!= b )
| ( A != a ) ),
inference(simp,[status(thm)],[29]) ).
thf(164,plain,
! [A: $i] :
( ( ( a @ ( A @ implies ) )
!= ( a @ ( b @ not @ implies ) ) )
| ( ( A @ not )
!= b ) ),
inference(simp,[status(thm)],[161]) ).
thf(34,plain,
! [B: $i,A: $i] :
( ( ( a @ ( b @ not @ implies ) )
!= ( B @ not @ ( A @ not @ implies ) ) )
| ( ( A @ ( B @ implies ) )
!= ( b @ ( a @ not @ implies ) ) )
| ( ( B @ not )
!= b )
| ( ( A @ not )
!= ( a @ not ) ) ),
inference(simp,[status(thm)],[33]) ).
thf(249,plain,
! [B: $i,A: $i] :
( ( ( B @ not @ ( A @ not @ implies ) )
!= ( b @ ( a @ not @ implies ) ) )
| ( ( a @ ( b @ not @ implies ) )
!= ( A @ ( B @ implies ) ) )
| ( ( A @ ( B @ implies ) )
!= ( b @ ( a @ not @ implies ) ) )
| ( ( B @ not )
!= b )
| ( ( A @ not )
!= ( a @ not ) ) ),
inference(eqfactor_ordered,[status(thm)],[34]) ).
thf(265,plain,
! [B: $i,A: $i] :
( ( ( B @ not )
!= b )
| ( ( A @ not )
!= ( a @ not ) )
| ( a != A )
| ( ( b @ not )
!= B )
| ( A != b )
| ( B
!= ( a @ not ) )
| ( ( B @ not )
!= b )
| ( A != a ) ),
inference(simp,[status(thm)],[249]) ).
thf(290,plain,
( ( ( a @ not @ not )
!= b )
| ( ( b @ not )
!= ( a @ not ) )
| ( b != a )
| ( ( a @ not @ not )
!= b ) ),
inference(simp,[status(thm)],[265]) ).
thf(319,plain,
( ( ( b @ not )
!= ( a @ not ) )
| ( b != a )
| ( ( a @ not @ not )
!= b ) ),
inference(simp,[status(thm)],[290]) ).
thf(320,plain,
( ( b != a )
| ( b != a )
| ( ( a @ not @ not )
!= b ) ),
inference(simp,[status(thm)],[319]) ).
thf(321,plain,
( ( b != a )
| ( ( a @ not @ not )
!= b ) ),
inference(simp,[status(thm)],[320]) ).
thf(150,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)],[81,137]) ).
thf(151,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[150]) ).
thf(160,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
!= a )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[151]) ).
thf(152,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11,137]) ).
thf(153,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( a @ is_a_theorem ) ),
inference(simp,[status(thm)],[152]) ).
thf(156,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ implies ) @ ( A @ implies ) )
!= a ),
inference(simp,[status(thm)],[153]) ).
thf(4,axiom,
! [C: $i,B: $i,A: $i] : ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mv_2) ).
thf(12,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)],[4]) ).
thf(25,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ ( b @ ( a @ not @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12,8]) ).
thf(26,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( a @ ( b @ not @ implies ) @ ( b @ ( a @ not @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[25]) ).
thf(27,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) )
!= ( a @ ( b @ not @ implies ) @ ( b @ ( a @ not @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[26]) ).
thf(85,plain,
( ( ( b @ not @ not )
!= b )
| ( ( a @ not )
!= ( a @ not ) ) ),
inference(simp,[status(thm)],[56]) ).
thf(86,plain,
( ( b @ not @ not )
!= b ),
inference(simp,[status(thm)],[85]) ).
thf(167,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ implies ) )
!= a )
| ( A
!= ( b @ not ) ) ),
inference(simp,[status(thm)],[145]) ).
thf(168,plain,
! [A: $i] :
( ( b @ not @ ( A @ implies ) )
!= a ),
inference(simp,[status(thm)],[167]) ).
thf(40,plain,
! [B: $i,A: $i] :
( ( ( B @ not )
!= a )
| ( ( b @ not )
!= ( A @ not ) )
| ( A != b )
| ( B
!= ( a @ not ) )
| ( ( B @ not )
!= b )
| ( ( A @ not )
!= ( a @ not ) ) ),
inference(simp,[status(thm)],[33]) ).
thf(51,plain,
( ( ( a @ not @ not )
!= a )
| ( ( a @ not @ not )
!= b )
| ( ( b @ not )
!= ( a @ not ) ) ),
inference(simp,[status(thm)],[40]) ).
thf(663,plain,
$false,
inference(e,[status(thm)],[115,24,13,145,50,11,186,8,126,10,56,14,184,125,157,189,20,29,164,321,28,160,137,156,9,34,17,22,27,12,86,81,7,168,51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL113-1 : TPTP v9.3.1. Released v1.0.0.
% 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
% 0.15/5.42 % Computer : n008.cluster.edu
% 0.15/5.42 % Model : x86_64 x86_64
% 0.15/5.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/5.42 % Memory : 8046.5625MB
% 0.15/5.42 % OS : Linux 6.8.0-71-generic
% 0.15/5.42 % CPULimit : 300
% 0.15/5.42 % WCLimit : 300
% 0.15/5.42 % DateTime : Fri Sep 25 21:53:15 UTC 2026
% 0.15/5.42 % CPUTime :
% 0.15/5.42 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
% 0.19/6.00 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.26/6.19 % [INFO] Parsing done (180ms).
% 1.39/6.20 % [INFO] Running in sequential loop mode.
% 1.99/6.61 % [INFO] eprover registered as external prover.
% 1.99/6.62 % [INFO] Scanning for conjecture ...
% 2.17/6.71 % [INFO] Found a conjecture (or negated_conjecture) and 5 axioms. Running axiom selection ...
% 2.17/6.74 % [INFO] Axiom selection finished. Selected 5 axioms (removed 0 axioms).
% 2.17/6.76 % [INFO] Problem is propositional (TPTP CNF).
% 2.17/6.76 % [INFO] Type checking passed.
% 2.17/6.76 % [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 ...
% 8.62/8.46 % External prover 'e' found a proof!
% 8.62/8.46 % [INFO] Killing All external provers ...
% 8.62/8.47 % Time passed: 2906ms (effective reasoning time: 2260ms)
% 8.62/8.47 % Axioms used in derivation (5): mv_5, mv_1, condensed_detachment, mv_2, mv_3
% 8.62/8.47 % No. of inferences in proof: 90
% 8.62/8.47 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2906 ms resp. 2260 ms w/o parsing
% 9.47/8.54 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 9.47/8.54 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------