%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL194-3 : TPTP v9.3.1. Released v2.3.0.
% 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 : n018.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 07:51:07 AM UTC 2026
% Result : Unsatisfiable 21.58s 6.41s
% Output : Refutation 18.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 9
% Syntax : Number of formulae : 104 ( 48 unt; 0 typ; 0 def)
% Number of atoms : 235 ( 86 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 1123 ( 121 ~; 87 |; 0 &; 915 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 218 ( 0 ^; 218 !; 0 ?; 218 :)
% Comments :
%------------------------------------------------------------------------------
thf(theorem_decl,type,
theorem: $i > $o ).
thf(implies_decl,type,
implies: $i > $i > $i ).
thf(q_decl,type,
q: $i ).
thf(r_decl,type,
r: $i ).
thf(or_decl,type,
or: $i > $i > $i ).
thf(p_decl,type,
p: $i ).
thf(axiom_decl,type,
axiom: $i > $o ).
thf(not_decl,type,
not: $i > $i ).
thf(1,negated_conjecture,
~ ( r @ ( p @ or ) @ ( p @ ( q @ or ) @ implies ) @ ( r @ ( q @ implies ) @ implies ) @ theorem ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
thf(10,plain,
~ ( r @ ( p @ or ) @ ( p @ ( q @ or ) @ implies ) @ ( r @ ( q @ implies ) @ implies ) @ theorem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(7,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) )
= ( B @ ( A @ not @ or ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',implies_definition) ).
thf(17,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) )
= ( B @ ( A @ not @ or ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(18,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ not @ or ) )
= ( B @ ( A @ implies ) ) ),
inference(lifteq,[status(thm)],[17]) ).
thf(11,plain,
~ ( r @ ( p @ or ) @ ( p @ ( q @ or ) @ implies ) @ ( r @ ( q @ implies ) @ implies ) @ theorem ),
inference(polarity_switch,[status(thm)],[10]) ).
thf(23,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( r @ ( p @ or ) ) )
| ~ ( B @ ( A @ implies ) @ ( p @ ( q @ or ) @ implies ) @ ( r @ ( q @ implies ) @ implies ) @ theorem ) ),
inference(paramod_ordered,[status(thm)],[18,11]) ).
thf(29,plain,
! [B: $i,A: $i] :
( ( B != r )
| ( ( A @ not )
!= p )
| ~ ( B @ ( A @ implies ) @ ( p @ ( q @ or ) @ implies ) @ ( r @ ( q @ implies ) @ implies ) @ theorem ) ),
inference(simp,[status(thm)],[23]) ).
thf(33,plain,
! [A: $i] :
( ( ( A @ not )
!= p )
| ~ ( r @ ( A @ implies ) @ ( p @ ( q @ or ) @ implies ) @ ( r @ ( q @ implies ) @ implies ) @ theorem ) ),
inference(simp,[status(thm)],[29]) ).
thf(35,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( p @ ( q @ or ) ) )
| ( ( C @ not )
!= p )
| ~ ( r @ ( C @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ ( r @ ( q @ implies ) @ implies ) @ theorem ) ),
inference(paramod_ordered,[status(thm)],[18,33]) ).
thf(36,plain,
! [C: $i,B: $i,A: $i] :
( ( B != p )
| ( ( A @ not )
!= q )
| ( ( C @ not )
!= p )
| ~ ( r @ ( C @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ ( r @ ( q @ implies ) @ implies ) @ theorem ) ),
inference(simp,[status(thm)],[35]) ).
thf(37,plain,
! [B: $i,A: $i] :
( ( ( A @ not )
!= q )
| ( ( B @ not )
!= p )
| ~ ( r @ ( B @ implies ) @ ( p @ ( A @ implies ) @ implies ) @ ( r @ ( q @ implies ) @ implies ) @ theorem ) ),
inference(simp,[status(thm)],[36]) ).
thf(4,axiom,
! [B: $i,A: $i] : ( A @ ( B @ or ) @ ( B @ ( A @ or ) @ implies ) @ axiom ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1_4) ).
thf(14,plain,
! [B: $i,A: $i] : ( A @ ( B @ or ) @ ( B @ ( A @ or ) @ implies ) @ axiom ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(3,axiom,
! [B: $i,A: $i] : ( A @ ( B @ or ) @ ( A @ implies ) @ axiom ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1_3) ).
thf(13,plain,
! [B: $i,A: $i] : ( A @ ( B @ or ) @ ( A @ implies ) @ axiom ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(27,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( C @ ( D @ or ) ) )
| ( B @ ( A @ implies ) @ ( C @ implies ) @ axiom ) ),
inference(paramod_ordered,[status(thm)],[18,13]) ).
thf(28,plain,
! [B: $i,A: $i] : ( A @ ( B @ implies ) @ ( A @ implies ) @ axiom ),
inference(pattern_uni,[status(thm)],[27:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( E @ not ))]]) ).
thf(32,plain,
! [B: $i,A: $i] : ( A @ ( B @ implies ) @ ( A @ implies ) @ axiom ),
inference(simp,[status(thm)],[28]) ).
thf(8,axiom,
! [A: $i] :
( ~ ( A @ axiom )
| ( A @ theorem ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_1) ).
thf(19,plain,
! [A: $i] :
( ~ ( A @ axiom )
| ( A @ theorem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(20,plain,
! [A: $i] :
( ~ ( A @ axiom )
| ( A @ theorem ) ),
inference(cnf,[status(esa)],[19]) ).
thf(72,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( A @ implies ) @ axiom )
!= ( C @ axiom ) )
| ~ $true
| ( C @ theorem ) ),
inference(paramod_ordered,[status(thm)],[32,20]) ).
thf(73,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( A @ implies ) @ axiom )
!= ( C @ axiom ) )
| ( C @ theorem ) ),
inference(simp,[status(thm)],[72]) ).
thf(74,plain,
! [B: $i,A: $i] : ( B @ ( A @ implies ) @ ( B @ implies ) @ theorem ),
inference(pattern_uni,[status(thm)],[73:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( G @ ( F @ implies ) @ ( G @ implies ) ))]]) ).
thf(85,plain,
! [B: $i,A: $i] : ( B @ ( A @ implies ) @ ( B @ implies ) @ theorem ),
inference(simp,[status(thm)],[74]) ).
thf(101,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ implies ) @ theorem )
!= ( r @ ( p @ or ) @ ( p @ ( q @ or ) @ implies ) @ ( r @ ( q @ implies ) @ implies ) @ theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[85,11]) ).
thf(102,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ implies ) @ theorem )
!= ( r @ ( p @ or ) @ ( p @ ( q @ or ) @ implies ) @ ( r @ ( q @ implies ) @ implies ) @ theorem ) ),
inference(simp,[status(thm)],[101]) ).
thf(111,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ implies ) )
!= ( r @ ( p @ or ) @ ( p @ ( q @ or ) @ implies ) @ ( r @ ( q @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[102]) ).
thf(222,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
!= ( r @ ( p @ or ) @ ( p @ ( q @ or ) @ implies ) ) )
| ( B
!= ( r @ ( q @ implies ) ) ) ),
inference(simp,[status(thm)],[111]) ).
thf(237,plain,
! [A: $i] :
( ( r @ ( q @ implies ) @ ( A @ implies ) )
!= ( r @ ( p @ or ) @ ( p @ ( q @ or ) @ implies ) ) ),
inference(simp,[status(thm)],[222]) ).
thf(239,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( r @ ( p @ or ) ) )
| ( ( B @ ( A @ implies ) @ ( p @ ( q @ or ) @ implies ) )
!= ( r @ ( q @ implies ) @ ( C @ implies ) ) ) ),
inference(paramod_ordered,[status(thm)],[18,237]) ).
thf(241,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( r @ ( p @ or ) ) )
| ( ( B @ ( A @ implies ) )
!= ( r @ ( q @ implies ) ) )
| ( ( p @ ( q @ or ) )
!= C ) ),
inference(simp,[status(thm)],[239]) ).
thf(247,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( r @ ( p @ or ) ) )
| ( ( B @ ( A @ implies ) )
!= ( r @ ( q @ implies ) ) ) ),
inference(simp,[status(thm)],[241]) ).
thf(476,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
!= ( r @ ( p @ or ) ) )
| ( ( B @ ( A @ implies ) )
!= ( r @ ( q @ implies ) ) ) ),
inference(rewrite,[status(thm)],[247,18]) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ~ ( B @ theorem )
| ~ ( A @ ( B @ implies ) @ theorem )
| ( A @ theorem ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_2) ).
thf(21,plain,
! [B: $i,A: $i] :
( ~ ( B @ theorem )
| ~ ( A @ ( B @ implies ) @ theorem )
| ( A @ theorem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(22,plain,
! [B: $i,A: $i] :
( ~ ( B @ theorem )
| ~ ( A @ ( B @ implies ) @ theorem )
| ( A @ theorem ) ),
inference(cnf,[status(esa)],[21]) ).
thf(41,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( C @ ( D @ or ) ) )
| ( B @ ( A @ implies ) @ ( D @ ( C @ or ) @ implies ) @ axiom ) ),
inference(paramod_ordered,[status(thm)],[18,14]) ).
thf(42,plain,
! [B: $i,A: $i] : ( A @ ( B @ implies ) @ ( B @ not @ ( A @ or ) @ implies ) @ axiom ),
inference(pattern_uni,[status(thm)],[41:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( E @ not ))]]) ).
thf(45,plain,
! [B: $i,A: $i] : ( A @ ( B @ implies ) @ ( B @ not @ ( A @ or ) @ implies ) @ axiom ),
inference(simp,[status(thm)],[42]) ).
thf(47,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( D @ not @ ( C @ or ) ) )
| ( C @ ( D @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ axiom ) ),
inference(paramod_ordered,[status(thm)],[18,45]) ).
thf(48,plain,
! [B: $i,A: $i] : ( A @ not @ ( B @ implies ) @ ( B @ not @ ( A @ implies ) @ implies ) @ axiom ),
inference(pattern_uni,[status(thm)],[47:[bind(A,$thf( E )),bind(B,$thf( F @ not )),bind(C,$thf( E @ not )),bind(D,$thf( F ))]]) ).
thf(49,plain,
! [B: $i,A: $i] : ( A @ not @ ( B @ implies ) @ ( B @ not @ ( A @ implies ) @ implies ) @ axiom ),
inference(simp,[status(thm)],[48]) ).
thf(78,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ not @ ( B @ implies ) @ ( B @ not @ ( A @ implies ) @ implies ) @ axiom )
!= ( C @ axiom ) )
| ~ $true
| ( C @ theorem ) ),
inference(paramod_ordered,[status(thm)],[49,20]) ).
thf(79,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ not @ ( B @ implies ) @ ( B @ not @ ( A @ implies ) @ implies ) @ axiom )
!= ( C @ axiom ) )
| ( C @ theorem ) ),
inference(simp,[status(thm)],[78]) ).
thf(80,plain,
! [B: $i,A: $i] : ( B @ not @ ( A @ implies ) @ ( A @ not @ ( B @ implies ) @ implies ) @ theorem ),
inference(pattern_uni,[status(thm)],[79:[bind(A,$thf( K )),bind(B,$thf( I )),bind(C,$thf( K @ not @ ( I @ implies ) @ ( I @ not @ ( K @ implies ) @ implies ) ))]]) ).
thf(81,plain,
! [B: $i,A: $i] : ( B @ not @ ( A @ implies ) @ ( A @ not @ ( B @ implies ) @ implies ) @ theorem ),
inference(simp,[status(thm)],[80]) ).
thf(2,axiom,
! [A: $i] : ( A @ ( A @ ( A @ or ) @ implies ) @ axiom ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1_2) ).
thf(12,plain,
! [A: $i] : ( A @ ( A @ ( A @ or ) @ implies ) @ axiom ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(75,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ or ) @ implies ) @ axiom )
!= ( B @ axiom ) )
| ~ $true
| ( B @ theorem ) ),
inference(paramod_ordered,[status(thm)],[12,20]) ).
thf(76,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ or ) @ implies ) @ axiom )
!= ( B @ axiom ) )
| ( B @ theorem ) ),
inference(simp,[status(thm)],[75]) ).
thf(77,plain,
! [A: $i] : ( A @ ( A @ ( A @ or ) @ implies ) @ theorem ),
inference(pattern_uni,[status(thm)],[76:[bind(A,$thf( D )),bind(B,$thf( D @ ( D @ ( D @ or ) @ implies ) ))]]) ).
thf(87,plain,
! [A: $i] : ( A @ ( A @ ( A @ or ) @ implies ) @ theorem ),
inference(simp,[status(thm)],[77]) ).
thf(25,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( C @ ( C @ or ) ) )
| ( C @ ( B @ ( A @ implies ) @ implies ) @ axiom ) ),
inference(paramod_ordered,[status(thm)],[18,12]) ).
thf(26,plain,
! [A: $i] : ( A @ not @ ( A @ not @ ( A @ implies ) @ implies ) @ axiom ),
inference(pattern_uni,[status(thm)],[25:[bind(A,$thf( E )),bind(B,$thf( E @ not )),bind(C,$thf( E @ not ))]]) ).
thf(31,plain,
! [A: $i] : ( A @ not @ ( A @ not @ ( A @ implies ) @ implies ) @ axiom ),
inference(simp,[status(thm)],[26]) ).
thf(63,plain,
! [B: $i,A: $i] :
( ( ( A @ not @ ( A @ not @ ( A @ implies ) @ implies ) @ axiom )
!= ( B @ axiom ) )
| ~ $true
| ( B @ theorem ) ),
inference(paramod_ordered,[status(thm)],[31,20]) ).
thf(64,plain,
! [B: $i,A: $i] :
( ( ( A @ not @ ( A @ not @ ( A @ implies ) @ implies ) @ axiom )
!= ( B @ axiom ) )
| ( B @ theorem ) ),
inference(simp,[status(thm)],[63]) ).
thf(65,plain,
! [A: $i] : ( A @ not @ ( A @ not @ ( A @ implies ) @ implies ) @ theorem ),
inference(pattern_uni,[status(thm)],[64:[bind(A,$thf( H )),bind(B,$thf( H @ not @ ( H @ not @ ( H @ implies ) @ implies ) ))]]) ).
thf(82,plain,
! [A: $i] : ( A @ not @ ( A @ not @ ( A @ implies ) @ implies ) @ theorem ),
inference(simp,[status(thm)],[65]) ).
thf(92,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ implies ) @ theorem )
!= ( r @ ( C @ implies ) @ ( p @ ( q @ or ) @ implies ) @ ( r @ ( q @ implies ) @ implies ) @ theorem ) )
| ( ( C @ not )
!= p )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[85,33]) ).
thf(93,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ implies ) @ theorem )
!= ( r @ ( C @ implies ) @ ( p @ ( q @ or ) @ implies ) @ ( r @ ( q @ implies ) @ implies ) @ theorem ) )
| ( ( C @ not )
!= p ) ),
inference(simp,[status(thm)],[92]) ).
thf(94,plain,
( ( q @ not )
!= p ),
inference(pattern_uni,[status(thm)],[93:[bind(A,$thf( p @ ( q @ or ) )),bind(B,$thf( r @ ( q @ implies ) )),bind(C,$thf( q ))]]) ).
thf(5,axiom,
! [C: $i,B: $i,A: $i] : ( C @ ( A @ or ) @ ( B @ or ) @ ( C @ ( B @ or ) @ ( A @ or ) @ implies ) @ axiom ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1_5) ).
thf(15,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( A @ or ) @ ( B @ or ) @ ( C @ ( B @ or ) @ ( A @ or ) @ implies ) @ axiom ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(243,plain,
! [C: $i,B: $i,A: $i] :
( ( B != r )
| ( ( A @ not )
!= p )
| ( ( B @ ( A @ implies ) )
!= ( r @ ( q @ implies ) ) )
| ( ( p @ ( q @ or ) )
!= C ) ),
inference(simp,[status(thm)],[239]) ).
thf(249,plain,
! [A: $i] :
( ( ( A @ not )
!= p )
| ( ( r @ ( A @ implies ) )
!= ( r @ ( q @ implies ) ) ) ),
inference(simp,[status(thm)],[243]) ).
thf(60,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ or ) @ ( A @ implies ) @ axiom )
!= ( C @ axiom ) )
| ~ $true
| ( C @ theorem ) ),
inference(paramod_ordered,[status(thm)],[13,20]) ).
thf(61,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ or ) @ ( A @ implies ) @ axiom )
!= ( C @ axiom ) )
| ( C @ theorem ) ),
inference(simp,[status(thm)],[60]) ).
thf(62,plain,
! [B: $i,A: $i] : ( B @ ( A @ or ) @ ( B @ implies ) @ theorem ),
inference(pattern_uni,[status(thm)],[61:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( G @ ( F @ or ) @ ( G @ implies ) ))]]) ).
thf(88,plain,
! [B: $i,A: $i] : ( B @ ( A @ or ) @ ( B @ implies ) @ theorem ),
inference(simp,[status(thm)],[62]) ).
thf(43,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( D @ ( C @ or ) ) )
| ( C @ ( D @ or ) @ ( B @ ( A @ implies ) @ implies ) @ axiom ) ),
inference(paramod_ordered,[status(thm)],[18,14]) ).
thf(44,plain,
! [B: $i,A: $i] : ( B @ not @ ( A @ or ) @ ( A @ ( B @ implies ) @ implies ) @ axiom ),
inference(pattern_uni,[status(thm)],[43:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( E @ not )),bind(D,$thf( B ))]]) ).
thf(46,plain,
! [B: $i,A: $i] : ( B @ not @ ( A @ or ) @ ( A @ ( B @ implies ) @ implies ) @ axiom ),
inference(simp,[status(thm)],[44]) ).
thf(238,plain,
! [A: $i] :
( ( ( r @ ( p @ or ) )
!= ( r @ ( q @ implies ) ) )
| ( A
!= ( p @ ( q @ or ) ) ) ),
inference(simp,[status(thm)],[237]) ).
thf(253,plain,
( ( r @ ( p @ or ) )
!= ( r @ ( q @ implies ) ) ),
inference(simp,[status(thm)],[238]) ).
thf(69,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( B @ not @ ( A @ or ) @ implies ) @ axiom )
!= ( C @ axiom ) )
| ~ $true
| ( C @ theorem ) ),
inference(paramod_ordered,[status(thm)],[45,20]) ).
thf(70,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( B @ not @ ( A @ or ) @ implies ) @ axiom )
!= ( C @ axiom ) )
| ( C @ theorem ) ),
inference(simp,[status(thm)],[69]) ).
thf(71,plain,
! [B: $i,A: $i] : ( B @ ( A @ implies ) @ ( A @ not @ ( B @ or ) @ implies ) @ theorem ),
inference(pattern_uni,[status(thm)],[70:[bind(A,$thf( J )),bind(B,$thf( I )),bind(C,$thf( J @ ( I @ implies ) @ ( I @ not @ ( J @ or ) @ implies ) ))]]) ).
thf(84,plain,
! [B: $i,A: $i] : ( B @ ( A @ implies ) @ ( A @ not @ ( B @ or ) @ implies ) @ theorem ),
inference(simp,[status(thm)],[71]) ).
thf(223,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( r @ ( p @ or ) ) )
| ( ( B @ ( A @ implies ) @ ( p @ ( q @ or ) @ implies ) @ ( r @ ( q @ implies ) @ implies ) )
!= ( D @ ( C @ implies ) @ ( D @ implies ) ) ) ),
inference(paramod_ordered,[status(thm)],[18,111]) ).
thf(227,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B != r )
| ( ( A @ not )
!= p )
| ( ( B @ ( A @ implies ) @ ( p @ ( q @ or ) @ implies ) )
!= ( D @ ( C @ implies ) ) )
| ( ( r @ ( q @ implies ) )
!= D ) ),
inference(simp,[status(thm)],[223]) ).
thf(233,plain,
! [B: $i,A: $i] :
( ( ( A @ not )
!= p )
| ( ( r @ ( A @ implies ) @ ( p @ ( q @ or ) @ implies ) )
!= ( r @ ( q @ implies ) @ ( B @ implies ) ) ) ),
inference(simp,[status(thm)],[227]) ).
thf(24,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( p @ ( q @ or ) ) )
| ~ ( r @ ( p @ or ) @ ( B @ ( A @ implies ) @ implies ) @ ( r @ ( q @ implies ) @ implies ) @ theorem ) ),
inference(paramod_ordered,[status(thm)],[18,11]) ).
thf(30,plain,
! [B: $i,A: $i] :
( ( B != p )
| ( ( A @ not )
!= q )
| ~ ( r @ ( p @ or ) @ ( B @ ( A @ implies ) @ implies ) @ ( r @ ( q @ implies ) @ implies ) @ theorem ) ),
inference(simp,[status(thm)],[24]) ).
thf(34,plain,
! [A: $i] :
( ( ( A @ not )
!= q )
| ~ ( r @ ( p @ or ) @ ( p @ ( A @ implies ) @ implies ) @ ( r @ ( q @ implies ) @ implies ) @ theorem ) ),
inference(simp,[status(thm)],[30]) ).
thf(53,plain,
! [B: $i,A: $i] :
( ~ $true
| ( ( A @ ( B @ implies ) @ theorem )
!= ( B @ theorem ) )
| ~ ( B @ theorem )
| ( A @ theorem ) ),
inference(eqfactor_ordered,[status(thm)],[22]) ).
thf(54,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ theorem )
!= ( B @ theorem ) )
| ~ ( B @ theorem )
| ( A @ theorem ) ),
inference(simp,[status(thm)],[53]) ).
thf(57,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ or ) @ ( B @ ( A @ or ) @ implies ) @ axiom )
!= ( C @ axiom ) )
| ~ $true
| ( C @ theorem ) ),
inference(paramod_ordered,[status(thm)],[14,20]) ).
thf(58,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ or ) @ ( B @ ( A @ or ) @ implies ) @ axiom )
!= ( C @ axiom ) )
| ( C @ theorem ) ),
inference(simp,[status(thm)],[57]) ).
thf(59,plain,
! [B: $i,A: $i] : ( B @ ( A @ or ) @ ( A @ ( B @ or ) @ implies ) @ theorem ),
inference(pattern_uni,[status(thm)],[58:[bind(A,$thf( I )),bind(B,$thf( H )),bind(C,$thf( I @ ( H @ or ) @ ( H @ ( I @ or ) @ implies ) ))]]) ).
thf(86,plain,
! [B: $i,A: $i] : ( B @ ( A @ or ) @ ( A @ ( B @ or ) @ implies ) @ theorem ),
inference(simp,[status(thm)],[59]) ).
thf(6,axiom,
! [C: $i,B: $i,A: $i] : ( B @ ( C @ or ) @ ( A @ ( C @ or ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ axiom ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1_6) ).
thf(16,plain,
! [C: $i,B: $i,A: $i] : ( B @ ( C @ or ) @ ( A @ ( C @ or ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ axiom ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(38,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( r @ ( p @ or ) ) )
| ( ( C @ not )
!= q )
| ~ ( B @ ( A @ implies ) @ ( p @ ( C @ implies ) @ implies ) @ ( r @ ( q @ implies ) @ implies ) @ theorem ) ),
inference(paramod_ordered,[status(thm)],[18,34]) ).
thf(39,plain,
! [C: $i,B: $i,A: $i] :
( ( B != r )
| ( ( A @ not )
!= p )
| ( ( C @ not )
!= q )
| ~ ( B @ ( A @ implies ) @ ( p @ ( C @ implies ) @ implies ) @ ( r @ ( q @ implies ) @ implies ) @ theorem ) ),
inference(simp,[status(thm)],[38]) ).
thf(40,plain,
! [B: $i,A: $i] :
( ( ( A @ not )
!= p )
| ( ( B @ not )
!= q )
| ~ ( r @ ( A @ implies ) @ ( p @ ( B @ implies ) @ implies ) @ ( r @ ( q @ implies ) @ implies ) @ theorem ) ),
inference(simp,[status(thm)],[39]) ).
thf(55,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ implies ) )
!= B )
| ~ ( B @ theorem )
| ( A @ theorem ) ),
inference(simp,[status(thm)],[53]) ).
thf(66,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ not @ ( A @ or ) @ ( A @ ( B @ implies ) @ implies ) @ axiom )
!= ( C @ axiom ) )
| ~ $true
| ( C @ theorem ) ),
inference(paramod_ordered,[status(thm)],[46,20]) ).
thf(67,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ not @ ( A @ or ) @ ( A @ ( B @ implies ) @ implies ) @ axiom )
!= ( C @ axiom ) )
| ( C @ theorem ) ),
inference(simp,[status(thm)],[66]) ).
thf(68,plain,
! [B: $i,A: $i] : ( B @ not @ ( A @ or ) @ ( A @ ( B @ implies ) @ implies ) @ theorem ),
inference(pattern_uni,[status(thm)],[67:[bind(A,$thf( H )),bind(B,$thf( J )),bind(C,$thf( J @ not @ ( H @ or ) @ ( H @ ( J @ implies ) @ implies ) ))]]) ).
thf(83,plain,
! [B: $i,A: $i] : ( B @ not @ ( A @ or ) @ ( A @ ( B @ implies ) @ implies ) @ theorem ),
inference(simp,[status(thm)],[68]) ).
thf(1220,plain,
$false,
inference(e,[status(thm)],[10,37,14,476,13,237,22,81,18,11,87,82,19,94,15,249,88,20,46,253,84,233,85,21,33,45,17,32,34,12,54,49,86,16,31,40,55,111,83]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL194-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.12 % 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
% 0.24/0.49 % Computer : n018.cluster.edu
% 0.24/0.49 % Model : x86_64 x86_64
% 0.24/0.49 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.24/0.49 % Memory : 8046.5625MB
% 0.24/0.49 % OS : Linux 6.8.0-71-generic
% 0.24/0.49 % CPULimit : 300
% 0.24/0.49 % WCLimit : 300
% 0.24/0.49 % DateTime : Fri Sep 25 22:01:35 UTC 2026
% 0.24/0.49 % CPUTime :
% 0.24/0.49 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
% 1.38/1.32 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.70/1.59 % [INFO] Parsing done (269ms).
% 1.91/1.61 % [INFO] Running in sequential loop mode.
% 2.72/2.19 % [INFO] eprover registered as external prover.
% 2.79/2.20 % [INFO] Scanning for conjecture ...
% 2.97/2.33 % [INFO] Found a conjecture (or negated_conjecture) and 8 axioms. Running axiom selection ...
% 2.97/2.37 % [INFO] Axiom selection finished. Selected 8 axioms (removed 0 axioms).
% 2.97/2.39 % [INFO] Problem is propositional (TPTP CNF).
% 3.14/2.40 % [INFO] Type checking passed.
% 3.14/2.41 % [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 ...
% 21.58/6.40 % External prover 'e' found a proof!
% 21.58/6.40 % [INFO] Killing All external provers ...
% 21.58/6.40 % Time passed: 5709ms (effective reasoning time: 4781ms)
% 21.58/6.41 % Axioms used in derivation (8): axiom_1_5, axiom_1_4, rule_1, axiom_1_3, implies_definition, axiom_1_2, rule_2, axiom_1_6
% 21.58/6.41 % No. of inferences in proof: 104
% 21.58/6.41 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 5709 ms resp. 4781 ms w/o parsing
% 18.72/6.53 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 18.72/6.53 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------