%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL249-3 : 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 : 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 07:51:21 AM UTC 2026
% Result : Unsatisfiable 16.98s 5.73s
% Output : Refutation 14.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 10
% Syntax : Number of formulae : 100 ( 65 unt; 0 typ; 0 def)
% Number of atoms : 181 ( 67 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 1013 ( 84 ~; 47 |; 0 &; 882 @)
% ( 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 : 12 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 183 ( 0 ^; 183 !; 0 ?; 183 :)
% Comments :
%------------------------------------------------------------------------------
thf(theorem_decl,type,
theorem: $i > $o ).
thf(implies_decl,type,
implies: $i > $i > $i ).
thf(p_decl,type,
p: $i ).
thf(r_decl,type,
r: $i ).
thf(and_decl,type,
and: $i > $i > $i ).
thf(q_decl,type,
q: $i ).
thf(axiom_decl,type,
axiom: $i > $o ).
thf(or_decl,type,
or: $i > $i > $i ).
thf(not_decl,type,
not: $i > $i ).
thf(3,axiom,
! [B: $i,A: $i] : ( A @ ( B @ or ) @ ( A @ implies ) @ axiom ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1_3) ).
thf(14,plain,
! [B: $i,A: $i] : ( A @ ( B @ or ) @ ( A @ implies ) @ axiom ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(7,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) )
= ( B @ ( A @ not @ or ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',implies_definition) ).
thf(18,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) )
= ( B @ ( A @ not @ or ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(19,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ not @ or ) )
= ( B @ ( A @ implies ) ) ),
inference(lifteq,[status(thm)],[18]) ).
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(15,plain,
! [B: $i,A: $i] : ( A @ ( B @ or ) @ ( B @ ( A @ or ) @ implies ) @ axiom ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(70,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)],[19,15]) ).
thf(71,plain,
! [B: $i,A: $i] : ( A @ ( B @ implies ) @ ( B @ not @ ( A @ or ) @ implies ) @ axiom ),
inference(pattern_uni,[status(thm)],[70:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( E @ not ))]]) ).
thf(74,plain,
! [B: $i,A: $i] : ( A @ ( B @ implies ) @ ( B @ not @ ( A @ or ) @ implies ) @ axiom ),
inference(simp,[status(thm)],[71]) ).
thf(2,axiom,
! [A: $i] : ( A @ ( A @ ( A @ or ) @ implies ) @ axiom ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1_2) ).
thf(13,plain,
! [A: $i] : ( A @ ( A @ ( A @ or ) @ implies ) @ axiom ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(8,axiom,
! [A: $i] :
( ~ ( A @ axiom )
| ( A @ theorem ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_1) ).
thf(20,plain,
! [A: $i] :
( ~ ( A @ axiom )
| ( A @ theorem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(21,plain,
! [A: $i] :
( ~ ( A @ axiom )
| ( A @ theorem ) ),
inference(cnf,[status(esa)],[20]) ).
thf(38,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ or ) @ implies ) @ axiom )
!= ( B @ axiom ) )
| ~ $true
| ( B @ theorem ) ),
inference(paramod_ordered,[status(thm)],[13,21]) ).
thf(39,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ or ) @ implies ) @ axiom )
!= ( B @ axiom ) )
| ( B @ theorem ) ),
inference(simp,[status(thm)],[38]) ).
thf(40,plain,
! [A: $i] : ( A @ ( A @ ( A @ or ) @ implies ) @ theorem ),
inference(pattern_uni,[status(thm)],[39:[bind(A,$thf( D )),bind(B,$thf( D @ ( D @ ( D @ or ) @ implies ) ))]]) ).
thf(45,plain,
! [A: $i] : ( A @ ( A @ ( A @ or ) @ implies ) @ theorem ),
inference(simp,[status(thm)],[40]) ).
thf(1,negated_conjecture,
~ ( r @ ( q @ ( p @ and ) @ implies ) @ ( r @ ( p @ implies ) @ implies ) @ theorem ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
thf(11,plain,
~ ( r @ ( q @ ( p @ and ) @ implies ) @ ( r @ ( p @ implies ) @ implies ) @ theorem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(12,plain,
~ ( r @ ( q @ ( p @ and ) @ implies ) @ ( r @ ( p @ implies ) @ implies ) @ theorem ),
inference(polarity_switch,[status(thm)],[11]) ).
thf(75,plain,
! [A: $i] :
( ( ( A @ ( A @ ( A @ or ) @ implies ) @ theorem )
!= ( r @ ( q @ ( p @ and ) @ implies ) @ ( r @ ( p @ implies ) @ implies ) @ theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[45,12]) ).
thf(76,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ or ) @ implies ) @ theorem )
!= ( r @ ( q @ ( p @ and ) @ implies ) @ ( r @ ( p @ implies ) @ implies ) @ theorem ) ),
inference(simp,[status(thm)],[75]) ).
thf(88,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ or ) @ implies ) )
!= ( r @ ( q @ ( p @ and ) @ implies ) @ ( r @ ( p @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[76]) ).
thf(10,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ and ) )
= ( B @ not @ ( A @ not @ or ) @ not ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_defn) ).
thf(24,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ and ) )
= ( B @ not @ ( A @ not @ or ) @ not ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(25,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ and ) )
= ( B @ not @ ( A @ not @ or ) @ not ) ),
inference(lifteq,[status(thm)],[24]) ).
thf(176,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ and ) )
= ( B @ not @ ( A @ implies ) @ not ) ),
inference(rewrite,[status(thm)],[25,19]) ).
thf(208,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ or ) @ implies ) )
!= ( r @ ( q @ not @ ( p @ implies ) @ not @ implies ) @ ( r @ ( p @ implies ) @ implies ) ) ),
inference(rewrite,[status(thm)],[88,176]) ).
thf(209,plain,
! [A: $i] :
( ( A
!= ( r @ ( q @ not @ ( p @ implies ) @ not @ implies ) ) )
| ( ( A @ ( A @ or ) )
!= ( r @ ( p @ implies ) ) ) ),
inference(simp,[status(thm)],[208]) ).
thf(212,plain,
( ( r @ ( q @ not @ ( p @ implies ) @ not @ implies ) @ ( r @ ( q @ not @ ( p @ implies ) @ not @ implies ) @ or ) )
!= ( r @ ( p @ implies ) ) ),
inference(simp,[status(thm)],[209]) ).
thf(227,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( r @ ( q @ not @ ( p @ implies ) @ not @ implies ) @ ( r @ ( q @ not @ ( p @ implies ) @ not @ implies ) @ or ) ) )
| ( ( B @ ( A @ implies ) )
!= ( r @ ( p @ implies ) ) ) ),
inference(paramod_ordered,[status(thm)],[19,212]) ).
thf(230,plain,
! [B: $i,A: $i] :
( ( B
!= ( r @ ( q @ not @ ( p @ implies ) @ not @ implies ) ) )
| ( ( A @ not )
!= ( r @ ( q @ not @ ( p @ implies ) @ not @ implies ) ) )
| ( B != r )
| ( A != p ) ),
inference(simp,[status(thm)],[227]) ).
thf(233,plain,
( ( ( r @ ( q @ not @ ( p @ implies ) @ not @ implies ) )
!= r )
| ( ( r @ ( q @ not @ ( p @ implies ) @ not @ implies ) )
!= ( p @ not ) ) ),
inference(simp,[status(thm)],[230]) ).
thf(68,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)],[19,15]) ).
thf(69,plain,
! [B: $i,A: $i] : ( B @ not @ ( A @ or ) @ ( A @ ( B @ implies ) @ implies ) @ axiom ),
inference(pattern_uni,[status(thm)],[68:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( E @ not )),bind(D,$thf( B ))]]) ).
thf(73,plain,
! [B: $i,A: $i] : ( B @ not @ ( A @ or ) @ ( A @ ( B @ implies ) @ implies ) @ axiom ),
inference(simp,[status(thm)],[69]) ).
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(22,plain,
! [B: $i,A: $i] :
( ~ ( B @ theorem )
| ~ ( A @ ( B @ implies ) @ theorem )
| ( A @ theorem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(23,plain,
! [B: $i,A: $i] :
( ~ ( B @ theorem )
| ~ ( A @ ( B @ implies ) @ theorem )
| ( A @ theorem ) ),
inference(cnf,[status(esa)],[22]) ).
thf(28,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)],[19,14]) ).
thf(29,plain,
! [B: $i,A: $i] : ( A @ ( B @ implies ) @ ( A @ implies ) @ axiom ),
inference(pattern_uni,[status(thm)],[28:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( E @ not ))]]) ).
thf(31,plain,
! [B: $i,A: $i] : ( A @ ( B @ implies ) @ ( A @ implies ) @ axiom ),
inference(simp,[status(thm)],[29]) ).
thf(41,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( A @ implies ) @ axiom )
!= ( C @ axiom ) )
| ~ $true
| ( C @ theorem ) ),
inference(paramod_ordered,[status(thm)],[31,21]) ).
thf(42,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( A @ implies ) @ axiom )
!= ( C @ axiom ) )
| ( C @ theorem ) ),
inference(simp,[status(thm)],[41]) ).
thf(43,plain,
! [B: $i,A: $i] : ( B @ ( A @ implies ) @ ( B @ implies ) @ theorem ),
inference(pattern_uni,[status(thm)],[42:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( G @ ( F @ implies ) @ ( G @ implies ) ))]]) ).
thf(46,plain,
! [B: $i,A: $i] : ( B @ ( A @ implies ) @ ( B @ implies ) @ theorem ),
inference(simp,[status(thm)],[43]) ).
thf(93,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ implies ) @ theorem )
!= ( r @ ( q @ ( p @ and ) @ implies ) @ ( r @ ( p @ implies ) @ implies ) @ theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[46,12]) ).
thf(94,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ implies ) @ theorem )
!= ( r @ ( q @ ( p @ and ) @ implies ) @ ( r @ ( p @ implies ) @ implies ) @ theorem ) ),
inference(simp,[status(thm)],[93]) ).
thf(104,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ implies ) )
!= ( r @ ( q @ ( p @ and ) @ implies ) @ ( r @ ( p @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[94]) ).
thf(214,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ implies ) )
!= ( r @ ( q @ not @ ( p @ implies ) @ not @ implies ) @ ( r @ ( p @ implies ) @ implies ) ) ),
inference(rewrite,[status(thm)],[104,176]) ).
thf(83,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( C @ ( C @ or ) ) )
| ( C @ ( B @ ( A @ implies ) @ implies ) @ theorem ) ),
inference(paramod_ordered,[status(thm)],[19,45]) ).
thf(84,plain,
! [A: $i] : ( A @ not @ ( A @ not @ ( A @ implies ) @ implies ) @ theorem ),
inference(pattern_uni,[status(thm)],[83:[bind(A,$thf( E )),bind(B,$thf( E @ not )),bind(C,$thf( E @ not ))]]) ).
thf(90,plain,
! [A: $i] : ( A @ not @ ( A @ not @ ( A @ implies ) @ implies ) @ theorem ),
inference(simp,[status(thm)],[84]) ).
thf(65,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)],[15,21]) ).
thf(66,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ or ) @ ( B @ ( A @ or ) @ implies ) @ axiom )
!= ( C @ axiom ) )
| ( C @ theorem ) ),
inference(simp,[status(thm)],[65]) ).
thf(67,plain,
! [B: $i,A: $i] : ( B @ ( A @ or ) @ ( A @ ( B @ or ) @ implies ) @ theorem ),
inference(pattern_uni,[status(thm)],[66:[bind(A,$thf( I )),bind(B,$thf( H )),bind(C,$thf( I @ ( H @ or ) @ ( H @ ( I @ or ) @ implies ) ))]]) ).
thf(72,plain,
! [B: $i,A: $i] : ( B @ ( A @ or ) @ ( A @ ( B @ or ) @ implies ) @ theorem ),
inference(simp,[status(thm)],[67]) ).
thf(168,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( D @ ( C @ or ) ) )
| ( B @ ( A @ implies ) @ ( C @ ( D @ or ) @ implies ) @ theorem ) ),
inference(paramod_ordered,[status(thm)],[19,72]) ).
thf(169,plain,
! [B: $i,A: $i] : ( A @ ( B @ implies ) @ ( B @ not @ ( A @ or ) @ implies ) @ theorem ),
inference(pattern_uni,[status(thm)],[168:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( E @ not )),bind(D,$thf( B ))]]) ).
thf(174,plain,
! [B: $i,A: $i] : ( A @ ( B @ implies ) @ ( B @ not @ ( A @ or ) @ implies ) @ theorem ),
inference(simp,[status(thm)],[169]) ).
thf(35,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ or ) @ ( A @ implies ) @ axiom )
!= ( C @ axiom ) )
| ~ $true
| ( C @ theorem ) ),
inference(paramod_ordered,[status(thm)],[14,21]) ).
thf(36,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ or ) @ ( A @ implies ) @ axiom )
!= ( C @ axiom ) )
| ( C @ theorem ) ),
inference(simp,[status(thm)],[35]) ).
thf(37,plain,
! [B: $i,A: $i] : ( B @ ( A @ or ) @ ( B @ implies ) @ theorem ),
inference(pattern_uni,[status(thm)],[36:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( G @ ( F @ or ) @ ( G @ implies ) ))]]) ).
thf(44,plain,
! [B: $i,A: $i] : ( B @ ( A @ or ) @ ( B @ implies ) @ theorem ),
inference(simp,[status(thm)],[37]) ).
thf(50,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ ( B @ implies ) @ theorem )
!= ( r @ ( q @ ( p @ and ) @ implies ) @ ( r @ ( p @ implies ) @ implies ) @ theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[44,12]) ).
thf(51,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ or ) @ ( B @ implies ) @ theorem )
!= ( r @ ( q @ ( p @ and ) @ implies ) @ ( r @ ( p @ implies ) @ implies ) @ theorem ) ),
inference(simp,[status(thm)],[50]) ).
thf(60,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ or ) @ ( B @ implies ) )
!= ( r @ ( q @ ( p @ and ) @ implies ) @ ( r @ ( p @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[51]) ).
thf(113,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ or ) )
!= ( r @ ( q @ ( p @ and ) @ implies ) ) )
| ( B
!= ( r @ ( p @ implies ) ) ) ),
inference(simp,[status(thm)],[60]) ).
thf(116,plain,
! [A: $i] :
( ( r @ ( p @ implies ) @ ( A @ or ) )
!= ( r @ ( q @ ( p @ and ) @ implies ) ) ),
inference(simp,[status(thm)],[113]) ).
thf(118,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( r @ ( p @ implies ) @ ( C @ or ) ) )
| ( ( B @ ( A @ implies ) )
!= ( r @ ( q @ ( p @ and ) @ implies ) ) ) ),
inference(paramod_ordered,[status(thm)],[19,116]) ).
thf(119,plain,
! [A: $i] :
( ( r @ ( p @ implies ) @ ( A @ implies ) )
!= ( r @ ( q @ ( p @ and ) @ implies ) ) ),
inference(pattern_uni,[status(thm)],[118:[bind(A,$thf( D )),bind(B,$thf( r @ ( p @ implies ) )),bind(C,$thf( D @ not ))]]) ).
thf(120,plain,
! [A: $i] :
( ( r @ ( p @ implies ) @ ( A @ implies ) )
!= ( r @ ( q @ ( p @ and ) @ implies ) ) ),
inference(simp,[status(thm)],[119]) ).
thf(136,plain,
! [A: $i] :
( ( ( r @ ( p @ implies ) )
!= r )
| ( A
!= ( q @ ( p @ and ) ) ) ),
inference(simp,[status(thm)],[120]) ).
thf(137,plain,
( ( r @ ( p @ implies ) )
!= r ),
inference(simp,[status(thm)],[136]) ).
thf(166,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( C @ ( D @ or ) ) )
| ( D @ ( C @ or ) @ ( B @ ( A @ implies ) @ implies ) @ theorem ) ),
inference(paramod_ordered,[status(thm)],[19,72]) ).
thf(167,plain,
! [B: $i,A: $i] : ( B @ not @ ( A @ or ) @ ( A @ ( B @ implies ) @ implies ) @ theorem ),
inference(pattern_uni,[status(thm)],[166:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( E @ not ))]]) ).
thf(173,plain,
! [B: $i,A: $i] : ( B @ not @ ( A @ or ) @ ( A @ ( B @ implies ) @ implies ) @ theorem ),
inference(simp,[status(thm)],[167]) ).
thf(32,plain,
! [B: $i,A: $i] :
( ~ $true
| ( ( A @ ( B @ implies ) @ theorem )
!= ( B @ theorem ) )
| ~ ( B @ theorem )
| ( A @ theorem ) ),
inference(eqfactor_ordered,[status(thm)],[23]) ).
thf(34,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ implies ) )
!= B )
| ~ ( B @ theorem )
| ( A @ theorem ) ),
inference(simp,[status(thm)],[32]) ).
thf(114,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( D @ ( C @ or ) ) )
| ( ( B @ ( A @ implies ) @ ( D @ implies ) )
!= ( r @ ( q @ ( p @ and ) @ implies ) @ ( r @ ( p @ implies ) @ implies ) ) ) ),
inference(paramod_ordered,[status(thm)],[19,60]) ).
thf(115,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ implies ) @ ( A @ implies ) )
!= ( r @ ( q @ ( p @ and ) @ implies ) @ ( r @ ( p @ implies ) @ implies ) ) ),
inference(pattern_uni,[status(thm)],[114:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( E @ not )),bind(D,$thf( B ))]]) ).
thf(117,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ implies ) @ ( A @ implies ) )
!= ( r @ ( q @ ( p @ and ) @ implies ) @ ( r @ ( p @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[115]) ).
thf(279,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ implies ) @ ( A @ implies ) )
!= ( r @ ( q @ not @ ( p @ implies ) @ not @ implies ) @ ( r @ ( p @ implies ) @ implies ) ) ),
inference(rewrite,[status(thm)],[117,176]) ).
thf(180,plain,
~ ( r @ ( q @ not @ ( p @ implies ) @ not @ implies ) @ ( r @ ( p @ implies ) @ implies ) @ theorem ),
inference(rewrite,[status(thm)],[12,176]) ).
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(17,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(121,plain,
! [A: $i] :
( ( ( A @ not @ ( A @ not @ ( A @ implies ) @ implies ) @ theorem )
!= ( r @ ( q @ ( p @ and ) @ implies ) @ ( r @ ( p @ implies ) @ implies ) @ theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[90,12]) ).
thf(122,plain,
! [A: $i] :
( ( A @ not @ ( A @ not @ ( A @ implies ) @ implies ) @ theorem )
!= ( r @ ( q @ ( p @ and ) @ implies ) @ ( r @ ( p @ implies ) @ implies ) @ theorem ) ),
inference(simp,[status(thm)],[121]) ).
thf(132,plain,
! [A: $i] :
( ( A @ not @ ( A @ not @ ( A @ implies ) @ implies ) )
!= ( r @ ( q @ ( p @ and ) @ implies ) @ ( r @ ( p @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[122]) ).
thf(282,plain,
! [A: $i] :
( ( A @ not @ ( A @ not @ ( A @ implies ) @ implies ) )
!= ( r @ ( q @ not @ ( p @ implies ) @ not @ implies ) @ ( r @ ( p @ implies ) @ implies ) ) ),
inference(rewrite,[status(thm)],[132,176]) ).
thf(177,plain,
! [A: $i] :
( ( r @ ( p @ implies ) @ ( A @ implies ) )
!= ( r @ ( q @ not @ ( p @ implies ) @ not @ implies ) ) ),
inference(rewrite,[status(thm)],[120,176]) ).
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(16,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(26,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)],[19,13]) ).
thf(27,plain,
! [A: $i] : ( A @ not @ ( A @ not @ ( A @ implies ) @ implies ) @ axiom ),
inference(pattern_uni,[status(thm)],[26:[bind(A,$thf( E )),bind(B,$thf( E @ not )),bind(C,$thf( E @ not ))]]) ).
thf(30,plain,
! [A: $i] : ( A @ not @ ( A @ not @ ( A @ implies ) @ implies ) @ axiom ),
inference(simp,[status(thm)],[27]) ).
thf(178,plain,
! [A: $i] :
( ( r @ ( p @ implies ) @ ( A @ or ) )
!= ( r @ ( q @ not @ ( p @ implies ) @ not @ implies ) ) ),
inference(rewrite,[status(thm)],[116,176]) ).
thf(659,plain,
$false,
inference(e,[status(thm)],[14,74,233,212,73,208,23,214,90,174,24,20,46,21,137,173,13,34,45,279,180,17,176,22,44,18,282,177,16,31,11,72,30,19,15,178]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL249-3 : 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
% 0.22/0.48 % Computer : n011.cluster.edu
% 0.22/0.48 % Model : x86_64 x86_64
% 0.22/0.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.22/0.48 % Memory : 8046.5625MB
% 0.22/0.48 % OS : Linux 6.8.0-71-generic
% 0.22/0.48 % CPULimit : 300
% 0.22/0.48 % WCLimit : 300
% 0.22/0.48 % DateTime : Fri Sep 25 22:07:14 UTC 2026
% 0.22/0.48 % CPUTime :
% 0.22/0.48 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
% 1.45/1.30 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.79/1.58 % [INFO] Parsing done (274ms).
% 2.06/1.60 % [INFO] Running in sequential loop mode.
% 3.15/2.21 % [INFO] eprover registered as external prover.
% 3.15/2.22 % [INFO] Scanning for conjecture ...
% 3.35/2.34 % [INFO] Found a conjecture (or negated_conjecture) and 9 axioms. Running axiom selection ...
% 3.35/2.39 % [INFO] Axiom selection finished. Selected 9 axioms (removed 0 axioms).
% 3.55/2.41 % [INFO] Problem is propositional (TPTP CNF).
% 3.55/2.42 % [INFO] Type checking passed.
% 3.55/2.43 % [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 ...
% 16.98/5.72 % External prover 'e' found a proof!
% 16.98/5.73 % [INFO] Killing All external provers ...
% 16.98/5.73 % Time passed: 5043ms (effective reasoning time: 4121ms)
% 16.98/5.73 % Axioms used in derivation (9): axiom_1_5, and_defn, axiom_1_4, rule_1, axiom_1_3, implies_definition, axiom_1_2, rule_2, axiom_1_6
% 16.98/5.73 % No. of inferences in proof: 100
% 16.98/5.73 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 5043 ms resp. 4121 ms w/o parsing
% 14.88/5.84 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 14.88/5.84 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------