%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL213-3 : TPTP v9.3.1. Released v2.3.0.
% 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 : n014.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 07:51:12 AM UTC 2026
% Result : Unsatisfiable 47.66s 11.42s
% Output : Refutation 47.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 9
% Syntax : Number of formulae : 95 ( 55 unt; 0 typ; 0 def)
% Number of atoms : 185 ( 65 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 985 ( 86 ~; 54 |; 0 &; 845 @)
% ( 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 : 10 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 179 ( 0 ^; 179 !; 0 ?; 179 :)
% Comments :
%------------------------------------------------------------------------------
thf(theorem_decl,type,
theorem: $i > $o ).
thf(implies_decl,type,
implies: $i > $i > $i ).
thf(p_decl,type,
p: $i ).
thf(q_decl,type,
q: $i ).
thf(not_decl,type,
not: $i > $i ).
thf(axiom_decl,type,
axiom: $i > $o ).
thf(or_decl,type,
or: $i > $i > $i ).
thf(1,negated_conjecture,
~ ( q @ ( q @ ( p @ not @ implies ) @ implies ) @ ( q @ ( p @ implies ) @ implies ) @ theorem ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
thf(10,plain,
~ ( q @ ( q @ ( p @ not @ implies ) @ implies ) @ ( q @ ( p @ implies ) @ implies ) @ theorem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(8,axiom,
! [A: $i] :
( ~ ( A @ axiom )
| ( A @ theorem ) ),
file('/export/starexec/sandbox/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(7,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) )
= ( B @ ( A @ not @ or ) ) ),
file('/export/starexec/sandbox/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(2,axiom,
! [A: $i] : ( A @ ( A @ ( A @ or ) @ implies ) @ axiom ),
file('/export/starexec/sandbox/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(38,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ or ) @ implies ) @ axiom )
!= ( B @ axiom ) )
| ~ $true
| ( B @ theorem ) ),
inference(paramod_ordered,[status(thm)],[12,20]) ).
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(43,plain,
! [A: $i] : ( A @ ( A @ ( A @ or ) @ implies ) @ theorem ),
inference(simp,[status(thm)],[40]) ).
thf(11,plain,
~ ( q @ ( q @ ( p @ not @ implies ) @ implies ) @ ( q @ ( p @ implies ) @ implies ) @ theorem ),
inference(polarity_switch,[status(thm)],[10]) ).
thf(98,plain,
! [A: $i] :
( ( ( A @ ( A @ ( A @ or ) @ implies ) @ theorem )
!= ( q @ ( q @ ( p @ not @ implies ) @ implies ) @ ( q @ ( p @ implies ) @ implies ) @ theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[43,11]) ).
thf(99,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ or ) @ implies ) @ theorem )
!= ( q @ ( q @ ( p @ not @ implies ) @ implies ) @ ( q @ ( p @ implies ) @ implies ) @ theorem ) ),
inference(simp,[status(thm)],[98]) ).
thf(100,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ or ) @ implies ) )
!= ( q @ ( q @ ( p @ not @ implies ) @ implies ) @ ( q @ ( p @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[99]) ).
thf(182,plain,
! [A: $i] :
( ( A
!= ( q @ ( q @ ( p @ not @ implies ) @ implies ) ) )
| ( ( A @ ( A @ or ) )
!= ( q @ ( p @ implies ) ) ) ),
inference(simp,[status(thm)],[100]) ).
thf(185,plain,
( ( q @ ( q @ ( p @ not @ implies ) @ implies ) @ ( q @ ( q @ ( p @ not @ implies ) @ implies ) @ or ) )
!= ( q @ ( p @ implies ) ) ),
inference(simp,[status(thm)],[182]) ).
thf(187,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( q @ ( q @ ( p @ not @ implies ) @ implies ) @ ( q @ ( q @ ( p @ not @ implies ) @ implies ) @ or ) ) )
| ( ( B @ ( A @ implies ) )
!= ( q @ ( p @ implies ) ) ) ),
inference(paramod_ordered,[status(thm)],[18,185]) ).
thf(190,plain,
! [B: $i,A: $i] :
( ( B
!= ( q @ ( q @ ( p @ not @ implies ) @ implies ) ) )
| ( ( A @ not )
!= ( q @ ( q @ ( p @ not @ implies ) @ implies ) ) )
| ( B != q )
| ( A != p ) ),
inference(simp,[status(thm)],[187]) ).
thf(193,plain,
( ( ( q @ ( q @ ( p @ not @ implies ) @ implies ) )
!= q )
| ( ( q @ ( q @ ( p @ not @ implies ) @ implies ) )
!= ( p @ not ) ) ),
inference(simp,[status(thm)],[190]) ).
thf(3,axiom,
! [B: $i,A: $i] : ( A @ ( B @ or ) @ ( A @ implies ) @ axiom ),
file('/export/starexec/sandbox/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(25,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(26,plain,
! [B: $i,A: $i] : ( A @ ( B @ implies ) @ ( A @ implies ) @ axiom ),
inference(pattern_uni,[status(thm)],[25:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( E @ not ))]]) ).
thf(28,plain,
! [B: $i,A: $i] : ( A @ ( B @ implies ) @ ( A @ implies ) @ axiom ),
inference(simp,[status(thm)],[26]) ).
thf(32,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( A @ implies ) @ axiom )
!= ( C @ axiom ) )
| ~ $true
| ( C @ theorem ) ),
inference(paramod_ordered,[status(thm)],[28,20]) ).
thf(33,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( A @ implies ) @ axiom )
!= ( C @ axiom ) )
| ( C @ theorem ) ),
inference(simp,[status(thm)],[32]) ).
thf(34,plain,
! [B: $i,A: $i] : ( B @ ( A @ implies ) @ ( B @ implies ) @ theorem ),
inference(pattern_uni,[status(thm)],[33:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( G @ ( F @ implies ) @ ( G @ implies ) ))]]) ).
thf(41,plain,
! [B: $i,A: $i] : ( B @ ( A @ implies ) @ ( B @ implies ) @ theorem ),
inference(simp,[status(thm)],[34]) ).
thf(53,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ implies ) @ theorem )
!= ( q @ ( q @ ( p @ not @ implies ) @ implies ) @ ( q @ ( p @ implies ) @ implies ) @ theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[41,11]) ).
thf(54,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ implies ) @ theorem )
!= ( q @ ( q @ ( p @ not @ implies ) @ implies ) @ ( q @ ( p @ implies ) @ implies ) @ theorem ) ),
inference(simp,[status(thm)],[53]) ).
thf(55,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ implies ) )
!= ( q @ ( q @ ( p @ not @ implies ) @ implies ) @ ( q @ ( p @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[54]) ).
thf(110,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
!= ( q @ ( q @ ( p @ not @ implies ) @ implies ) ) )
| ( B
!= ( q @ ( p @ implies ) ) ) ),
inference(simp,[status(thm)],[55]) ).
thf(111,plain,
! [A: $i] :
( ( q @ ( p @ implies ) @ ( A @ implies ) )
!= ( q @ ( q @ ( p @ not @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[110]) ).
thf(112,plain,
! [A: $i] :
( ( ( q @ ( p @ implies ) )
!= q )
| ( A
!= ( q @ ( p @ not @ implies ) ) ) ),
inference(simp,[status(thm)],[111]) ).
thf(113,plain,
( ( q @ ( p @ implies ) )
!= q ),
inference(simp,[status(thm)],[112]) ).
thf(4,axiom,
! [B: $i,A: $i] : ( A @ ( B @ or ) @ ( B @ ( A @ or ) @ implies ) @ axiom ),
file('/export/starexec/sandbox/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(64,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(65,plain,
! [B: $i,A: $i] : ( B @ not @ ( A @ or ) @ ( A @ ( B @ implies ) @ implies ) @ axiom ),
inference(pattern_uni,[status(thm)],[64:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( E @ not )),bind(D,$thf( B ))]]) ).
thf(66,plain,
! [B: $i,A: $i] : ( B @ not @ ( A @ or ) @ ( A @ ( B @ implies ) @ implies ) @ axiom ),
inference(simp,[status(thm)],[65]) ).
thf(93,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)],[18,43]) ).
thf(94,plain,
! [A: $i] : ( A @ not @ ( A @ not @ ( A @ implies ) @ implies ) @ theorem ),
inference(pattern_uni,[status(thm)],[93:[bind(A,$thf( E )),bind(B,$thf( E @ not )),bind(C,$thf( E @ not ))]]) ).
thf(104,plain,
! [A: $i] : ( A @ not @ ( A @ not @ ( A @ implies ) @ implies ) @ theorem ),
inference(simp,[status(thm)],[94]) ).
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)],[13,20]) ).
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(42,plain,
! [B: $i,A: $i] : ( B @ ( A @ or ) @ ( B @ implies ) @ theorem ),
inference(simp,[status(thm)],[37]) ).
thf(80,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ ( B @ implies ) @ theorem )
!= ( q @ ( q @ ( p @ not @ implies ) @ implies ) @ ( q @ ( p @ implies ) @ implies ) @ theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[42,11]) ).
thf(81,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ or ) @ ( B @ implies ) @ theorem )
!= ( q @ ( q @ ( p @ not @ implies ) @ implies ) @ ( q @ ( p @ implies ) @ implies ) @ theorem ) ),
inference(simp,[status(thm)],[80]) ).
thf(82,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ or ) @ ( B @ implies ) )
!= ( q @ ( q @ ( p @ not @ implies ) @ implies ) @ ( q @ ( p @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[81]) ).
thf(59,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(60,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ or ) @ ( B @ ( A @ or ) @ implies ) @ axiom )
!= ( C @ axiom ) )
| ( C @ theorem ) ),
inference(simp,[status(thm)],[59]) ).
thf(61,plain,
! [B: $i,A: $i] : ( B @ ( A @ or ) @ ( A @ ( B @ or ) @ implies ) @ theorem ),
inference(pattern_uni,[status(thm)],[60:[bind(A,$thf( I )),bind(B,$thf( H )),bind(C,$thf( I @ ( H @ or ) @ ( H @ ( I @ or ) @ implies ) ))]]) ).
thf(67,plain,
! [B: $i,A: $i] : ( B @ ( A @ or ) @ ( A @ ( B @ or ) @ implies ) @ theorem ),
inference(simp,[status(thm)],[61]) ).
thf(156,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)],[18,67]) ).
thf(157,plain,
! [B: $i,A: $i] : ( A @ ( B @ implies ) @ ( B @ not @ ( A @ or ) @ implies ) @ theorem ),
inference(pattern_uni,[status(thm)],[156:[bind(A,$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)],[157]) ).
thf(123,plain,
! [A: $i] :
( ( ( A @ not @ ( A @ not @ ( A @ implies ) @ implies ) @ theorem )
!= ( q @ ( q @ ( p @ not @ implies ) @ implies ) @ ( q @ ( p @ implies ) @ implies ) @ theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[104,11]) ).
thf(124,plain,
! [A: $i] :
( ( A @ not @ ( A @ not @ ( A @ implies ) @ implies ) @ theorem )
!= ( q @ ( q @ ( p @ not @ implies ) @ implies ) @ ( q @ ( p @ implies ) @ implies ) @ theorem ) ),
inference(simp,[status(thm)],[123]) ).
thf(125,plain,
! [A: $i] :
( ( A @ not @ ( A @ not @ ( A @ implies ) @ implies ) )
!= ( q @ ( q @ ( p @ not @ implies ) @ implies ) @ ( q @ ( p @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[124]) ).
thf(129,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ or ) )
!= ( q @ ( q @ ( p @ not @ implies ) @ implies ) ) )
| ( B
!= ( q @ ( p @ implies ) ) ) ),
inference(simp,[status(thm)],[82]) ).
thf(132,plain,
! [A: $i] :
( ( q @ ( p @ implies ) @ ( A @ or ) )
!= ( q @ ( q @ ( p @ not @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[129]) ).
thf(130,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( D @ ( C @ or ) ) )
| ( ( B @ ( A @ implies ) @ ( D @ implies ) )
!= ( q @ ( q @ ( p @ not @ implies ) @ implies ) @ ( q @ ( p @ implies ) @ implies ) ) ) ),
inference(paramod_ordered,[status(thm)],[18,82]) ).
thf(131,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ implies ) @ ( A @ implies ) )
!= ( q @ ( q @ ( p @ not @ implies ) @ implies ) @ ( q @ ( p @ implies ) @ implies ) ) ),
inference(pattern_uni,[status(thm)],[130:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( E @ not )),bind(D,$thf( B ))]]) ).
thf(133,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ implies ) @ ( A @ implies ) )
!= ( q @ ( q @ ( p @ not @ implies ) @ implies ) @ ( q @ ( p @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[131]) ).
thf(189,plain,
! [B: $i,A: $i] :
( ( B
!= ( q @ ( q @ ( p @ not @ implies ) @ implies ) ) )
| ( ( A @ not )
!= ( q @ ( q @ ( p @ not @ implies ) @ implies ) ) )
| ( ( B @ ( A @ implies ) )
!= ( q @ ( p @ implies ) ) ) ),
inference(simp,[status(thm)],[187]) ).
thf(192,plain,
! [A: $i] :
( ( ( A @ not )
!= ( q @ ( q @ ( p @ not @ implies ) @ implies ) ) )
| ( ( q @ ( q @ ( p @ not @ implies ) @ implies ) @ ( A @ implies ) )
!= ( q @ ( p @ implies ) ) ) ),
inference(simp,[status(thm)],[189]) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ~ ( B @ theorem )
| ~ ( A @ ( B @ implies ) @ theorem )
| ( A @ theorem ) ),
file('/export/starexec/sandbox/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(154,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)],[18,67]) ).
thf(155,plain,
! [B: $i,A: $i] : ( B @ not @ ( A @ or ) @ ( A @ ( B @ implies ) @ implies ) @ theorem ),
inference(pattern_uni,[status(thm)],[154:[bind(A,$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)],[155]) ).
thf(22,plain,
! [B: $i,A: $i] :
( ~ ( B @ theorem )
| ~ ( A @ ( B @ implies ) @ theorem )
| ( A @ theorem ) ),
inference(cnf,[status(esa)],[21]) ).
thf(23,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(24,plain,
! [A: $i] : ( A @ not @ ( A @ not @ ( A @ implies ) @ implies ) @ axiom ),
inference(pattern_uni,[status(thm)],[23:[bind(A,$thf( E )),bind(B,$thf( E @ not )),bind(C,$thf( E @ not ))]]) ).
thf(27,plain,
! [A: $i] : ( A @ not @ ( A @ not @ ( A @ implies ) @ implies ) @ axiom ),
inference(simp,[status(thm)],[24]) ).
thf(178,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( D @ not @ ( C @ or ) ) )
| ( B @ ( A @ implies ) @ ( C @ ( D @ implies ) @ implies ) @ axiom ) ),
inference(paramod_ordered,[status(thm)],[18,66]) ).
thf(179,plain,
! [B: $i,A: $i] : ( B @ not @ ( A @ implies ) @ ( A @ not @ ( B @ implies ) @ implies ) @ axiom ),
inference(pattern_uni,[status(thm)],[178:[bind(A,$thf( E )),bind(B,$thf( F @ not )),bind(C,$thf( E @ not )),bind(D,$thf( F ))]]) ).
thf(181,plain,
! [B: $i,A: $i] : ( B @ not @ ( A @ implies ) @ ( A @ not @ ( B @ implies ) @ implies ) @ axiom ),
inference(simp,[status(thm)],[179]) ).
thf(6,axiom,
! [C: $i,B: $i,A: $i] : ( B @ ( C @ or ) @ ( A @ ( C @ or ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ axiom ),
file('/export/starexec/sandbox/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(29,plain,
! [B: $i,A: $i] :
( ~ $true
| ( ( A @ ( B @ implies ) @ theorem )
!= ( B @ theorem ) )
| ~ ( B @ theorem )
| ( A @ theorem ) ),
inference(eqfactor_ordered,[status(thm)],[22]) ).
thf(31,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ implies ) )
!= B )
| ~ ( B @ theorem )
| ( A @ theorem ) ),
inference(simp,[status(thm)],[29]) ).
thf(258,plain,
! [A: $i] :
( ( ( A @ not )
!= ( q @ ( q @ ( p @ not @ implies ) @ implies ) ) )
| ( ( A @ not @ ( A @ implies ) )
!= ( q @ ( p @ implies ) ) ) ),
inference(simp,[status(thm)],[125]) ).
thf(30,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ theorem )
!= ( B @ theorem ) )
| ~ ( B @ theorem )
| ( A @ theorem ) ),
inference(simp,[status(thm)],[29]) ).
thf(5,axiom,
! [C: $i,B: $i,A: $i] : ( C @ ( A @ or ) @ ( B @ or ) @ ( C @ ( B @ or ) @ ( A @ or ) @ implies ) @ axiom ),
file('/export/starexec/sandbox/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(62,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(63,plain,
! [B: $i,A: $i] : ( A @ ( B @ implies ) @ ( B @ not @ ( A @ or ) @ implies ) @ axiom ),
inference(pattern_uni,[status(thm)],[62:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( E @ not ))]]) ).
thf(68,plain,
! [B: $i,A: $i] : ( A @ ( B @ implies ) @ ( B @ not @ ( A @ or ) @ implies ) @ axiom ),
inference(simp,[status(thm)],[63]) ).
thf(13889,plain,
$false,
inference(e,[status(thm)],[10,20,193,17,113,66,18,104,82,174,185,42,14,125,132,133,28,192,21,173,13,41,22,27,12,181,67,16,31,11,43,258,55,30,19,15,68,111,100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL213-3 : TPTP v9.3.1. Released v2.3.0.
% 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
% 0.13/0.40 % Computer : n014.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Fri Sep 25 22:01:17 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 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
% 0.81/0.95 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.05/1.12 % [INFO] Parsing done (169ms).
% 1.05/1.14 % [INFO] Running in sequential loop mode.
% 1.79/1.64 % [INFO] eprover registered as external prover.
% 1.79/1.65 % [INFO] Scanning for conjecture ...
% 1.92/1.76 % [INFO] Found a conjecture (or negated_conjecture) and 8 axioms. Running axiom selection ...
% 2.04/1.80 % [INFO] Axiom selection finished. Selected 8 axioms (removed 0 axioms).
% 2.04/1.82 % [INFO] Problem is propositional (TPTP CNF).
% 2.04/1.83 % [INFO] Type checking passed.
% 2.04/1.84 % [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 ...
% 47.66/11.41 % External prover 'e' found a proof!
% 47.66/11.41 % [INFO] Killing All external provers ...
% 47.66/11.42 % Time passed: 10894ms (effective reasoning time: 10271ms)
% 47.66/11.42 % 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
% 47.66/11.42 % No. of inferences in proof: 95
% 47.66/11.42 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 10894 ms resp. 10271 ms w/o parsing
% 47.66/11.48 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 47.66/11.48 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------