%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL298-3 : 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 : n003.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 07:51:27 AM UTC 2026
% Result : Unsatisfiable 19.24s 6.34s
% Output : Refutation 16.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 11
% Syntax : Number of formulae : 100 ( 64 unt; 0 typ; 0 def)
% Number of atoms : 180 ( 55 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 1184 ( 78 ~; 46 |; 0 &;1060 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 180 ( 0 ^; 180 !; 0 ?; 180 :)
% Comments :
%------------------------------------------------------------------------------
thf(theorem_decl,type,
theorem: $i > $o ).
thf(equivalent_decl,type,
equivalent: $i > $i > $i ).
thf(not_decl,type,
not: $i > $i ).
thf(and_decl,type,
and: $i > $i > $i ).
thf(p_decl,type,
p: $i ).
thf(q_decl,type,
q: $i ).
thf(or_decl,type,
or: $i > $i > $i ).
thf(axiom_decl,type,
axiom: $i > $o ).
thf(implies_decl,type,
implies: $i > $i > $i ).
thf(10,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ and ) )
= ( B @ not @ ( A @ not @ or ) @ not ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_defn) ).
thf(25,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ and ) )
= ( B @ not @ ( A @ not @ or ) @ not ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(26,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ and ) )
= ( B @ not @ ( A @ not @ or ) @ not ) ),
inference(lifteq,[status(thm)],[25]) ).
thf(1,negated_conjecture,
~ ( q @ not @ ( p @ not @ or ) @ ( q @ ( p @ and ) @ not @ equivalent ) @ theorem ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
thf(12,plain,
~ ( q @ not @ ( p @ not @ or ) @ ( q @ ( p @ and ) @ not @ equivalent ) @ theorem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(13,plain,
~ ( q @ not @ ( p @ not @ or ) @ ( q @ ( p @ and ) @ not @ equivalent ) @ theorem ),
inference(polarity_switch,[status(thm)],[12]) ).
thf(84,plain,
! [B: $i,A: $i] :
( ( ( B @ not @ ( A @ not @ or ) @ not )
!= ( p @ not ) )
| ~ ( q @ not @ ( B @ ( A @ and ) @ or ) @ ( q @ ( p @ and ) @ not @ equivalent ) @ theorem ) ),
inference(paramod_ordered,[status(thm)],[26,13]) ).
thf(101,plain,
! [B: $i,A: $i] :
( ( ( B @ not @ ( A @ not @ or ) )
!= p )
| ~ ( q @ not @ ( B @ ( A @ and ) @ or ) @ ( q @ ( p @ and ) @ not @ equivalent ) @ theorem ) ),
inference(simp,[status(thm)],[84]) ).
thf(2,axiom,
! [A: $i] : ( A @ ( A @ ( A @ or ) @ implies ) @ axiom ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1_2) ).
thf(14,plain,
! [A: $i] : ( A @ ( A @ ( A @ or ) @ implies ) @ axiom ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(85,plain,
! [B: $i,A: $i] :
( ( ( B @ not @ ( A @ not @ or ) @ not )
!= ( q @ ( p @ and ) @ not ) )
| ~ ( q @ not @ ( p @ not @ or ) @ ( B @ ( A @ and ) @ equivalent ) @ theorem ) ),
inference(paramod_ordered,[status(thm)],[26,13]) ).
thf(102,plain,
! [B: $i,A: $i] :
( ( ( B @ not @ ( A @ not @ or ) )
!= ( q @ ( p @ and ) ) )
| ~ ( q @ not @ ( p @ not @ or ) @ ( B @ ( A @ and ) @ equivalent ) @ theorem ) ),
inference(simp,[status(thm)],[85]) ).
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(18,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(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(16,plain,
! [B: $i,A: $i] : ( A @ ( B @ or ) @ ( B @ ( A @ or ) @ implies ) @ axiom ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(7,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) )
= ( B @ ( A @ not @ or ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',implies_definition) ).
thf(19,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) )
= ( B @ ( A @ not @ or ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(20,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) )
= ( B @ ( A @ not @ or ) ) ),
inference(lifteq,[status(thm)],[19]) ).
thf(43,plain,
! [B: $i,A: $i] : ( A @ ( B @ or ) @ ( B @ ( A @ or ) @ not @ or ) @ axiom ),
inference(rewrite,[status(thm)],[16,20]) ).
thf(3,axiom,
! [B: $i,A: $i] : ( A @ ( B @ or ) @ ( A @ implies ) @ axiom ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1_3) ).
thf(15,plain,
! [B: $i,A: $i] : ( A @ ( B @ or ) @ ( A @ implies ) @ axiom ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(30,plain,
! [B: $i,A: $i] : ( A @ ( B @ or ) @ ( A @ not @ or ) @ axiom ),
inference(rewrite,[status(thm)],[15,20]) ).
thf(8,axiom,
! [A: $i] :
( ~ ( A @ axiom )
| ( A @ theorem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_1) ).
thf(21,plain,
! [A: $i] :
( ~ ( A @ axiom )
| ( A @ theorem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(22,plain,
! [A: $i] :
( ~ ( A @ axiom )
| ( A @ theorem ) ),
inference(cnf,[status(esa)],[21]) ).
thf(39,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ or ) @ ( A @ not @ or ) @ axiom )
!= ( C @ axiom ) )
| ~ $true
| ( C @ theorem ) ),
inference(paramod_ordered,[status(thm)],[30,22]) ).
thf(40,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ or ) @ ( A @ not @ or ) @ axiom )
!= ( C @ axiom ) )
| ( C @ theorem ) ),
inference(simp,[status(thm)],[39]) ).
thf(41,plain,
! [B: $i,A: $i] : ( B @ ( A @ or ) @ ( B @ not @ or ) @ theorem ),
inference(pattern_uni,[status(thm)],[40:[bind(A,$thf( H )),bind(B,$thf( G )),bind(C,$thf( H @ ( G @ or ) @ ( H @ not @ or ) ))]]) ).
thf(42,plain,
! [B: $i,A: $i] : ( B @ ( A @ or ) @ ( B @ not @ or ) @ theorem ),
inference(simp,[status(thm)],[41]) ).
thf(29,plain,
! [A: $i] : ( A @ ( A @ ( A @ or ) @ not @ or ) @ axiom ),
inference(rewrite,[status(thm)],[14,20]) ).
thf(35,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ or ) @ not @ or ) @ axiom )
!= ( B @ axiom ) )
| ~ $true
| ( B @ theorem ) ),
inference(paramod_ordered,[status(thm)],[29,22]) ).
thf(36,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ or ) @ not @ or ) @ axiom )
!= ( B @ axiom ) )
| ( B @ theorem ) ),
inference(simp,[status(thm)],[35]) ).
thf(37,plain,
! [A: $i] : ( A @ ( A @ ( A @ or ) @ not @ or ) @ theorem ),
inference(pattern_uni,[status(thm)],[36:[bind(A,$thf( D )),bind(B,$thf( D @ ( D @ ( D @ or ) @ not @ or ) ))]]) ).
thf(38,plain,
! [A: $i] : ( A @ ( A @ ( A @ or ) @ not @ or ) @ theorem ),
inference(simp,[status(thm)],[37]) ).
thf(80,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ not @ ( A @ not @ or ) @ not )
!= ( C @ ( C @ or ) @ not ) )
| ( C @ ( B @ ( A @ and ) @ or ) @ theorem ) ),
inference(paramod_ordered,[status(thm)],[26,38]) ).
thf(81,plain,
! [A: $i] : ( A @ not @ ( A @ ( A @ and ) @ or ) @ theorem ),
inference(pattern_uni,[status(thm)],[80:[bind(A,$thf( B )),bind(B,$thf( B )),bind(C,$thf( B @ not ))]]) ).
thf(108,plain,
! [A: $i] : ( A @ not @ ( A @ ( A @ and ) @ or ) @ theorem ),
inference(simp,[status(thm)],[81]) ).
thf(82,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ and ) )
!= ( q @ ( p @ and ) ) )
| ~ ( q @ not @ ( p @ not @ or ) @ ( B @ not @ ( A @ not @ or ) @ not @ not @ equivalent ) @ theorem ) ),
inference(paramod_ordered,[status(thm)],[26,13]) ).
thf(83,plain,
~ ( q @ not @ ( p @ not @ or ) @ ( q @ not @ ( p @ not @ or ) @ not @ not @ equivalent ) @ theorem ),
inference(pattern_uni,[status(thm)],[82:[bind(A,$thf( p )),bind(B,$thf( q ))]]) ).
thf(206,plain,
! [A: $i] :
( ( ( A @ not @ ( A @ ( A @ and ) @ or ) @ theorem )
!= ( q @ not @ ( p @ not @ or ) @ ( q @ not @ ( p @ not @ or ) @ not @ not @ equivalent ) @ theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[108,83]) ).
thf(207,plain,
! [A: $i] :
( ( A @ not @ ( A @ ( A @ and ) @ or ) @ theorem )
!= ( q @ not @ ( p @ not @ or ) @ ( q @ not @ ( p @ not @ or ) @ not @ not @ equivalent ) @ theorem ) ),
inference(simp,[status(thm)],[206]) ).
thf(211,plain,
! [A: $i] :
( ( A @ not @ ( A @ ( A @ and ) @ or ) )
!= ( q @ not @ ( p @ not @ or ) @ ( q @ not @ ( p @ not @ or ) @ not @ not @ equivalent ) ) ),
inference(simp,[status(thm)],[207]) ).
thf(99,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ not @ ( A @ not @ or ) @ not )
!= ( C @ ( C @ or ) @ not ) )
| ( C @ ( B @ ( A @ and ) @ or ) @ axiom ) ),
inference(paramod_ordered,[status(thm)],[26,29]) ).
thf(100,plain,
! [A: $i] : ( A @ not @ ( A @ ( A @ and ) @ or ) @ axiom ),
inference(pattern_uni,[status(thm)],[99:[bind(A,$thf( B )),bind(B,$thf( B )),bind(C,$thf( B @ not ))]]) ).
thf(106,plain,
! [A: $i] : ( A @ not @ ( A @ ( A @ and ) @ or ) @ axiom ),
inference(simp,[status(thm)],[100]) ).
thf(48,plain,
! [A: $i] :
( ( ( A @ ( A @ ( A @ or ) @ not @ or ) @ theorem )
!= ( q @ not @ ( p @ not @ or ) @ ( q @ ( p @ and ) @ not @ equivalent ) @ theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[38,13]) ).
thf(49,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ or ) @ not @ or ) @ theorem )
!= ( q @ not @ ( p @ not @ or ) @ ( q @ ( p @ and ) @ not @ equivalent ) @ theorem ) ),
inference(simp,[status(thm)],[48]) ).
thf(59,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ or ) @ not @ or ) )
!= ( q @ not @ ( p @ not @ or ) @ ( q @ ( p @ and ) @ not @ equivalent ) ) ),
inference(simp,[status(thm)],[49]) ).
thf(131,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ not @ ( A @ not @ or ) @ not )
!= ( C @ ( C @ or ) @ not ) )
| ( ( C @ ( B @ ( A @ and ) @ or ) )
!= ( q @ not @ ( p @ not @ or ) @ ( q @ ( p @ and ) @ not @ equivalent ) ) ) ),
inference(paramod_ordered,[status(thm)],[26,59]) ).
thf(132,plain,
! [A: $i] :
( ( A @ not @ ( A @ ( A @ and ) @ or ) )
!= ( q @ not @ ( p @ not @ or ) @ ( q @ ( p @ and ) @ not @ equivalent ) ) ),
inference(pattern_uni,[status(thm)],[131:[bind(A,$thf( B )),bind(B,$thf( B )),bind(C,$thf( B @ not ))]]) ).
thf(133,plain,
! [A: $i] :
( ( A @ not @ ( A @ ( A @ and ) @ or ) )
!= ( q @ not @ ( p @ not @ or ) @ ( q @ ( p @ and ) @ not @ equivalent ) ) ),
inference(simp,[status(thm)],[132]) ).
thf(11,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ equivalent ) )
= ( A @ ( B @ implies ) @ ( B @ ( A @ implies ) @ and ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equivalent_defn) ).
thf(27,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ equivalent ) )
= ( A @ ( B @ implies ) @ ( B @ ( A @ implies ) @ and ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(28,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ implies ) @ ( B @ ( A @ implies ) @ and ) )
= ( B @ ( A @ equivalent ) ) ),
inference(lifteq,[status(thm)],[27]) ).
thf(392,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ not @ or ) @ ( B @ ( A @ not @ or ) @ and ) )
= ( B @ ( A @ equivalent ) ) ),
inference(rewrite,[status(thm)],[28,20]) ).
thf(419,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ or ) @ ( B @ ( A @ not @ or ) @ and ) )
!= ( C @ ( C @ and ) ) )
| ( C @ not @ ( B @ ( A @ equivalent ) @ or ) @ theorem ) ),
inference(paramod_ordered,[status(thm)],[392,108]) ).
thf(420,plain,
! [A: $i] : ( A @ ( A @ not @ or ) @ not @ ( A @ ( A @ equivalent ) @ or ) @ theorem ),
inference(pattern_uni,[status(thm)],[419:[bind(A,$thf( E )),bind(B,$thf( E )),bind(C,$thf( E @ ( E @ not @ or ) ))]]) ).
thf(428,plain,
! [A: $i] : ( A @ ( A @ not @ or ) @ not @ ( A @ ( A @ equivalent ) @ or ) @ theorem ),
inference(simp,[status(thm)],[420]) ).
thf(312,plain,
! [C: $i,B: $i,A: $i] : ( B @ ( C @ or ) @ ( A @ ( C @ or ) @ implies ) @ ( B @ ( A @ implies ) @ not @ or ) @ axiom ),
inference(rewrite,[status(thm)],[18,20]) ).
thf(63,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ ( B @ not @ or ) @ theorem )
!= ( q @ not @ ( p @ not @ or ) @ ( q @ ( p @ and ) @ not @ equivalent ) @ theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[42,13]) ).
thf(64,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ or ) @ ( B @ not @ or ) @ theorem )
!= ( q @ not @ ( p @ not @ or ) @ ( q @ ( p @ and ) @ not @ equivalent ) @ theorem ) ),
inference(simp,[status(thm)],[63]) ).
thf(74,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ or ) @ ( B @ not @ or ) )
!= ( q @ not @ ( p @ not @ or ) @ ( q @ ( p @ and ) @ not @ equivalent ) ) ),
inference(simp,[status(thm)],[64]) ).
thf(44,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ or ) @ ( B @ ( A @ or ) @ not @ or ) @ axiom )
!= ( C @ axiom ) )
| ~ $true
| ( C @ theorem ) ),
inference(paramod_ordered,[status(thm)],[43,22]) ).
thf(45,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ or ) @ ( B @ ( A @ or ) @ not @ or ) @ axiom )
!= ( C @ axiom ) )
| ( C @ theorem ) ),
inference(simp,[status(thm)],[44]) ).
thf(46,plain,
! [B: $i,A: $i] : ( B @ ( A @ or ) @ ( A @ ( B @ or ) @ not @ or ) @ theorem ),
inference(pattern_uni,[status(thm)],[45:[bind(A,$thf( J )),bind(B,$thf( I )),bind(C,$thf( J @ ( I @ or ) @ ( I @ ( J @ or ) @ not @ or ) ))]]) ).
thf(47,plain,
! [B: $i,A: $i] : ( B @ ( A @ or ) @ ( A @ ( B @ or ) @ not @ or ) @ theorem ),
inference(simp,[status(thm)],[46]) ).
thf(248,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ not @ ( A @ not @ or ) @ not )
!= ( C @ ( D @ or ) @ not ) )
| ( D @ ( C @ or ) @ ( B @ ( A @ and ) @ or ) @ theorem ) ),
inference(paramod_ordered,[status(thm)],[26,47]) ).
thf(249,plain,
! [B: $i,A: $i] : ( A @ not @ ( B @ not @ or ) @ ( B @ ( A @ and ) @ or ) @ theorem ),
inference(pattern_uni,[status(thm)],[248:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( F @ not )),bind(D,$thf( E @ not ))]]) ).
thf(260,plain,
! [B: $i,A: $i] : ( A @ not @ ( B @ not @ or ) @ ( B @ ( A @ and ) @ or ) @ theorem ),
inference(simp,[status(thm)],[249]) ).
thf(156,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ and ) )
!= ( C @ ( C @ and ) ) )
| ( ( C @ not @ ( B @ not @ ( A @ not @ or ) @ not @ or ) )
!= ( q @ not @ ( p @ not @ or ) @ ( q @ ( p @ and ) @ not @ equivalent ) ) ) ),
inference(paramod_ordered,[status(thm)],[26,133]) ).
thf(157,plain,
! [A: $i] :
( ( A @ not @ ( A @ not @ ( A @ not @ or ) @ not @ or ) )
!= ( q @ not @ ( p @ not @ or ) @ ( q @ ( p @ and ) @ not @ equivalent ) ) ),
inference(pattern_uni,[status(thm)],[156:[bind(A,$thf( B )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(160,plain,
! [A: $i] :
( ( A @ not @ ( A @ not @ ( A @ not @ or ) @ not @ or ) )
!= ( q @ not @ ( p @ not @ or ) @ ( q @ ( p @ and ) @ not @ equivalent ) ) ),
inference(simp,[status(thm)],[157]) ).
thf(113,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ ( B @ not @ or ) @ theorem )
!= ( q @ not @ ( p @ not @ or ) @ ( q @ not @ ( p @ not @ or ) @ not @ not @ equivalent ) @ theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[42,83]) ).
thf(114,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ or ) @ ( B @ not @ or ) @ theorem )
!= ( q @ not @ ( p @ not @ or ) @ ( q @ not @ ( p @ not @ or ) @ not @ not @ equivalent ) @ theorem ) ),
inference(simp,[status(thm)],[113]) ).
thf(129,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ or ) @ ( B @ not @ or ) )
!= ( q @ not @ ( p @ not @ or ) @ ( q @ not @ ( p @ not @ or ) @ not @ not @ equivalent ) ) ),
inference(simp,[status(thm)],[114]) ).
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(23,plain,
! [B: $i,A: $i] :
( ~ ( B @ theorem )
| ~ ( A @ ( B @ implies ) @ theorem )
| ( A @ theorem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(24,plain,
! [B: $i,A: $i] :
( ~ ( B @ theorem )
| ~ ( A @ ( B @ implies ) @ theorem )
| ( A @ theorem ) ),
inference(cnf,[status(esa)],[23]) ).
thf(31,plain,
! [B: $i,A: $i] :
( ~ ( B @ theorem )
| ~ ( A @ ( B @ not @ or ) @ theorem )
| ( A @ theorem ) ),
inference(rewrite,[status(thm)],[24,20]) ).
thf(32,plain,
! [B: $i,A: $i] :
( ~ $true
| ( ( A @ ( B @ not @ or ) @ theorem )
!= ( B @ theorem ) )
| ~ ( B @ theorem )
| ( A @ theorem ) ),
inference(eqfactor_ordered,[status(thm)],[31]) ).
thf(34,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ not @ or ) )
!= B )
| ~ ( B @ theorem )
| ( A @ theorem ) ),
inference(simp,[status(thm)],[32]) ).
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(17,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(86,plain,
! [B: $i,A: $i] :
( ( ( B @ not @ ( A @ not @ or ) @ not )
!= ( q @ not ) )
| ~ ( B @ ( A @ and ) @ ( p @ not @ or ) @ ( q @ ( p @ and ) @ not @ equivalent ) @ theorem ) ),
inference(paramod_ordered,[status(thm)],[26,13]) ).
thf(103,plain,
! [B: $i,A: $i] :
( ( ( B @ not @ ( A @ not @ or ) )
!= q )
| ~ ( B @ ( A @ and ) @ ( p @ not @ or ) @ ( q @ ( p @ and ) @ not @ equivalent ) @ theorem ) ),
inference(simp,[status(thm)],[86]) ).
thf(183,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( A @ or ) @ ( B @ or ) @ ( C @ ( B @ or ) @ ( A @ or ) @ not @ or ) @ axiom ),
inference(rewrite,[status(thm)],[17,20]) ).
thf(115,plain,
! [A: $i] :
( ( ( A @ ( A @ ( A @ or ) @ not @ or ) @ theorem )
!= ( q @ not @ ( p @ not @ or ) @ ( q @ not @ ( p @ not @ or ) @ not @ not @ equivalent ) @ theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[38,83]) ).
thf(116,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ or ) @ not @ or ) @ theorem )
!= ( q @ not @ ( p @ not @ or ) @ ( q @ not @ ( p @ not @ or ) @ not @ not @ equivalent ) @ theorem ) ),
inference(simp,[status(thm)],[115]) ).
thf(126,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ or ) @ not @ or ) )
!= ( q @ not @ ( p @ not @ or ) @ ( q @ not @ ( p @ not @ or ) @ not @ not @ equivalent ) ) ),
inference(simp,[status(thm)],[116]) ).
thf(408,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ or ) @ ( B @ ( A @ not @ or ) @ and ) )
!= ( C @ ( C @ and ) ) )
| ( C @ not @ ( B @ ( A @ equivalent ) @ or ) @ axiom ) ),
inference(paramod_ordered,[status(thm)],[392,106]) ).
thf(409,plain,
! [A: $i] : ( A @ ( A @ not @ or ) @ not @ ( A @ ( A @ equivalent ) @ or ) @ axiom ),
inference(pattern_uni,[status(thm)],[408:[bind(A,$thf( E )),bind(B,$thf( E )),bind(C,$thf( E @ ( E @ not @ or ) ))]]) ).
thf(437,plain,
! [A: $i] : ( A @ ( A @ not @ or ) @ not @ ( A @ ( A @ equivalent ) @ or ) @ axiom ),
inference(simp,[status(thm)],[409]) ).
thf(91,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ not @ ( A @ not @ or ) @ not )
!= ( D @ ( C @ or ) @ not ) )
| ( C @ ( D @ or ) @ ( B @ ( A @ and ) @ or ) @ axiom ) ),
inference(paramod_ordered,[status(thm)],[26,43]) ).
thf(92,plain,
! [B: $i,A: $i] : ( A @ not @ ( B @ not @ or ) @ ( B @ ( A @ and ) @ or ) @ axiom ),
inference(pattern_uni,[status(thm)],[91:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( E @ not )),bind(D,$thf( F @ not ))]]) ).
thf(111,plain,
! [B: $i,A: $i] : ( A @ not @ ( B @ not @ or ) @ ( B @ ( A @ and ) @ or ) @ axiom ),
inference(simp,[status(thm)],[92]) ).
thf(452,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ not @ ( A @ not @ or ) @ not )
!= ( C @ ( C @ not @ or ) @ not ) )
| ( B @ ( A @ and ) @ ( C @ ( C @ equivalent ) @ or ) @ theorem ) ),
inference(paramod_ordered,[status(thm)],[26,428]) ).
thf(453,plain,
! [A: $i] : ( A @ ( A @ not @ and ) @ ( A @ not @ ( A @ not @ equivalent ) @ or ) @ theorem ),
inference(pattern_uni,[status(thm)],[452:[bind(A,$thf( D @ not )),bind(B,$thf( D )),bind(C,$thf( D @ not ))]]) ).
thf(469,plain,
! [A: $i] : ( A @ ( A @ not @ and ) @ ( A @ not @ ( A @ not @ equivalent ) @ or ) @ theorem ),
inference(simp,[status(thm)],[453]) ).
thf(695,plain,
$false,
inference(e,[status(thm)],[101,14,102,12,18,43,42,25,20,29,211,106,133,428,312,74,260,38,160,392,21,13,129,34,17,22,59,27,103,108,16,31,26,23,30,183,19,126,437,47,15,111,469,83]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL298-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.07 % 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
% 0.12/0.39 % Computer : n003.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Fri Sep 25 22:14:23 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 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
% 1.31/1.22 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.83/1.55 % [INFO] Parsing done (327ms).
% 1.83/1.58 % [INFO] Running in sequential loop mode.
% 3.12/2.27 % [INFO] eprover registered as external prover.
% 3.12/2.28 % [INFO] Scanning for conjecture ...
% 3.50/2.43 % [INFO] Found a conjecture (or negated_conjecture) and 10 axioms. Running axiom selection ...
% 3.50/2.48 % [INFO] Axiom selection finished. Selected 10 axioms (removed 0 axioms).
% 3.72/2.52 % [INFO] Problem is propositional (TPTP CNF).
% 3.72/2.53 % [INFO] Type checking passed.
% 3.72/2.54 % [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 ...
% 19.24/6.33 % External prover 'e' found a proof!
% 19.24/6.33 % [INFO] Killing All external provers ...
% 19.24/6.33 % Time passed: 5800ms (effective reasoning time: 4745ms)
% 19.24/6.34 % Axioms used in derivation (10): axiom_1_5, equivalent_defn, and_defn, axiom_1_4, rule_1, axiom_1_3, implies_definition, axiom_1_2, rule_2, axiom_1_6
% 19.24/6.34 % No. of inferences in proof: 100
% 19.24/6.34 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 5800 ms resp. 4745 ms w/o parsing
% 16.75/6.47 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 16.75/6.47 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------