%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL198-3 : 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 : n015.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 07:51:08 AM UTC 2026
% Result : Unsatisfiable 14.88s 4.71s
% Output : Refutation 14.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 9
% Syntax : Number of formulae : 98 ( 60 unt; 0 typ; 0 def)
% Number of atoms : 185 ( 63 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 971 ( 84 ~; 51 |; 0 &; 836 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 7 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 : 186 ( 0 ^; 186 !; 0 ?; 186 :)
% Comments :
%------------------------------------------------------------------------------
thf(theorem_decl,type,
theorem: $i > $o ).
thf(implies_decl,type,
implies: $i > $i > $i ).
thf(or_decl,type,
or: $i > $i > $i ).
thf(not_decl,type,
not: $i > $i ).
thf(p_decl,type,
p: $i ).
thf(q_decl,type,
q: $i ).
thf(axiom_decl,type,
axiom: $i > $o ).
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(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(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(36,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ or ) @ implies ) @ axiom )
!= ( B @ axiom ) )
| ~ $true
| ( B @ theorem ) ),
inference(paramod_ordered,[status(thm)],[12,20]) ).
thf(37,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ or ) @ implies ) @ axiom )
!= ( B @ axiom ) )
| ( B @ theorem ) ),
inference(simp,[status(thm)],[36]) ).
thf(38,plain,
! [A: $i] : ( A @ ( A @ ( A @ or ) @ implies ) @ theorem ),
inference(pattern_uni,[status(thm)],[37:[bind(A,$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)],[38]) ).
thf(75,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(76,plain,
! [A: $i] : ( A @ not @ ( A @ not @ ( A @ implies ) @ implies ) @ theorem ),
inference(pattern_uni,[status(thm)],[75:[bind(A,$thf( E )),bind(B,$thf( E @ not )),bind(C,$thf( E @ not ))]]) ).
thf(82,plain,
! [A: $i] : ( A @ not @ ( A @ not @ ( A @ implies ) @ implies ) @ theorem ),
inference(simp,[status(thm)],[76]) ).
thf(1,negated_conjecture,
~ ( q @ ( p @ implies ) @ ( q @ ( p @ implies ) @ ( p @ not @ or ) @ implies ) @ theorem ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
thf(10,plain,
~ ( q @ ( p @ implies ) @ ( q @ ( p @ implies ) @ ( p @ not @ or ) @ implies ) @ theorem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(11,plain,
~ ( q @ ( p @ implies ) @ ( q @ ( p @ implies ) @ ( p @ not @ or ) @ implies ) @ theorem ),
inference(polarity_switch,[status(thm)],[10]) ).
thf(23,plain,
~ ( q @ ( p @ implies ) @ ( q @ ( p @ implies ) @ ( p @ implies ) @ implies ) @ theorem ),
inference(rewrite,[status(thm)],[11,18]) ).
thf(113,plain,
! [A: $i] :
( ( ( A @ not @ ( A @ not @ ( A @ implies ) @ implies ) @ theorem )
!= ( q @ ( p @ implies ) @ ( q @ ( p @ implies ) @ ( p @ implies ) @ implies ) @ theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[82,23]) ).
thf(114,plain,
! [A: $i] :
( ( A @ not @ ( A @ not @ ( A @ implies ) @ implies ) @ theorem )
!= ( q @ ( p @ implies ) @ ( q @ ( p @ implies ) @ ( p @ implies ) @ implies ) @ theorem ) ),
inference(simp,[status(thm)],[113]) ).
thf(115,plain,
! [A: $i] :
( ( A @ not @ ( A @ not @ ( A @ implies ) @ implies ) )
!= ( q @ ( p @ implies ) @ ( q @ ( p @ implies ) @ ( p @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[114]) ).
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(33,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(34,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ or ) @ ( A @ implies ) @ axiom )
!= ( C @ axiom ) )
| ( C @ theorem ) ),
inference(simp,[status(thm)],[33]) ).
thf(35,plain,
! [B: $i,A: $i] : ( B @ ( A @ or ) @ ( B @ implies ) @ theorem ),
inference(pattern_uni,[status(thm)],[34:[bind(A,$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)],[35]) ).
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(53,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ ( B @ implies ) @ theorem )
!= ( q @ ( p @ implies ) @ ( q @ ( p @ implies ) @ ( p @ implies ) @ implies ) @ theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[42,23]) ).
thf(54,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ or ) @ ( B @ implies ) @ theorem )
!= ( q @ ( p @ implies ) @ ( q @ ( p @ implies ) @ ( p @ implies ) @ implies ) @ theorem ) ),
inference(simp,[status(thm)],[53]) ).
thf(55,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ or ) @ ( B @ implies ) )
!= ( q @ ( p @ implies ) @ ( q @ ( p @ implies ) @ ( p @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[54]) ).
thf(99,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ or ) )
!= ( q @ ( p @ implies ) ) )
| ( B
!= ( q @ ( p @ implies ) @ ( p @ implies ) ) ) ),
inference(simp,[status(thm)],[55]) ).
thf(102,plain,
! [A: $i] :
( ( q @ ( p @ implies ) @ ( p @ implies ) @ ( A @ or ) )
!= ( q @ ( p @ implies ) ) ),
inference(simp,[status(thm)],[99]) ).
thf(77,plain,
! [A: $i] :
( ( ( A @ ( A @ ( A @ or ) @ implies ) @ theorem )
!= ( q @ ( p @ implies ) @ ( q @ ( p @ implies ) @ ( p @ implies ) @ implies ) @ theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[43,23]) ).
thf(78,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ or ) @ implies ) @ theorem )
!= ( q @ ( p @ implies ) @ ( q @ ( p @ implies ) @ ( p @ implies ) @ implies ) @ theorem ) ),
inference(simp,[status(thm)],[77]) ).
thf(79,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ or ) @ implies ) )
!= ( q @ ( p @ implies ) @ ( q @ ( p @ implies ) @ ( p @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[78]) ).
thf(63,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(64,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ or ) @ ( B @ ( A @ or ) @ implies ) @ axiom )
!= ( C @ axiom ) )
| ( C @ theorem ) ),
inference(simp,[status(thm)],[63]) ).
thf(65,plain,
! [B: $i,A: $i] : ( B @ ( A @ or ) @ ( A @ ( B @ or ) @ implies ) @ theorem ),
inference(pattern_uni,[status(thm)],[64:[bind(A,$thf( I )),bind(B,$thf( H )),bind(C,$thf( I @ ( H @ or ) @ ( H @ ( I @ or ) @ implies ) ))]]) ).
thf(66,plain,
! [B: $i,A: $i] : ( B @ ( A @ or ) @ ( A @ ( B @ or ) @ implies ) @ theorem ),
inference(simp,[status(thm)],[65]) ).
thf(139,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)],[18,66]) ).
thf(140,plain,
! [B: $i,A: $i] : ( B @ not @ ( A @ or ) @ ( A @ ( B @ implies ) @ implies ) @ theorem ),
inference(pattern_uni,[status(thm)],[139:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( E @ not ))]]) ).
thf(152,plain,
! [B: $i,A: $i] : ( B @ not @ ( A @ or ) @ ( A @ ( B @ implies ) @ implies ) @ theorem ),
inference(simp,[status(thm)],[140]) ).
thf(26,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(27,plain,
! [B: $i,A: $i] : ( A @ ( B @ implies ) @ ( A @ implies ) @ axiom ),
inference(pattern_uni,[status(thm)],[26:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( E @ not ))]]) ).
thf(29,plain,
! [B: $i,A: $i] : ( A @ ( B @ implies ) @ ( A @ implies ) @ axiom ),
inference(simp,[status(thm)],[27]) ).
thf(168,plain,
! [A: $i] :
( ( A
!= ( q @ ( p @ implies ) ) )
| ( ( A @ ( A @ or ) )
!= ( q @ ( p @ implies ) @ ( p @ implies ) ) ) ),
inference(simp,[status(thm)],[79]) ).
thf(171,plain,
( ( q @ ( p @ implies ) @ ( q @ ( p @ implies ) @ or ) )
!= ( q @ ( p @ implies ) @ ( p @ implies ) ) ),
inference(simp,[status(thm)],[168]) ).
thf(173,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( q @ ( p @ implies ) @ ( q @ ( p @ implies ) @ or ) ) )
| ( ( B @ ( A @ implies ) )
!= ( q @ ( p @ implies ) @ ( p @ implies ) ) ) ),
inference(paramod_ordered,[status(thm)],[18,171]) ).
thf(175,plain,
! [B: $i,A: $i] :
( ( B
!= ( q @ ( p @ implies ) ) )
| ( ( A @ not )
!= ( q @ ( p @ implies ) ) )
| ( ( B @ ( A @ implies ) )
!= ( q @ ( p @ implies ) @ ( p @ implies ) ) ) ),
inference(simp,[status(thm)],[173]) ).
thf(179,plain,
! [A: $i] :
( ( ( A @ not )
!= ( q @ ( p @ implies ) ) )
| ( ( q @ ( p @ implies ) @ ( A @ implies ) )
!= ( q @ ( p @ implies ) @ ( p @ implies ) ) ) ),
inference(simp,[status(thm)],[175]) ).
thf(104,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( q @ ( p @ implies ) @ ( p @ implies ) @ ( C @ or ) ) )
| ( ( B @ ( A @ implies ) )
!= ( q @ ( p @ implies ) ) ) ),
inference(paramod_ordered,[status(thm)],[18,102]) ).
thf(105,plain,
! [A: $i] :
( ( q @ ( p @ implies ) @ ( p @ implies ) @ ( A @ implies ) )
!= ( q @ ( p @ implies ) ) ),
inference(pattern_uni,[status(thm)],[104:[bind(A,$thf( D )),bind(B,$thf( q @ ( p @ implies ) @ ( p @ implies ) )),bind(C,$thf( D @ not ))]]) ).
thf(106,plain,
! [A: $i] :
( ( q @ ( p @ implies ) @ ( p @ implies ) @ ( A @ implies ) )
!= ( q @ ( p @ implies ) ) ),
inference(simp,[status(thm)],[105]) ).
thf(24,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(25,plain,
! [A: $i] : ( A @ not @ ( A @ not @ ( A @ implies ) @ implies ) @ axiom ),
inference(pattern_uni,[status(thm)],[24:[bind(A,$thf( E )),bind(B,$thf( E @ not )),bind(C,$thf( E @ not ))]]) ).
thf(28,plain,
! [A: $i] : ( A @ not @ ( A @ not @ ( A @ implies ) @ implies ) @ axiom ),
inference(simp,[status(thm)],[25]) ).
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(137,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)],[18,66]) ).
thf(138,plain,
! [B: $i,A: $i] : ( A @ ( B @ implies ) @ ( B @ not @ ( A @ or ) @ implies ) @ theorem ),
inference(pattern_uni,[status(thm)],[137:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( E @ not )),bind(D,$thf( B ))]]) ).
thf(151,plain,
! [B: $i,A: $i] : ( A @ ( B @ implies ) @ ( B @ not @ ( A @ or ) @ implies ) @ theorem ),
inference(simp,[status(thm)],[138]) ).
thf(180,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( D @ not @ ( C @ or ) ) )
| ( C @ ( D @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ theorem ) ),
inference(paramod_ordered,[status(thm)],[18,151]) ).
thf(181,plain,
! [B: $i,A: $i] : ( A @ not @ ( B @ implies ) @ ( B @ not @ ( A @ implies ) @ implies ) @ theorem ),
inference(pattern_uni,[status(thm)],[180:[bind(A,$thf( E )),bind(B,$thf( F @ not )),bind(C,$thf( E @ not )),bind(D,$thf( F ))]]) ).
thf(191,plain,
! [B: $i,A: $i] : ( A @ not @ ( B @ implies ) @ ( B @ not @ ( A @ implies ) @ implies ) @ theorem ),
inference(simp,[status(thm)],[181]) ).
thf(22,plain,
! [B: $i,A: $i] :
( ~ ( B @ theorem )
| ~ ( A @ ( B @ implies ) @ theorem )
| ( A @ theorem ) ),
inference(cnf,[status(esa)],[21]) ).
thf(39,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( A @ implies ) @ axiom )
!= ( C @ axiom ) )
| ~ $true
| ( C @ theorem ) ),
inference(paramod_ordered,[status(thm)],[29,20]) ).
thf(40,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( A @ implies ) @ axiom )
!= ( C @ axiom ) )
| ( C @ theorem ) ),
inference(simp,[status(thm)],[39]) ).
thf(41,plain,
! [B: $i,A: $i] : ( B @ ( A @ implies ) @ ( B @ implies ) @ theorem ),
inference(pattern_uni,[status(thm)],[40:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( G @ ( F @ implies ) @ ( G @ implies ) ))]]) ).
thf(44,plain,
! [B: $i,A: $i] : ( B @ ( A @ implies ) @ ( B @ implies ) @ theorem ),
inference(simp,[status(thm)],[41]) ).
thf(59,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(60,plain,
! [B: $i,A: $i] : ( B @ not @ ( A @ or ) @ ( A @ ( B @ implies ) @ implies ) @ axiom ),
inference(pattern_uni,[status(thm)],[59:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( E @ not )),bind(D,$thf( B ))]]) ).
thf(67,plain,
! [B: $i,A: $i] : ( B @ not @ ( A @ or ) @ ( A @ ( B @ implies ) @ implies ) @ axiom ),
inference(simp,[status(thm)],[60]) ).
thf(154,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)],[18,67]) ).
thf(155,plain,
! [B: $i,A: $i] : ( B @ not @ ( A @ implies ) @ ( A @ not @ ( B @ implies ) @ implies ) @ axiom ),
inference(pattern_uni,[status(thm)],[154:[bind(A,$thf( E )),bind(B,$thf( F @ not )),bind(C,$thf( E @ not )),bind(D,$thf( F ))]]) ).
thf(159,plain,
! [B: $i,A: $i] : ( B @ not @ ( A @ implies ) @ ( A @ not @ ( B @ implies ) @ implies ) @ axiom ),
inference(simp,[status(thm)],[155]) ).
thf(100,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( D @ ( C @ or ) ) )
| ( ( B @ ( A @ implies ) @ ( D @ implies ) )
!= ( q @ ( p @ implies ) @ ( q @ ( p @ implies ) @ ( p @ implies ) @ implies ) ) ) ),
inference(paramod_ordered,[status(thm)],[18,55]) ).
thf(101,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ implies ) @ ( A @ implies ) )
!= ( q @ ( p @ implies ) @ ( q @ ( p @ implies ) @ ( p @ implies ) @ implies ) ) ),
inference(pattern_uni,[status(thm)],[100:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( E @ not )),bind(D,$thf( B ))]]) ).
thf(103,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ implies ) @ ( A @ implies ) )
!= ( q @ ( p @ implies ) @ ( q @ ( p @ implies ) @ ( p @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[101]) ).
thf(83,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ implies ) @ theorem )
!= ( q @ ( p @ implies ) @ ( q @ ( p @ implies ) @ ( p @ implies ) @ implies ) @ theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[44,23]) ).
thf(84,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ implies ) @ theorem )
!= ( q @ ( p @ implies ) @ ( q @ ( p @ implies ) @ ( p @ implies ) @ implies ) @ theorem ) ),
inference(simp,[status(thm)],[83]) ).
thf(91,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ implies ) )
!= ( q @ ( p @ implies ) @ ( q @ ( p @ implies ) @ ( p @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[84]) ).
thf(176,plain,
! [B: $i,A: $i] :
( ( B
!= ( q @ ( p @ implies ) ) )
| ( ( A @ not )
!= ( q @ ( p @ implies ) ) )
| ( B
!= ( q @ ( p @ implies ) ) )
| ( A != p ) ),
inference(simp,[status(thm)],[173]) ).
thf(177,plain,
( ( q @ ( p @ implies ) )
!= ( p @ not ) ),
inference(simp,[status(thm)],[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(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(30,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 ) @ theorem )
!= ( B @ theorem ) )
| ~ ( B @ theorem )
| ( A @ theorem ) ),
inference(simp,[status(thm)],[30]) ).
thf(118,plain,
! [A: $i] :
( ( ( q @ ( p @ implies ) @ ( p @ implies ) )
!= q )
| ( A != p ) ),
inference(simp,[status(thm)],[106]) ).
thf(119,plain,
( ( q @ ( p @ implies ) @ ( p @ implies ) )
!= q ),
inference(simp,[status(thm)],[118]) ).
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(61,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(62,plain,
! [B: $i,A: $i] : ( A @ ( B @ implies ) @ ( B @ not @ ( A @ or ) @ implies ) @ axiom ),
inference(pattern_uni,[status(thm)],[61:[bind(A,$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)],[62]) ).
thf(1107,plain,
$false,
inference(e,[status(thm)],[115,10,42,14,102,13,17,18,43,79,20,152,29,179,106,28,21,191,22,44,12,159,103,91,66,67,177,16,31,55,171,23,119,82,151,19,15,68]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL198-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.07 % 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
% 0.12/0.41 % Computer : n015.cluster.edu
% 0.12/0.41 % Model : x86_64 x86_64
% 0.12/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.41 % Memory : 8046.5625MB
% 0.12/0.41 % OS : Linux 6.8.0-71-generic
% 0.12/0.41 % CPULimit : 300
% 0.12/0.41 % WCLimit : 300
% 0.12/0.41 % DateTime : Fri Sep 25 22:03:43 UTC 2026
% 0.12/0.41 % CPUTime :
% 0.12/0.41 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
% 1.34/1.23 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.84/1.51 % [INFO] Parsing done (280ms).
% 1.84/1.54 % [INFO] Running in sequential loop mode.
% 2.74/2.06 % [INFO] eprover registered as external prover.
% 2.74/2.07 % [INFO] Scanning for conjecture ...
% 2.95/2.16 % [INFO] Found a conjecture (or negated_conjecture) and 8 axioms. Running axiom selection ...
% 2.95/2.19 % [INFO] Axiom selection finished. Selected 8 axioms (removed 0 axioms).
% 3.07/2.21 % [INFO] Problem is propositional (TPTP CNF).
% 3.07/2.22 % [INFO] Type checking passed.
% 3.07/2.22 % [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 ...
% 14.88/4.71 % External prover 'e' found a proof!
% 14.88/4.71 % [INFO] Killing All external provers ...
% 14.88/4.71 % Time passed: 4082ms (effective reasoning time: 3162ms)
% 14.88/4.71 % 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
% 14.88/4.71 % No. of inferences in proof: 98
% 14.88/4.71 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 4082 ms resp. 3162 ms w/o parsing
% 14.88/4.79 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 14.88/4.79 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------