%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL230-3 : 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 : n019.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 07:51:17 AM UTC 2026
% Result : Unsatisfiable 26.88s 6.84s
% Output : Refutation 23.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of formulae : 99 ( 44 unt; 0 typ; 0 def)
% Number of atoms : 213 ( 90 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 1312 ( 135 ~; 94 |; 0 &;1083 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 9 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 : 213 ( 0 ^; 213 !; 0 ?; 213 :)
% 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(p_decl,type,
p: $i ).
thf(q_decl,type,
q: $i ).
thf(r_decl,type,
r: $i ).
thf(axiom_decl,type,
axiom: $i > $o ).
thf(not_decl,type,
not: $i > $i ).
thf(1,negated_conjecture,
~ ( r @ ( q @ implies ) @ ( p @ or ) @ ( r @ ( p @ or ) @ ( q @ ( p @ or ) @ implies ) @ implies ) @ theorem ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
thf(10,plain,
~ ( r @ ( q @ implies ) @ ( p @ or ) @ ( r @ ( p @ or ) @ ( q @ ( p @ or ) @ 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(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(63,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(64,plain,
! [B: $i,A: $i] : ( A @ ( B @ implies ) @ ( B @ not @ ( A @ or ) @ implies ) @ axiom ),
inference(pattern_uni,[status(thm)],[63:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( E @ not ))]]) ).
thf(65,plain,
! [B: $i,A: $i] : ( A @ ( B @ implies ) @ ( B @ not @ ( A @ or ) @ implies ) @ axiom ),
inference(simp,[status(thm)],[64]) ).
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(162,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(163,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ or ) @ ( A @ implies ) @ axiom )
!= ( C @ axiom ) )
| ( C @ theorem ) ),
inference(simp,[status(thm)],[162]) ).
thf(164,plain,
! [B: $i,A: $i] : ( B @ ( A @ or ) @ ( B @ implies ) @ theorem ),
inference(pattern_uni,[status(thm)],[163:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( G @ ( F @ or ) @ ( G @ implies ) ))]]) ).
thf(193,plain,
! [B: $i,A: $i] : ( B @ ( A @ or ) @ ( B @ implies ) @ theorem ),
inference(simp,[status(thm)],[164]) ).
thf(11,plain,
~ ( r @ ( q @ implies ) @ ( p @ or ) @ ( r @ ( p @ or ) @ ( q @ ( p @ or ) @ implies ) @ implies ) @ theorem ),
inference(polarity_switch,[status(thm)],[10]) ).
thf(25,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( r @ ( q @ implies ) @ ( p @ or ) ) )
| ~ ( B @ ( A @ implies ) @ ( r @ ( p @ or ) @ ( q @ ( p @ or ) @ implies ) @ implies ) @ theorem ) ),
inference(paramod_ordered,[status(thm)],[18,11]) ).
thf(32,plain,
! [B: $i,A: $i] :
( ( B
!= ( r @ ( q @ implies ) ) )
| ( ( A @ not )
!= p )
| ~ ( B @ ( A @ implies ) @ ( r @ ( p @ or ) @ ( q @ ( p @ or ) @ implies ) @ implies ) @ theorem ) ),
inference(simp,[status(thm)],[25]) ).
thf(33,plain,
! [A: $i] :
( ( ( A @ not )
!= p )
| ~ ( r @ ( q @ implies ) @ ( A @ implies ) @ ( r @ ( p @ or ) @ ( q @ ( p @ or ) @ implies ) @ implies ) @ theorem ) ),
inference(simp,[status(thm)],[32]) ).
thf(38,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( r @ ( p @ or ) ) )
| ( ( C @ not )
!= p )
| ~ ( r @ ( q @ implies ) @ ( C @ implies ) @ ( B @ ( A @ implies ) @ ( q @ ( p @ or ) @ implies ) @ implies ) @ theorem ) ),
inference(paramod_ordered,[status(thm)],[18,33]) ).
thf(40,plain,
! [C: $i,B: $i,A: $i] :
( ( B != r )
| ( ( A @ not )
!= p )
| ( ( C @ not )
!= p )
| ~ ( r @ ( q @ implies ) @ ( C @ implies ) @ ( B @ ( A @ implies ) @ ( q @ ( p @ or ) @ implies ) @ implies ) @ theorem ) ),
inference(simp,[status(thm)],[38]) ).
thf(42,plain,
! [B: $i,A: $i] :
( ( ( A @ not )
!= p )
| ( ( B @ not )
!= p )
| ~ ( r @ ( q @ implies ) @ ( B @ implies ) @ ( r @ ( A @ implies ) @ ( q @ ( p @ or ) @ implies ) @ implies ) @ theorem ) ),
inference(simp,[status(thm)],[40]) ).
thf(57,plain,
! [B: $i,A: $i] :
( ( p != p )
| ( ( A @ not )
!= ( B @ not ) )
| ( ( B @ not )
!= p )
| ~ ( r @ ( q @ implies ) @ ( B @ implies ) @ ( r @ ( A @ implies ) @ ( q @ ( p @ or ) @ implies ) @ implies ) @ theorem ) ),
inference(eqfactor_ordered,[status(thm)],[42]) ).
thf(59,plain,
! [A: $i] :
( ( ( A @ not )
!= p )
| ~ ( r @ ( q @ implies ) @ ( A @ implies ) @ ( r @ ( A @ implies ) @ ( q @ ( p @ or ) @ implies ) @ implies ) @ theorem ) ),
inference(pattern_uni,[status(thm)],[57:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(61,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(62,plain,
! [B: $i,A: $i] : ( B @ not @ ( A @ or ) @ ( A @ ( B @ implies ) @ implies ) @ axiom ),
inference(pattern_uni,[status(thm)],[61:[bind(A,$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)],[62]) ).
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)],[18,13]) ).
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(35,plain,
! [B: $i,A: $i] : ( A @ ( B @ implies ) @ ( A @ implies ) @ axiom ),
inference(simp,[status(thm)],[29]) ).
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(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)],[18,12]) ).
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(34,plain,
! [A: $i] : ( A @ not @ ( A @ not @ ( A @ implies ) @ implies ) @ axiom ),
inference(simp,[status(thm)],[27]) ).
thf(165,plain,
! [B: $i,A: $i] :
( ( ( A @ not @ ( A @ not @ ( A @ implies ) @ implies ) @ axiom )
!= ( B @ axiom ) )
| ~ $true
| ( B @ theorem ) ),
inference(paramod_ordered,[status(thm)],[34,20]) ).
thf(166,plain,
! [B: $i,A: $i] :
( ( ( A @ not @ ( A @ not @ ( A @ implies ) @ implies ) @ axiom )
!= ( B @ axiom ) )
| ( B @ theorem ) ),
inference(simp,[status(thm)],[165]) ).
thf(167,plain,
! [A: $i] : ( A @ not @ ( A @ not @ ( A @ implies ) @ implies ) @ theorem ),
inference(pattern_uni,[status(thm)],[166:[bind(A,$thf( H )),bind(B,$thf( H @ not @ ( H @ not @ ( H @ implies ) @ implies ) ))]]) ).
thf(194,plain,
! [A: $i] : ( A @ not @ ( A @ not @ ( A @ implies ) @ implies ) @ theorem ),
inference(simp,[status(thm)],[167]) ).
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(189,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ or ) @ implies ) @ axiom )
!= ( B @ axiom ) )
| ~ $true
| ( B @ theorem ) ),
inference(paramod_ordered,[status(thm)],[12,20]) ).
thf(190,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ or ) @ implies ) @ axiom )
!= ( B @ axiom ) )
| ( B @ theorem ) ),
inference(simp,[status(thm)],[189]) ).
thf(191,plain,
! [A: $i] : ( A @ ( A @ ( A @ or ) @ implies ) @ theorem ),
inference(pattern_uni,[status(thm)],[190:[bind(A,$thf( D )),bind(B,$thf( D @ ( D @ ( D @ or ) @ implies ) ))]]) ).
thf(203,plain,
! [A: $i] : ( A @ ( A @ ( A @ or ) @ implies ) @ theorem ),
inference(simp,[status(thm)],[191]) ).
thf(24,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( r @ ( p @ or ) ) )
| ~ ( r @ ( q @ implies ) @ ( p @ or ) @ ( B @ ( A @ implies ) @ ( q @ ( p @ or ) @ implies ) @ implies ) @ theorem ) ),
inference(paramod_ordered,[status(thm)],[18,11]) ).
thf(31,plain,
! [B: $i,A: $i] :
( ( B != r )
| ( ( A @ not )
!= p )
| ~ ( r @ ( q @ implies ) @ ( p @ or ) @ ( B @ ( A @ implies ) @ ( q @ ( p @ or ) @ implies ) @ implies ) @ theorem ) ),
inference(simp,[status(thm)],[24]) ).
thf(37,plain,
! [A: $i] :
( ( ( A @ not )
!= p )
| ~ ( r @ ( q @ implies ) @ ( p @ or ) @ ( r @ ( A @ implies ) @ ( q @ ( p @ or ) @ implies ) @ implies ) @ theorem ) ),
inference(simp,[status(thm)],[31]) ).
thf(51,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( q @ ( p @ or ) ) )
| ( ( C @ not )
!= p )
| ~ ( r @ ( q @ implies ) @ ( p @ or ) @ ( r @ ( C @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ theorem ) ),
inference(paramod_ordered,[status(thm)],[18,37]) ).
thf(53,plain,
! [C: $i,B: $i,A: $i] :
( ( B != q )
| ( ( A @ not )
!= p )
| ( ( C @ not )
!= p )
| ~ ( r @ ( q @ implies ) @ ( p @ or ) @ ( r @ ( C @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ theorem ) ),
inference(simp,[status(thm)],[51]) ).
thf(55,plain,
! [B: $i,A: $i] :
( ( ( A @ not )
!= p )
| ( ( B @ not )
!= p )
| ~ ( r @ ( q @ implies ) @ ( p @ or ) @ ( r @ ( B @ implies ) @ ( q @ ( A @ implies ) @ implies ) @ implies ) @ theorem ) ),
inference(simp,[status(thm)],[53]) ).
thf(228,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ ( B @ implies ) @ theorem )
!= ( r @ ( q @ implies ) @ ( p @ or ) @ ( r @ ( p @ or ) @ ( q @ ( p @ or ) @ implies ) @ implies ) @ theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[193,11]) ).
thf(229,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ or ) @ ( B @ implies ) @ theorem )
!= ( r @ ( q @ implies ) @ ( p @ or ) @ ( r @ ( p @ or ) @ ( q @ ( p @ or ) @ implies ) @ implies ) @ theorem ) ),
inference(simp,[status(thm)],[228]) ).
thf(235,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ or ) @ ( B @ implies ) )
!= ( r @ ( q @ implies ) @ ( p @ or ) @ ( r @ ( p @ or ) @ ( q @ ( p @ or ) @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[229]) ).
thf(39,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( q @ ( p @ or ) ) )
| ( ( C @ not )
!= p )
| ~ ( r @ ( q @ implies ) @ ( C @ implies ) @ ( r @ ( p @ or ) @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ theorem ) ),
inference(paramod_ordered,[status(thm)],[18,33]) ).
thf(41,plain,
! [C: $i,B: $i,A: $i] :
( ( B != q )
| ( ( A @ not )
!= p )
| ( ( C @ not )
!= p )
| ~ ( r @ ( q @ implies ) @ ( C @ implies ) @ ( r @ ( p @ or ) @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ theorem ) ),
inference(simp,[status(thm)],[39]) ).
thf(43,plain,
! [B: $i,A: $i] :
( ( ( A @ not )
!= p )
| ( ( B @ not )
!= p )
| ~ ( r @ ( q @ implies ) @ ( B @ implies ) @ ( r @ ( p @ or ) @ ( q @ ( A @ implies ) @ implies ) @ implies ) @ theorem ) ),
inference(simp,[status(thm)],[41]) ).
thf(77,plain,
! [B: $i,A: $i] :
( ( p != p )
| ( ( A @ not )
!= ( B @ not ) )
| ( ( B @ not )
!= p )
| ~ ( r @ ( q @ implies ) @ ( B @ implies ) @ ( r @ ( p @ or ) @ ( q @ ( A @ implies ) @ implies ) @ implies ) @ theorem ) ),
inference(eqfactor_ordered,[status(thm)],[43]) ).
thf(79,plain,
! [A: $i] :
( ( ( A @ not )
!= p )
| ~ ( r @ ( q @ implies ) @ ( A @ implies ) @ ( r @ ( p @ or ) @ ( q @ ( A @ implies ) @ implies ) @ implies ) @ theorem ) ),
inference(pattern_uni,[status(thm)],[77:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
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(92,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( E @ ( C @ or ) ) )
| ( B @ ( A @ implies ) @ ( D @ or ) @ ( E @ ( D @ or ) @ ( C @ or ) @ implies ) @ axiom ) ),
inference(paramod_ordered,[status(thm)],[18,15]) ).
thf(93,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( C @ implies ) @ ( B @ or ) @ ( A @ ( B @ or ) @ ( C @ not @ or ) @ implies ) @ axiom ),
inference(pattern_uni,[status(thm)],[92:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( F @ not )),bind(D,$thf( D )),bind(E,$thf( B ))]]) ).
thf(100,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( C @ implies ) @ ( B @ or ) @ ( A @ ( B @ or ) @ ( C @ not @ or ) @ implies ) @ axiom ),
inference(simp,[status(thm)],[93]) ).
thf(122,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( C @ implies ) @ ( B @ or ) @ ( A @ ( B @ or ) @ ( C @ implies ) @ implies ) @ axiom ),
inference(rewrite,[status(thm)],[100,18]) ).
thf(67,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)],[18,65]) ).
thf(68,plain,
! [B: $i,A: $i] : ( A @ not @ ( B @ implies ) @ ( B @ not @ ( A @ implies ) @ implies ) @ axiom ),
inference(pattern_uni,[status(thm)],[67:[bind(A,$thf( E )),bind(B,$thf( F @ not )),bind(C,$thf( E @ not )),bind(D,$thf( F ))]]) ).
thf(69,plain,
! [B: $i,A: $i] : ( A @ not @ ( B @ implies ) @ ( B @ not @ ( A @ implies ) @ implies ) @ axiom ),
inference(simp,[status(thm)],[68]) ).
thf(94,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( E @ ( C @ or ) @ ( D @ or ) ) )
| ( B @ ( A @ implies ) @ ( E @ ( D @ or ) @ ( C @ or ) @ implies ) @ axiom ) ),
inference(paramod_ordered,[status(thm)],[18,15]) ).
thf(95,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ or ) @ ( A @ implies ) @ ( C @ ( A @ not @ or ) @ ( B @ or ) @ implies ) @ axiom ),
inference(pattern_uni,[status(thm)],[94:[bind(A,$thf( F )),bind(B,$thf( H @ ( G @ or ) )),bind(C,$thf( G )),bind(D,$thf( F @ not )),bind(E,$thf( H ))]]) ).
thf(101,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ or ) @ ( A @ implies ) @ ( C @ ( A @ not @ or ) @ ( B @ or ) @ implies ) @ axiom ),
inference(simp,[status(thm)],[95]) ).
thf(138,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ or ) @ ( A @ implies ) @ ( C @ ( A @ implies ) @ ( B @ or ) @ implies ) @ axiom ),
inference(rewrite,[status(thm)],[101,18]) ).
thf(23,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( q @ ( p @ or ) ) )
| ~ ( r @ ( q @ implies ) @ ( p @ or ) @ ( r @ ( p @ or ) @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ theorem ) ),
inference(paramod_ordered,[status(thm)],[18,11]) ).
thf(30,plain,
! [B: $i,A: $i] :
( ( B != q )
| ( ( A @ not )
!= p )
| ~ ( r @ ( q @ implies ) @ ( p @ or ) @ ( r @ ( p @ or ) @ ( B @ ( A @ implies ) @ implies ) @ implies ) @ theorem ) ),
inference(simp,[status(thm)],[23]) ).
thf(36,plain,
! [A: $i] :
( ( ( A @ not )
!= p )
| ~ ( r @ ( q @ implies ) @ ( p @ or ) @ ( r @ ( p @ or ) @ ( q @ ( A @ implies ) @ implies ) @ implies ) @ theorem ) ),
inference(simp,[status(thm)],[30]) ).
thf(44,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( r @ ( p @ or ) ) )
| ( ( C @ not )
!= p )
| ~ ( r @ ( q @ implies ) @ ( p @ or ) @ ( B @ ( A @ implies ) @ ( q @ ( C @ implies ) @ implies ) @ implies ) @ theorem ) ),
inference(paramod_ordered,[status(thm)],[18,36]) ).
thf(46,plain,
! [C: $i,B: $i,A: $i] :
( ( B != r )
| ( ( A @ not )
!= p )
| ( ( C @ not )
!= p )
| ~ ( r @ ( q @ implies ) @ ( p @ or ) @ ( B @ ( A @ implies ) @ ( q @ ( C @ implies ) @ implies ) @ implies ) @ theorem ) ),
inference(simp,[status(thm)],[44]) ).
thf(48,plain,
! [B: $i,A: $i] :
( ( ( A @ not )
!= p )
| ( ( B @ not )
!= p )
| ~ ( r @ ( q @ implies ) @ ( p @ or ) @ ( r @ ( A @ implies ) @ ( q @ ( B @ implies ) @ implies ) @ implies ) @ theorem ) ),
inference(simp,[status(thm)],[46]) ).
thf(86,plain,
! [B: $i,A: $i] :
( ( p != p )
| ( ( A @ not )
!= ( B @ not ) )
| ( ( B @ not )
!= p )
| ~ ( r @ ( q @ implies ) @ ( p @ or ) @ ( r @ ( A @ implies ) @ ( q @ ( B @ implies ) @ implies ) @ implies ) @ theorem ) ),
inference(eqfactor_ordered,[status(thm)],[48]) ).
thf(88,plain,
! [A: $i] :
( ( ( A @ not )
!= p )
| ~ ( r @ ( q @ implies ) @ ( p @ or ) @ ( r @ ( A @ implies ) @ ( q @ ( A @ implies ) @ implies ) @ implies ) @ theorem ) ),
inference(pattern_uni,[status(thm)],[86:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(171,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( A @ implies ) @ axiom )
!= ( C @ axiom ) )
| ~ $true
| ( C @ theorem ) ),
inference(paramod_ordered,[status(thm)],[35,20]) ).
thf(172,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( A @ implies ) @ axiom )
!= ( C @ axiom ) )
| ( C @ theorem ) ),
inference(simp,[status(thm)],[171]) ).
thf(173,plain,
! [B: $i,A: $i] : ( B @ ( A @ implies ) @ ( B @ implies ) @ theorem ),
inference(pattern_uni,[status(thm)],[172:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( G @ ( F @ implies ) @ ( G @ implies ) ))]]) ).
thf(196,plain,
! [B: $i,A: $i] : ( B @ ( A @ implies ) @ ( B @ implies ) @ theorem ),
inference(simp,[status(thm)],[173]) ).
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(50,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( r @ ( q @ implies ) @ ( p @ or ) ) )
| ( ( C @ not )
!= p )
| ~ ( B @ ( A @ implies ) @ ( r @ ( C @ implies ) @ ( q @ ( p @ or ) @ implies ) @ implies ) @ theorem ) ),
inference(paramod_ordered,[status(thm)],[18,37]) ).
thf(52,plain,
! [C: $i,B: $i,A: $i] :
( ( B
!= ( r @ ( q @ implies ) ) )
| ( ( A @ not )
!= p )
| ( ( C @ not )
!= p )
| ~ ( B @ ( A @ implies ) @ ( r @ ( C @ implies ) @ ( q @ ( p @ or ) @ implies ) @ implies ) @ theorem ) ),
inference(simp,[status(thm)],[50]) ).
thf(54,plain,
! [B: $i,A: $i] :
( ( ( A @ not )
!= p )
| ( ( B @ not )
!= p )
| ~ ( r @ ( q @ implies ) @ ( A @ implies ) @ ( r @ ( B @ implies ) @ ( q @ ( p @ or ) @ implies ) @ implies ) @ theorem ) ),
inference(simp,[status(thm)],[52]) ).
thf(45,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( r @ ( q @ implies ) @ ( p @ or ) ) )
| ( ( C @ not )
!= p )
| ~ ( B @ ( A @ implies ) @ ( r @ ( p @ or ) @ ( q @ ( C @ implies ) @ implies ) @ implies ) @ theorem ) ),
inference(paramod_ordered,[status(thm)],[18,36]) ).
thf(47,plain,
! [C: $i,B: $i,A: $i] :
( ( B
!= ( r @ ( q @ implies ) ) )
| ( ( A @ not )
!= p )
| ( ( C @ not )
!= p )
| ~ ( B @ ( A @ implies ) @ ( r @ ( p @ or ) @ ( q @ ( C @ implies ) @ implies ) @ implies ) @ theorem ) ),
inference(simp,[status(thm)],[45]) ).
thf(49,plain,
! [B: $i,A: $i] :
( ( ( A @ not )
!= p )
| ( ( B @ not )
!= p )
| ~ ( r @ ( q @ implies ) @ ( A @ implies ) @ ( r @ ( p @ or ) @ ( q @ ( B @ implies ) @ implies ) @ implies ) @ theorem ) ),
inference(simp,[status(thm)],[47]) ).
thf(328,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ or ) )
!= ( r @ ( q @ implies ) @ ( p @ or ) ) )
| ( B
!= ( r @ ( p @ or ) @ ( q @ ( p @ or ) @ implies ) ) ) ),
inference(simp,[status(thm)],[235]) ).
thf(350,plain,
! [A: $i] :
( ( r @ ( p @ or ) @ ( q @ ( p @ or ) @ implies ) @ ( A @ or ) )
!= ( r @ ( q @ implies ) @ ( p @ or ) ) ),
inference(simp,[status(thm)],[328]) ).
thf(1447,plain,
$false,
inference(e,[status(thm)],[10,20,65,193,13,59,66,35,194,16,203,55,235,79,15,122,69,138,88,42,37,14,196,21,33,34,17,12,54,49,350,48,18,11,43,36,19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL230-3 : 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
% 0.14/0.62 % Computer : n019.cluster.edu
% 0.14/0.62 % Model : x86_64 x86_64
% 0.14/0.62 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.62 % Memory : 8046.5625MB
% 0.14/0.62 % OS : Linux 6.8.0-71-generic
% 0.14/0.62 % CPULimit : 300
% 0.14/0.62 % WCLimit : 300
% 0.14/0.62 % DateTime : Fri Sep 25 22:04:20 UTC 2026
% 0.14/0.62 % CPUTime :
% 0.14/0.62 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
% 0.87/1.11 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.45/1.31 % [INFO] Parsing done (201ms).
% 1.45/1.33 % [INFO] Running in sequential loop mode.
% 2.23/1.73 % [INFO] eprover registered as external prover.
% 2.23/1.74 % [INFO] Scanning for conjecture ...
% 2.45/1.88 % [INFO] Found a conjecture (or negated_conjecture) and 8 axioms. Running axiom selection ...
% 2.62/1.93 % [INFO] Axiom selection finished. Selected 8 axioms (removed 0 axioms).
% 2.62/1.95 % [INFO] Problem is propositional (TPTP CNF).
% 2.62/1.96 % [INFO] Type checking passed.
% 2.62/1.97 % [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 ...
% 26.88/6.83 % External prover 'e' found a proof!
% 26.88/6.83 % [INFO] Killing All external provers ...
% 26.88/6.84 % Time passed: 6074ms (effective reasoning time: 5496ms)
% 26.88/6.84 % 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
% 26.88/6.84 % No. of inferences in proof: 99
% 26.88/6.84 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 6074 ms resp. 5496 ms w/o parsing
% 23.20/6.95 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 23.20/6.96 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------