%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL224-1 : TPTP v9.3.1. Released v1.1.0.
% 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 : n005.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 07:51:15 AM UTC 2026
% Result : Unsatisfiable 16.32s 5.86s
% Output : Refutation 19.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 9
% Syntax : Number of formulae : 114 ( 44 unt; 0 typ; 0 def)
% Number of atoms : 329 ( 53 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 1909 ( 169 ~; 111 |; 0 &;1629 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 229 ( 0 ^; 229 !; 0 ?; 229 :)
% Comments :
%------------------------------------------------------------------------------
thf(theorem_decl,type,
theorem: $i > $o ).
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(r_decl,type,
r: $i ).
thf(axiom_decl,type,
axiom: $i > $o ).
thf(4,axiom,
! [B: $i,A: $i] : ( A @ ( B @ or ) @ ( B @ ( A @ or ) @ not @ or ) @ axiom ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1_4) ).
thf(14,plain,
! [B: $i,A: $i] : ( A @ ( B @ or ) @ ( B @ ( A @ or ) @ not @ or ) @ axiom ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(8,axiom,
! [B: $i,A: $i] :
( ~ ( B @ theorem )
| ~ ( A @ ( B @ not @ or ) @ axiom )
| ( A @ theorem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_2) ).
thf(19,plain,
! [B: $i,A: $i] :
( ~ ( B @ theorem )
| ~ ( A @ ( B @ not @ or ) @ axiom )
| ( A @ theorem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(20,plain,
! [B: $i,A: $i] :
( ~ ( B @ theorem )
| ~ ( A @ ( B @ not @ or ) @ axiom )
| ( A @ theorem ) ),
inference(cnf,[status(esa)],[19]) ).
thf(23,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ or ) @ ( B @ ( A @ or ) @ not @ or ) @ axiom )
!= ( C @ ( D @ not @ or ) @ axiom ) )
| ~ ( D @ theorem )
| ~ $true
| ( C @ theorem ) ),
inference(paramod_ordered,[status(thm)],[14,20]) ).
thf(24,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ or ) @ ( B @ ( A @ or ) @ not @ or ) @ axiom )
!= ( C @ ( D @ not @ or ) @ axiom ) )
| ~ ( D @ theorem )
| ( C @ theorem ) ),
inference(simp,[status(thm)],[23]) ).
thf(25,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ or ) @ theorem )
| ( B @ ( A @ or ) @ theorem ) ),
inference(pattern_uni,[status(thm)],[24:[bind(A,$thf( H )),bind(B,$thf( G )),bind(C,$thf( H @ ( G @ or ) )),bind(D,$thf( G @ ( H @ or ) ))]]) ).
thf(32,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ or ) @ theorem )
| ( B @ ( A @ or ) @ theorem ) ),
inference(simp,[status(thm)],[25]) ).
thf(9,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ not @ or ) @ theorem )
| ~ ( C @ ( A @ not @ or ) @ axiom )
| ( B @ ( A @ not @ or ) @ theorem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_3) ).
thf(21,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ not @ or ) @ theorem )
| ~ ( C @ ( A @ not @ or ) @ axiom )
| ( B @ ( A @ not @ or ) @ theorem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(22,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ not @ or ) @ theorem )
| ~ ( C @ ( A @ not @ or ) @ axiom )
| ( B @ ( A @ not @ or ) @ theorem ) ),
inference(cnf,[status(esa)],[21]) ).
thf(1,negated_conjecture,
~ ( r @ ( p @ or ) @ ( q @ ( p @ or ) @ not @ or ) @ ( r @ ( q @ not @ or ) @ ( p @ or ) @ not @ or ) @ theorem ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
thf(10,plain,
~ ( r @ ( p @ or ) @ ( q @ ( p @ or ) @ not @ or ) @ ( r @ ( q @ not @ or ) @ ( p @ or ) @ not @ or ) @ theorem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(11,plain,
~ ( r @ ( p @ or ) @ ( q @ ( p @ or ) @ not @ or ) @ ( r @ ( q @ not @ or ) @ ( p @ or ) @ not @ or ) @ theorem ),
inference(polarity_switch,[status(thm)],[10]) ).
thf(50,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) @ theorem )
!= ( r @ ( p @ or ) @ ( q @ ( p @ or ) @ not @ or ) @ ( r @ ( q @ not @ or ) @ ( p @ or ) @ not @ or ) @ theorem ) )
| ~ $true
| ~ ( B @ ( C @ not @ or ) @ theorem )
| ~ ( C @ ( A @ not @ or ) @ axiom ) ),
inference(paramod_ordered,[status(thm)],[22,11]) ).
thf(51,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) @ theorem )
!= ( r @ ( p @ or ) @ ( q @ ( p @ or ) @ not @ or ) @ ( r @ ( q @ not @ or ) @ ( p @ or ) @ not @ or ) @ theorem ) )
| ~ ( B @ ( C @ not @ or ) @ theorem )
| ~ ( C @ ( A @ not @ or ) @ axiom ) ),
inference(simp,[status(thm)],[50]) ).
thf(52,plain,
! [A: $i] :
( ~ ( r @ ( p @ or ) @ ( q @ ( p @ or ) @ not @ or ) @ ( A @ not @ or ) @ theorem )
| ~ ( A @ ( r @ ( q @ not @ or ) @ ( p @ or ) @ not @ or ) @ axiom ) ),
inference(pattern_uni,[status(thm)],[51:[bind(A,$thf( r @ ( q @ not @ or ) @ ( p @ or ) )),bind(B,$thf( r @ ( p @ or ) @ ( q @ ( p @ or ) @ not @ or ) )),bind(C,$thf( C ))]]) ).
thf(54,plain,
! [A: $i] :
( ~ ( r @ ( p @ or ) @ ( q @ ( p @ or ) @ not @ or ) @ ( A @ not @ or ) @ theorem )
| ~ ( A @ ( r @ ( q @ not @ or ) @ ( p @ or ) @ not @ or ) @ axiom ) ),
inference(simp,[status(thm)],[52]) ).
thf(66,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ or ) @ ( B @ ( A @ or ) @ not @ or ) @ axiom )
!= ( C @ ( r @ ( q @ not @ or ) @ ( p @ or ) @ not @ or ) @ axiom ) )
| ~ ( r @ ( p @ or ) @ ( q @ ( p @ or ) @ not @ or ) @ ( C @ not @ or ) @ theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[14,54]) ).
thf(67,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ or ) @ ( B @ ( A @ or ) @ not @ or ) @ axiom )
!= ( C @ ( r @ ( q @ not @ or ) @ ( p @ or ) @ not @ or ) @ axiom ) )
| ~ ( r @ ( p @ or ) @ ( q @ ( p @ or ) @ not @ or ) @ ( C @ not @ or ) @ theorem ) ),
inference(simp,[status(thm)],[66]) ).
thf(68,plain,
~ ( r @ ( p @ or ) @ ( q @ ( p @ or ) @ not @ or ) @ ( p @ ( r @ ( q @ not @ or ) @ or ) @ not @ or ) @ theorem ),
inference(pattern_uni,[status(thm)],[67:[bind(A,$thf( p )),bind(B,$thf( r @ ( q @ not @ or ) )),bind(C,$thf( p @ ( r @ ( q @ not @ or ) @ or ) ))]]) ).
thf(274,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ theorem )
!= ( r @ ( p @ or ) @ ( q @ ( p @ or ) @ not @ or ) @ ( p @ ( r @ ( q @ not @ or ) @ or ) @ not @ or ) @ theorem ) )
| ~ $true
| ~ ( A @ ( B @ or ) @ theorem ) ),
inference(paramod_ordered,[status(thm)],[32,68]) ).
thf(275,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ theorem )
!= ( r @ ( p @ or ) @ ( q @ ( p @ or ) @ not @ or ) @ ( p @ ( r @ ( q @ not @ or ) @ or ) @ not @ or ) @ theorem ) )
| ~ ( A @ ( B @ or ) @ theorem ) ),
inference(simp,[status(thm)],[274]) ).
thf(276,plain,
~ ( p @ ( r @ ( q @ not @ or ) @ or ) @ not @ ( r @ ( p @ or ) @ ( q @ ( p @ or ) @ not @ or ) @ or ) @ theorem ),
inference(pattern_uni,[status(thm)],[275:[bind(A,$thf( p @ ( r @ ( q @ not @ or ) @ or ) @ not )),bind(B,$thf( r @ ( p @ or ) @ ( q @ ( p @ or ) @ not @ or ) ))]]) ).
thf(3,axiom,
! [B: $i,A: $i] : ( A @ ( B @ or ) @ ( A @ not @ or ) @ axiom ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1_3) ).
thf(13,plain,
! [B: $i,A: $i] : ( A @ ( B @ or ) @ ( A @ not @ or ) @ axiom ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(83,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) @ theorem )
!= ( r @ ( p @ or ) @ ( q @ ( p @ or ) @ not @ or ) @ ( p @ ( r @ ( q @ not @ or ) @ or ) @ not @ or ) @ theorem ) )
| ~ $true
| ~ ( B @ ( C @ not @ or ) @ theorem )
| ~ ( C @ ( A @ not @ or ) @ axiom ) ),
inference(paramod_ordered,[status(thm)],[22,68]) ).
thf(84,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) @ theorem )
!= ( r @ ( p @ or ) @ ( q @ ( p @ or ) @ not @ or ) @ ( p @ ( r @ ( q @ not @ or ) @ or ) @ not @ or ) @ theorem ) )
| ~ ( B @ ( C @ not @ or ) @ theorem )
| ~ ( C @ ( A @ not @ or ) @ axiom ) ),
inference(simp,[status(thm)],[83]) ).
thf(85,plain,
! [A: $i] :
( ~ ( r @ ( p @ or ) @ ( q @ ( p @ or ) @ not @ or ) @ ( A @ not @ or ) @ theorem )
| ~ ( A @ ( p @ ( r @ ( q @ not @ or ) @ or ) @ not @ or ) @ axiom ) ),
inference(pattern_uni,[status(thm)],[84:[bind(A,$thf( p @ ( r @ ( q @ not @ or ) @ or ) )),bind(B,$thf( r @ ( p @ or ) @ ( q @ ( p @ or ) @ not @ or ) )),bind(C,$thf( C ))]]) ).
thf(86,plain,
! [A: $i] :
( ~ ( r @ ( p @ or ) @ ( q @ ( p @ or ) @ not @ or ) @ ( A @ not @ or ) @ theorem )
| ~ ( A @ ( p @ ( r @ ( q @ not @ or ) @ or ) @ not @ or ) @ axiom ) ),
inference(simp,[status(thm)],[85]) ).
thf(167,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ or ) @ ( A @ not @ or ) @ axiom )
!= ( C @ ( p @ ( r @ ( q @ not @ or ) @ or ) @ not @ or ) @ axiom ) )
| ~ ( r @ ( p @ or ) @ ( q @ ( p @ or ) @ not @ or ) @ ( C @ not @ or ) @ theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13,86]) ).
thf(168,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ or ) @ ( A @ not @ or ) @ axiom )
!= ( C @ ( p @ ( r @ ( q @ not @ or ) @ or ) @ not @ or ) @ axiom ) )
| ~ ( r @ ( p @ or ) @ ( q @ ( p @ or ) @ not @ or ) @ ( C @ not @ or ) @ theorem ) ),
inference(simp,[status(thm)],[167]) ).
thf(169,plain,
! [A: $i] :
~ ( r @ ( p @ or ) @ ( q @ ( p @ or ) @ not @ or ) @ ( p @ ( r @ ( q @ not @ or ) @ or ) @ ( A @ or ) @ not @ or ) @ theorem ),
inference(pattern_uni,[status(thm)],[168:[bind(A,$thf( p @ ( r @ ( q @ not @ or ) @ or ) )),bind(B,$thf( I )),bind(C,$thf( p @ ( r @ ( q @ not @ or ) @ or ) @ ( I @ or ) ))]]) ).
thf(185,plain,
! [A: $i] :
~ ( r @ ( p @ or ) @ ( q @ ( p @ or ) @ not @ or ) @ ( p @ ( r @ ( q @ not @ or ) @ or ) @ ( A @ or ) @ not @ or ) @ theorem ),
inference(simp,[status(thm)],[169]) ).
thf(7,axiom,
! [A: $i] :
( ~ ( A @ axiom )
| ( A @ theorem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_1) ).
thf(17,plain,
! [A: $i] :
( ~ ( A @ axiom )
| ( A @ theorem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(18,plain,
! [A: $i] :
( ~ ( A @ axiom )
| ( A @ theorem ) ),
inference(cnf,[status(esa)],[17]) ).
thf(109,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ or ) @ ( A @ not @ or ) @ axiom )
!= ( C @ axiom ) )
| ~ $true
| ( C @ theorem ) ),
inference(paramod_ordered,[status(thm)],[13,18]) ).
thf(110,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ or ) @ ( A @ not @ or ) @ axiom )
!= ( C @ axiom ) )
| ( C @ theorem ) ),
inference(simp,[status(thm)],[109]) ).
thf(111,plain,
! [B: $i,A: $i] : ( B @ ( A @ or ) @ ( B @ not @ or ) @ theorem ),
inference(pattern_uni,[status(thm)],[110:[bind(A,$thf( H )),bind(B,$thf( G )),bind(C,$thf( H @ ( G @ or ) @ ( H @ not @ or ) ))]]) ).
thf(125,plain,
! [B: $i,A: $i] : ( B @ ( A @ or ) @ ( B @ not @ or ) @ theorem ),
inference(simp,[status(thm)],[111]) ).
thf(259,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ ( B @ not @ or ) @ theorem )
!= ( C @ ( D @ or ) @ theorem ) )
| ~ $true
| ( D @ ( C @ or ) @ theorem ) ),
inference(paramod_ordered,[status(thm)],[125,32]) ).
thf(260,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ ( B @ not @ or ) @ theorem )
!= ( C @ ( D @ or ) @ theorem ) )
| ( D @ ( C @ or ) @ theorem ) ),
inference(simp,[status(thm)],[259]) ).
thf(261,plain,
! [B: $i,A: $i] : ( B @ not @ ( B @ ( A @ or ) @ or ) @ theorem ),
inference(pattern_uni,[status(thm)],[260:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( G @ ( F @ or ) )),bind(D,$thf( G @ not ))]]) ).
thf(280,plain,
! [B: $i,A: $i] : ( B @ not @ ( B @ ( A @ or ) @ or ) @ theorem ),
inference(simp,[status(thm)],[261]) ).
thf(2,axiom,
! [A: $i] : ( A @ ( A @ ( A @ or ) @ not @ or ) @ axiom ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1_2) ).
thf(12,plain,
! [A: $i] : ( A @ ( A @ ( A @ or ) @ not @ or ) @ axiom ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(199,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ ( B @ not @ or ) @ theorem )
!= ( r @ ( p @ or ) @ ( q @ ( p @ or ) @ not @ or ) @ ( C @ not @ or ) @ theorem ) )
| ~ $true
| ~ ( C @ ( r @ ( q @ not @ or ) @ ( p @ or ) @ not @ or ) @ axiom ) ),
inference(paramod_ordered,[status(thm)],[125,54]) ).
thf(200,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ ( B @ not @ or ) @ theorem )
!= ( r @ ( p @ or ) @ ( q @ ( p @ or ) @ not @ or ) @ ( C @ not @ or ) @ theorem ) )
| ~ ( C @ ( r @ ( q @ not @ or ) @ ( p @ or ) @ not @ or ) @ axiom ) ),
inference(simp,[status(thm)],[199]) ).
thf(201,plain,
~ ( r @ ( p @ or ) @ ( r @ ( q @ not @ or ) @ ( p @ or ) @ not @ or ) @ axiom ),
inference(pattern_uni,[status(thm)],[200:[bind(A,$thf( q @ ( p @ or ) @ not )),bind(B,$thf( r @ ( p @ or ) )),bind(C,$thf( r @ ( p @ or ) ))]]) ).
thf(219,plain,
! [A: $i] :
( ( ( A @ ( A @ ( A @ or ) @ not @ or ) @ axiom )
!= ( r @ ( p @ or ) @ ( r @ ( q @ not @ or ) @ ( p @ or ) @ not @ or ) @ axiom ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12,201]) ).
thf(220,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ or ) @ not @ or ) @ axiom )
!= ( r @ ( p @ or ) @ ( r @ ( q @ not @ or ) @ ( p @ or ) @ not @ or ) @ axiom ) ),
inference(simp,[status(thm)],[219]) ).
thf(224,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ or ) @ not @ or ) )
!= ( r @ ( p @ or ) @ ( r @ ( q @ not @ or ) @ ( p @ or ) @ not @ or ) ) ),
inference(simp,[status(thm)],[220]) ).
thf(115,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ or ) @ not @ or ) @ axiom )
!= ( B @ axiom ) )
| ~ $true
| ( B @ theorem ) ),
inference(paramod_ordered,[status(thm)],[12,18]) ).
thf(116,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ or ) @ not @ or ) @ axiom )
!= ( B @ axiom ) )
| ( B @ theorem ) ),
inference(simp,[status(thm)],[115]) ).
thf(117,plain,
! [A: $i] : ( A @ ( A @ ( A @ or ) @ not @ or ) @ theorem ),
inference(pattern_uni,[status(thm)],[116:[bind(A,$thf( D )),bind(B,$thf( D @ ( D @ ( D @ or ) @ not @ or ) ))]]) ).
thf(122,plain,
! [A: $i] : ( A @ ( A @ ( A @ or ) @ not @ or ) @ theorem ),
inference(simp,[status(thm)],[117]) ).
thf(256,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ or ) @ not @ or ) @ theorem )
!= ( B @ ( C @ or ) @ theorem ) )
| ~ $true
| ( C @ ( B @ or ) @ theorem ) ),
inference(paramod_ordered,[status(thm)],[122,32]) ).
thf(257,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ or ) @ not @ or ) @ theorem )
!= ( B @ ( C @ or ) @ theorem ) )
| ( C @ ( B @ or ) @ theorem ) ),
inference(simp,[status(thm)],[256]) ).
thf(258,plain,
! [A: $i] : ( A @ ( A @ or ) @ not @ ( A @ or ) @ theorem ),
inference(pattern_uni,[status(thm)],[257:[bind(A,$thf( F )),bind(B,$thf( F )),bind(C,$thf( F @ ( F @ or ) @ not ))]]) ).
thf(278,plain,
! [A: $i] : ( A @ ( A @ or ) @ not @ ( A @ or ) @ theorem ),
inference(simp,[status(thm)],[258]) ).
thf(6,axiom,
! [C: $i,B: $i,A: $i] : ( B @ ( C @ or ) @ ( A @ ( C @ or ) @ not @ or ) @ ( B @ ( A @ not @ or ) @ not @ or ) @ 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 ) @ not @ or ) @ ( B @ ( A @ not @ or ) @ not @ or ) @ axiom ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(106,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)],[14,18]) ).
thf(107,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ or ) @ ( B @ ( A @ or ) @ not @ or ) @ axiom )
!= ( C @ axiom ) )
| ( C @ theorem ) ),
inference(simp,[status(thm)],[106]) ).
thf(108,plain,
! [B: $i,A: $i] : ( B @ ( A @ or ) @ ( A @ ( B @ or ) @ not @ or ) @ theorem ),
inference(pattern_uni,[status(thm)],[107:[bind(A,$thf( J )),bind(B,$thf( I )),bind(C,$thf( J @ ( I @ or ) @ ( I @ ( J @ or ) @ not @ or ) ))]]) ).
thf(124,plain,
! [B: $i,A: $i] : ( B @ ( A @ or ) @ ( A @ ( B @ or ) @ not @ or ) @ theorem ),
inference(simp,[status(thm)],[108]) ).
thf(382,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ ( A @ ( B @ or ) @ not @ or ) @ theorem )
!= ( r @ ( p @ or ) @ ( q @ ( p @ or ) @ not @ or ) @ ( C @ not @ or ) @ theorem ) )
| ~ $true
| ~ ( C @ ( p @ ( r @ ( q @ not @ or ) @ or ) @ not @ or ) @ axiom ) ),
inference(paramod_ordered,[status(thm)],[124,86]) ).
thf(383,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ ( A @ ( B @ or ) @ not @ or ) @ theorem )
!= ( r @ ( p @ or ) @ ( q @ ( p @ or ) @ not @ or ) @ ( C @ not @ or ) @ theorem ) )
| ~ ( C @ ( p @ ( r @ ( q @ not @ or ) @ or ) @ not @ or ) @ axiom ) ),
inference(simp,[status(thm)],[382]) ).
thf(384,plain,
~ ( q @ ( p @ or ) @ not @ ( r @ ( p @ or ) @ or ) @ ( p @ ( r @ ( q @ not @ or ) @ or ) @ not @ or ) @ axiom ),
inference(pattern_uni,[status(thm)],[383:[bind(A,$thf( q @ ( p @ or ) @ not )),bind(B,$thf( r @ ( p @ or ) )),bind(C,$thf( q @ ( p @ or ) @ not @ ( r @ ( p @ or ) @ or ) ))]]) ).
thf(379,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ ( A @ ( B @ or ) @ not @ or ) @ theorem )
!= ( r @ ( p @ or ) @ ( q @ ( p @ or ) @ not @ or ) @ ( C @ not @ or ) @ theorem ) )
| ~ $true
| ~ ( C @ ( r @ ( q @ not @ or ) @ ( p @ or ) @ not @ or ) @ axiom ) ),
inference(paramod_ordered,[status(thm)],[124,54]) ).
thf(380,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ ( A @ ( B @ or ) @ not @ or ) @ theorem )
!= ( r @ ( p @ or ) @ ( q @ ( p @ or ) @ not @ or ) @ ( C @ not @ or ) @ theorem ) )
| ~ ( C @ ( r @ ( q @ not @ or ) @ ( p @ or ) @ not @ or ) @ axiom ) ),
inference(simp,[status(thm)],[379]) ).
thf(381,plain,
~ ( q @ ( p @ or ) @ not @ ( r @ ( p @ or ) @ or ) @ ( r @ ( q @ not @ or ) @ ( p @ or ) @ not @ or ) @ axiom ),
inference(pattern_uni,[status(thm)],[380:[bind(A,$thf( q @ ( p @ or ) @ not )),bind(B,$thf( r @ ( p @ or ) )),bind(C,$thf( q @ ( p @ or ) @ not @ ( r @ ( p @ or ) @ or ) ))]]) ).
thf(367,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ ( A @ ( B @ or ) @ not @ or ) @ theorem )
!= ( C @ ( D @ or ) @ theorem ) )
| ~ $true
| ( D @ ( C @ or ) @ theorem ) ),
inference(paramod_ordered,[status(thm)],[124,32]) ).
thf(368,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ ( A @ ( B @ or ) @ not @ or ) @ theorem )
!= ( C @ ( D @ or ) @ theorem ) )
| ( D @ ( C @ or ) @ theorem ) ),
inference(simp,[status(thm)],[367]) ).
thf(369,plain,
! [B: $i,A: $i] : ( A @ ( B @ or ) @ not @ ( B @ ( A @ or ) @ or ) @ theorem ),
inference(pattern_uni,[status(thm)],[368:[bind(A,$thf( H )),bind(B,$thf( I )),bind(C,$thf( I @ ( H @ or ) )),bind(D,$thf( H @ ( I @ or ) @ not ))]]) ).
thf(392,plain,
! [B: $i,A: $i] : ( A @ ( B @ or ) @ not @ ( B @ ( A @ or ) @ or ) @ theorem ),
inference(simp,[status(thm)],[369]) ).
thf(26,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ or ) @ ( A @ not @ or ) @ axiom )
!= ( C @ ( D @ not @ or ) @ axiom ) )
| ~ ( D @ theorem )
| ~ $true
| ( C @ theorem ) ),
inference(paramod_ordered,[status(thm)],[13,20]) ).
thf(27,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ or ) @ ( A @ not @ or ) @ axiom )
!= ( C @ ( D @ not @ or ) @ axiom ) )
| ~ ( D @ theorem )
| ( C @ theorem ) ),
inference(simp,[status(thm)],[26]) ).
thf(28,plain,
! [B: $i,A: $i] :
( ~ ( B @ theorem )
| ( B @ ( A @ or ) @ theorem ) ),
inference(pattern_uni,[status(thm)],[27:[bind(A,$thf( F )),bind(B,$thf( E )),bind(C,$thf( F @ ( E @ or ) )),bind(D,$thf( F ))]]) ).
thf(33,plain,
! [B: $i,A: $i] :
( ~ ( B @ theorem )
| ( B @ ( A @ or ) @ theorem ) ),
inference(simp,[status(thm)],[28]) ).
thf(5,axiom,
! [C: $i,B: $i,A: $i] : ( C @ ( A @ or ) @ ( B @ or ) @ ( C @ ( B @ or ) @ ( A @ or ) @ not @ or ) @ 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 ) @ not @ or ) @ axiom ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(75,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ or ) @ ( B @ or ) @ ( C @ ( B @ or ) @ ( A @ or ) @ not @ or ) @ axiom )
!= ( D @ ( r @ ( q @ not @ or ) @ ( p @ or ) @ not @ or ) @ axiom ) )
| ~ ( r @ ( p @ or ) @ ( q @ ( p @ or ) @ not @ or ) @ ( D @ not @ or ) @ theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[15,54]) ).
thf(76,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ or ) @ ( B @ or ) @ ( C @ ( B @ or ) @ ( A @ or ) @ not @ or ) @ axiom )
!= ( D @ ( r @ ( q @ not @ or ) @ ( p @ or ) @ not @ or ) @ axiom ) )
| ~ ( r @ ( p @ or ) @ ( q @ ( p @ or ) @ not @ or ) @ ( D @ not @ or ) @ theorem ) ),
inference(simp,[status(thm)],[75]) ).
thf(77,plain,
~ ( r @ ( p @ or ) @ ( q @ ( p @ or ) @ not @ or ) @ ( r @ ( p @ or ) @ ( q @ not @ or ) @ not @ or ) @ theorem ),
inference(pattern_uni,[status(thm)],[76:[bind(A,$thf( p )),bind(B,$thf( q @ not )),bind(C,$thf( r )),bind(D,$thf( r @ ( p @ or ) @ ( q @ not @ or ) ))]]) ).
thf(29,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ or ) @ not @ or ) @ axiom )
!= ( B @ ( C @ not @ or ) @ axiom ) )
| ~ ( C @ theorem )
| ~ $true
| ( B @ theorem ) ),
inference(paramod_ordered,[status(thm)],[12,20]) ).
thf(30,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ or ) @ not @ or ) @ axiom )
!= ( B @ ( C @ not @ or ) @ axiom ) )
| ~ ( C @ theorem )
| ( B @ theorem ) ),
inference(simp,[status(thm)],[29]) ).
thf(31,plain,
! [A: $i] :
( ~ ( A @ ( A @ or ) @ theorem )
| ( A @ theorem ) ),
inference(pattern_uni,[status(thm)],[30:[bind(A,$thf( E )),bind(B,$thf( E )),bind(C,$thf( E @ ( E @ or ) ))]]) ).
thf(34,plain,
! [A: $i] :
( ~ ( A @ ( A @ or ) @ theorem )
| ( A @ theorem ) ),
inference(simp,[status(thm)],[31]) ).
thf(202,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ ( B @ not @ or ) @ theorem )
!= ( r @ ( p @ or ) @ ( q @ ( p @ or ) @ not @ or ) @ ( C @ not @ or ) @ theorem ) )
| ~ $true
| ~ ( C @ ( p @ ( r @ ( q @ not @ or ) @ or ) @ not @ or ) @ axiom ) ),
inference(paramod_ordered,[status(thm)],[125,86]) ).
thf(203,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ ( B @ not @ or ) @ theorem )
!= ( r @ ( p @ or ) @ ( q @ ( p @ or ) @ not @ or ) @ ( C @ not @ or ) @ theorem ) )
| ~ ( C @ ( p @ ( r @ ( q @ not @ or ) @ or ) @ not @ or ) @ axiom ) ),
inference(simp,[status(thm)],[202]) ).
thf(204,plain,
~ ( r @ ( p @ or ) @ ( p @ ( r @ ( q @ not @ or ) @ or ) @ not @ or ) @ axiom ),
inference(pattern_uni,[status(thm)],[203:[bind(A,$thf( q @ ( p @ or ) @ not )),bind(B,$thf( r @ ( p @ or ) )),bind(C,$thf( r @ ( p @ or ) ))]]) ).
thf(69,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ or ) @ ( A @ not @ or ) @ axiom )
!= ( C @ ( r @ ( q @ not @ or ) @ ( p @ or ) @ not @ or ) @ axiom ) )
| ~ ( r @ ( p @ or ) @ ( q @ ( p @ or ) @ not @ or ) @ ( C @ not @ or ) @ theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13,54]) ).
thf(70,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ or ) @ ( A @ not @ or ) @ axiom )
!= ( C @ ( r @ ( q @ not @ or ) @ ( p @ or ) @ not @ or ) @ axiom ) )
| ~ ( r @ ( p @ or ) @ ( q @ ( p @ or ) @ not @ or ) @ ( C @ not @ or ) @ theorem ) ),
inference(simp,[status(thm)],[69]) ).
thf(71,plain,
! [A: $i] :
~ ( r @ ( p @ or ) @ ( q @ ( p @ or ) @ not @ or ) @ ( r @ ( q @ not @ or ) @ ( p @ or ) @ ( A @ or ) @ not @ or ) @ theorem ),
inference(pattern_uni,[status(thm)],[70:[bind(A,$thf( r @ ( q @ not @ or ) @ ( p @ or ) )),bind(B,$thf( I )),bind(C,$thf( r @ ( q @ not @ or ) @ ( p @ or ) @ ( I @ or ) ))]]) ).
thf(81,plain,
! [A: $i] :
~ ( r @ ( p @ or ) @ ( q @ ( p @ or ) @ not @ or ) @ ( r @ ( q @ not @ or ) @ ( p @ or ) @ ( A @ or ) @ not @ or ) @ theorem ),
inference(simp,[status(thm)],[71]) ).
thf(488,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ theorem )
!= ( r @ ( p @ or ) @ ( q @ ( p @ or ) @ not @ or ) @ ( p @ ( r @ ( q @ not @ or ) @ or ) @ ( C @ or ) @ not @ or ) @ theorem ) )
| ~ $true
| ~ ( B @ theorem ) ),
inference(paramod_ordered,[status(thm)],[33,185]) ).
thf(489,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ theorem )
!= ( r @ ( p @ or ) @ ( q @ ( p @ or ) @ not @ or ) @ ( p @ ( r @ ( q @ not @ or ) @ or ) @ ( C @ or ) @ not @ or ) @ theorem ) )
| ~ ( B @ theorem ) ),
inference(simp,[status(thm)],[488]) ).
thf(490,plain,
~ ( r @ ( p @ or ) @ ( q @ ( p @ or ) @ not @ or ) @ theorem ),
inference(pattern_uni,[status(thm)],[489:[bind(A,$thf( p @ ( r @ ( q @ not @ or ) @ or ) @ ( E @ or ) @ not )),bind(B,$thf( r @ ( p @ or ) @ ( q @ ( p @ or ) @ not @ or ) )),bind(C,$thf( E ))]]) ).
thf(597,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ theorem )
!= ( r @ ( p @ or ) @ ( q @ ( p @ or ) @ not @ or ) @ theorem ) )
| ~ $true
| ~ ( B @ theorem ) ),
inference(paramod_ordered,[status(thm)],[33,490]) ).
thf(598,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ theorem )
!= ( r @ ( p @ or ) @ ( q @ ( p @ or ) @ not @ or ) @ theorem ) )
| ~ ( B @ theorem ) ),
inference(simp,[status(thm)],[597]) ).
thf(599,plain,
~ ( r @ ( p @ or ) @ theorem ),
inference(pattern_uni,[status(thm)],[598:[bind(A,$thf( q @ ( p @ or ) @ not )),bind(B,$thf( r @ ( p @ or ) ))]]) ).
thf(138,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ or ) @ not @ or ) @ theorem )
!= ( r @ ( p @ or ) @ ( q @ ( p @ or ) @ not @ or ) @ ( B @ not @ or ) @ theorem ) )
| ~ $true
| ~ ( B @ ( r @ ( q @ not @ or ) @ ( p @ or ) @ not @ or ) @ axiom ) ),
inference(paramod_ordered,[status(thm)],[122,54]) ).
thf(139,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ or ) @ not @ or ) @ theorem )
!= ( r @ ( p @ or ) @ ( q @ ( p @ or ) @ not @ or ) @ ( B @ not @ or ) @ theorem ) )
| ~ ( B @ ( r @ ( q @ not @ or ) @ ( p @ or ) @ not @ or ) @ axiom ) ),
inference(simp,[status(thm)],[138]) ).
thf(140,plain,
~ ( r @ ( p @ or ) @ ( q @ ( p @ or ) @ not @ or ) @ ( r @ ( p @ or ) @ ( q @ ( p @ or ) @ not @ or ) @ or ) @ ( r @ ( q @ not @ or ) @ ( p @ or ) @ not @ or ) @ axiom ),
inference(pattern_uni,[status(thm)],[139:[bind(A,$thf( r @ ( p @ or ) @ ( q @ ( p @ or ) @ not @ or ) )),bind(B,$thf( r @ ( p @ or ) @ ( q @ ( p @ or ) @ not @ or ) @ ( r @ ( p @ or ) @ ( q @ ( p @ or ) @ not @ or ) @ or ) ))]]) ).
thf(624,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ theorem )
!= ( r @ ( p @ or ) @ theorem ) )
| ~ $true
| ~ ( B @ theorem ) ),
inference(paramod_ordered,[status(thm)],[33,599]) ).
thf(625,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ theorem )
!= ( r @ ( p @ or ) @ theorem ) )
| ~ ( B @ theorem ) ),
inference(simp,[status(thm)],[624]) ).
thf(626,plain,
~ ( r @ theorem ),
inference(pattern_uni,[status(thm)],[625:[bind(A,$thf( p )),bind(B,$thf( r ))]]) ).
thf(485,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ theorem )
!= ( p @ ( r @ ( q @ not @ or ) @ or ) @ not @ ( r @ ( p @ or ) @ ( q @ ( p @ or ) @ not @ or ) @ or ) @ theorem ) )
| ~ $true
| ~ ( B @ theorem ) ),
inference(paramod_ordered,[status(thm)],[33,276]) ).
thf(486,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ theorem )
!= ( p @ ( r @ ( q @ not @ or ) @ or ) @ not @ ( r @ ( p @ or ) @ ( q @ ( p @ or ) @ not @ or ) @ or ) @ theorem ) )
| ~ ( B @ theorem ) ),
inference(simp,[status(thm)],[485]) ).
thf(487,plain,
~ ( p @ ( r @ ( q @ not @ or ) @ or ) @ not @ theorem ),
inference(pattern_uni,[status(thm)],[486:[bind(A,$thf( r @ ( p @ or ) @ ( q @ ( p @ or ) @ not @ or ) )),bind(B,$thf( p @ ( r @ ( q @ not @ or ) @ or ) @ not ))]]) ).
thf(949,plain,
$false,
inference(e,[status(thm)],[276,185,20,280,224,13,278,18,16,11,19,122,10,384,14,125,201,381,392,21,33,124,77,17,32,34,22,204,12,54,86,81,599,140,626,490,487,15,68]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL224-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.12 % 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
% 0.25/0.50 % Computer : n005.cluster.edu
% 0.25/0.50 % Model : x86_64 x86_64
% 0.25/0.50 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.25/0.50 % Memory : 8046.5625MB
% 0.25/0.50 % OS : Linux 6.8.0-71-generic
% 0.25/0.50 % CPULimit : 300
% 0.25/0.50 % WCLimit : 300
% 0.25/0.50 % DateTime : Fri Sep 25 22:02:50 UTC 2026
% 0.25/0.50 % CPUTime :
% 0.25/0.50 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
% 1.12/1.13 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.63/1.30 % [INFO] Parsing done (163ms).
% 1.63/1.31 % [INFO] Running in sequential loop mode.
% 2.67/1.93 % [INFO] eprover registered as external prover.
% 2.67/1.94 % [INFO] Scanning for conjecture ...
% 2.95/2.07 % [INFO] Found a conjecture (or negated_conjecture) and 8 axioms. Running axiom selection ...
% 2.95/2.12 % [INFO] Axiom selection finished. Selected 8 axioms (removed 0 axioms).
% 2.95/2.15 % [INFO] Problem is propositional (TPTP CNF).
% 2.95/2.15 % [INFO] Type checking passed.
% 3.13/2.16 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 16.32/5.85 % External prover 'e' found a proof!
% 16.32/5.85 % [INFO] Killing All external provers ...
% 16.32/5.86 % Time passed: 5213ms (effective reasoning time: 4534ms)
% 16.32/5.86 % Axioms used in derivation (8): axiom_1_5, axiom_1_4, rule_1, axiom_1_3, rule_3, axiom_1_2, rule_2, axiom_1_6
% 16.32/5.86 % No. of inferences in proof: 114
% 16.32/5.86 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 5213 ms resp. 4534 ms w/o parsing
% 19.77/6.01 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 19.77/6.02 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------