%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL192-1 : TPTP v9.3.1. Released v1.1.0.
% 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 : n020.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 07:51:06 AM UTC 2026
% Result : Unsatisfiable 10.18s 3.80s
% Output : Refutation 10.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 9
% Syntax : Number of formulae : 113 ( 45 unt; 0 typ; 0 def)
% Number of atoms : 324 ( 53 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 1688 ( 168 ~; 107 |; 0 &;1413 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 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 : 224 ( 0 ^; 224 !; 0 ?; 224 :)
% 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(1,negated_conjecture,
~ ( r @ ( q @ or ) @ ( p @ or ) @ ( r @ ( q @ ( p @ or ) @ or ) @ not @ or ) @ theorem ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
thf(10,plain,
~ ( r @ ( q @ or ) @ ( p @ or ) @ ( r @ ( q @ ( p @ or ) @ or ) @ not @ or ) @ theorem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(4,axiom,
! [B: $i,A: $i] : ( A @ ( B @ or ) @ ( B @ ( A @ or ) @ not @ or ) @ axiom ),
file('/export/starexec/sandbox2/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/sandbox2/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(11,plain,
~ ( r @ ( q @ or ) @ ( p @ or ) @ ( r @ ( q @ ( p @ or ) @ or ) @ not @ or ) @ theorem ),
inference(polarity_switch,[status(thm)],[10]) ).
thf(255,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ theorem )
!= ( r @ ( q @ or ) @ ( p @ or ) @ ( r @ ( q @ ( p @ or ) @ or ) @ not @ or ) @ theorem ) )
| ~ $true
| ~ ( A @ ( B @ or ) @ theorem ) ),
inference(paramod_ordered,[status(thm)],[32,11]) ).
thf(256,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ theorem )
!= ( r @ ( q @ or ) @ ( p @ or ) @ ( r @ ( q @ ( p @ or ) @ or ) @ not @ or ) @ theorem ) )
| ~ ( A @ ( B @ or ) @ theorem ) ),
inference(simp,[status(thm)],[255]) ).
thf(257,plain,
~ ( r @ ( q @ ( p @ or ) @ or ) @ not @ ( r @ ( q @ or ) @ ( p @ or ) @ or ) @ theorem ),
inference(pattern_uni,[status(thm)],[256:[bind(A,$thf( r @ ( q @ ( p @ or ) @ or ) @ not )),bind(B,$thf( r @ ( q @ or ) @ ( p @ or ) ))]]) ).
thf(2,axiom,
! [A: $i] : ( A @ ( A @ ( A @ or ) @ not @ or ) @ axiom ),
file('/export/starexec/sandbox2/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(7,axiom,
! [A: $i] :
( ~ ( A @ axiom )
| ( A @ theorem ) ),
file('/export/starexec/sandbox2/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(111,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(112,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ or ) @ not @ or ) @ axiom )
!= ( B @ axiom ) )
| ( B @ theorem ) ),
inference(simp,[status(thm)],[111]) ).
thf(113,plain,
! [A: $i] : ( A @ ( A @ ( A @ or ) @ not @ or ) @ theorem ),
inference(pattern_uni,[status(thm)],[112:[bind(A,$thf( D )),bind(B,$thf( D @ ( D @ ( D @ or ) @ not @ or ) ))]]) ).
thf(117,plain,
! [A: $i] : ( A @ ( A @ ( A @ or ) @ not @ or ) @ theorem ),
inference(simp,[status(thm)],[113]) ).
thf(231,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)],[117,32]) ).
thf(232,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)],[231]) ).
thf(233,plain,
! [A: $i] : ( A @ ( A @ or ) @ not @ ( A @ or ) @ theorem ),
inference(pattern_uni,[status(thm)],[232:[bind(A,$thf( F )),bind(B,$thf( F )),bind(C,$thf( F @ ( F @ or ) @ not ))]]) ).
thf(265,plain,
! [A: $i] : ( A @ ( A @ or ) @ not @ ( A @ or ) @ theorem ),
inference(simp,[status(thm)],[233]) ).
thf(3,axiom,
! [B: $i,A: $i] : ( A @ ( B @ or ) @ ( A @ not @ or ) @ axiom ),
file('/export/starexec/sandbox2/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(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(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/sandbox2/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(50,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) @ theorem )
!= ( r @ ( q @ or ) @ ( p @ or ) @ ( r @ ( q @ ( p @ or ) @ 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 @ ( q @ or ) @ ( p @ or ) @ ( r @ ( q @ ( p @ or ) @ or ) @ not @ or ) @ theorem ) )
| ~ ( B @ ( C @ not @ or ) @ theorem )
| ~ ( C @ ( A @ not @ or ) @ axiom ) ),
inference(simp,[status(thm)],[50]) ).
thf(52,plain,
! [A: $i] :
( ~ ( r @ ( q @ or ) @ ( p @ or ) @ ( A @ not @ or ) @ theorem )
| ~ ( A @ ( r @ ( q @ ( p @ or ) @ or ) @ not @ or ) @ axiom ) ),
inference(pattern_uni,[status(thm)],[51:[bind(A,$thf( r @ ( q @ ( p @ or ) @ or ) )),bind(B,$thf( r @ ( q @ or ) @ ( p @ or ) )),bind(C,$thf( C ))]]) ).
thf(54,plain,
! [A: $i] :
( ~ ( r @ ( q @ or ) @ ( p @ or ) @ ( A @ not @ or ) @ theorem )
| ~ ( A @ ( r @ ( q @ ( p @ or ) @ or ) @ not @ or ) @ axiom ) ),
inference(simp,[status(thm)],[52]) ).
thf(69,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ or ) @ ( A @ not @ or ) @ axiom )
!= ( C @ ( r @ ( q @ ( p @ or ) @ or ) @ not @ or ) @ axiom ) )
| ~ ( r @ ( q @ or ) @ ( p @ 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 @ ( p @ or ) @ or ) @ not @ or ) @ axiom ) )
| ~ ( r @ ( q @ or ) @ ( p @ or ) @ ( C @ not @ or ) @ theorem ) ),
inference(simp,[status(thm)],[69]) ).
thf(71,plain,
! [A: $i] :
~ ( r @ ( q @ or ) @ ( p @ or ) @ ( r @ ( q @ ( p @ or ) @ or ) @ ( A @ or ) @ not @ or ) @ theorem ),
inference(pattern_uni,[status(thm)],[70:[bind(A,$thf( r @ ( q @ ( p @ or ) @ or ) )),bind(B,$thf( H )),bind(C,$thf( r @ ( q @ ( p @ or ) @ or ) @ ( H @ or ) ))]]) ).
thf(81,plain,
! [A: $i] :
~ ( r @ ( q @ or ) @ ( p @ or ) @ ( r @ ( q @ ( p @ or ) @ or ) @ ( A @ or ) @ not @ or ) @ theorem ),
inference(simp,[status(thm)],[71]) ).
thf(535,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ theorem )
!= ( r @ ( q @ or ) @ ( p @ or ) @ ( r @ ( q @ ( p @ or ) @ or ) @ ( C @ or ) @ not @ or ) @ theorem ) )
| ~ $true
| ~ ( B @ theorem ) ),
inference(paramod_ordered,[status(thm)],[33,81]) ).
thf(536,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ theorem )
!= ( r @ ( q @ or ) @ ( p @ or ) @ ( r @ ( q @ ( p @ or ) @ or ) @ ( C @ or ) @ not @ or ) @ theorem ) )
| ~ ( B @ theorem ) ),
inference(simp,[status(thm)],[535]) ).
thf(537,plain,
~ ( r @ ( q @ or ) @ ( p @ or ) @ theorem ),
inference(pattern_uni,[status(thm)],[536:[bind(A,$thf( r @ ( q @ ( p @ or ) @ or ) @ ( E @ or ) @ not )),bind(B,$thf( r @ ( q @ or ) @ ( p @ or ) )),bind(C,$thf( E ))]]) ).
thf(252,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ theorem )
!= ( r @ ( q @ or ) @ ( p @ or ) @ ( r @ ( q @ ( p @ or ) @ or ) @ ( C @ or ) @ not @ or ) @ theorem ) )
| ~ $true
| ~ ( A @ ( B @ or ) @ theorem ) ),
inference(paramod_ordered,[status(thm)],[32,81]) ).
thf(253,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ theorem )
!= ( r @ ( q @ or ) @ ( p @ or ) @ ( r @ ( q @ ( p @ or ) @ or ) @ ( C @ or ) @ not @ or ) @ theorem ) )
| ~ ( A @ ( B @ or ) @ theorem ) ),
inference(simp,[status(thm)],[252]) ).
thf(254,plain,
! [A: $i] :
~ ( r @ ( q @ ( p @ or ) @ or ) @ ( A @ or ) @ not @ ( r @ ( q @ or ) @ ( p @ or ) @ or ) @ theorem ),
inference(pattern_uni,[status(thm)],[253:[bind(A,$thf( r @ ( q @ ( p @ or ) @ or ) @ ( E @ or ) @ not )),bind(B,$thf( r @ ( q @ or ) @ ( p @ or ) )),bind(C,$thf( E ))]]) ).
thf(267,plain,
! [A: $i] :
~ ( r @ ( q @ ( p @ or ) @ or ) @ ( A @ or ) @ not @ ( r @ ( q @ or ) @ ( p @ or ) @ or ) @ theorem ),
inference(simp,[status(thm)],[254]) ).
thf(66,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ or ) @ ( B @ ( A @ or ) @ not @ or ) @ axiom )
!= ( C @ ( r @ ( q @ ( p @ or ) @ or ) @ not @ or ) @ axiom ) )
| ~ ( r @ ( q @ or ) @ ( p @ or ) @ ( C @ not @ or ) @ theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[14,54]) ).
thf(67,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ or ) @ ( B @ ( A @ or ) @ not @ or ) @ axiom )
!= ( C @ ( r @ ( q @ ( p @ or ) @ or ) @ not @ or ) @ axiom ) )
| ~ ( r @ ( q @ or ) @ ( p @ or ) @ ( C @ not @ or ) @ theorem ) ),
inference(simp,[status(thm)],[66]) ).
thf(68,plain,
~ ( r @ ( q @ or ) @ ( p @ or ) @ ( q @ ( p @ or ) @ ( r @ or ) @ not @ or ) @ theorem ),
inference(pattern_uni,[status(thm)],[67:[bind(A,$thf( q @ ( p @ or ) )),bind(B,$thf( r )),bind(C,$thf( q @ ( p @ or ) @ ( r @ or ) ))]]) ).
thf(258,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ theorem )
!= ( r @ ( q @ or ) @ ( p @ or ) @ ( q @ ( p @ or ) @ ( r @ or ) @ not @ or ) @ theorem ) )
| ~ $true
| ~ ( A @ ( B @ or ) @ theorem ) ),
inference(paramod_ordered,[status(thm)],[32,68]) ).
thf(259,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ theorem )
!= ( r @ ( q @ or ) @ ( p @ or ) @ ( q @ ( p @ or ) @ ( r @ or ) @ not @ or ) @ theorem ) )
| ~ ( A @ ( B @ or ) @ theorem ) ),
inference(simp,[status(thm)],[258]) ).
thf(260,plain,
~ ( q @ ( p @ or ) @ ( r @ or ) @ not @ ( r @ ( q @ or ) @ ( p @ or ) @ or ) @ theorem ),
inference(pattern_uni,[status(thm)],[259:[bind(A,$thf( q @ ( p @ or ) @ ( r @ or ) @ not )),bind(B,$thf( r @ ( q @ or ) @ ( p @ or ) ))]]) ).
thf(514,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ theorem )
!= ( q @ ( p @ or ) @ ( r @ or ) @ not @ ( r @ ( q @ or ) @ ( p @ or ) @ or ) @ theorem ) )
| ~ $true
| ~ ( B @ theorem ) ),
inference(paramod_ordered,[status(thm)],[33,260]) ).
thf(515,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ theorem )
!= ( q @ ( p @ or ) @ ( r @ or ) @ not @ ( r @ ( q @ or ) @ ( p @ or ) @ or ) @ theorem ) )
| ~ ( B @ theorem ) ),
inference(simp,[status(thm)],[514]) ).
thf(516,plain,
~ ( q @ ( p @ or ) @ ( r @ or ) @ not @ theorem ),
inference(pattern_uni,[status(thm)],[515:[bind(A,$thf( r @ ( q @ or ) @ ( p @ or ) )),bind(B,$thf( q @ ( p @ or ) @ ( r @ or ) @ not ))]]) ).
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/sandbox2/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(105,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(106,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ or ) @ ( A @ not @ or ) @ axiom )
!= ( C @ axiom ) )
| ( C @ theorem ) ),
inference(simp,[status(thm)],[105]) ).
thf(107,plain,
! [B: $i,A: $i] : ( B @ ( A @ or ) @ ( B @ not @ or ) @ theorem ),
inference(pattern_uni,[status(thm)],[106:[bind(A,$thf( H )),bind(B,$thf( G )),bind(C,$thf( H @ ( G @ or ) @ ( H @ not @ or ) ))]]) ).
thf(120,plain,
! [B: $i,A: $i] : ( B @ ( A @ or ) @ ( B @ not @ or ) @ theorem ),
inference(simp,[status(thm)],[107]) ).
thf(83,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) @ theorem )
!= ( r @ ( q @ or ) @ ( p @ or ) @ ( q @ ( p @ or ) @ ( r @ 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 @ ( q @ or ) @ ( p @ or ) @ ( q @ ( p @ or ) @ ( r @ or ) @ not @ or ) @ theorem ) )
| ~ ( B @ ( C @ not @ or ) @ theorem )
| ~ ( C @ ( A @ not @ or ) @ axiom ) ),
inference(simp,[status(thm)],[83]) ).
thf(85,plain,
! [A: $i] :
( ~ ( r @ ( q @ or ) @ ( p @ or ) @ ( A @ not @ or ) @ theorem )
| ~ ( A @ ( q @ ( p @ or ) @ ( r @ or ) @ not @ or ) @ axiom ) ),
inference(pattern_uni,[status(thm)],[84:[bind(A,$thf( q @ ( p @ or ) @ ( r @ or ) )),bind(B,$thf( r @ ( q @ or ) @ ( p @ or ) )),bind(C,$thf( C ))]]) ).
thf(86,plain,
! [A: $i] :
( ~ ( r @ ( q @ or ) @ ( p @ or ) @ ( A @ not @ or ) @ theorem )
| ~ ( A @ ( q @ ( p @ or ) @ ( r @ or ) @ not @ or ) @ axiom ) ),
inference(simp,[status(thm)],[85]) ).
thf(399,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ ( B @ not @ or ) @ theorem )
!= ( r @ ( q @ or ) @ ( p @ or ) @ ( C @ not @ or ) @ theorem ) )
| ~ $true
| ~ ( C @ ( q @ ( p @ or ) @ ( r @ or ) @ not @ or ) @ axiom ) ),
inference(paramod_ordered,[status(thm)],[120,86]) ).
thf(400,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ ( B @ not @ or ) @ theorem )
!= ( r @ ( q @ or ) @ ( p @ or ) @ ( C @ not @ or ) @ theorem ) )
| ~ ( C @ ( q @ ( p @ or ) @ ( r @ or ) @ not @ or ) @ axiom ) ),
inference(simp,[status(thm)],[399]) ).
thf(401,plain,
~ ( r @ ( q @ or ) @ ( q @ ( p @ or ) @ ( r @ or ) @ not @ or ) @ axiom ),
inference(pattern_uni,[status(thm)],[400:[bind(A,$thf( p )),bind(B,$thf( r @ ( q @ or ) )),bind(C,$thf( r @ ( q @ or ) ))]]) ).
thf(102,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(103,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ or ) @ ( B @ ( A @ or ) @ not @ or ) @ axiom )
!= ( C @ axiom ) )
| ( C @ theorem ) ),
inference(simp,[status(thm)],[102]) ).
thf(104,plain,
! [B: $i,A: $i] : ( B @ ( A @ or ) @ ( A @ ( B @ or ) @ not @ or ) @ theorem ),
inference(pattern_uni,[status(thm)],[103:[bind(A,$thf( J )),bind(B,$thf( I )),bind(C,$thf( J @ ( I @ or ) @ ( I @ ( J @ or ) @ not @ or ) ))]]) ).
thf(119,plain,
! [B: $i,A: $i] : ( B @ ( A @ or ) @ ( A @ ( B @ or ) @ not @ or ) @ theorem ),
inference(simp,[status(thm)],[104]) ).
thf(484,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ theorem )
!= ( r @ ( q @ ( p @ or ) @ or ) @ not @ ( r @ ( q @ or ) @ ( p @ or ) @ or ) @ theorem ) )
| ~ $true
| ~ ( B @ theorem ) ),
inference(paramod_ordered,[status(thm)],[33,257]) ).
thf(485,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ theorem )
!= ( r @ ( q @ ( p @ or ) @ or ) @ not @ ( r @ ( q @ or ) @ ( p @ or ) @ or ) @ theorem ) )
| ~ ( B @ theorem ) ),
inference(simp,[status(thm)],[484]) ).
thf(486,plain,
~ ( r @ ( q @ ( p @ or ) @ or ) @ not @ theorem ),
inference(pattern_uni,[status(thm)],[485:[bind(A,$thf( r @ ( q @ or ) @ ( p @ or ) )),bind(B,$thf( r @ ( q @ ( p @ or ) @ or ) @ not ))]]) ).
thf(200,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ ( A @ ( B @ or ) @ not @ or ) @ theorem )
!= ( r @ ( q @ or ) @ ( p @ or ) @ ( C @ not @ or ) @ theorem ) )
| ~ $true
| ~ ( C @ ( r @ ( q @ ( p @ or ) @ or ) @ not @ or ) @ axiom ) ),
inference(paramod_ordered,[status(thm)],[119,54]) ).
thf(201,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ ( A @ ( B @ or ) @ not @ or ) @ theorem )
!= ( r @ ( q @ or ) @ ( p @ or ) @ ( C @ not @ or ) @ theorem ) )
| ~ ( C @ ( r @ ( q @ ( p @ or ) @ or ) @ not @ or ) @ axiom ) ),
inference(simp,[status(thm)],[200]) ).
thf(202,plain,
~ ( p @ ( r @ ( q @ or ) @ or ) @ ( r @ ( q @ ( p @ or ) @ or ) @ not @ or ) @ axiom ),
inference(pattern_uni,[status(thm)],[201:[bind(A,$thf( p )),bind(B,$thf( r @ ( q @ or ) )),bind(C,$thf( p @ ( r @ ( q @ or ) @ or ) ))]]) ).
thf(570,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ theorem )
!= ( r @ ( q @ or ) @ ( p @ or ) @ theorem ) )
| ~ $true
| ~ ( B @ theorem ) ),
inference(paramod_ordered,[status(thm)],[33,537]) ).
thf(571,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ theorem )
!= ( r @ ( q @ or ) @ ( p @ or ) @ theorem ) )
| ~ ( B @ theorem ) ),
inference(simp,[status(thm)],[570]) ).
thf(572,plain,
~ ( r @ ( q @ or ) @ theorem ),
inference(pattern_uni,[status(thm)],[571:[bind(A,$thf( p )),bind(B,$thf( r @ ( q @ or ) ))]]) ).
thf(596,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ theorem )
!= ( r @ ( q @ or ) @ theorem ) )
| ~ $true
| ~ ( B @ theorem ) ),
inference(paramod_ordered,[status(thm)],[33,572]) ).
thf(597,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ theorem )
!= ( r @ ( q @ or ) @ theorem ) )
| ~ ( B @ theorem ) ),
inference(simp,[status(thm)],[596]) ).
thf(598,plain,
~ ( r @ theorem ),
inference(pattern_uni,[status(thm)],[597:[bind(A,$thf( q )),bind(B,$thf( r ))]]) ).
thf(132,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ or ) @ not @ or ) @ theorem )
!= ( r @ ( q @ or ) @ ( p @ or ) @ ( B @ not @ or ) @ theorem ) )
| ~ $true
| ~ ( B @ ( r @ ( q @ ( p @ or ) @ or ) @ not @ or ) @ axiom ) ),
inference(paramod_ordered,[status(thm)],[117,54]) ).
thf(133,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ or ) @ not @ or ) @ theorem )
!= ( r @ ( q @ or ) @ ( p @ or ) @ ( B @ not @ or ) @ theorem ) )
| ~ ( B @ ( r @ ( q @ ( p @ or ) @ or ) @ not @ or ) @ axiom ) ),
inference(simp,[status(thm)],[132]) ).
thf(134,plain,
~ ( r @ ( q @ or ) @ ( p @ or ) @ ( r @ ( q @ or ) @ ( p @ or ) @ or ) @ ( r @ ( q @ ( p @ or ) @ or ) @ not @ or ) @ axiom ),
inference(pattern_uni,[status(thm)],[133:[bind(A,$thf( r @ ( q @ or ) @ ( p @ or ) )),bind(B,$thf( r @ ( q @ or ) @ ( p @ or ) @ ( r @ ( q @ or ) @ ( p @ or ) @ or ) ))]]) ).
thf(396,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ ( A @ ( B @ or ) @ not @ or ) @ theorem )
!= ( r @ ( q @ or ) @ ( p @ or ) @ ( C @ not @ or ) @ theorem ) )
| ~ $true
| ~ ( C @ ( q @ ( p @ or ) @ ( r @ or ) @ not @ or ) @ axiom ) ),
inference(paramod_ordered,[status(thm)],[119,86]) ).
thf(397,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ ( A @ ( B @ or ) @ not @ or ) @ theorem )
!= ( r @ ( q @ or ) @ ( p @ or ) @ ( C @ not @ or ) @ theorem ) )
| ~ ( C @ ( q @ ( p @ or ) @ ( r @ or ) @ not @ or ) @ axiom ) ),
inference(simp,[status(thm)],[396]) ).
thf(398,plain,
~ ( p @ ( r @ ( q @ or ) @ or ) @ ( q @ ( p @ or ) @ ( r @ or ) @ not @ or ) @ axiom ),
inference(pattern_uni,[status(thm)],[397:[bind(A,$thf( p )),bind(B,$thf( r @ ( q @ or ) )),bind(C,$thf( p @ ( r @ ( q @ or ) @ or ) ))]]) ).
thf(246,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)],[120,32]) ).
thf(247,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)],[246]) ).
thf(248,plain,
! [B: $i,A: $i] : ( B @ not @ ( B @ ( A @ or ) @ or ) @ theorem ),
inference(pattern_uni,[status(thm)],[247:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( G @ ( F @ or ) )),bind(D,$thf( G @ not ))]]) ).
thf(264,plain,
! [B: $i,A: $i] : ( B @ not @ ( B @ ( A @ or ) @ or ) @ theorem ),
inference(simp,[status(thm)],[248]) ).
thf(152,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ ( B @ not @ or ) @ theorem )
!= ( r @ ( q @ or ) @ ( p @ or ) @ ( C @ not @ or ) @ theorem ) )
| ~ $true
| ~ ( C @ ( r @ ( q @ ( p @ or ) @ or ) @ not @ or ) @ axiom ) ),
inference(paramod_ordered,[status(thm)],[120,54]) ).
thf(153,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ ( B @ not @ or ) @ theorem )
!= ( r @ ( q @ or ) @ ( p @ or ) @ ( C @ not @ or ) @ theorem ) )
| ~ ( C @ ( r @ ( q @ ( p @ or ) @ or ) @ not @ or ) @ axiom ) ),
inference(simp,[status(thm)],[152]) ).
thf(154,plain,
~ ( r @ ( q @ or ) @ ( r @ ( q @ ( p @ or ) @ or ) @ not @ or ) @ axiom ),
inference(pattern_uni,[status(thm)],[153:[bind(A,$thf( p )),bind(B,$thf( r @ ( q @ or ) )),bind(C,$thf( r @ ( q @ or ) ))]]) ).
thf(164,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ or ) @ ( A @ not @ or ) @ axiom )
!= ( r @ ( q @ or ) @ ( r @ ( q @ ( p @ or ) @ or ) @ not @ or ) @ axiom ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13,154]) ).
thf(165,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ or ) @ ( A @ not @ or ) @ axiom )
!= ( r @ ( q @ or ) @ ( r @ ( q @ ( p @ or ) @ or ) @ not @ or ) @ axiom ) ),
inference(simp,[status(thm)],[164]) ).
thf(172,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ or ) @ ( A @ not @ or ) )
!= ( r @ ( q @ or ) @ ( r @ ( q @ ( p @ or ) @ or ) @ not @ or ) ) ),
inference(simp,[status(thm)],[165]) ).
thf(243,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)],[119,32]) ).
thf(244,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)],[243]) ).
thf(245,plain,
! [B: $i,A: $i] : ( A @ ( B @ or ) @ not @ ( B @ ( A @ or ) @ or ) @ theorem ),
inference(pattern_uni,[status(thm)],[244:[bind(A,$thf( H )),bind(B,$thf( I )),bind(C,$thf( I @ ( H @ or ) )),bind(D,$thf( H @ ( I @ or ) @ not ))]]) ).
thf(262,plain,
! [B: $i,A: $i] : ( A @ ( B @ or ) @ not @ ( B @ ( A @ or ) @ or ) @ theorem ),
inference(simp,[status(thm)],[245]) ).
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/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 ) @ not @ or ) @ axiom ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(784,plain,
$false,
inference(e,[status(thm)],[10,257,14,20,265,117,537,13,22,267,516,18,16,401,119,486,120,202,260,598,21,33,134,398,32,264,17,12,54,572,86,172,81,154,11,262,19,15,68]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL192-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.08 % 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
% 0.13/0.40 % Computer : n020.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Fri Sep 25 22:00:18 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 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
% 0.87/0.98 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.25/1.18 % [INFO] Parsing done (189ms).
% 1.25/1.19 % [INFO] Running in sequential loop mode.
% 1.83/1.58 % [INFO] eprover registered as external prover.
% 1.83/1.59 % [INFO] Scanning for conjecture ...
% 2.02/1.68 % [INFO] Found a conjecture (or negated_conjecture) and 8 axioms. Running axiom selection ...
% 2.20/1.72 % [INFO] Axiom selection finished. Selected 8 axioms (removed 0 axioms).
% 2.20/1.74 % [INFO] Problem is propositional (TPTP CNF).
% 2.20/1.74 % [INFO] Type checking passed.
% 2.20/1.75 % [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 ...
% 9.54/3.80 % External prover 'e' found a proof!
% 10.18/3.80 % [INFO] Killing All external provers ...
% 10.18/3.80 % Time passed: 3258ms (effective reasoning time: 2603ms)
% 10.18/3.80 % 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
% 10.18/3.80 % No. of inferences in proof: 113
% 10.18/3.80 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3258 ms resp. 2603 ms w/o parsing
% 10.18/3.90 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 10.18/3.90 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------