%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL185-3 : 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 07:51:05 AM UTC 2026
% Result : Unsatisfiable 7.49s 3.11s
% Output : Refutation 7.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 9
% Syntax : Number of formulae : 101 ( 52 unt; 0 typ; 0 def)
% Number of atoms : 199 ( 86 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 886 ( 108 ~; 66 |; 0 &; 712 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 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 : 198 ( 0 ^; 198 !; 0 ?; 198 :)
% Comments :
%------------------------------------------------------------------------------
thf(theorem_decl,type,
theorem: $i > $o ).
thf(implies_decl,type,
implies: $i > $i > $i ).
thf(p_decl,type,
p: $i ).
thf(or_decl,type,
or: $i > $i > $i ).
thf(q_decl,type,
q: $i ).
thf(axiom_decl,type,
axiom: $i > $o ).
thf(not_decl,type,
not: $i > $i ).
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(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(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(35,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(36,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ or ) @ ( A @ implies ) @ axiom )
!= ( C @ axiom ) )
| ( C @ theorem ) ),
inference(simp,[status(thm)],[35]) ).
thf(37,plain,
! [B: $i,A: $i] : ( B @ ( A @ or ) @ ( B @ implies ) @ theorem ),
inference(pattern_uni,[status(thm)],[36:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( G @ ( F @ or ) @ ( G @ implies ) ))]]) ).
thf(44,plain,
! [B: $i,A: $i] : ( B @ ( A @ or ) @ ( B @ implies ) @ theorem ),
inference(simp,[status(thm)],[37]) ).
thf(1,negated_conjecture,
~ ( q @ ( p @ or ) @ ( p @ implies ) @ theorem ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
thf(10,plain,
~ ( q @ ( p @ or ) @ ( p @ implies ) @ theorem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(11,plain,
~ ( q @ ( p @ or ) @ ( p @ implies ) @ theorem ),
inference(polarity_switch,[status(thm)],[10]) ).
thf(51,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ ( B @ implies ) @ theorem )
!= ( q @ ( p @ or ) @ ( p @ implies ) @ theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[44,11]) ).
thf(52,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ or ) @ ( B @ implies ) @ theorem )
!= ( q @ ( p @ or ) @ ( p @ implies ) @ theorem ) ),
inference(simp,[status(thm)],[51]) ).
thf(59,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ or ) @ ( B @ implies ) )
!= ( q @ ( p @ or ) @ ( p @ implies ) ) ),
inference(simp,[status(thm)],[52]) ).
thf(113,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( q @ ( p @ or ) ) )
| ( ( B @ ( A @ implies ) @ ( p @ implies ) )
!= ( D @ ( C @ or ) @ ( D @ implies ) ) ) ),
inference(paramod_ordered,[status(thm)],[18,59]) ).
thf(116,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B != q )
| ( ( A @ not )
!= p )
| ( ( B @ ( A @ implies ) )
!= ( D @ ( C @ or ) ) )
| ( p != D ) ),
inference(simp,[status(thm)],[113]) ).
thf(120,plain,
! [B: $i,A: $i] :
( ( ( A @ not )
!= p )
| ( ( q @ ( A @ implies ) )
!= ( p @ ( B @ or ) ) ) ),
inference(simp,[status(thm)],[116]) ).
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(110,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ or ) )
!= ( q @ ( p @ or ) ) )
| ( B != p ) ),
inference(simp,[status(thm)],[59]) ).
thf(121,plain,
! [A: $i] :
( ( p @ ( A @ or ) )
!= ( q @ ( p @ or ) ) ),
inference(simp,[status(thm)],[110]) ).
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(38,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ or ) @ implies ) @ axiom )
!= ( B @ axiom ) )
| ~ $true
| ( B @ theorem ) ),
inference(paramod_ordered,[status(thm)],[12,20]) ).
thf(39,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ or ) @ implies ) @ axiom )
!= ( B @ axiom ) )
| ( B @ theorem ) ),
inference(simp,[status(thm)],[38]) ).
thf(40,plain,
! [A: $i] : ( A @ ( A @ ( A @ or ) @ implies ) @ theorem ),
inference(pattern_uni,[status(thm)],[39:[bind(A,$thf( D )),bind(B,$thf( D @ ( D @ ( D @ or ) @ implies ) ))]]) ).
thf(45,plain,
! [A: $i] : ( A @ ( A @ ( A @ or ) @ implies ) @ theorem ),
inference(simp,[status(thm)],[40]) ).
thf(78,plain,
! [A: $i] :
( ( ( A @ ( A @ ( A @ or ) @ implies ) @ theorem )
!= ( q @ ( p @ or ) @ ( p @ implies ) @ theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[45,11]) ).
thf(79,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ or ) @ implies ) @ theorem )
!= ( q @ ( p @ or ) @ ( p @ implies ) @ theorem ) ),
inference(simp,[status(thm)],[78]) ).
thf(87,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ or ) @ implies ) )
!= ( q @ ( p @ or ) @ ( p @ implies ) ) ),
inference(simp,[status(thm)],[79]) ).
thf(169,plain,
! [A: $i] :
( ( A
!= ( q @ ( p @ or ) ) )
| ( ( A @ ( A @ or ) )
!= p ) ),
inference(simp,[status(thm)],[87]) ).
thf(176,plain,
( ( q @ ( p @ or ) @ ( q @ ( p @ or ) @ or ) )
!= p ),
inference(simp,[status(thm)],[169]) ).
thf(182,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( q @ ( p @ or ) ) )
| ( ( q @ ( p @ or ) @ ( B @ ( A @ implies ) @ or ) )
!= p ) ),
inference(paramod_ordered,[status(thm)],[18,176]) ).
thf(185,plain,
! [B: $i,A: $i] :
( ( B != q )
| ( ( A @ not )
!= p )
| ( ( q @ ( p @ or ) @ ( B @ ( A @ implies ) @ or ) )
!= p ) ),
inference(simp,[status(thm)],[182]) ).
thf(188,plain,
! [A: $i] :
( ( ( A @ not )
!= p )
| ( ( q @ ( p @ or ) @ ( q @ ( A @ implies ) @ or ) )
!= p ) ),
inference(simp,[status(thm)],[185]) ).
thf(64,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(65,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ or ) @ ( B @ ( A @ or ) @ implies ) @ axiom )
!= ( C @ axiom ) )
| ( C @ theorem ) ),
inference(simp,[status(thm)],[64]) ).
thf(66,plain,
! [B: $i,A: $i] : ( B @ ( A @ or ) @ ( A @ ( B @ or ) @ implies ) @ theorem ),
inference(pattern_uni,[status(thm)],[65:[bind(A,$thf( I )),bind(B,$thf( H )),bind(C,$thf( I @ ( H @ or ) @ ( H @ ( I @ or ) @ implies ) ))]]) ).
thf(71,plain,
! [B: $i,A: $i] : ( B @ ( A @ or ) @ ( A @ ( B @ or ) @ implies ) @ theorem ),
inference(simp,[status(thm)],[66]) ).
thf(196,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)],[18,71]) ).
thf(197,plain,
! [B: $i,A: $i] : ( A @ ( B @ implies ) @ ( B @ not @ ( A @ or ) @ implies ) @ theorem ),
inference(pattern_uni,[status(thm)],[196:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( E @ not )),bind(D,$thf( B ))]]) ).
thf(212,plain,
! [B: $i,A: $i] : ( A @ ( B @ implies ) @ ( B @ not @ ( A @ or ) @ implies ) @ theorem ),
inference(simp,[status(thm)],[197]) ).
thf(181,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( q @ ( p @ or ) @ ( q @ ( p @ or ) @ or ) ) )
| ( ( B @ ( A @ implies ) )
!= p ) ),
inference(paramod_ordered,[status(thm)],[18,176]) ).
thf(184,plain,
! [B: $i,A: $i] :
( ( B
!= ( q @ ( p @ or ) ) )
| ( ( A @ not )
!= ( q @ ( p @ or ) ) )
| ( ( B @ ( A @ implies ) )
!= p ) ),
inference(simp,[status(thm)],[181]) ).
thf(187,plain,
! [A: $i] :
( ( ( A @ not )
!= ( q @ ( p @ or ) ) )
| ( ( q @ ( p @ or ) @ ( A @ implies ) )
!= p ) ),
inference(simp,[status(thm)],[184]) ).
thf(198,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)],[18,71]) ).
thf(199,plain,
! [B: $i,A: $i] : ( B @ not @ ( A @ or ) @ ( A @ ( B @ implies ) @ implies ) @ theorem ),
inference(pattern_uni,[status(thm)],[198:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( E @ not ))]]) ).
thf(213,plain,
! [B: $i,A: $i] : ( B @ not @ ( A @ or ) @ ( A @ ( B @ implies ) @ implies ) @ theorem ),
inference(simp,[status(thm)],[199]) ).
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(74,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)],[18,45]) ).
thf(75,plain,
! [A: $i] : ( A @ not @ ( A @ not @ ( A @ implies ) @ implies ) @ theorem ),
inference(pattern_uni,[status(thm)],[74:[bind(A,$thf( E )),bind(B,$thf( E @ not )),bind(C,$thf( E @ not ))]]) ).
thf(90,plain,
! [A: $i] : ( A @ not @ ( A @ not @ ( A @ implies ) @ implies ) @ theorem ),
inference(simp,[status(thm)],[75]) ).
thf(183,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( q @ ( p @ or ) ) )
| ( ( B @ ( A @ implies ) @ ( q @ ( p @ or ) @ or ) )
!= p ) ),
inference(paramod_ordered,[status(thm)],[18,176]) ).
thf(186,plain,
! [B: $i,A: $i] :
( ( B != q )
| ( ( A @ not )
!= p )
| ( ( B @ ( A @ implies ) @ ( q @ ( p @ or ) @ or ) )
!= p ) ),
inference(simp,[status(thm)],[183]) ).
thf(189,plain,
! [A: $i] :
( ( ( A @ not )
!= p )
| ( ( q @ ( A @ implies ) @ ( q @ ( p @ or ) @ or ) )
!= p ) ),
inference(simp,[status(thm)],[186]) ).
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(30,plain,
! [B: $i,A: $i] : ( A @ ( B @ implies ) @ ( A @ implies ) @ axiom ),
inference(simp,[status(thm)],[27]) ).
thf(41,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( A @ implies ) @ axiom )
!= ( C @ axiom ) )
| ~ $true
| ( C @ theorem ) ),
inference(paramod_ordered,[status(thm)],[30,20]) ).
thf(42,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( A @ implies ) @ axiom )
!= ( C @ axiom ) )
| ( C @ theorem ) ),
inference(simp,[status(thm)],[41]) ).
thf(43,plain,
! [B: $i,A: $i] : ( B @ ( A @ implies ) @ ( B @ implies ) @ theorem ),
inference(pattern_uni,[status(thm)],[42:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( G @ ( F @ implies ) @ ( G @ implies ) ))]]) ).
thf(46,plain,
! [B: $i,A: $i] : ( B @ ( A @ implies ) @ ( B @ implies ) @ theorem ),
inference(simp,[status(thm)],[43]) ).
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(29,plain,
! [A: $i] : ( A @ not @ ( A @ not @ ( A @ implies ) @ implies ) @ axiom ),
inference(simp,[status(thm)],[25]) ).
thf(111,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( D @ ( C @ or ) ) )
| ( ( B @ ( A @ implies ) @ ( D @ implies ) )
!= ( q @ ( p @ or ) @ ( p @ implies ) ) ) ),
inference(paramod_ordered,[status(thm)],[18,59]) ).
thf(112,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ implies ) @ ( A @ implies ) )
!= ( q @ ( p @ or ) @ ( p @ implies ) ) ),
inference(pattern_uni,[status(thm)],[111:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( E @ not )),bind(D,$thf( B ))]]) ).
thf(117,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ implies ) @ ( A @ implies ) )
!= ( q @ ( p @ or ) @ ( p @ implies ) ) ),
inference(simp,[status(thm)],[112]) ).
thf(93,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ implies ) @ theorem )
!= ( q @ ( p @ or ) @ ( p @ implies ) @ theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[46,11]) ).
thf(94,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ implies ) @ theorem )
!= ( q @ ( p @ or ) @ ( p @ implies ) @ theorem ) ),
inference(simp,[status(thm)],[93]) ).
thf(102,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ implies ) )
!= ( q @ ( p @ or ) @ ( p @ implies ) ) ),
inference(simp,[status(thm)],[94]) ).
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(22,plain,
! [B: $i,A: $i] :
( ~ ( B @ theorem )
| ~ ( A @ ( B @ implies ) @ theorem )
| ( A @ theorem ) ),
inference(cnf,[status(esa)],[21]) ).
thf(32,plain,
! [B: $i,A: $i] :
( ~ $true
| ( ( A @ ( B @ implies ) @ theorem )
!= ( B @ theorem ) )
| ~ ( B @ theorem )
| ( A @ theorem ) ),
inference(eqfactor_ordered,[status(thm)],[22]) ).
thf(33,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ theorem )
!= ( B @ theorem ) )
| ~ ( B @ theorem )
| ( A @ theorem ) ),
inference(simp,[status(thm)],[32]) ).
thf(69,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(70,plain,
! [B: $i,A: $i] : ( A @ ( B @ implies ) @ ( B @ not @ ( A @ or ) @ implies ) @ axiom ),
inference(pattern_uni,[status(thm)],[69:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( E @ not ))]]) ).
thf(73,plain,
! [B: $i,A: $i] : ( A @ ( B @ implies ) @ ( B @ not @ ( A @ or ) @ implies ) @ axiom ),
inference(simp,[status(thm)],[70]) ).
thf(123,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( p @ ( C @ or ) ) )
| ( ( B @ ( A @ implies ) )
!= ( q @ ( p @ or ) ) ) ),
inference(paramod_ordered,[status(thm)],[18,121]) ).
thf(124,plain,
! [A: $i] :
( ( p @ ( A @ implies ) )
!= ( q @ ( p @ or ) ) ),
inference(pattern_uni,[status(thm)],[123:[bind(A,$thf( D )),bind(B,$thf( p )),bind(C,$thf( D @ not ))]]) ).
thf(128,plain,
! [A: $i] :
( ( p @ ( A @ implies ) )
!= ( q @ ( p @ or ) ) ),
inference(simp,[status(thm)],[124]) ).
thf(144,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( q @ ( p @ or ) ) )
| ( ( B @ ( A @ implies ) )
!= ( p @ ( C @ implies ) ) ) ),
inference(paramod_ordered,[status(thm)],[18,128]) ).
thf(146,plain,
! [C: $i,B: $i,A: $i] :
( ( B != q )
| ( ( A @ not )
!= p )
| ( ( B @ ( A @ implies ) )
!= ( p @ ( C @ implies ) ) ) ),
inference(simp,[status(thm)],[144]) ).
thf(149,plain,
! [B: $i,A: $i] :
( ( ( A @ not )
!= p )
| ( ( q @ ( A @ implies ) )
!= ( p @ ( B @ implies ) ) ) ),
inference(simp,[status(thm)],[146]) ).
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(122,plain,
! [A: $i] :
( ( q != p )
| ( A != p ) ),
inference(simp,[status(thm)],[121]) ).
thf(127,plain,
q != p,
inference(simp,[status(thm)],[122]) ).
thf(23,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( q @ ( p @ or ) ) )
| ~ ( B @ ( A @ implies ) @ ( p @ implies ) @ theorem ) ),
inference(paramod_ordered,[status(thm)],[18,11]) ).
thf(28,plain,
! [B: $i,A: $i] :
( ( B != q )
| ( ( A @ not )
!= p )
| ~ ( B @ ( A @ implies ) @ ( p @ implies ) @ theorem ) ),
inference(simp,[status(thm)],[23]) ).
thf(31,plain,
! [A: $i] :
( ( ( A @ not )
!= p )
| ~ ( q @ ( A @ implies ) @ ( p @ implies ) @ theorem ) ),
inference(simp,[status(thm)],[28]) ).
thf(67,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(68,plain,
! [B: $i,A: $i] : ( B @ not @ ( A @ or ) @ ( A @ ( B @ implies ) @ implies ) @ axiom ),
inference(pattern_uni,[status(thm)],[67:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( E @ not )),bind(D,$thf( B ))]]) ).
thf(72,plain,
! [B: $i,A: $i] : ( B @ not @ ( A @ or ) @ ( A @ ( B @ implies ) @ implies ) @ axiom ),
inference(simp,[status(thm)],[68]) ).
thf(414,plain,
$false,
inference(e,[status(thm)],[120,10,14,121,188,212,13,187,213,18,87,15,90,189,20,46,29,117,102,21,33,73,128,45,17,149,176,22,44,59,71,12,16,127,31,11,72,30,19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL185-3 : 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
% 0.13/0.40 % Computer : n015.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 22:01:43 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
% 0.86/1.00 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.23/1.19 % [INFO] Parsing done (191ms).
% 1.39/1.21 % [INFO] Running in sequential loop mode.
% 2.09/1.60 % [INFO] eprover registered as external prover.
% 2.09/1.61 % [INFO] Scanning for conjecture ...
% 2.26/1.70 % [INFO] Found a conjecture (or negated_conjecture) and 8 axioms. Running axiom selection ...
% 2.26/1.73 % [INFO] Axiom selection finished. Selected 8 axioms (removed 0 axioms).
% 2.26/1.75 % [INFO] Problem is propositional (TPTP CNF).
% 2.26/1.76 % [INFO] Type checking passed.
% 2.26/1.76 % [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 ...
% 7.49/3.10 % External prover 'e' found a proof!
% 7.49/3.10 % [INFO] Killing All external provers ...
% 7.49/3.11 % Time passed: 2560ms (effective reasoning time: 1895ms)
% 7.49/3.11 % 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
% 7.49/3.11 % No. of inferences in proof: 101
% 7.49/3.11 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2560 ms resp. 1895 ms w/o parsing
% 7.22/3.18 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 7.22/3.18 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------