%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL048-1 : TPTP v9.3.1. Released v1.0.0.
% 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 : 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 07:50:40 AM UTC 2026
% Result : Unsatisfiable 27.42s 7.59s
% Output : Refutation 26.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 5
% Syntax : Number of formulae : 112 ( 47 unt; 0 typ; 0 def)
% Number of atoms : 310 ( 112 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 1648 ( 173 ~; 102 |; 0 &;1373 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 307 ( 0 ^; 307 !; 0 ?; 307 :)
% Comments :
%------------------------------------------------------------------------------
thf(is_a_theorem_decl,type,
is_a_theorem: $i > $o ).
thf(implies_decl,type,
implies: $i > $i > $i ).
thf(a_decl,type,
a: $i ).
thf(b_decl,type,
b: $i ).
thf(c_decl,type,
c: $i ).
thf(not_decl,type,
not: $i > $i ).
thf(5,axiom,
! [B: $i,A: $i] : ( B @ ( A @ not @ implies ) @ ( A @ implies ) @ is_a_theorem ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cn_3) ).
thf(12,plain,
! [B: $i,A: $i] : ( B @ ( A @ not @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(2,axiom,
! [B: $i,A: $i] :
( ( B @ is_a_theorem )
| ~ ( A @ is_a_theorem )
| ~ ( B @ ( A @ implies ) @ is_a_theorem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',condensed_detachment) ).
thf(8,plain,
! [B: $i,A: $i] :
( ( B @ is_a_theorem )
| ~ ( A @ is_a_theorem )
| ~ ( B @ ( A @ implies ) @ is_a_theorem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(9,plain,
! [B: $i,A: $i] :
( ( B @ is_a_theorem )
| ~ ( A @ is_a_theorem )
| ~ ( B @ ( A @ implies ) @ is_a_theorem ) ),
inference(cnf,[status(esa)],[8]) ).
thf(35,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ ( C @ implies ) @ is_a_theorem ) )
| ( D @ is_a_theorem )
| ~ ( C @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12,9]) ).
thf(36,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ ( C @ implies ) @ is_a_theorem ) )
| ( D @ is_a_theorem )
| ~ ( C @ is_a_theorem ) ),
inference(simp,[status(thm)],[35]) ).
thf(37,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ not @ implies ) @ is_a_theorem )
| ~ ( B @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[36:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( G )),bind(D,$thf( F @ ( G @ not @ implies ) ))]]) ).
thf(51,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ not @ implies ) @ is_a_theorem )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[37]) ).
thf(66,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( C @ ( D @ not @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12,51]) ).
thf(67,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( C @ ( D @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[66]) ).
thf(68,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[67:[bind(A,$thf( I )),bind(B,$thf( H )),bind(C,$thf( C )),bind(D,$thf( H @ ( I @ not @ implies ) @ ( I @ implies ) ))]]) ).
thf(79,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[68]) ).
thf(1,negated_conjecture,
~ ( c @ ( b @ implies ) @ ( c @ ( b @ ( a @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_cn_19) ).
thf(6,plain,
~ ( c @ ( b @ implies ) @ ( c @ ( b @ ( a @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(7,plain,
~ ( c @ ( b @ implies ) @ ( c @ ( b @ ( a @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
inference(polarity_switch,[status(thm)],[6]) ).
thf(69,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ is_a_theorem )
!= ( c @ ( b @ implies ) @ ( c @ ( b @ ( a @ implies ) @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[51,7]) ).
thf(70,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ is_a_theorem )
!= ( c @ ( b @ implies ) @ ( c @ ( b @ ( a @ implies ) @ implies ) @ implies ) @ is_a_theorem ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[69]) ).
thf(77,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) )
!= ( c @ ( b @ implies ) @ ( c @ ( b @ ( a @ implies ) @ implies ) @ implies ) ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[70]) ).
thf(99,plain,
! [B: $i,A: $i] :
( ( A
!= ( c @ ( b @ implies ) ) )
| ( ( B @ not )
!= ( c @ ( b @ ( a @ implies ) @ implies ) ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[77]) ).
thf(116,plain,
! [A: $i] :
( ( ( A @ not )
!= ( c @ ( b @ ( a @ implies ) @ implies ) ) )
| ~ ( A @ is_a_theorem ) ),
inference(simp,[status(thm)],[99]) ).
thf(133,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ not )
!= ( c @ ( b @ ( a @ implies ) @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[79,116]) ).
thf(134,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ not )
!= ( c @ ( b @ ( a @ implies ) @ implies ) ) ) ),
inference(simp,[status(thm)],[133]) ).
thf(135,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ implies ) @ not )
!= ( c @ ( b @ ( a @ implies ) @ implies ) ) ),
inference(pattern_uni,[status(thm)],[134:[bind(A,$thf( F )),bind(B,$thf( K )),bind(C,$thf( L )),bind(D,$thf( F @ ( K @ ( L @ not @ implies ) @ ( L @ implies ) @ not @ implies ) ))]]) ).
thf(138,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ implies ) @ not )
!= ( c @ ( b @ ( a @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[135]) ).
thf(109,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( C @ ( D @ not @ implies ) )
!= ( c @ ( b @ implies ) @ ( c @ ( b @ ( a @ implies ) @ implies ) @ implies ) ) )
| ~ $true
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[51,77]) ).
thf(110,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( C @ ( D @ not @ implies ) )
!= ( c @ ( b @ implies ) @ ( c @ ( b @ ( a @ implies ) @ implies ) @ implies ) ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[109]) ).
thf(111,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) )
!= ( c @ ( b @ implies ) @ ( c @ ( b @ ( a @ implies ) @ implies ) @ implies ) ) )
| ~ ( C @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[110:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( C )),bind(D,$thf( F @ ( G @ not @ implies ) ))]]) ).
thf(120,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) )
!= ( c @ ( b @ implies ) @ ( c @ ( b @ ( a @ implies ) @ implies ) @ implies ) ) )
| ~ ( C @ is_a_theorem ) ),
inference(simp,[status(thm)],[111]) ).
thf(3,axiom,
! [C: $i,B: $i,A: $i] : ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cn_1) ).
thf(10,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(22,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ ( b @ implies ) @ ( c @ ( b @ ( a @ implies ) @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10,7]) ).
thf(23,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ ( b @ implies ) @ ( c @ ( b @ ( a @ implies ) @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[22]) ).
thf(24,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) )
!= ( c @ ( b @ implies ) @ ( c @ ( b @ ( a @ implies ) @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[23]) ).
thf(4,axiom,
! [A: $i] : ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cn_2) ).
thf(11,plain,
! [A: $i] : ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(13,plain,
! [A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ ( b @ implies ) @ ( c @ ( b @ ( a @ implies ) @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11,7]) ).
thf(14,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ ( b @ implies ) @ ( c @ ( b @ ( a @ implies ) @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[13]) ).
thf(15,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ not @ implies ) @ implies ) )
!= ( c @ ( b @ implies ) @ ( c @ ( b @ ( a @ implies ) @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[14]) ).
thf(19,plain,
! [A: $i] :
( ( A
!= ( c @ ( b @ implies ) ) )
| ( ( A @ ( A @ not @ implies ) )
!= ( c @ ( b @ ( a @ implies ) @ implies ) ) ) ),
inference(simp,[status(thm)],[15]) ).
thf(20,plain,
( ( c @ ( b @ implies ) @ ( c @ ( b @ implies ) @ not @ implies ) )
!= ( c @ ( b @ ( a @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[19]) ).
thf(124,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( C @ not )
!= ( c @ ( b @ ( a @ implies ) @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12,116]) ).
thf(125,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( C @ not )
!= ( c @ ( b @ ( a @ implies ) @ implies ) ) ) ),
inference(simp,[status(thm)],[124]) ).
thf(126,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ not @ implies ) @ ( B @ implies ) @ not )
!= ( c @ ( b @ ( a @ implies ) @ implies ) ) ),
inference(pattern_uni,[status(thm)],[125:[bind(A,$thf( H )),bind(B,$thf( G )),bind(C,$thf( G @ ( H @ not @ implies ) @ ( H @ implies ) ))]]) ).
thf(140,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ not @ implies ) @ ( B @ implies ) @ not )
!= ( c @ ( b @ ( a @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[126]) ).
thf(71,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( B @ ( C @ not @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11,51]) ).
thf(72,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( B @ ( C @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[71]) ).
thf(73,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[72:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( E @ ( E @ ( E @ not @ implies ) @ implies ) ))]]) ).
thf(80,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[73]) ).
thf(155,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( C @ ( D @ not @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[80,51]) ).
thf(156,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( C @ ( D @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[155]) ).
thf(157,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[156:[bind(A,$thf( F )),bind(B,$thf( I )),bind(C,$thf( C )),bind(D,$thf( F @ ( I @ ( I @ ( I @ not @ implies ) @ implies ) @ not @ implies ) ))]]) ).
thf(162,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[157]) ).
thf(16,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( b @ implies ) @ ( c @ ( b @ ( a @ implies ) @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12,7]) ).
thf(17,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( b @ implies ) @ ( c @ ( b @ ( a @ implies ) @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[16]) ).
thf(18,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ not @ implies ) @ ( A @ implies ) )
!= ( c @ ( b @ implies ) @ ( c @ ( b @ ( a @ implies ) @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[17]) ).
thf(25,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ not @ implies ) )
!= ( c @ ( b @ implies ) ) )
| ( A
!= ( c @ ( b @ ( a @ implies ) @ implies ) ) ) ),
inference(simp,[status(thm)],[18]) ).
thf(26,plain,
! [A: $i] :
( ( A @ ( c @ ( b @ ( a @ implies ) @ implies ) @ not @ implies ) )
!= ( c @ ( b @ implies ) ) ),
inference(simp,[status(thm)],[25]) ).
thf(27,plain,
! [A: $i] :
( ( A != c )
| ( ( c @ ( b @ ( a @ implies ) @ implies ) @ not )
!= b ) ),
inference(simp,[status(thm)],[26]) ).
thf(28,plain,
( ( c @ ( b @ ( a @ implies ) @ implies ) @ not )
!= b ),
inference(simp,[status(thm)],[27]) ).
thf(21,plain,
( ( ( c @ ( b @ implies ) )
!= c )
| ( ( c @ ( b @ implies ) @ not )
!= ( b @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[20]) ).
thf(130,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( C @ not )
!= ( c @ ( b @ ( a @ implies ) @ implies ) ) )
| ~ $true
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[51,116]) ).
thf(131,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( C @ not )
!= ( c @ ( b @ ( a @ implies ) @ implies ) ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[130]) ).
thf(132,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ not )
!= ( c @ ( b @ ( a @ implies ) @ implies ) ) )
| ~ ( B @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[131:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( E @ ( F @ not @ implies ) ))]]) ).
thf(137,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ not )
!= ( c @ ( b @ ( a @ implies ) @ implies ) ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[132]) ).
thf(47,plain,
! [B: $i,A: $i] :
( ~ $true
| ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( A @ is_a_theorem ) )
| ( B @ is_a_theorem )
| ~ ( A @ is_a_theorem ) ),
inference(eqfactor_ordered,[status(thm)],[9]) ).
thf(49,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
!= A )
| ~ ( A @ is_a_theorem )
| ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[47]) ).
thf(92,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( D @ ( E @ not @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[79,51]) ).
thf(93,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( D @ ( E @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[92]) ).
thf(94,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[93:[bind(A,$thf( G )),bind(B,$thf( L )),bind(C,$thf( M )),bind(D,$thf( D )),bind(E,$thf( G @ ( L @ ( M @ not @ implies ) @ ( M @ implies ) @ not @ implies ) ))]]) ).
thf(98,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[94]) ).
thf(279,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( E @ ( F @ not @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[98,51]) ).
thf(280,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ( E @ ( F @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[279]) ).
thf(281,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( D @ ( E @ not @ implies ) @ ( E @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[280:[bind(A,$thf( H )),bind(B,$thf( K )),bind(C,$thf( P )),bind(D,$thf( Q )),bind(E,$thf( E )),bind(F,$thf( H @ ( K @ ( P @ ( Q @ not @ implies ) @ ( Q @ implies ) @ not @ implies ) @ not @ implies ) ))]]) ).
thf(299,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( D @ ( E @ not @ implies ) @ ( E @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[281]) ).
thf(48,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( A @ is_a_theorem ) )
| ~ ( A @ is_a_theorem )
| ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[47]) ).
thf(90,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( c @ ( b @ implies ) @ ( c @ ( b @ ( a @ implies ) @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[79,7]) ).
thf(91,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( c @ ( b @ implies ) @ ( c @ ( b @ ( a @ implies ) @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[90]) ).
thf(95,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ implies ) )
!= ( c @ ( b @ implies ) @ ( c @ ( b @ ( a @ implies ) @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[91]) ).
thf(32,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( E @ is_a_theorem )
| ~ $true
| ~ ( E @ ( D @ implies ) @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[10,9]) ).
thf(33,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( E @ is_a_theorem )
| ~ ( E @ ( D @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[32]) ).
thf(34,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ is_a_theorem )
| ~ ( A @ ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ ( B @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[33:[bind(A,$thf( N )),bind(B,$thf( L )),bind(C,$thf( O )),bind(D,$thf( O @ ( N @ implies ) @ ( O @ ( L @ implies ) @ implies ) @ ( L @ ( N @ implies ) @ implies ) )),bind(E,$thf( E ))]]) ).
thf(50,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ is_a_theorem )
| ~ ( A @ ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ ( B @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[34]) ).
thf(176,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( C @ ( D @ not @ implies ) @ not )
!= ( c @ ( b @ ( a @ implies ) @ implies ) ) )
| ~ $true
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[51,137]) ).
thf(177,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( C @ ( D @ not @ implies ) @ not )
!= ( c @ ( b @ ( a @ implies ) @ implies ) ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[176]) ).
thf(178,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ not )
!= ( c @ ( b @ ( a @ implies ) @ implies ) ) )
| ~ ( C @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[177:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( C )),bind(D,$thf( F @ ( G @ not @ implies ) ))]]) ).
thf(182,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ not )
!= ( c @ ( b @ ( a @ implies ) @ implies ) ) )
| ~ ( C @ is_a_theorem ) ),
inference(simp,[status(thm)],[178]) ).
thf(170,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( C @ ( D @ not @ implies ) @ not )
!= ( c @ ( b @ ( a @ implies ) @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[80,137]) ).
thf(171,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( C @ ( D @ not @ implies ) @ not )
!= ( c @ ( b @ ( a @ implies ) @ implies ) ) ) ),
inference(simp,[status(thm)],[170]) ).
thf(172,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ not )
!= ( c @ ( b @ ( a @ implies ) @ implies ) ) ),
inference(pattern_uni,[status(thm)],[171:[bind(A,$thf( F )),bind(B,$thf( I )),bind(C,$thf( C )),bind(D,$thf( F @ ( I @ ( I @ ( I @ not @ implies ) @ implies ) @ not @ implies ) ))]]) ).
thf(186,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ not )
!= ( c @ ( b @ ( a @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[172]) ).
thf(121,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ not )
!= ( c @ ( b @ ( a @ implies ) @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10,116]) ).
thf(122,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ not )
!= ( c @ ( b @ ( a @ implies ) @ implies ) ) ) ),
inference(simp,[status(thm)],[121]) ).
thf(123,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ ( A @ ( B @ implies ) @ implies ) @ not )
!= ( c @ ( b @ ( a @ implies ) @ implies ) ) ),
inference(pattern_uni,[status(thm)],[122:[bind(A,$thf( M )),bind(B,$thf( K )),bind(C,$thf( N )),bind(D,$thf( N @ ( M @ implies ) @ ( N @ ( K @ implies ) @ implies ) @ ( K @ ( M @ implies ) @ implies ) ))]]) ).
thf(139,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ ( A @ ( B @ implies ) @ implies ) @ not )
!= ( c @ ( b @ ( a @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[123]) ).
thf(106,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( B @ ( C @ not @ implies ) )
!= ( c @ ( b @ implies ) @ ( c @ ( b @ ( a @ implies ) @ implies ) @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11,77]) ).
thf(107,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( B @ ( C @ not @ implies ) )
!= ( c @ ( b @ implies ) @ ( c @ ( b @ ( a @ implies ) @ implies ) @ implies ) ) ) ),
inference(simp,[status(thm)],[106]) ).
thf(108,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) )
!= ( c @ ( b @ implies ) @ ( c @ ( b @ ( a @ implies ) @ implies ) @ implies ) ) ),
inference(pattern_uni,[status(thm)],[107:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( E @ ( E @ ( E @ not @ implies ) @ implies ) ))]]) ).
thf(119,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) )
!= ( c @ ( b @ implies ) @ ( c @ ( b @ ( a @ implies ) @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[108]) ).
thf(179,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( D @ ( E @ not @ implies ) @ not )
!= ( c @ ( b @ ( a @ implies ) @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[79,137]) ).
thf(180,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( D @ ( E @ not @ implies ) @ not )
!= ( c @ ( b @ ( a @ implies ) @ implies ) ) ) ),
inference(simp,[status(thm)],[179]) ).
thf(181,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ implies ) @ not @ implies ) @ not )
!= ( c @ ( b @ ( a @ implies ) @ implies ) ) ),
inference(pattern_uni,[status(thm)],[180:[bind(A,$thf( G )),bind(B,$thf( L )),bind(C,$thf( M )),bind(D,$thf( D )),bind(E,$thf( G @ ( L @ ( M @ not @ implies ) @ ( M @ implies ) @ not @ implies ) ))]]) ).
thf(183,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ implies ) @ not @ implies ) @ not )
!= ( c @ ( b @ ( a @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[181]) ).
thf(127,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( B @ is_a_theorem ) )
| ( ( B @ not )
!= ( c @ ( b @ ( a @ implies ) @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11,116]) ).
thf(128,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( B @ is_a_theorem ) )
| ( ( B @ not )
!= ( c @ ( b @ ( a @ implies ) @ implies ) ) ) ),
inference(simp,[status(thm)],[127]) ).
thf(129,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not )
!= ( c @ ( b @ ( a @ implies ) @ implies ) ) ),
inference(pattern_uni,[status(thm)],[128:[bind(A,$thf( D )),bind(B,$thf( D @ ( D @ ( D @ not @ implies ) @ implies ) ))]]) ).
thf(136,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not )
!= ( c @ ( b @ ( a @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[129]) ).
thf(141,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( C @ not )
!= ( c @ ( b @ ( a @ implies ) @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[80,116]) ).
thf(142,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( C @ not )
!= ( c @ ( b @ ( a @ implies ) @ implies ) ) ) ),
inference(simp,[status(thm)],[141]) ).
thf(143,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) @ not )
!= ( c @ ( b @ ( a @ implies ) @ implies ) ) ),
inference(pattern_uni,[status(thm)],[142:[bind(A,$thf( E )),bind(B,$thf( H )),bind(C,$thf( E @ ( H @ ( H @ ( H @ not @ implies ) @ implies ) @ not @ implies ) ))]]) ).
thf(163,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) @ not )
!= ( c @ ( b @ ( a @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[143]) ).
thf(6632,plain,
$false,
inference(e,[status(thm)],[138,120,10,24,20,116,6,9,77,140,162,11,28,21,137,12,49,7,98,299,80,48,18,95,50,182,26,186,139,8,119,51,183,136,79,15,163]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL048-1 : TPTP v9.3.1. Released v1.0.0.
% 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
% 0.13/0.40 % 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 21:47:03 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 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
% 0.82/0.97 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.19/1.15 % [INFO] Parsing done (172ms).
% 1.19/1.16 % [INFO] Running in sequential loop mode.
% 1.86/1.66 % [INFO] eprover registered as external prover.
% 1.86/1.67 % [INFO] Scanning for conjecture ...
% 1.93/1.76 % [INFO] Found a conjecture (or negated_conjecture) and 4 axioms. Running axiom selection ...
% 1.93/1.79 % [INFO] Axiom selection finished. Selected 4 axioms (removed 0 axioms).
% 2.08/1.80 % [INFO] Problem is propositional (TPTP CNF).
% 2.08/1.80 % [INFO] Type checking passed.
% 2.08/1.81 % [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 ...
% 27.42/7.59 % External prover 'e' found a proof!
% 27.42/7.59 % [INFO] Killing All external provers ...
% 27.42/7.59 % Time passed: 7045ms (effective reasoning time: 6421ms)
% 27.42/7.59 % Axioms used in derivation (4): cn_3, condensed_detachment, cn_1, cn_2
% 27.42/7.59 % No. of inferences in proof: 112
% 27.42/7.59 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 7045 ms resp. 6421 ms w/o parsing
% 26.27/7.64 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 26.27/7.64 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------