%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL390-10 : TPTP v9.3.1. Released v7.5.0.
% 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 : n004.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 07:51:41 AM UTC 2026
% Result : Unsatisfiable 57.06s 12.55s
% Output : Refutation 47.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 6
% Syntax : Number of formulae : 97 ( 57 unt; 0 typ; 0 def)
% Number of atoms : 165 ( 164 equ; 0 cnn)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 1321 ( 115 ~; 68 |; 0 &;1138 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 4 con; 0-4 aty)
% Number of variables : 191 ( 0 ^; 191 !; 0 ?; 191 :)
% Comments :
%------------------------------------------------------------------------------
thf(is_a_theorem_decl,type,
is_a_theorem: $i > $i ).
thf(implies_decl,type,
implies: $i > $i > $i ).
thf(not_decl,type,
not: $i > $i ).
thf(x_decl,type,
x: $i ).
thf(y_decl,type,
y: $i ).
thf(true_decl,type,
true: $i ).
thf(ifeq_decl,type,
ifeq: $i > $i > $i > $i > $i ).
thf(4,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cn_1) ).
thf(14,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(15,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
= true ),
inference(lifteq,[status(thm)],[14]) ).
thf(1,negated_conjecture,
( ( y @ ( y @ ( x @ implies ) @ implies ) @ ( y @ ( x @ not @ implies ) @ implies ) @ is_a_theorem )
!= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_cn_53) ).
thf(7,plain,
( ( y @ ( y @ ( x @ implies ) @ implies ) @ ( y @ ( x @ not @ implies ) @ implies ) @ is_a_theorem )
!= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(8,plain,
( ( y @ ( y @ ( x @ implies ) @ implies ) @ ( y @ ( x @ not @ implies ) @ implies ) @ is_a_theorem )
!= true ),
inference(polarity_switch,[status(thm)],[7]) ).
thf(9,plain,
( ( y @ ( y @ ( x @ implies ) @ implies ) @ ( y @ ( x @ not @ implies ) @ implies ) @ is_a_theorem )
!= true ),
inference(lifteq,[status(thm)],[8]) ).
thf(64,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( y @ ( y @ ( x @ implies ) @ implies ) @ ( y @ ( x @ not @ implies ) @ implies ) @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[15,9]) ).
thf(65,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( y @ ( y @ ( x @ implies ) @ implies ) @ ( y @ ( x @ not @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[64]) ).
thf(80,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) )
!= ( y @ ( y @ ( x @ implies ) @ implies ) @ ( y @ ( x @ not @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[65]) ).
thf(147,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) )
!= ( y @ ( y @ ( x @ implies ) @ implies ) ) )
| ( ( B @ ( A @ implies ) )
!= ( y @ ( x @ not @ implies ) ) ) ),
inference(simp,[status(thm)],[80]) ).
thf(240,plain,
! [C: $i,B: $i,A: $i] :
( ( ( y @ ( y @ ( x @ implies ) @ implies ) )
!= ( B @ ( A @ implies ) ) )
| ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) )
!= ( y @ ( x @ not @ implies ) ) )
| ( ( B @ ( A @ implies ) )
!= ( y @ ( x @ not @ implies ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[147]) ).
thf(245,plain,
! [C: $i,B: $i,A: $i] :
( ( y != B )
| ( ( y @ ( x @ implies ) )
!= A )
| ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) )
!= ( y @ ( x @ not @ implies ) ) )
| ( B != y )
| ( A
!= ( x @ not ) ) ),
inference(simp,[status(thm)],[240]) ).
thf(260,plain,
! [A: $i] :
( ( ( y @ ( x @ implies ) )
!= ( x @ not ) )
| ( ( A @ ( x @ not @ implies ) @ ( A @ ( y @ implies ) @ implies ) )
!= ( y @ ( x @ not @ implies ) ) ) ),
inference(simp,[status(thm)],[245]) ).
thf(5,axiom,
! [A: $i] :
( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cn_2) ).
thf(16,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(17,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
= true ),
inference(lifteq,[status(thm)],[16]) ).
thf(6,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cn_3) ).
thf(18,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(19,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
= true ),
inference(lifteq,[status(thm)],[18]) ).
thf(3,axiom,
! [B: $i,A: $i] :
( ( true @ ( true @ ( B @ is_a_theorem @ ( true @ ( A @ is_a_theorem @ ifeq ) ) ) @ ( true @ ( B @ ( A @ implies ) @ is_a_theorem @ ifeq ) ) ) )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',condensed_detachment) ).
thf(12,plain,
! [B: $i,A: $i] :
( ( true @ ( true @ ( B @ is_a_theorem @ ( true @ ( A @ is_a_theorem @ ifeq ) ) ) @ ( true @ ( B @ ( A @ implies ) @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(13,plain,
! [B: $i,A: $i] :
( ( true @ ( true @ ( B @ is_a_theorem @ ( true @ ( A @ is_a_theorem @ ifeq ) ) ) @ ( true @ ( B @ ( A @ implies ) @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(lifteq,[status(thm)],[12]) ).
thf(47,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ ( C @ implies ) @ is_a_theorem ) )
| ( ( true @ ( true @ ( D @ is_a_theorem @ ( true @ ( C @ is_a_theorem @ ifeq ) ) ) @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[19,13]) ).
thf(48,plain,
! [B: $i,A: $i] :
( ( true @ ( true @ ( A @ ( B @ not @ implies ) @ is_a_theorem @ ( true @ ( B @ is_a_theorem @ ifeq ) ) ) @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[47:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( G )),bind(D,$thf( F @ ( G @ not @ implies ) ))]]) ).
thf(53,plain,
! [B: $i,A: $i] :
( ( true @ ( true @ ( A @ ( B @ not @ implies ) @ is_a_theorem @ ( true @ ( B @ is_a_theorem @ ifeq ) ) ) @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[48]) ).
thf(2,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( A @ ifeq ) ) ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom) ).
thf(10,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( A @ ifeq ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(11,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( A @ ifeq ) ) ) )
= B ),
inference(lifteq,[status(thm)],[10]) ).
thf(84,plain,
! [B: $i,A: $i] :
( ( true @ ( A @ ( B @ not @ implies ) @ is_a_theorem @ ( true @ ( B @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(rewrite,[status(thm)],[53,11]) ).
thf(100,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( true @ ( B @ ( C @ not @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[17,84]) ).
thf(101,plain,
! [B: $i,A: $i] :
( ( true @ ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[100:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( E @ ( E @ ( E @ not @ implies ) @ implies ) ))]]) ).
thf(109,plain,
! [B: $i,A: $i] :
( ( true @ ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[101]) ).
thf(191,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem )
= true ),
inference(rewrite,[status(thm)],[109,11]) ).
thf(196,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( y @ ( y @ ( x @ implies ) @ implies ) @ ( y @ ( x @ not @ implies ) @ implies ) @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[191,9]) ).
thf(197,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( y @ ( y @ ( x @ implies ) @ implies ) @ ( y @ ( x @ not @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[196]) ).
thf(224,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) )
!= ( y @ ( y @ ( x @ implies ) @ implies ) @ ( y @ ( x @ not @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[197]) ).
thf(93,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( true @ ( C @ ( D @ not @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[19,84]) ).
thf(94,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[93:[bind(A,$thf( I )),bind(B,$thf( H )),bind(C,$thf( C )),bind(D,$thf( H @ ( I @ not @ implies ) @ ( I @ implies ) ))]]) ).
thf(113,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[94]) ).
thf(464,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ implies ) @ is_a_theorem )
= true ),
inference(rewrite,[status(thm)],[113,11]) ).
thf(38,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ ( B @ implies ) @ is_a_theorem ) )
| ( ( true @ ( true @ ( C @ is_a_theorem @ ( true @ ( B @ is_a_theorem @ ifeq ) ) ) @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[17,13]) ).
thf(39,plain,
! [A: $i] :
( ( true @ ( true @ ( A @ is_a_theorem @ ( true @ ( A @ ( A @ not @ implies ) @ is_a_theorem @ ifeq ) ) ) @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[38:[bind(A,$thf( E )),bind(B,$thf( E @ ( E @ not @ implies ) )),bind(C,$thf( E ))]]) ).
thf(60,plain,
! [A: $i] :
( ( true @ ( true @ ( A @ is_a_theorem @ ( true @ ( A @ ( A @ not @ implies ) @ is_a_theorem @ ifeq ) ) ) @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[39]) ).
thf(152,plain,
! [A: $i] :
( ( true @ ( A @ is_a_theorem @ ( true @ ( A @ ( A @ not @ implies ) @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(rewrite,[status(thm)],[60,11]) ).
thf(486,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( D @ ( D @ not @ implies ) @ is_a_theorem ) )
| ( ( true @ ( D @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[464,152]) ).
thf(487,plain,
! [B: $i,A: $i] :
( ( true @ ( A @ ( B @ not @ implies ) @ ( B @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[486:[bind(A,$thf( M @ ( N @ not @ implies ) @ ( N @ implies ) )),bind(B,$thf( M )),bind(C,$thf( N )),bind(D,$thf( M @ ( N @ not @ implies ) @ ( N @ implies ) ))]]) ).
thf(520,plain,
! [B: $i,A: $i] :
( ( true @ ( A @ ( B @ not @ implies ) @ ( B @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[487]) ).
thf(535,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ not @ implies ) @ ( B @ implies ) @ is_a_theorem )
= true ),
inference(rewrite,[status(thm)],[520,11]) ).
thf(236,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) )
!= ( y @ ( y @ ( x @ implies ) @ implies ) ) )
| ( B != y )
| ( A
!= ( x @ not ) ) ),
inference(simp,[status(thm)],[147]) ).
thf(255,plain,
! [A: $i] :
( ( A @ ( x @ not @ implies ) @ ( A @ ( y @ implies ) @ implies ) )
!= ( y @ ( y @ ( x @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[236]) ).
thf(247,plain,
! [C: $i,B: $i,A: $i] :
( ( y != B )
| ( ( y @ ( x @ implies ) )
!= A )
| ( ( C @ ( A @ implies ) )
!= y )
| ( ( C @ ( B @ implies ) )
!= ( x @ not ) )
| ( B != y )
| ( A
!= ( x @ not ) ) ),
inference(simp,[status(thm)],[240]) ).
thf(262,plain,
! [A: $i] :
( ( ( y @ ( x @ implies ) )
!= ( x @ not ) )
| ( ( A @ ( x @ not @ implies ) )
!= y )
| ( ( A @ ( y @ implies ) )
!= ( x @ not ) ) ),
inference(simp,[status(thm)],[247]) ).
thf(27,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( y @ ( y @ ( x @ implies ) @ implies ) @ ( y @ ( x @ not @ implies ) @ implies ) @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[19,9]) ).
thf(28,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( y @ ( y @ ( x @ implies ) @ implies ) @ ( y @ ( x @ not @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[27]) ).
thf(29,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ not @ implies ) @ ( A @ implies ) )
!= ( y @ ( y @ ( x @ implies ) @ implies ) @ ( y @ ( x @ not @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[28]) ).
thf(141,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ not @ implies ) )
!= ( y @ ( y @ ( x @ implies ) @ implies ) ) )
| ( A
!= ( y @ ( x @ not @ implies ) ) ) ),
inference(simp,[status(thm)],[29]) ).
thf(142,plain,
! [A: $i] :
( ( A @ ( y @ ( x @ not @ implies ) @ not @ implies ) )
!= ( y @ ( y @ ( x @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[141]) ).
thf(246,plain,
! [C: $i,B: $i,A: $i] :
( ( y != B )
| ( ( y @ ( x @ implies ) )
!= A )
| ( ( C @ ( A @ implies ) )
!= y )
| ( ( C @ ( B @ implies ) )
!= ( x @ not ) )
| ( ( B @ ( A @ implies ) )
!= ( y @ ( x @ not @ implies ) ) ) ),
inference(simp,[status(thm)],[240]) ).
thf(261,plain,
! [A: $i] :
( ( ( A @ ( y @ ( x @ implies ) @ implies ) )
!= y )
| ( ( A @ ( y @ implies ) )
!= ( x @ not ) )
| ( ( y @ ( y @ ( x @ implies ) @ implies ) )
!= ( y @ ( x @ not @ implies ) ) ) ),
inference(simp,[status(thm)],[246]) ).
thf(542,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ ( B @ implies ) @ is_a_theorem )
!= ( y @ ( y @ ( x @ implies ) @ implies ) @ ( y @ ( x @ not @ implies ) @ implies ) @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[535,9]) ).
thf(543,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ not @ implies ) @ ( B @ implies ) @ is_a_theorem )
!= ( y @ ( y @ ( x @ implies ) @ implies ) @ ( y @ ( x @ not @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[542]) ).
thf(591,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ not @ implies ) @ ( B @ implies ) )
!= ( y @ ( y @ ( x @ implies ) @ implies ) @ ( y @ ( x @ not @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[543]) ).
thf(232,plain,
! [B: $i,A: $i] :
( ( A
!= ( y @ ( y @ ( x @ implies ) @ implies ) ) )
| ( ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not )
!= ( y @ ( x @ not @ implies ) ) ) ),
inference(simp,[status(thm)],[224]) ).
thf(233,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not )
!= ( y @ ( x @ not @ implies ) ) ),
inference(simp,[status(thm)],[232]) ).
thf(533,plain,
! [A: $i] :
( ( ( A @ ( y @ ( x @ implies ) @ implies ) )
!= y )
| ( ( A @ ( y @ implies ) )
!= ( x @ not ) )
| ( y != y )
| ( ( y @ ( x @ implies ) )
!= ( x @ not ) ) ),
inference(simp,[status(thm)],[261]) ).
thf(534,plain,
! [A: $i] :
( ( ( A @ ( y @ ( x @ implies ) @ implies ) )
!= y )
| ( ( A @ ( y @ implies ) )
!= ( x @ not ) )
| ( ( y @ ( x @ implies ) )
!= ( x @ not ) ) ),
inference(simp,[status(thm)],[533]) ).
thf(41,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ ( A @ ifeq ) ) ) )
!= ( true @ ( true @ ( E @ is_a_theorem @ ( true @ ( D @ is_a_theorem @ ifeq ) ) ) @ ( true @ ( E @ ( D @ implies ) @ is_a_theorem @ ifeq ) ) ) ) )
| ( B = true ) ),
inference(paramod_ordered,[status(thm)],[11,13]) ).
thf(50,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C != true )
| ( B
!= ( true @ ( E @ is_a_theorem @ ( true @ ( D @ is_a_theorem @ ifeq ) ) ) ) )
| ( A != true )
| ( A
!= ( E @ ( D @ implies ) @ is_a_theorem ) )
| ( B = true ) ),
inference(simp,[status(thm)],[41]) ).
thf(55,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= true )
| ( ( true @ ( B @ is_a_theorem @ ( true @ ( A @ is_a_theorem @ ifeq ) ) ) )
= true ) ),
inference(simp,[status(thm)],[50]) ).
thf(321,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( D @ ( C @ implies ) @ is_a_theorem ) )
| ( true != true )
| ( ( true @ ( D @ is_a_theorem @ ( true @ ( C @ is_a_theorem @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[191,55]) ).
thf(322,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( D @ ( C @ implies ) @ is_a_theorem ) )
| ( ( true @ ( D @ is_a_theorem @ ( true @ ( C @ is_a_theorem @ ifeq ) ) ) )
= true ) ),
inference(simp,[status(thm)],[321]) ).
thf(323,plain,
! [B: $i,A: $i] :
( ( true @ ( A @ is_a_theorem @ ( true @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[322:[bind(A,$thf( A )),bind(B,$thf( G )),bind(C,$thf( G @ ( G @ ( G @ not @ implies ) @ implies ) @ not )),bind(D,$thf( A ))]]) ).
thf(328,plain,
! [B: $i,A: $i] :
( ( true @ ( A @ is_a_theorem @ ( true @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[323]) ).
thf(238,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) )
!= y )
| ( ( C @ ( B @ implies ) )
!= ( y @ ( x @ implies ) ) )
| ( B != y )
| ( A
!= ( x @ not ) ) ),
inference(simp,[status(thm)],[147]) ).
thf(256,plain,
! [A: $i] :
( ( ( A @ ( x @ not @ implies ) )
!= y )
| ( ( A @ ( y @ implies ) )
!= ( y @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[238]) ).
thf(20,plain,
! [A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( y @ ( y @ ( x @ implies ) @ implies ) @ ( y @ ( x @ not @ implies ) @ implies ) @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[17,9]) ).
thf(21,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( y @ ( y @ ( x @ implies ) @ implies ) @ ( y @ ( x @ not @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[20]) ).
thf(22,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ not @ implies ) @ implies ) )
!= ( y @ ( y @ ( x @ implies ) @ implies ) @ ( y @ ( x @ not @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[21]) ).
thf(30,plain,
! [A: $i] :
( ( A
!= ( y @ ( y @ ( x @ implies ) @ implies ) ) )
| ( ( A @ ( A @ not @ implies ) )
!= ( y @ ( x @ not @ implies ) ) ) ),
inference(simp,[status(thm)],[22]) ).
thf(31,plain,
( ( y @ ( y @ ( x @ implies ) @ implies ) @ ( y @ ( y @ ( x @ implies ) @ implies ) @ not @ implies ) )
!= ( y @ ( x @ not @ implies ) ) ),
inference(simp,[status(thm)],[30]) ).
thf(32,plain,
( ( ( y @ ( y @ ( x @ implies ) @ implies ) )
!= y )
| ( ( y @ ( y @ ( x @ implies ) @ implies ) @ not )
!= ( x @ not ) ) ),
inference(simp,[status(thm)],[31]) ).
thf(143,plain,
! [A: $i] :
( ( A != y )
| ( ( y @ ( x @ not @ implies ) @ not )
!= ( y @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[142]) ).
thf(144,plain,
( ( y @ ( x @ not @ implies ) @ not )
!= ( y @ ( x @ implies ) ) ),
inference(simp,[status(thm)],[143]) ).
thf(270,plain,
! [A: $i] :
( ( ( A @ ( x @ not @ implies ) )
!= y )
| ( A != y )
| ( y != x ) ),
inference(simp,[status(thm)],[256]) ).
thf(271,plain,
( ( ( y @ ( x @ not @ implies ) )
!= y )
| ( y != x ) ),
inference(simp,[status(thm)],[270]) ).
thf(63,plain,
( ( ( y @ ( y @ ( x @ implies ) @ implies ) )
!= y )
| ( ( y @ ( y @ ( x @ implies ) @ implies ) )
!= x ) ),
inference(simp,[status(thm)],[32]) ).
thf(243,plain,
! [C: $i,B: $i,A: $i] :
( ( ( y @ ( y @ ( x @ implies ) @ implies ) )
!= ( B @ ( A @ implies ) ) )
| ( ( C @ ( A @ implies ) )
!= y )
| ( ( C @ ( B @ implies ) )
!= ( x @ not ) )
| ( B != y )
| ( A
!= ( x @ not ) ) ),
inference(simp,[status(thm)],[240]) ).
thf(258,plain,
! [A: $i] :
( ( ( y @ ( y @ ( x @ implies ) @ implies ) )
!= ( y @ ( x @ not @ implies ) ) )
| ( ( A @ ( x @ not @ implies ) )
!= y )
| ( ( A @ ( y @ implies ) )
!= ( x @ not ) ) ),
inference(simp,[status(thm)],[243]) ).
thf(95,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( C @ ( D @ not @ implies ) @ is_a_theorem ) )
| ( ( true @ ( true @ ( true @ ( D @ is_a_theorem @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[19,84]) ).
thf(96,plain,
! [A: $i] :
( ( true @ ( true @ ( true @ ( A @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[95:[bind(A,$thf( I @ not )),bind(B,$thf( G )),bind(C,$thf( G @ ( I @ not @ not @ implies ) )),bind(D,$thf( I ))]]) ).
thf(107,plain,
! [A: $i] :
( ( true @ ( true @ ( true @ ( A @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[96]) ).
thf(34,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( B @ is_a_theorem ) )
| ( ( true @ ( true @ ( C @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) @ ( true @ ( C @ ( B @ implies ) @ is_a_theorem @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[17,13]) ).
thf(35,plain,
! [B: $i,A: $i] :
( ( true @ ( true @ ( A @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) @ ( true @ ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[34:[bind(A,$thf( E )),bind(B,$thf( E @ ( E @ ( E @ not @ implies ) @ implies ) )),bind(C,$thf( C ))]]) ).
thf(56,plain,
! [B: $i,A: $i] :
( ( true @ ( true @ ( A @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) @ ( true @ ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[35]) ).
thf(400,plain,
! [B: $i,A: $i] :
( ( true @ ( A @ is_a_theorem @ ( true @ ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(rewrite,[status(thm)],[56,11]) ).
thf(10576,plain,
$false,
inference(e,[status(thm)],[14,147,260,224,9,13,535,80,255,11,262,10,142,152,261,29,591,84,233,534,328,256,32,17,191,22,12,144,7,271,63,18,16,31,258,55,107,400,464,15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL390-10 : TPTP v9.3.1. Released v7.5.0.
% 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
% 0.18/0.43 % Computer : n004.cluster.edu
% 0.18/0.43 % Model : x86_64 x86_64
% 0.18/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.43 % Memory : 8046.5625MB
% 0.18/0.43 % OS : Linux 6.8.0-71-generic
% 0.18/0.43 % CPULimit : 300
% 0.18/0.43 % WCLimit : 300
% 0.18/0.43 % DateTime : Fri Sep 25 22:24:07 UTC 2026
% 0.18/0.43 % CPUTime :
% 0.18/0.43 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
% 1.08/1.07 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.38/1.25 % [INFO] Parsing done (174ms).
% 1.38/1.26 % [INFO] Running in sequential loop mode.
% 1.97/1.68 % [INFO] eprover registered as external prover.
% 1.97/1.69 % [INFO] Scanning for conjecture ...
% 2.18/1.78 % [INFO] Found a conjecture (or negated_conjecture) and 5 axioms. Running axiom selection ...
% 2.38/1.81 % [INFO] Axiom selection finished. Selected 5 axioms (removed 0 axioms).
% 2.38/1.82 % [INFO] Problem is propositional (TPTP CNF).
% 2.38/1.83 % [INFO] Type checking passed.
% 2.38/1.84 % [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 ...
% 57.06/12.54 % External prover 'e' found a proof!
% 57.06/12.54 % [INFO] Killing All external provers ...
% 57.06/12.54 % Time passed: 11917ms (effective reasoning time: 11274ms)
% 57.06/12.54 % Axioms used in derivation (5): cn_2, ifeq_axiom, condensed_detachment, cn_1, cn_3
% 57.06/12.54 % No. of inferences in proof: 97
% 57.06/12.55 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 11917 ms resp. 11274 ms w/o parsing
% 47.26/12.61 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 47.26/12.61 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------