%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL367-1 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:51:36 AM UTC 2026
% Result : Unsatisfiable 26.12s 6.18s
% Output : Refutation 21.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 5
% Syntax : Number of formulae : 114 ( 49 unt; 0 typ; 0 def)
% Number of atoms : 316 ( 109 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 1477 ( 171 ~; 102 |; 0 &;1204 @)
% ( 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 : 8 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 321 ( 0 ^; 321 !; 0 ?; 321 :)
% Comments :
%------------------------------------------------------------------------------
thf(is_a_theorem_decl,type,
is_a_theorem: $i > $o ).
thf(implies_decl,type,
implies: $i > $i > $i ).
thf(x_decl,type,
x: $i ).
thf(y_decl,type,
y: $i ).
thf(not_decl,type,
not: $i > $i ).
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(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(34,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(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 ) ),
inference(simp,[status(thm)],[34]) ).
thf(36,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ not @ implies ) @ is_a_theorem )
| ~ ( B @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[35:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( G )),bind(D,$thf( F @ ( G @ not @ implies ) ))]]) ).
thf(50,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ not @ implies ) @ is_a_theorem )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[36]) ).
thf(1,negated_conjecture,
~ ( x @ ( x @ ( y @ implies ) @ implies ) @ ( x @ implies ) @ is_a_theorem ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_cn_17) ).
thf(6,plain,
~ ( x @ ( x @ ( y @ implies ) @ implies ) @ ( x @ implies ) @ is_a_theorem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(7,plain,
~ ( x @ ( x @ ( y @ implies ) @ implies ) @ ( x @ implies ) @ is_a_theorem ),
inference(polarity_switch,[status(thm)],[6]) ).
thf(68,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ is_a_theorem )
!= ( x @ ( x @ ( y @ implies ) @ implies ) @ ( x @ implies ) @ is_a_theorem ) )
| ~ $true
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[50,7]) ).
thf(69,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ is_a_theorem )
!= ( x @ ( x @ ( y @ implies ) @ implies ) @ ( x @ implies ) @ is_a_theorem ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[68]) ).
thf(76,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) )
!= ( x @ ( x @ ( y @ implies ) @ implies ) @ ( x @ implies ) ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[69]) ).
thf(113,plain,
! [B: $i,A: $i] :
( ( A
!= ( x @ ( x @ ( y @ implies ) @ implies ) ) )
| ( ( B @ not )
!= x )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[76]) ).
thf(133,plain,
! [A: $i] :
( ( ( A @ not )
!= x )
| ~ ( A @ is_a_theorem ) ),
inference(simp,[status(thm)],[113]) ).
thf(142,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( C @ not )
!= x )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12,133]) ).
thf(143,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( C @ not )
!= x ) ),
inference(simp,[status(thm)],[142]) ).
thf(144,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ not @ implies ) @ ( B @ implies ) @ not )
!= x ),
inference(pattern_uni,[status(thm)],[143:[bind(A,$thf( H )),bind(B,$thf( G )),bind(C,$thf( G @ ( H @ not @ implies ) @ ( H @ implies ) ))]]) ).
thf(157,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ not @ implies ) @ ( B @ implies ) @ not )
!= x ),
inference(simp,[status(thm)],[144]) ).
thf(65,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)],[12,50]) ).
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 ) ),
inference(simp,[status(thm)],[65]) ).
thf(67,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[66:[bind(A,$thf( I )),bind(B,$thf( H )),bind(C,$thf( C )),bind(D,$thf( H @ ( I @ not @ implies ) @ ( I @ implies ) ))]]) ).
thf(78,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[67]) ).
thf(91,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)],[78,50]) ).
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 ) ),
inference(simp,[status(thm)],[91]) ).
thf(93,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[92:[bind(A,$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(97,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)],[93]) ).
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(73,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)],[11,50]) ).
thf(74,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)],[73]) ).
thf(75,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[74:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( E @ ( E @ ( E @ not @ implies ) @ implies ) ))]]) ).
thf(81,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[75]) ).
thf(154,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 )
!= x )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[81,133]) ).
thf(155,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 )
!= x ) ),
inference(simp,[status(thm)],[154]) ).
thf(156,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) @ not )
!= x ),
inference(pattern_uni,[status(thm)],[155:[bind(A,$thf( E )),bind(B,$thf( H )),bind(C,$thf( E @ ( H @ ( H @ ( H @ not @ implies ) @ implies ) @ not @ implies ) ))]]) ).
thf(161,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) @ not )
!= x ),
inference(simp,[status(thm)],[156]) ).
thf(145,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( C @ not )
!= x )
| ~ $true
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[50,133]) ).
thf(146,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( C @ not )
!= x )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[145]) ).
thf(147,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ not )
!= x )
| ~ ( B @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[146:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( E @ ( F @ not @ implies ) ))]]) ).
thf(158,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ not )
!= x )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[147]) ).
thf(89,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( x @ ( x @ ( y @ implies ) @ implies ) @ ( x @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[78,7]) ).
thf(90,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( x @ ( x @ ( y @ implies ) @ implies ) @ ( x @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[89]) ).
thf(94,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ implies ) )
!= ( x @ ( x @ ( y @ implies ) @ implies ) @ ( x @ implies ) ) ),
inference(simp,[status(thm)],[90]) ).
thf(104,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)],[81,50]) ).
thf(105,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)],[104]) ).
thf(106,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[105:[bind(A,$thf( F )),bind(B,$thf( I )),bind(C,$thf( C )),bind(D,$thf( F @ ( I @ ( I @ ( I @ not @ implies ) @ implies ) @ not @ implies ) ))]]) ).
thf(112,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)],[106]) ).
thf(311,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( D @ ( E @ not @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[112,50]) ).
thf(312,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( D @ ( E @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[311]) ).
thf(313,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( D @ ( D @ ( D @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[312:[bind(A,$thf( G )),bind(B,$thf( J )),bind(C,$thf( M )),bind(D,$thf( D )),bind(E,$thf( G @ ( J @ ( M @ ( M @ ( M @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) ))]]) ).
thf(337,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( D @ ( D @ ( D @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[313]) ).
thf(172,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)],[97,50]) ).
thf(173,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)],[172]) ).
thf(174,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( D @ ( E @ not @ implies ) @ ( E @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[173:[bind(A,$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(185,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)],[174]) ).
thf(23,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( x @ ( x @ ( y @ implies ) @ implies ) @ ( x @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10,7]) ).
thf(24,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( x @ ( x @ ( y @ implies ) @ implies ) @ ( x @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[23]) ).
thf(25,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) )
!= ( x @ ( x @ ( y @ implies ) @ implies ) @ ( x @ implies ) ) ),
inference(simp,[status(thm)],[24]) ).
thf(13,plain,
! [A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( x @ ( x @ ( y @ implies ) @ implies ) @ ( x @ 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 )
!= ( x @ ( x @ ( y @ implies ) @ implies ) @ ( x @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[13]) ).
thf(15,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ not @ implies ) @ implies ) )
!= ( x @ ( x @ ( y @ implies ) @ implies ) @ ( x @ implies ) ) ),
inference(simp,[status(thm)],[14]) ).
thf(19,plain,
! [A: $i] :
( ( A
!= ( x @ ( x @ ( y @ implies ) @ implies ) ) )
| ( ( A @ ( A @ not @ implies ) )
!= x ) ),
inference(simp,[status(thm)],[15]) ).
thf(20,plain,
( ( x @ ( x @ ( y @ implies ) @ implies ) @ ( x @ ( x @ ( y @ implies ) @ implies ) @ not @ implies ) )
!= x ),
inference(simp,[status(thm)],[19]) ).
thf(151,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 )
!= x )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[78,133]) ).
thf(152,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 )
!= x ) ),
inference(simp,[status(thm)],[151]) ).
thf(153,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ implies ) @ not )
!= x ),
inference(pattern_uni,[status(thm)],[152:[bind(A,$thf( F )),bind(B,$thf( K )),bind(C,$thf( L )),bind(D,$thf( F @ ( K @ ( L @ not @ implies ) @ ( L @ implies ) @ not @ implies ) ))]]) ).
thf(160,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ implies ) @ not )
!= x ),
inference(simp,[status(thm)],[153]) ).
thf(120,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( C @ ( D @ not @ implies ) )
!= ( x @ ( x @ ( y @ implies ) @ implies ) @ ( x @ implies ) ) )
| ~ $true
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[50,76]) ).
thf(121,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( C @ ( D @ not @ implies ) )
!= ( x @ ( x @ ( y @ implies ) @ implies ) @ ( x @ implies ) ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[120]) ).
thf(122,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) )
!= ( x @ ( x @ ( y @ implies ) @ implies ) @ ( x @ implies ) ) )
| ~ ( C @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[121:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( C )),bind(D,$thf( F @ ( G @ not @ implies ) ))]]) ).
thf(137,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) )
!= ( x @ ( x @ ( y @ implies ) @ implies ) @ ( x @ implies ) ) )
| ~ ( C @ is_a_theorem ) ),
inference(simp,[status(thm)],[122]) ).
thf(107,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( x @ ( x @ ( y @ implies ) @ implies ) @ ( x @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[81,7]) ).
thf(108,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( x @ ( x @ ( y @ implies ) @ implies ) @ ( x @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[107]) ).
thf(109,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) )
!= ( x @ ( x @ ( y @ implies ) @ implies ) @ ( x @ implies ) ) ),
inference(simp,[status(thm)],[108]) ).
thf(204,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 )
!= x )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[81,158]) ).
thf(205,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 )
!= x ) ),
inference(simp,[status(thm)],[204]) ).
thf(206,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ not )
!= x ),
inference(pattern_uni,[status(thm)],[205:[bind(A,$thf( F )),bind(B,$thf( I )),bind(C,$thf( C )),bind(D,$thf( F @ ( I @ ( I @ ( I @ not @ implies ) @ implies ) @ not @ implies ) ))]]) ).
thf(212,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ not )
!= x ),
inference(simp,[status(thm)],[206]) ).
thf(16,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( x @ ( x @ ( y @ implies ) @ implies ) @ ( x @ 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 )
!= ( x @ ( x @ ( y @ implies ) @ implies ) @ ( x @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[16]) ).
thf(18,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ not @ implies ) @ ( A @ implies ) )
!= ( x @ ( x @ ( y @ implies ) @ implies ) @ ( x @ implies ) ) ),
inference(simp,[status(thm)],[17]) ).
thf(21,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ not @ implies ) )
!= ( x @ ( x @ ( y @ implies ) @ implies ) ) )
| ( A != x ) ),
inference(simp,[status(thm)],[18]) ).
thf(22,plain,
! [A: $i] :
( ( A @ ( x @ not @ implies ) )
!= ( x @ ( x @ ( y @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[21]) ).
thf(26,plain,
! [A: $i] :
( ( A != x )
| ( ( x @ ( y @ implies ) )
!= ( x @ not ) ) ),
inference(simp,[status(thm)],[22]) ).
thf(27,plain,
( ( x @ ( y @ implies ) )
!= ( x @ not ) ),
inference(simp,[status(thm)],[26]) ).
thf(31,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(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 )
| ~ ( E @ ( D @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[31]) ).
thf(33,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ is_a_theorem )
| ~ ( A @ ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ ( B @ ( C @ implies ) @ implies ) @ implies ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[32:[bind(A,$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(49,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)],[33]) ).
thf(148,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( B @ is_a_theorem ) )
| ( ( B @ not )
!= x )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11,133]) ).
thf(149,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( B @ is_a_theorem ) )
| ( ( B @ not )
!= x ) ),
inference(simp,[status(thm)],[148]) ).
thf(150,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not )
!= x ),
inference(pattern_uni,[status(thm)],[149:[bind(A,$thf( D )),bind(B,$thf( D @ ( D @ ( D @ not @ implies ) @ implies ) ))]]) ).
thf(159,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not )
!= x ),
inference(simp,[status(thm)],[150]) ).
thf(195,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 )
!= x )
| ~ $true
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[50,158]) ).
thf(196,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 )
!= x )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[195]) ).
thf(197,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ not )
!= x )
| ~ ( C @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[196:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( C )),bind(D,$thf( F @ ( G @ not @ implies ) ))]]) ).
thf(208,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ not )
!= x )
| ~ ( C @ is_a_theorem ) ),
inference(simp,[status(thm)],[197]) ).
thf(139,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 )
!= x )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10,133]) ).
thf(140,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 )
!= x ) ),
inference(simp,[status(thm)],[139]) ).
thf(141,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ ( A @ ( B @ implies ) @ implies ) @ not )
!= x ),
inference(pattern_uni,[status(thm)],[140:[bind(A,$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(162,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ ( A @ ( B @ implies ) @ implies ) @ not )
!= x ),
inference(simp,[status(thm)],[141]) ).
thf(46,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(48,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
!= A )
| ~ ( A @ is_a_theorem )
| ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[46]) ).
thf(163,plain,
! [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 )
!= ( E @ is_a_theorem ) )
| ( ( E @ not )
!= x )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[97,133]) ).
thf(164,plain,
! [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 )
!= ( E @ is_a_theorem ) )
| ( ( E @ not )
!= x ) ),
inference(simp,[status(thm)],[163]) ).
thf(165,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ implies ) @ not @ implies ) @ not )
!= x ),
inference(pattern_uni,[status(thm)],[164:[bind(A,$thf( G )),bind(B,$thf( J )),bind(C,$thf( O )),bind(D,$thf( P )),bind(E,$thf( G @ ( J @ ( O @ ( P @ not @ implies ) @ ( P @ implies ) @ not @ implies ) @ not @ implies ) ))]]) ).
thf(182,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ implies ) @ not @ implies ) @ not )
!= x ),
inference(simp,[status(thm)],[165]) ).
thf(47,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)],[46]) ).
thf(2988,plain,
$false,
inference(e,[status(thm)],[10,157,133,6,97,9,161,11,158,8,94,337,185,25,20,78,160,137,109,212,22,27,12,49,159,81,76,7,208,162,112,48,18,50,182,47,15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL367-1 : TPTP v9.3.1. Released v2.3.0.
% 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
% 0.14/0.40 % Computer : n005.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.40 % CPULimit : 300
% 0.14/0.40 % WCLimit : 300
% 0.14/0.40 % DateTime : Fri Sep 25 22:19:46 UTC 2026
% 0.14/0.40 % CPUTime :
% 0.14/0.40 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
% 0.85/0.98 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.10/1.15 % [INFO] Parsing done (169ms).
% 1.28/1.15 % [INFO] Running in sequential loop mode.
% 1.53/1.35 % [INFO] eprover registered as external prover.
% 1.53/1.36 % [INFO] Scanning for conjecture ...
% 1.77/1.40 % [INFO] Found a conjecture (or negated_conjecture) and 4 axioms. Running axiom selection ...
% 1.77/1.42 % [INFO] Axiom selection finished. Selected 4 axioms (removed 0 axioms).
% 1.77/1.42 % [INFO] Problem is propositional (TPTP CNF).
% 1.77/1.42 % [INFO] Type checking passed.
% 1.77/1.43 % [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 ...
% 26.12/6.18 % External prover 'e' found a proof!
% 26.12/6.18 % [INFO] Killing All external provers ...
% 26.12/6.18 % Time passed: 5635ms (effective reasoning time: 5022ms)
% 26.12/6.18 % Axioms used in derivation (4): cn_1, cn_3, condensed_detachment, cn_2
% 26.12/6.18 % No. of inferences in proof: 114
% 26.12/6.18 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 5635 ms resp. 5022 ms w/o parsing
% 21.87/6.28 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 21.87/6.28 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------