%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL384-1 : 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 : n007.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 07:51:40 AM UTC 2026
% Result : Unsatisfiable 36.20s 8.44s
% Output : Refutation 30.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 5
% Syntax : Number of formulae : 110 ( 47 unt; 0 typ; 0 def)
% Number of atoms : 301 ( 116 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 1776 ( 172 ~; 99 |; 0 &;1505 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 7 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 : 294 ( 0 ^; 294 !; 0 ?; 294 :)
% 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(z_decl,type,
z: $i ).
thf(not_decl,type,
not: $i > $i ).
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(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(31,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(32,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)],[31]) ).
thf(33,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ not @ implies ) @ is_a_theorem )
| ~ ( B @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[32:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( G )),bind(D,$thf( F @ ( G @ not @ implies ) ))]]) ).
thf(46,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ not @ implies ) @ is_a_theorem )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[33]) ).
thf(69,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)],[11,46]) ).
thf(70,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)],[69]) ).
thf(71,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[70:[bind(A,$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)],[71]) ).
thf(130,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)],[80,46]) ).
thf(131,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)],[130]) ).
thf(132,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[131:[bind(A,$thf( F )),bind(B,$thf( I )),bind(C,$thf( C )),bind(D,$thf( F @ ( I @ ( I @ ( I @ not @ implies ) @ implies ) @ not @ implies ) ))]]) ).
thf(138,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)],[132]) ).
thf(1,negated_conjecture,
~ ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) @ ( z @ ( y @ implies ) @ ( x @ implies ) @ implies ) @ is_a_theorem ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_cn_45) ).
thf(6,plain,
~ ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) @ ( z @ ( y @ implies ) @ ( x @ implies ) @ implies ) @ is_a_theorem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(7,plain,
~ ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) @ ( z @ ( y @ implies ) @ ( x @ implies ) @ implies ) @ is_a_theorem ),
inference(polarity_switch,[status(thm)],[6]) ).
thf(67,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ is_a_theorem )
!= ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) @ ( z @ ( y @ implies ) @ ( x @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[46,7]) ).
thf(68,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ is_a_theorem )
!= ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) @ ( z @ ( y @ implies ) @ ( x @ implies ) @ implies ) @ is_a_theorem ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[67]) ).
thf(78,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) )
!= ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) @ ( z @ ( y @ implies ) @ ( x @ implies ) @ implies ) ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[68]) ).
thf(85,plain,
! [B: $i,A: $i] :
( ( A
!= ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) ) )
| ( ( B @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[78]) ).
thf(99,plain,
! [A: $i] :
( ( ( A @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ~ ( A @ is_a_theorem ) ),
inference(simp,[status(thm)],[85]) ).
thf(112,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( C @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12,99]) ).
thf(113,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( C @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[112]) ).
thf(114,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ not @ implies ) @ ( B @ implies ) @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ),
inference(pattern_uni,[status(thm)],[113:[bind(A,$thf( H )),bind(B,$thf( G )),bind(C,$thf( G @ ( H @ not @ implies ) @ ( H @ implies ) ))]]) ).
thf(115,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ not @ implies ) @ ( B @ implies ) @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ),
inference(simp,[status(thm)],[114]) ).
thf(13,plain,
! [A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) @ ( z @ ( y @ implies ) @ ( x @ 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 )
!= ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) @ ( z @ ( y @ implies ) @ ( x @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[13]) ).
thf(17,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ not @ implies ) @ implies ) )
!= ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) @ ( z @ ( y @ implies ) @ ( x @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[14]) ).
thf(22,plain,
! [A: $i] :
( ( A
!= ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) ) )
| ( ( A @ ( A @ not @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[17]) ).
thf(23,plain,
( ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) @ ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) @ not @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ),
inference(simp,[status(thm)],[22]) ).
thf(24,plain,
( ( ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) )
!= ( z @ ( y @ implies ) ) )
| ( ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) @ not )
!= x ) ),
inference(simp,[status(thm)],[23]) ).
thf(52,plain,
( ( ( z @ ( x @ implies ) )
!= z )
| ( ( y @ ( z @ not @ implies ) )
!= y )
| ( ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) @ not )
!= x ) ),
inference(simp,[status(thm)],[24]) ).
thf(75,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)],[12,46]) ).
thf(76,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)],[75]) ).
thf(77,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[76:[bind(A,$thf( I )),bind(B,$thf( H )),bind(C,$thf( C )),bind(D,$thf( H @ ( I @ not @ implies ) @ ( I @ implies ) ))]]) ).
thf(83,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[77]) ).
thf(200,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 )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[83,99]) ).
thf(201,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 )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[200]) ).
thf(202,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ implies ) @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ),
inference(pattern_uni,[status(thm)],[201:[bind(A,$thf( F )),bind(B,$thf( K )),bind(C,$thf( L )),bind(D,$thf( F @ ( K @ ( L @ not @ implies ) @ ( L @ implies ) @ not @ implies ) ))]]) ).
thf(213,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ implies ) @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ),
inference(simp,[status(thm)],[202]) ).
thf(15,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) @ ( z @ ( y @ implies ) @ ( x @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12,7]) ).
thf(16,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) @ ( z @ ( y @ implies ) @ ( x @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[15]) ).
thf(18,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ not @ implies ) @ ( A @ implies ) )
!= ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) @ ( z @ ( y @ implies ) @ ( x @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[16]) ).
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(53,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ not @ implies ) )
!= ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) ) )
| ( A
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[18]) ).
thf(54,plain,
! [A: $i] :
( ( A @ ( z @ ( y @ implies ) @ ( x @ implies ) @ not @ implies ) )
!= ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[53]) ).
thf(55,plain,
! [A: $i] :
( ( A
!= ( z @ ( x @ implies ) ) )
| ( ( y @ ( z @ not @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) @ not ) ) ),
inference(simp,[status(thm)],[54]) ).
thf(56,plain,
( ( y @ ( z @ not @ implies ) )
!= ( z @ ( y @ implies ) @ ( x @ implies ) @ not ) ),
inference(simp,[status(thm)],[55]) ).
thf(103,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( B @ is_a_theorem ) )
| ( ( B @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11,99]) ).
thf(104,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( B @ is_a_theorem ) )
| ( ( B @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[103]) ).
thf(105,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ),
inference(pattern_uni,[status(thm)],[104:[bind(A,$thf( D )),bind(B,$thf( D @ ( D @ ( D @ not @ implies ) @ implies ) ))]]) ).
thf(116,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ),
inference(simp,[status(thm)],[105]) ).
thf(231,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[138,99]) ).
thf(232,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( D @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[231]) ).
thf(233,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ),
inference(pattern_uni,[status(thm)],[232:[bind(A,$thf( F )),bind(B,$thf( I )),bind(C,$thf( L )),bind(D,$thf( F @ ( I @ ( L @ ( L @ ( L @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) ))]]) ).
thf(243,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ),
inference(simp,[status(thm)],[233]) ).
thf(106,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 )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10,99]) ).
thf(107,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 )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[106]) ).
thf(108,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ ( A @ ( B @ implies ) @ implies ) @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ),
inference(pattern_uni,[status(thm)],[107:[bind(A,$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(117,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ ( A @ ( B @ implies ) @ implies ) @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ),
inference(simp,[status(thm)],[108]) ).
thf(109,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( C @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ~ $true
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[46,99]) ).
thf(110,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( C @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[109]) ).
thf(111,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ~ ( B @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[110:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( E @ ( F @ not @ implies ) ))]]) ).
thf(118,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[111]) ).
thf(257,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 )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[83,118]) ).
thf(258,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 )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[257]) ).
thf(259,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ implies ) @ not @ implies ) @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ),
inference(pattern_uni,[status(thm)],[258:[bind(A,$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(270,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ implies ) @ not @ implies ) @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ),
inference(simp,[status(thm)],[259]) ).
thf(19,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) @ ( z @ ( y @ implies ) @ ( x @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10,7]) ).
thf(20,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) @ ( z @ ( y @ implies ) @ ( x @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[19]) ).
thf(21,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) )
!= ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) @ ( z @ ( y @ implies ) @ ( x @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[20]) ).
thf(127,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 )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[80,99]) ).
thf(128,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 )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[127]) ).
thf(129,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ),
inference(pattern_uni,[status(thm)],[128:[bind(A,$thf( E )),bind(B,$thf( H )),bind(C,$thf( E @ ( H @ ( H @ ( H @ not @ implies ) @ implies ) @ not @ implies ) ))]]) ).
thf(137,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) ),
inference(simp,[status(thm)],[129]) ).
thf(263,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 )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ~ $true
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[46,118]) ).
thf(264,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 )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[263]) ).
thf(265,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ~ ( C @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[264:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( C )),bind(D,$thf( F @ ( G @ not @ implies ) ))]]) ).
thf(272,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ~ ( C @ is_a_theorem ) ),
inference(simp,[status(thm)],[265]) ).
thf(291,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( C @ ( D @ ( E @ not @ implies ) @ not @ implies ) @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ~ $true
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[46,272]) ).
thf(292,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( C @ ( D @ ( E @ not @ implies ) @ not @ implies ) @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[291]) ).
thf(293,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( D @ not @ implies ) @ not @ implies ) @ not @ implies ) @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ~ ( D @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[292:[bind(A,$thf( G )),bind(B,$thf( H )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( G @ ( H @ not @ implies ) ))]]) ).
thf(298,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( D @ not @ implies ) @ not @ implies ) @ not @ implies ) @ not )
!= ( z @ ( y @ implies ) @ ( x @ implies ) ) )
| ~ ( D @ is_a_theorem ) ),
inference(simp,[status(thm)],[293]) ).
thf(43,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(45,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
!= A )
| ~ ( A @ is_a_theorem )
| ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[43]) ).
thf(44,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)],[43]) ).
thf(234,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)],[138,46]) ).
thf(235,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)],[234]) ).
thf(236,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( D @ ( D @ ( D @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[235:[bind(A,$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(245,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)],[236]) ).
thf(95,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 ) )
!= ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) @ ( z @ ( y @ implies ) @ ( x @ implies ) @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12,78]) ).
thf(96,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 ) )
!= ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) @ ( z @ ( y @ implies ) @ ( x @ implies ) @ implies ) ) ) ),
inference(simp,[status(thm)],[95]) ).
thf(97,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ implies ) )
!= ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) @ ( z @ ( y @ implies ) @ ( x @ implies ) @ implies ) ) ),
inference(pattern_uni,[status(thm)],[96:[bind(A,$thf( I )),bind(B,$thf( H )),bind(C,$thf( C )),bind(D,$thf( H @ ( I @ not @ implies ) @ ( I @ implies ) ))]]) ).
thf(98,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ implies ) )
!= ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) @ ( z @ ( y @ implies ) @ ( x @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[97]) ).
thf(203,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)],[83,46]) ).
thf(204,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)],[203]) ).
thf(205,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[204:[bind(A,$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(215,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)],[205]) ).
thf(86,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( B @ ( C @ not @ implies ) )
!= ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) @ ( z @ ( y @ implies ) @ ( x @ implies ) @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11,78]) ).
thf(87,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( B @ ( C @ not @ implies ) )
!= ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) @ ( z @ ( y @ implies ) @ ( x @ implies ) @ implies ) ) ) ),
inference(simp,[status(thm)],[86]) ).
thf(88,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) )
!= ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) @ ( z @ ( y @ implies ) @ ( x @ implies ) @ implies ) ) ),
inference(pattern_uni,[status(thm)],[87:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( E @ ( E @ ( E @ not @ implies ) @ implies ) ))]]) ).
thf(100,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) )
!= ( z @ ( x @ implies ) @ ( y @ ( z @ not @ implies ) @ implies ) @ ( z @ ( y @ implies ) @ ( x @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[88]) ).
thf(6469,plain,
$false,
inference(e,[status(thm)],[138,115,24,52,9,213,80,18,11,99,23,10,56,46,78,116,243,6,117,270,21,137,298,45,17,44,118,12,54,7,245,98,8,272,83,215,100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL384-1 : 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
% 0.12/0.39 % Computer : n007.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Fri Sep 25 22:21:09 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 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
% 1.03/1.09 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.31/1.26 % [INFO] Parsing done (163ms).
% 1.31/1.27 % [INFO] Running in sequential loop mode.
% 1.86/1.67 % [INFO] eprover registered as external prover.
% 1.86/1.68 % [INFO] Scanning for conjecture ...
% 2.05/1.77 % [INFO] Found a conjecture (or negated_conjecture) and 4 axioms. Running axiom selection ...
% 2.19/1.80 % [INFO] Axiom selection finished. Selected 4 axioms (removed 0 axioms).
% 2.19/1.81 % [INFO] Problem is propositional (TPTP CNF).
% 2.19/1.81 % [INFO] Type checking passed.
% 2.19/1.82 % [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 ...
% 36.20/8.43 % External prover 'e' found a proof!
% 36.20/8.43 % [INFO] Killing All external provers ...
% 36.20/8.44 % Time passed: 7829ms (effective reasoning time: 7158ms)
% 36.20/8.44 % Axioms used in derivation (4): cn_2, cn_3, condensed_detachment, cn_1
% 36.20/8.44 % No. of inferences in proof: 110
% 36.20/8.44 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 7829 ms resp. 7158 ms w/o parsing
% 30.35/8.52 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 30.35/8.52 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------