%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL365+1 : TPTP v9.3.1. Released v9.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n009.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 07:51:35 AM UTC 2026
% Result : Theorem 37.75s 10.89s
% Output : Refutation 30.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 5
% Syntax : Number of formulae : 115 ( 54 unt; 0 typ; 0 def)
% Number of atoms : 305 ( 108 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 2010 ( 156 ~; 90 |; 2 &;1760 @)
% ( 0 <=>; 2 =>; 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 : 10 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 318 ( 0 ^; 318 !; 0 ?; 318 :)
% 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(u_decl,type,
u: $i ).
thf(not_decl,type,
not: $i > $i ).
thf(6,axiom,
! [A: $i,B: $i] : ( B @ ( A @ not @ implies ) @ ( A @ implies ) @ is_a_theorem ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cn_3) ).
thf(14,plain,
! [A: $i,B: $i] : ( B @ ( A @ not @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(15,plain,
! [B: $i,A: $i] : ( B @ ( A @ not @ implies ) @ ( A @ implies ) @ is_a_theorem ),
inference(cnf,[status(esa)],[14]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( ( A @ is_a_theorem )
& ( B @ ( A @ implies ) @ is_a_theorem ) )
=> ( B @ is_a_theorem ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',condensed_detachment) ).
thf(8,plain,
! [A: $i,B: $i] :
( ( ( A @ is_a_theorem )
& ( B @ ( A @ implies ) @ is_a_theorem ) )
=> ( B @ is_a_theorem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
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(40,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)],[15,9]) ).
thf(41,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)],[40]) ).
thf(42,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ not @ implies ) @ is_a_theorem )
| ~ ( B @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[41:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( G )),bind(D,$thf( F @ ( G @ not @ implies ) ))]]) ).
thf(52,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ not @ implies ) @ is_a_theorem )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[42]) ).
thf(1,conjecture,
u @ ( y @ ( z @ not @ implies ) @ implies ) @ ( u @ ( z @ ( z @ ( y @ implies ) @ implies ) @ ( x @ implies ) @ implies ) @ implies ) @ is_a_theorem,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_cn_14) ).
thf(2,negated_conjecture,
~ ( u @ ( y @ ( z @ not @ implies ) @ implies ) @ ( u @ ( z @ ( z @ ( y @ implies ) @ implies ) @ ( x @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(7,plain,
~ ( u @ ( y @ ( z @ not @ implies ) @ implies ) @ ( u @ ( z @ ( z @ ( y @ implies ) @ implies ) @ ( x @ implies ) @ implies ) @ implies ) @ is_a_theorem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(72,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ is_a_theorem )
!= ( u @ ( y @ ( z @ not @ implies ) @ implies ) @ ( u @ ( z @ ( z @ ( y @ implies ) @ implies ) @ ( x @ implies ) @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[52,7]) ).
thf(73,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ is_a_theorem )
!= ( u @ ( y @ ( z @ not @ implies ) @ implies ) @ ( u @ ( z @ ( z @ ( y @ implies ) @ implies ) @ ( x @ implies ) @ implies ) @ implies ) @ is_a_theorem ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[72]) ).
thf(80,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) )
!= ( u @ ( y @ ( z @ not @ implies ) @ implies ) @ ( u @ ( z @ ( z @ ( y @ implies ) @ implies ) @ ( x @ implies ) @ implies ) @ implies ) ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[73]) ).
thf(102,plain,
! [B: $i,A: $i] :
( ( A
!= ( u @ ( y @ ( z @ not @ implies ) @ implies ) ) )
| ( ( B @ not )
!= ( u @ ( z @ ( z @ ( y @ implies ) @ implies ) @ ( x @ implies ) @ implies ) ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[80]) ).
thf(120,plain,
! [A: $i] :
( ( ( A @ not )
!= ( u @ ( z @ ( z @ ( y @ implies ) @ implies ) @ ( x @ implies ) @ implies ) ) )
| ~ ( A @ is_a_theorem ) ),
inference(simp,[status(thm)],[102]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i] : ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cn_1) ).
thf(10,plain,
! [A: $i,B: $i,C: $i] : ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(11,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem ),
inference(cnf,[status(esa)],[10]) ).
thf(22,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( u @ ( y @ ( z @ not @ implies ) @ implies ) @ ( u @ ( z @ ( z @ ( y @ implies ) @ implies ) @ ( x @ implies ) @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11,7]) ).
thf(23,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( u @ ( y @ ( z @ not @ implies ) @ implies ) @ ( u @ ( z @ ( z @ ( y @ implies ) @ implies ) @ ( x @ 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 ) )
!= ( u @ ( y @ ( z @ not @ implies ) @ implies ) @ ( u @ ( z @ ( z @ ( y @ implies ) @ implies ) @ ( x @ implies ) @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[23]) ).
thf(5,axiom,
! [A: $i] : ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cn_2) ).
thf(12,plain,
! [A: $i] : ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(13,plain,
! [A: $i] : ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem ),
inference(cnf,[status(esa)],[12]) ).
thf(16,plain,
! [A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( u @ ( y @ ( z @ not @ implies ) @ implies ) @ ( u @ ( z @ ( z @ ( y @ implies ) @ implies ) @ ( x @ implies ) @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13,7]) ).
thf(17,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( u @ ( y @ ( z @ not @ implies ) @ implies ) @ ( u @ ( z @ ( z @ ( y @ implies ) @ implies ) @ ( x @ implies ) @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[16]) ).
thf(20,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ not @ implies ) @ implies ) )
!= ( u @ ( y @ ( z @ not @ implies ) @ implies ) @ ( u @ ( z @ ( z @ ( y @ implies ) @ implies ) @ ( x @ implies ) @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[17]) ).
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)],[13,52]) ).
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(83,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[71]) ).
thf(87,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)],[83,52]) ).
thf(88,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)],[87]) ).
thf(89,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[88:[bind(A,$thf( F )),bind(B,$thf( I )),bind(C,$thf( C )),bind(D,$thf( F @ ( I @ ( I @ ( I @ not @ implies ) @ implies ) @ not @ implies ) ))]]) ).
thf(99,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)],[89]) ).
thf(219,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 )
!= ( u @ ( z @ ( z @ ( y @ implies ) @ implies ) @ ( x @ implies ) @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[99,120]) ).
thf(220,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 )
!= ( u @ ( z @ ( z @ ( y @ implies ) @ implies ) @ ( x @ implies ) @ implies ) ) ) ),
inference(simp,[status(thm)],[219]) ).
thf(221,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ not )
!= ( u @ ( z @ ( z @ ( y @ implies ) @ implies ) @ ( x @ implies ) @ implies ) ) ),
inference(pattern_uni,[status(thm)],[220:[bind(A,$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(248,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( C @ ( C @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ not )
!= ( u @ ( z @ ( z @ ( y @ implies ) @ implies ) @ ( x @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[221]) ).
thf(18,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( u @ ( y @ ( z @ not @ implies ) @ implies ) @ ( u @ ( z @ ( z @ ( y @ implies ) @ implies ) @ ( x @ implies ) @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[15,7]) ).
thf(19,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( u @ ( y @ ( z @ not @ implies ) @ implies ) @ ( u @ ( z @ ( z @ ( y @ implies ) @ implies ) @ ( x @ implies ) @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[18]) ).
thf(21,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ not @ implies ) @ ( A @ implies ) )
!= ( u @ ( y @ ( z @ not @ implies ) @ implies ) @ ( u @ ( z @ ( z @ ( y @ implies ) @ implies ) @ ( x @ implies ) @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[19]) ).
thf(130,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 )
!= ( u @ ( z @ ( z @ ( y @ implies ) @ implies ) @ ( x @ implies ) @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11,120]) ).
thf(131,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 )
!= ( u @ ( z @ ( z @ ( y @ implies ) @ implies ) @ ( x @ implies ) @ implies ) ) ) ),
inference(simp,[status(thm)],[130]) ).
thf(132,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ ( A @ ( B @ implies ) @ implies ) @ not )
!= ( u @ ( z @ ( z @ ( y @ implies ) @ implies ) @ ( x @ implies ) @ implies ) ) ),
inference(pattern_uni,[status(thm)],[131:[bind(A,$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(140,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ ( A @ ( B @ implies ) @ implies ) @ not )
!= ( u @ ( z @ ( z @ ( y @ implies ) @ implies ) @ ( x @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[132]) ).
thf(55,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ not @ implies ) )
!= ( u @ ( y @ ( z @ not @ implies ) @ implies ) ) )
| ( A
!= ( u @ ( z @ ( z @ ( y @ implies ) @ implies ) @ ( x @ implies ) @ implies ) ) ) ),
inference(simp,[status(thm)],[21]) ).
thf(56,plain,
! [A: $i] :
( ( A @ ( u @ ( z @ ( z @ ( y @ implies ) @ implies ) @ ( x @ implies ) @ implies ) @ not @ implies ) )
!= ( u @ ( y @ ( z @ not @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[55]) ).
thf(136,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 )
!= ( u @ ( z @ ( z @ ( y @ implies ) @ implies ) @ ( x @ implies ) @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[83,120]) ).
thf(137,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 )
!= ( u @ ( z @ ( z @ ( y @ implies ) @ implies ) @ ( x @ implies ) @ implies ) ) ) ),
inference(simp,[status(thm)],[136]) ).
thf(138,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) @ not )
!= ( u @ ( z @ ( z @ ( y @ implies ) @ implies ) @ ( x @ implies ) @ implies ) ) ),
inference(pattern_uni,[status(thm)],[137:[bind(A,$thf( E )),bind(B,$thf( H )),bind(C,$thf( E @ ( H @ ( H @ ( H @ not @ implies ) @ implies ) @ not @ implies ) ))]]) ).
thf(142,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) @ not )
!= ( u @ ( z @ ( z @ ( y @ implies ) @ implies ) @ ( x @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[138]) ).
thf(77,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)],[15,52]) ).
thf(78,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)],[77]) ).
thf(79,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[78:[bind(A,$thf( I )),bind(B,$thf( H )),bind(C,$thf( C )),bind(D,$thf( H @ ( I @ not @ implies ) @ ( I @ implies ) ))]]) ).
thf(86,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[79]) ).
thf(147,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)],[86,52]) ).
thf(148,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)],[147]) ).
thf(149,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[148:[bind(A,$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(164,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)],[149]) ).
thf(74,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 )
!= ( E @ is_a_theorem ) )
| ( D @ ( E @ not @ implies ) @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11,52]) ).
thf(75,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 )
!= ( E @ is_a_theorem ) )
| ( D @ ( E @ not @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[74]) ).
thf(76,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ ( B @ ( C @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[75:[bind(A,$thf( N )),bind(B,$thf( L )),bind(C,$thf( O )),bind(D,$thf( D )),bind(E,$thf( O @ ( N @ implies ) @ ( O @ ( L @ implies ) @ implies ) @ ( L @ ( N @ implies ) @ implies ) ))]]) ).
thf(84,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( D @ ( C @ implies ) @ ( D @ ( B @ implies ) @ implies ) @ ( B @ ( C @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[76]) ).
thf(253,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)],[164,52]) ).
thf(254,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)],[253]) ).
thf(255,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( D @ ( E @ not @ implies ) @ ( E @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[254:[bind(A,$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(280,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)],[255]) ).
thf(222,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)],[99,52]) ).
thf(223,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)],[222]) ).
thf(224,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( D @ ( D @ ( D @ not @ implies ) @ implies ) @ not @ implies ) @ not @ implies ) @ not @ implies ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[223:[bind(A,$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(243,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)],[224]) ).
thf(133,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( C @ not )
!= ( u @ ( z @ ( z @ ( y @ implies ) @ implies ) @ ( x @ implies ) @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[15,120]) ).
thf(134,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( C @ not )
!= ( u @ ( z @ ( z @ ( y @ implies ) @ implies ) @ ( x @ implies ) @ implies ) ) ) ),
inference(simp,[status(thm)],[133]) ).
thf(135,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ not @ implies ) @ ( B @ implies ) @ not )
!= ( u @ ( z @ ( z @ ( y @ implies ) @ implies ) @ ( x @ implies ) @ implies ) ) ),
inference(pattern_uni,[status(thm)],[134:[bind(A,$thf( H )),bind(B,$thf( G )),bind(C,$thf( G @ ( H @ not @ implies ) @ ( H @ implies ) ))]]) ).
thf(141,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ not @ implies ) @ ( B @ implies ) @ not )
!= ( u @ ( z @ ( z @ ( y @ implies ) @ implies ) @ ( x @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[135]) ).
thf(25,plain,
! [A: $i] :
( ( A
!= ( u @ ( y @ ( z @ not @ implies ) @ implies ) ) )
| ( ( A @ ( A @ not @ implies ) )
!= ( u @ ( z @ ( z @ ( y @ implies ) @ implies ) @ ( x @ implies ) @ implies ) ) ) ),
inference(simp,[status(thm)],[20]) ).
thf(26,plain,
( ( u @ ( y @ ( z @ not @ implies ) @ implies ) @ ( u @ ( y @ ( z @ not @ implies ) @ implies ) @ not @ implies ) )
!= ( u @ ( z @ ( z @ ( y @ implies ) @ implies ) @ ( x @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[25]) ).
thf(27,plain,
( ( ( u @ ( y @ ( z @ not @ implies ) @ implies ) )
!= u )
| ( ( u @ ( y @ ( z @ not @ implies ) @ implies ) @ not )
!= ( z @ ( z @ ( y @ implies ) @ implies ) @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[26]) ).
thf(58,plain,
! [A: $i] :
( ( A != u )
| ( ( u @ ( z @ ( z @ ( y @ implies ) @ implies ) @ ( x @ implies ) @ implies ) @ not )
!= ( y @ ( z @ not @ implies ) ) ) ),
inference(simp,[status(thm)],[56]) ).
thf(59,plain,
( ( u @ ( z @ ( z @ ( y @ implies ) @ implies ) @ ( x @ implies ) @ implies ) @ not )
!= ( y @ ( z @ not @ implies ) ) ),
inference(simp,[status(thm)],[58]) ).
thf(112,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 ) )
!= ( u @ ( y @ ( z @ not @ implies ) @ implies ) @ ( u @ ( z @ ( z @ ( y @ implies ) @ implies ) @ ( x @ implies ) @ implies ) @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[15,80]) ).
thf(113,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 ) )
!= ( u @ ( y @ ( z @ not @ implies ) @ implies ) @ ( u @ ( z @ ( z @ ( y @ implies ) @ implies ) @ ( x @ implies ) @ implies ) @ implies ) ) ) ),
inference(simp,[status(thm)],[112]) ).
thf(114,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ implies ) )
!= ( u @ ( y @ ( z @ not @ implies ) @ implies ) @ ( u @ ( z @ ( z @ ( y @ implies ) @ implies ) @ ( x @ implies ) @ implies ) @ implies ) ) ),
inference(pattern_uni,[status(thm)],[113:[bind(A,$thf( I )),bind(B,$thf( H )),bind(C,$thf( C )),bind(D,$thf( H @ ( I @ not @ implies ) @ ( I @ implies ) ))]]) ).
thf(118,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ implies ) )
!= ( u @ ( y @ ( z @ not @ implies ) @ implies ) @ ( u @ ( z @ ( z @ ( y @ implies ) @ implies ) @ ( x @ implies ) @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[114]) ).
thf(96,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( u @ ( y @ ( z @ not @ implies ) @ implies ) @ ( u @ ( z @ ( z @ ( y @ implies ) @ implies ) @ ( x @ implies ) @ implies ) @ implies ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[83,7]) ).
thf(97,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( u @ ( y @ ( z @ not @ implies ) @ implies ) @ ( u @ ( z @ ( z @ ( y @ implies ) @ implies ) @ ( x @ implies ) @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[96]) ).
thf(98,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) )
!= ( u @ ( y @ ( z @ not @ implies ) @ implies ) @ ( u @ ( z @ ( z @ ( y @ implies ) @ implies ) @ ( x @ implies ) @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[97]) ).
thf(250,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 )
!= ( u @ ( z @ ( z @ ( y @ implies ) @ implies ) @ ( x @ implies ) @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[164,120]) ).
thf(251,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 )
!= ( u @ ( z @ ( z @ ( y @ implies ) @ implies ) @ ( x @ implies ) @ implies ) ) ) ),
inference(simp,[status(thm)],[250]) ).
thf(252,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ implies ) @ not @ implies ) @ not )
!= ( u @ ( z @ ( z @ ( y @ implies ) @ implies ) @ ( x @ implies ) @ implies ) ) ),
inference(pattern_uni,[status(thm)],[251:[bind(A,$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(278,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( D @ not @ implies ) @ ( D @ implies ) @ not @ implies ) @ not @ implies ) @ not )
!= ( u @ ( z @ ( z @ ( y @ implies ) @ implies ) @ ( x @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[252]) ).
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(124,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( C @ not )
!= ( u @ ( z @ ( z @ ( y @ implies ) @ implies ) @ ( x @ implies ) @ implies ) ) )
| ~ $true
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[52,120]) ).
thf(125,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( C @ not )
!= ( u @ ( z @ ( z @ ( y @ implies ) @ implies ) @ ( x @ implies ) @ implies ) ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[124]) ).
thf(126,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ not )
!= ( u @ ( z @ ( z @ ( y @ implies ) @ implies ) @ ( x @ implies ) @ implies ) ) )
| ~ ( B @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[125:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( E @ ( F @ not @ implies ) ))]]) ).
thf(143,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ not )
!= ( u @ ( z @ ( z @ ( y @ implies ) @ implies ) @ ( x @ implies ) @ implies ) ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[126]) ).
thf(281,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 )
!= ( u @ ( z @ ( z @ ( y @ implies ) @ implies ) @ ( x @ implies ) @ implies ) ) )
| ~ $true
| ~ ( B @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[52,143]) ).
thf(282,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 )
!= ( u @ ( z @ ( z @ ( y @ implies ) @ implies ) @ ( x @ implies ) @ implies ) ) )
| ~ ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[281]) ).
thf(283,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ not )
!= ( u @ ( z @ ( z @ ( y @ implies ) @ implies ) @ ( x @ implies ) @ implies ) ) )
| ~ ( C @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[282:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( C )),bind(D,$thf( F @ ( G @ not @ implies ) ))]]) ).
thf(310,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ not @ implies ) @ not )
!= ( u @ ( z @ ( z @ ( y @ implies ) @ implies ) @ ( x @ implies ) @ implies ) ) )
| ~ ( C @ is_a_theorem ) ),
inference(simp,[status(thm)],[283]) ).
thf(127,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( B @ is_a_theorem ) )
| ( ( B @ not )
!= ( u @ ( z @ ( z @ ( y @ implies ) @ implies ) @ ( x @ implies ) @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13,120]) ).
thf(128,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( B @ is_a_theorem ) )
| ( ( B @ not )
!= ( u @ ( z @ ( z @ ( y @ implies ) @ implies ) @ ( x @ implies ) @ implies ) ) ) ),
inference(simp,[status(thm)],[127]) ).
thf(129,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not )
!= ( u @ ( z @ ( z @ ( y @ implies ) @ implies ) @ ( x @ implies ) @ implies ) ) ),
inference(pattern_uni,[status(thm)],[128:[bind(A,$thf( D )),bind(B,$thf( D @ ( D @ ( D @ not @ implies ) @ implies ) ))]]) ).
thf(139,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not )
!= ( u @ ( z @ ( z @ ( y @ implies ) @ implies ) @ ( x @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[129]) ).
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(144,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 )
!= ( u @ ( z @ ( z @ ( y @ implies ) @ implies ) @ ( x @ implies ) @ implies ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[86,120]) ).
thf(145,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 )
!= ( u @ ( z @ ( z @ ( y @ implies ) @ implies ) @ ( x @ implies ) @ implies ) ) ) ),
inference(simp,[status(thm)],[144]) ).
thf(146,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ implies ) @ not )
!= ( u @ ( z @ ( z @ ( y @ implies ) @ implies ) @ ( x @ implies ) @ implies ) ) ),
inference(pattern_uni,[status(thm)],[145:[bind(A,$thf( F )),bind(B,$thf( K )),bind(C,$thf( L )),bind(D,$thf( F @ ( K @ ( L @ not @ implies ) @ ( L @ implies ) @ not @ implies ) ))]]) ).
thf(163,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ implies ) @ not )
!= ( u @ ( z @ ( z @ ( y @ implies ) @ implies ) @ ( x @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[146]) ).
thf(2512,plain,
$false,
inference(e,[status(thm)],[120,24,20,248,21,13,140,99,8,83,10,56,142,52,14,164,84,280,243,9,141,27,59,118,12,86,7,98,278,80,48,310,11,143,26,139,47,15,163]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LCL365+1 : TPTP v9.3.1. Released v9.1.0.
% 0.00/0.11 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.24/0.48 % Computer : n009.cluster.edu
% 0.24/0.48 % Model : x86_64 x86_64
% 0.24/0.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.24/0.48 % Memory : 8046.5625MB
% 0.24/0.48 % OS : Linux 6.8.0-71-generic
% 0.24/0.48 % CPULimit : 300
% 0.24/0.48 % WCLimit : 300
% 0.24/0.48 % DateTime : Fri Sep 25 22:19:44 UTC 2026
% 0.24/0.49 % CPUTime :
% 0.24/0.49 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 1.22/1.29 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.70/1.55 % [INFO] Parsing done (253ms).
% 1.70/1.57 % [INFO] Running in sequential loop mode.
% 2.56/2.08 % [INFO] eprover registered as external prover.
% 2.56/2.09 % [INFO] Scanning for conjecture ...
% 2.82/2.21 % [INFO] Found a conjecture (or negated_conjecture) and 4 axioms. Running axiom selection ...
% 2.82/2.26 % [INFO] Axiom selection finished. Selected 4 axioms (removed 0 axioms).
% 2.82/2.29 % [INFO] Problem is first-order (TPTP FOF).
% 3.01/2.30 % [INFO] Type checking passed.
% 3.01/2.31 % [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 ...
% 37.75/10.88 % External prover 'e' found a proof!
% 37.75/10.88 % [INFO] Killing All external provers ...
% 37.75/10.88 % Time passed: 10199ms (effective reasoning time: 9306ms)
% 37.75/10.88 % Solved by 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)>
% 37.75/10.89 % Axioms used in derivation (4): cn_3, condensed_detachment, cn_1, cn_2
% 37.75/10.89 % No. of inferences in proof: 115
% 37.75/10.89 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 10199 ms resp. 9306 ms w/o parsing
% 30.26/10.98 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 30.26/10.98 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------