%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL024-10 : TPTP v9.3.1. Released v7.5.0.
% 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 : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:50:36 AM UTC 2026
% Result : Unsatisfiable 49.48s 22.63s
% Output : Refutation 40.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 4
% Syntax : Number of formulae : 101 ( 54 unt; 0 typ; 0 def)
% Number of atoms : 185 ( 184 equ; 0 cnn)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 1956 ( 115 ~; 84 |; 0 &;1757 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 5 con; 0-4 aty)
% Number of variables : 361 ( 0 ^; 361 !; 0 ?; 361 :)
% Comments :
%------------------------------------------------------------------------------
thf(is_a_theorem_decl,type,
is_a_theorem: $i > $i ).
thf(equivalent_decl,type,
equivalent: $i > $i > $i ).
thf(a_decl,type,
a: $i ).
thf(b_decl,type,
b: $i ).
thf(c_decl,type,
c: $i ).
thf(true_decl,type,
true: $i ).
thf(ifeq_decl,type,
ifeq: $i > $i > $i > $i > $i ).
thf(4,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ equivalent ) @ ( A @ ( C @ equivalent ) @ ( B @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ is_a_theorem )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xgk) ).
thf(12,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ equivalent ) @ ( A @ ( C @ equivalent ) @ ( B @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ is_a_theorem )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(13,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ equivalent ) @ ( A @ ( C @ equivalent ) @ ( B @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ is_a_theorem )
= true ),
inference(lifteq,[status(thm)],[12]) ).
thf(3,axiom,
! [B: $i,A: $i] :
( ( true @ ( true @ ( B @ is_a_theorem @ ( true @ ( A @ is_a_theorem @ ifeq ) ) ) @ ( true @ ( B @ ( A @ equivalent ) @ is_a_theorem @ ifeq ) ) ) )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',condensed_detachment) ).
thf(10,plain,
! [B: $i,A: $i] :
( ( true @ ( true @ ( B @ is_a_theorem @ ( true @ ( A @ is_a_theorem @ ifeq ) ) ) @ ( true @ ( B @ ( A @ equivalent ) @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(11,plain,
! [B: $i,A: $i] :
( ( true @ ( true @ ( B @ is_a_theorem @ ( true @ ( A @ is_a_theorem @ ifeq ) ) ) @ ( true @ ( B @ ( A @ equivalent ) @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(lifteq,[status(thm)],[10]) ).
thf(32,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ equivalent ) @ ( A @ ( C @ equivalent ) @ ( B @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ is_a_theorem )
!= ( E @ ( D @ equivalent ) @ is_a_theorem ) )
| ( ( true @ ( true @ ( E @ is_a_theorem @ ( true @ ( D @ is_a_theorem @ ifeq ) ) ) @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[13,11]) ).
thf(33,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( true @ ( C @ ( B @ equivalent ) @ ( A @ ( B @ equivalent ) @ ( C @ equivalent ) @ equivalent ) @ is_a_theorem @ ( true @ ( A @ is_a_theorem @ ifeq ) ) ) @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[32:[bind(A,$thf( K )),bind(B,$thf( M )),bind(C,$thf( L )),bind(D,$thf( K )),bind(E,$thf( M @ ( L @ equivalent ) @ ( K @ ( L @ equivalent ) @ ( M @ equivalent ) @ equivalent ) ))]]) ).
thf(35,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( true @ ( C @ ( B @ equivalent ) @ ( A @ ( B @ equivalent ) @ ( C @ equivalent ) @ equivalent ) @ is_a_theorem @ ( true @ ( A @ is_a_theorem @ ifeq ) ) ) @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[33]) ).
thf(2,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( A @ ifeq ) ) ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom) ).
thf(8,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( A @ ifeq ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(9,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( A @ ifeq ) ) ) )
= B ),
inference(lifteq,[status(thm)],[8]) ).
thf(41,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( C @ ( B @ equivalent ) @ ( A @ ( B @ equivalent ) @ ( C @ equivalent ) @ equivalent ) @ is_a_theorem @ ( true @ ( A @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(rewrite,[status(thm)],[35,9]) ).
thf(46,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( true @ ( C @ ( B @ equivalent ) @ ( A @ ( B @ equivalent ) @ ( C @ equivalent ) @ equivalent ) @ is_a_theorem @ ( true @ ( A @ is_a_theorem @ ifeq ) ) ) )
!= ( true @ ( E @ is_a_theorem @ ( true @ ( D @ is_a_theorem @ ifeq ) ) ) ) )
| ( ( true @ ( true @ ( true @ ( E @ ( D @ equivalent ) @ is_a_theorem @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[41,11]) ).
thf(47,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( true @ ( true @ ( C @ ( B @ equivalent ) @ ( A @ ( B @ equivalent ) @ ( C @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[46:[bind(A,$thf( K )),bind(B,$thf( L )),bind(C,$thf( M )),bind(D,$thf( K )),bind(E,$thf( M @ ( L @ equivalent ) @ ( K @ ( L @ equivalent ) @ ( M @ equivalent ) @ equivalent ) ))]]) ).
thf(59,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( true @ ( true @ ( C @ ( B @ equivalent ) @ ( A @ ( B @ equivalent ) @ ( C @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[47]) ).
thf(88,plain,
( ( true @ ( true @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(rewrite,[status(thm)],[59,13]) ).
thf(14,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( true @ ( true @ ( B @ is_a_theorem @ ( true @ ( A @ is_a_theorem @ ifeq ) ) ) @ ( true @ ( B @ ( A @ equivalent ) @ is_a_theorem @ ifeq ) ) ) )
!= ( E @ ( D @ ( C @ ( C @ ifeq ) ) ) ) )
| ( true = D ) ),
inference(paramod_ordered,[status(thm)],[11,9]) ).
thf(18,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true != E )
| ( ( true @ ( B @ is_a_theorem @ ( true @ ( A @ is_a_theorem @ ifeq ) ) ) )
!= D )
| ( true != C )
| ( ( B @ ( A @ equivalent ) @ is_a_theorem )
!= C )
| ( true = D ) ),
inference(simp,[status(thm)],[14]) ).
thf(22,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ equivalent ) @ is_a_theorem )
!= true )
| ( ( true @ ( B @ is_a_theorem @ ( true @ ( A @ is_a_theorem @ ifeq ) ) ) )
= true ) ),
inference(simp,[status(thm)],[18]) ).
thf(30,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ equivalent ) @ ( A @ ( C @ equivalent ) @ ( B @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( true @ ( true @ ( true @ ( true @ ( D @ is_a_theorem @ ifeq ) ) ) @ ( true @ ( E @ ( D @ equivalent ) @ is_a_theorem @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[13,11]) ).
thf(31,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( true @ ( true @ ( true @ ( A @ is_a_theorem @ ifeq ) ) ) @ ( true @ ( D @ ( C @ equivalent ) @ ( B @ ( C @ equivalent ) @ ( D @ equivalent ) @ equivalent ) @ ( B @ equivalent ) @ ( A @ equivalent ) @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[30:[bind(A,$thf( M )),bind(B,$thf( O )),bind(C,$thf( N )),bind(D,$thf( D )),bind(E,$thf( O @ ( N @ equivalent ) @ ( M @ ( N @ equivalent ) @ ( O @ equivalent ) @ equivalent ) @ ( M @ equivalent ) ))]]) ).
thf(37,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( true @ ( true @ ( true @ ( A @ is_a_theorem @ ifeq ) ) ) @ ( true @ ( D @ ( C @ equivalent ) @ ( B @ ( C @ equivalent ) @ ( D @ equivalent ) @ equivalent ) @ ( B @ equivalent ) @ ( A @ equivalent ) @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[31]) ).
thf(181,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( true @ ( B @ is_a_theorem @ ( true @ ( A @ is_a_theorem @ ifeq ) ) ) )
!= ( true @ ( true @ ( true @ ( C @ is_a_theorem @ ifeq ) ) ) ) )
| ( ( true @ ( true @ ( true @ ( F @ ( E @ equivalent ) @ ( D @ ( E @ equivalent ) @ ( F @ equivalent ) @ equivalent ) @ ( D @ equivalent ) @ ( C @ equivalent ) @ is_a_theorem @ ifeq ) ) ) )
= true )
| ( ( B @ ( A @ equivalent ) @ is_a_theorem )
!= true ) ),
inference(paramod_ordered,[status(thm)],[22,37]) ).
thf(215,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true != true )
| ( ( B @ is_a_theorem )
!= true )
| ( true != true )
| ( ( A @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( B @ ( A @ equivalent ) @ is_a_theorem )
!= true )
| ( ( true @ ( true @ ( true @ ( F @ ( E @ equivalent ) @ ( D @ ( E @ equivalent ) @ ( F @ equivalent ) @ equivalent ) @ ( D @ equivalent ) @ ( C @ equivalent ) @ is_a_theorem @ ifeq ) ) ) )
= true ) ),
inference(simp,[status(thm)],[181]) ).
thf(228,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ is_a_theorem )
!= true )
| ( ( A @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( B @ ( A @ equivalent ) @ is_a_theorem )
!= true )
| ( ( true @ ( true @ ( true @ ( F @ ( E @ equivalent ) @ ( D @ ( E @ equivalent ) @ ( F @ equivalent ) @ equivalent ) @ ( D @ equivalent ) @ ( C @ equivalent ) @ is_a_theorem @ ifeq ) ) ) )
= true ) ),
inference(simp,[status(thm)],[215]) ).
thf(51,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ equivalent ) @ ( A @ ( C @ equivalent ) @ ( B @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( true @ ( F @ ( E @ equivalent ) @ ( D @ ( E @ equivalent ) @ ( F @ equivalent ) @ equivalent ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[13,41]) ).
thf(52,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( B @ ( A @ equivalent ) @ ( E @ ( D @ equivalent ) @ ( C @ ( D @ equivalent ) @ ( E @ equivalent ) @ equivalent ) @ ( C @ equivalent ) @ ( A @ equivalent ) @ ( B @ equivalent ) @ equivalent ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[51:[bind(A,$thf( N )),bind(B,$thf( P )),bind(C,$thf( O )),bind(D,$thf( P @ ( O @ equivalent ) @ ( N @ ( O @ equivalent ) @ ( P @ equivalent ) @ equivalent ) @ ( N @ equivalent ) )),bind(E,$thf( E )),bind(F,$thf( F ))]]) ).
thf(56,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( B @ ( A @ equivalent ) @ ( E @ ( D @ equivalent ) @ ( C @ ( D @ equivalent ) @ ( E @ equivalent ) @ equivalent ) @ ( C @ equivalent ) @ ( A @ equivalent ) @ ( B @ equivalent ) @ equivalent ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[52]) ).
thf(473,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ equivalent ) @ ( E @ ( D @ equivalent ) @ ( C @ ( D @ equivalent ) @ ( E @ equivalent ) @ equivalent ) @ ( C @ equivalent ) @ ( A @ equivalent ) @ ( B @ equivalent ) @ equivalent ) @ is_a_theorem )
= true ),
inference(rewrite,[status(thm)],[56,9]) ).
thf(1,negated_conjecture,
( ( a @ ( b @ equivalent ) @ ( c @ ( c @ ( b @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
!= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_pyo) ).
thf(5,plain,
( ( a @ ( b @ equivalent ) @ ( c @ ( c @ ( b @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
!= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(6,plain,
( ( a @ ( b @ equivalent ) @ ( c @ ( c @ ( b @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
!= true ),
inference(polarity_switch,[status(thm)],[5]) ).
thf(7,plain,
( ( a @ ( b @ equivalent ) @ ( c @ ( c @ ( b @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
!= true ),
inference(lifteq,[status(thm)],[6]) ).
thf(536,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ equivalent ) @ ( E @ ( D @ equivalent ) @ ( C @ ( D @ equivalent ) @ ( E @ equivalent ) @ equivalent ) @ ( C @ equivalent ) @ ( A @ equivalent ) @ ( B @ equivalent ) @ equivalent ) @ is_a_theorem )
!= ( a @ ( b @ equivalent ) @ ( c @ ( c @ ( b @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[473,7]) ).
thf(537,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ equivalent ) @ ( E @ ( D @ equivalent ) @ ( C @ ( D @ equivalent ) @ ( E @ equivalent ) @ equivalent ) @ ( C @ equivalent ) @ ( A @ equivalent ) @ ( B @ equivalent ) @ equivalent ) @ is_a_theorem )
!= ( a @ ( b @ equivalent ) @ ( c @ ( c @ ( b @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[536]) ).
thf(538,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ equivalent ) @ ( E @ ( D @ equivalent ) @ ( C @ ( D @ equivalent ) @ ( E @ equivalent ) @ equivalent ) @ ( C @ equivalent ) @ ( A @ equivalent ) @ ( B @ equivalent ) @ equivalent ) )
!= ( a @ ( b @ equivalent ) @ ( c @ ( c @ ( b @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) ) ),
inference(simp,[status(thm)],[537]) ).
thf(564,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ equivalent ) )
!= ( a @ ( b @ equivalent ) ) )
| ( ( E @ ( D @ equivalent ) @ ( C @ ( D @ equivalent ) @ ( E @ equivalent ) @ equivalent ) @ ( C @ equivalent ) @ ( A @ equivalent ) @ ( B @ equivalent ) )
!= ( c @ ( c @ ( b @ equivalent ) @ ( a @ equivalent ) @ equivalent ) ) ) ),
inference(simp,[status(thm)],[538]) ).
thf(565,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ equivalent ) )
!= ( a @ ( b @ equivalent ) ) )
| ( ( E @ ( D @ equivalent ) @ ( C @ ( D @ equivalent ) @ ( E @ equivalent ) @ equivalent ) @ ( C @ equivalent ) @ ( A @ equivalent ) )
!= c )
| ( B
!= ( c @ ( b @ equivalent ) @ ( a @ equivalent ) ) ) ),
inference(simp,[status(thm)],[564]) ).
thf(591,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c @ ( b @ equivalent ) @ ( a @ equivalent ) @ ( A @ equivalent ) )
!= ( a @ ( b @ equivalent ) ) )
| ( ( D @ ( C @ equivalent ) @ ( B @ ( C @ equivalent ) @ ( D @ equivalent ) @ equivalent ) @ ( B @ equivalent ) @ ( A @ equivalent ) )
!= c ) ),
inference(simp,[status(thm)],[565]) ).
thf(28,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ equivalent ) @ ( A @ ( C @ equivalent ) @ ( B @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( true @ ( true @ ( E @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) @ ( true @ ( E @ ( D @ equivalent ) @ is_a_theorem @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[13,11]) ).
thf(29,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( true @ ( A @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) @ ( true @ ( A @ ( D @ ( C @ equivalent ) @ ( B @ ( C @ equivalent ) @ ( D @ equivalent ) @ equivalent ) @ ( B @ equivalent ) @ equivalent ) @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[28:[bind(A,$thf( M )),bind(B,$thf( O )),bind(C,$thf( N )),bind(D,$thf( O @ ( N @ equivalent ) @ ( M @ ( N @ equivalent ) @ ( O @ equivalent ) @ equivalent ) @ ( M @ equivalent ) )),bind(E,$thf( E ))]]) ).
thf(36,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( true @ ( A @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) @ ( true @ ( A @ ( D @ ( C @ equivalent ) @ ( B @ ( C @ equivalent ) @ ( D @ equivalent ) @ equivalent ) @ ( B @ equivalent ) @ equivalent ) @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[29]) ).
thf(108,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( A @ is_a_theorem @ ( true @ ( A @ ( D @ ( C @ equivalent ) @ ( B @ ( C @ equivalent ) @ ( D @ equivalent ) @ equivalent ) @ ( B @ equivalent ) @ equivalent ) @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(rewrite,[status(thm)],[36,9]) ).
thf(499,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ equivalent ) @ ( E @ ( D @ equivalent ) @ ( C @ ( D @ equivalent ) @ ( E @ equivalent ) @ equivalent ) @ ( C @ equivalent ) @ ( A @ equivalent ) @ ( B @ equivalent ) @ equivalent ) @ is_a_theorem )
!= ( F @ ( I @ ( H @ equivalent ) @ ( G @ ( H @ equivalent ) @ ( I @ equivalent ) @ equivalent ) @ ( G @ equivalent ) @ equivalent ) @ is_a_theorem ) )
| ( ( true @ ( F @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[473,108]) ).
thf(500,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( A @ ( A @ ( D @ equivalent ) @ ( C @ ( B @ equivalent ) @ ( D @ ( B @ equivalent ) @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[499:[bind(A,$thf( W @ ( ZH @ equivalent ) @ ( ZG @ ( ZF @ equivalent ) @ ( ZH @ ( ZF @ equivalent ) @ ( ZG @ equivalent ) @ equivalent ) @ equivalent ) )),bind(B,$thf( W )),bind(C,$thf( ZH )),bind(D,$thf( ZF )),bind(E,$thf( ZG )),bind(F,$thf( W @ ( W @ ( ZH @ equivalent ) @ ( ZG @ ( ZF @ equivalent ) @ ( ZH @ ( ZF @ equivalent ) @ ( ZG @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) )),bind(G,$thf( W )),bind(H,$thf( ZH )),bind(I,$thf( ZG @ ( ZF @ equivalent ) @ ( ZH @ ( ZF @ equivalent ) @ ( ZG @ equivalent ) @ equivalent ) ))]]) ).
thf(558,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( A @ ( A @ ( D @ equivalent ) @ ( C @ ( B @ equivalent ) @ ( D @ ( B @ equivalent ) @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[500]) ).
thf(674,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( D @ equivalent ) @ ( C @ ( B @ equivalent ) @ ( D @ ( B @ equivalent ) @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
= true ),
inference(rewrite,[status(thm)],[558,9]) ).
thf(691,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ equivalent ) @ ( C @ ( B @ equivalent ) @ ( D @ ( B @ equivalent ) @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
!= ( F @ ( E @ equivalent ) @ is_a_theorem ) )
| ( true != true )
| ( ( true @ ( F @ is_a_theorem @ ( true @ ( E @ is_a_theorem @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[674,22]) ).
thf(692,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ equivalent ) @ ( C @ ( B @ equivalent ) @ ( D @ ( B @ equivalent ) @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
!= ( F @ ( E @ equivalent ) @ is_a_theorem ) )
| ( ( true @ ( F @ is_a_theorem @ ( true @ ( E @ is_a_theorem @ ifeq ) ) ) )
= true ) ),
inference(simp,[status(thm)],[691]) ).
thf(693,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( D @ is_a_theorem @ ( true @ ( D @ ( C @ equivalent ) @ ( B @ ( A @ equivalent ) @ ( C @ ( A @ equivalent ) @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[692:[bind(A,$thf( R )),bind(B,$thf( O )),bind(C,$thf( P )),bind(D,$thf( Q )),bind(E,$thf( R @ ( Q @ equivalent ) @ ( P @ ( O @ equivalent ) @ ( Q @ ( O @ equivalent ) @ ( P @ equivalent ) @ equivalent ) @ equivalent ) )),bind(F,$thf( R ))]]) ).
thf(778,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( D @ is_a_theorem @ ( true @ ( D @ ( C @ equivalent ) @ ( B @ ( A @ equivalent ) @ ( C @ ( A @ equivalent ) @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[693]) ).
thf(26,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ equivalent ) @ ( A @ ( C @ equivalent ) @ ( B @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ is_a_theorem )
!= ( a @ ( b @ equivalent ) @ ( c @ ( c @ ( b @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[13,7]) ).
thf(27,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ equivalent ) @ ( A @ ( C @ equivalent ) @ ( B @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ is_a_theorem )
!= ( a @ ( b @ equivalent ) @ ( c @ ( c @ ( b @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[26]) ).
thf(34,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ equivalent ) @ ( A @ ( C @ equivalent ) @ ( B @ equivalent ) @ equivalent ) @ ( A @ equivalent ) )
!= ( a @ ( b @ equivalent ) @ ( c @ ( c @ ( b @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) ) ),
inference(simp,[status(thm)],[27]) ).
thf(38,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ equivalent ) @ ( A @ ( C @ equivalent ) @ ( B @ equivalent ) @ equivalent ) )
!= ( a @ ( b @ equivalent ) ) )
| ( A
!= ( c @ ( c @ ( b @ equivalent ) @ ( a @ equivalent ) @ equivalent ) ) ) ),
inference(simp,[status(thm)],[34]) ).
thf(39,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ equivalent ) @ ( c @ ( c @ ( b @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ ( B @ equivalent ) @ ( A @ equivalent ) @ equivalent ) )
!= ( a @ ( b @ equivalent ) ) ),
inference(simp,[status(thm)],[38]) ).
thf(40,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ equivalent ) )
!= a )
| ( ( c @ ( c @ ( b @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ ( B @ equivalent ) @ ( A @ equivalent ) )
!= b ) ),
inference(simp,[status(thm)],[39]) ).
thf(566,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B != a )
| ( A != b )
| ( ( E @ ( D @ equivalent ) @ ( C @ ( D @ equivalent ) @ ( E @ equivalent ) @ equivalent ) @ ( C @ equivalent ) @ ( A @ equivalent ) @ ( B @ equivalent ) )
!= ( c @ ( c @ ( b @ equivalent ) @ ( a @ equivalent ) @ equivalent ) ) ) ),
inference(simp,[status(thm)],[564]) ).
thf(592,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ equivalent ) @ ( A @ ( B @ equivalent ) @ ( C @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ ( b @ equivalent ) @ ( a @ equivalent ) )
!= ( c @ ( c @ ( b @ equivalent ) @ ( a @ equivalent ) @ equivalent ) ) ),
inference(simp,[status(thm)],[566]) ).
thf(791,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ equivalent ) @ ( C @ ( B @ equivalent ) @ ( D @ ( B @ equivalent ) @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
!= ( H @ ( G @ equivalent ) @ ( F @ ( E @ equivalent ) @ ( G @ ( E @ equivalent ) @ ( F @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
| ( ( true @ ( H @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[674,778]) ).
thf(792,plain,
! [A: $i] :
( ( true @ ( A @ ( A @ equivalent ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[791:[bind(A,$thf( R @ ( R @ equivalent ) @ ( M @ equivalent ) )),bind(B,$thf( R )),bind(C,$thf( M )),bind(D,$thf( R )),bind(E,$thf( R )),bind(F,$thf( R @ ( R @ equivalent ) @ ( M @ equivalent ) )),bind(G,$thf( M )),bind(H,$thf( R @ ( R @ equivalent ) ))]]) ).
thf(848,plain,
! [A: $i] :
( ( true @ ( A @ ( A @ equivalent ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[792]) ).
thf(1099,plain,
! [A: $i] :
( ( A @ ( A @ equivalent ) @ is_a_theorem )
= true ),
inference(rewrite,[status(thm)],[848,9]) ).
thf(1190,plain,
! [A: $i] :
( ( ( A @ ( A @ equivalent ) @ is_a_theorem )
!= ( a @ ( b @ equivalent ) @ ( c @ ( c @ ( b @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[1099,7]) ).
thf(1191,plain,
! [A: $i] :
( ( A @ ( A @ equivalent ) @ is_a_theorem )
!= ( a @ ( b @ equivalent ) @ ( c @ ( c @ ( b @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[1190]) ).
thf(1192,plain,
! [A: $i] :
( ( A @ ( A @ equivalent ) )
!= ( a @ ( b @ equivalent ) @ ( c @ ( c @ ( b @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) ) ),
inference(simp,[status(thm)],[1191]) ).
thf(1399,plain,
! [A: $i] :
( ( A
!= ( a @ ( b @ equivalent ) ) )
| ( A
!= ( c @ ( c @ ( b @ equivalent ) @ ( a @ equivalent ) @ equivalent ) ) ) ),
inference(simp,[status(thm)],[1192]) ).
thf(1400,plain,
( ( c @ ( c @ ( b @ equivalent ) @ ( a @ equivalent ) @ equivalent ) )
!= ( a @ ( b @ equivalent ) ) ),
inference(simp,[status(thm)],[1399]) ).
thf(1401,plain,
( ( c != a )
| ( ( c @ ( b @ equivalent ) @ ( a @ equivalent ) )
!= b ) ),
inference(simp,[status(thm)],[1400]) ).
thf(16,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ ( A @ ifeq ) ) ) )
!= ( true @ ( E @ is_a_theorem @ ( true @ ( D @ is_a_theorem @ ifeq ) ) ) ) )
| ( ( true @ ( B @ ( true @ ( E @ ( D @ equivalent ) @ is_a_theorem @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[9,11]) ).
thf(20,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C != true )
| ( B
!= ( E @ is_a_theorem ) )
| ( A != true )
| ( A
!= ( D @ is_a_theorem ) )
| ( ( true @ ( B @ ( true @ ( E @ ( D @ equivalent ) @ is_a_theorem @ ifeq ) ) ) )
= true ) ),
inference(simp,[status(thm)],[16]) ).
thf(24,plain,
! [B: $i,A: $i] :
( ( ( A @ is_a_theorem )
!= true )
| ( ( true @ ( B @ is_a_theorem @ ( true @ ( B @ ( A @ equivalent ) @ is_a_theorem @ ifeq ) ) ) )
= true ) ),
inference(simp,[status(thm)],[20]) ).
thf(1144,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ equivalent ) @ is_a_theorem )
!= ( B @ is_a_theorem ) )
| ( true != true )
| ( ( true @ ( C @ is_a_theorem @ ( true @ ( C @ ( B @ equivalent ) @ is_a_theorem @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[1099,24]) ).
thf(1145,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ equivalent ) @ is_a_theorem )
!= ( B @ is_a_theorem ) )
| ( ( true @ ( C @ is_a_theorem @ ( true @ ( C @ ( B @ equivalent ) @ is_a_theorem @ ifeq ) ) ) )
= true ) ),
inference(simp,[status(thm)],[1144]) ).
thf(1146,plain,
! [B: $i,A: $i] :
( ( true @ ( A @ is_a_theorem @ ( true @ ( A @ ( B @ ( B @ equivalent ) @ equivalent ) @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[1145:[bind(A,$thf( E )),bind(B,$thf( E @ ( E @ equivalent ) )),bind(C,$thf( C ))]]) ).
thf(1222,plain,
! [B: $i,A: $i] :
( ( true @ ( A @ is_a_theorem @ ( true @ ( A @ ( B @ ( B @ equivalent ) @ equivalent ) @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[1146]) ).
thf(17,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( true @ ( true @ ( B @ is_a_theorem @ ( true @ ( A @ is_a_theorem @ ifeq ) ) ) @ ( true @ ( B @ ( A @ equivalent ) @ is_a_theorem @ ifeq ) ) ) )
!= ( true @ ( D @ is_a_theorem @ ( true @ ( C @ is_a_theorem @ ifeq ) ) ) ) )
| ( ( true @ ( true @ ( true @ ( D @ ( C @ equivalent ) @ is_a_theorem @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[11,11]) ).
thf(21,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( true != true )
| ( ( true @ ( B @ is_a_theorem @ ( true @ ( A @ is_a_theorem @ ifeq ) ) ) )
!= ( D @ is_a_theorem ) )
| ( true != true )
| ( ( B @ ( A @ equivalent ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( true @ ( true @ ( true @ ( D @ ( C @ equivalent ) @ is_a_theorem @ ifeq ) ) ) )
= true ) ),
inference(simp,[status(thm)],[17]) ).
thf(25,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( true @ ( B @ is_a_theorem @ ( true @ ( A @ is_a_theorem @ ifeq ) ) ) )
!= ( D @ is_a_theorem ) )
| ( ( B @ ( A @ equivalent ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( true @ ( true @ ( true @ ( D @ ( C @ equivalent ) @ is_a_theorem @ ifeq ) ) ) )
= true ) ),
inference(simp,[status(thm)],[21]) ).
thf(256,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( true @ ( true @ ( true @ ( F @ ( E @ equivalent ) @ ( D @ ( E @ equivalent ) @ ( F @ equivalent ) @ equivalent ) @ ( D @ equivalent ) @ ( C @ equivalent ) @ is_a_theorem @ ifeq ) ) ) )
!= ( true @ ( H @ is_a_theorem @ ( true @ ( G @ is_a_theorem @ ifeq ) ) ) ) )
| ( ( true @ ( true @ ( true @ ( H @ ( G @ equivalent ) @ is_a_theorem @ ifeq ) ) ) )
= true )
| ( ( B @ is_a_theorem )
!= true )
| ( ( A @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( B @ ( A @ equivalent ) @ is_a_theorem )
!= true ) ),
inference(paramod_ordered,[status(thm)],[228,11]) ).
thf(287,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true != true )
| ( ( H @ is_a_theorem )
!= true )
| ( true != true )
| ( ( F @ ( E @ equivalent ) @ ( D @ ( E @ equivalent ) @ ( F @ equivalent ) @ equivalent ) @ ( D @ equivalent ) @ ( C @ equivalent ) @ is_a_theorem )
!= ( G @ is_a_theorem ) )
| ( ( B @ is_a_theorem )
!= true )
| ( ( A @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( B @ ( A @ equivalent ) @ is_a_theorem )
!= true )
| ( ( true @ ( true @ ( true @ ( H @ ( G @ equivalent ) @ is_a_theorem @ ifeq ) ) ) )
= true ) ),
inference(simp,[status(thm)],[256]) ).
thf(317,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( H @ is_a_theorem )
!= true )
| ( ( F @ ( E @ equivalent ) @ ( D @ ( E @ equivalent ) @ ( F @ equivalent ) @ equivalent ) @ ( D @ equivalent ) @ ( C @ equivalent ) @ is_a_theorem )
!= ( G @ is_a_theorem ) )
| ( ( B @ is_a_theorem )
!= true )
| ( ( A @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( B @ ( A @ equivalent ) @ is_a_theorem )
!= true )
| ( ( true @ ( true @ ( true @ ( H @ ( G @ equivalent ) @ is_a_theorem @ ifeq ) ) ) )
= true ) ),
inference(simp,[status(thm)],[287]) ).
thf(567,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B != a )
| ( A != b )
| ( ( E @ ( D @ equivalent ) @ ( C @ ( D @ equivalent ) @ ( E @ equivalent ) @ equivalent ) @ ( C @ equivalent ) @ ( A @ equivalent ) )
!= c )
| ( B
!= ( c @ ( b @ equivalent ) @ ( a @ equivalent ) ) ) ),
inference(simp,[status(thm)],[564]) ).
thf(593,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c @ ( b @ equivalent ) @ ( a @ equivalent ) )
!= a )
| ( ( C @ ( B @ equivalent ) @ ( A @ ( B @ equivalent ) @ ( C @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ ( b @ equivalent ) )
!= c ) ),
inference(simp,[status(thm)],[567]) ).
thf(123,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( true @ ( A @ is_a_theorem @ ( true @ ( A @ ( D @ ( C @ equivalent ) @ ( B @ ( C @ equivalent ) @ ( D @ equivalent ) @ equivalent ) @ ( B @ equivalent ) @ equivalent ) @ is_a_theorem @ ifeq ) ) ) )
!= ( true @ ( F @ is_a_theorem @ ( true @ ( E @ is_a_theorem @ ifeq ) ) ) ) )
| ( ( true @ ( true @ ( true @ ( F @ ( E @ equivalent ) @ is_a_theorem @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[108,11]) ).
thf(124,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( true @ ( true @ ( A @ ( A @ ( D @ ( C @ equivalent ) @ ( B @ ( C @ equivalent ) @ ( D @ equivalent ) @ equivalent ) @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[123:[bind(A,$thf( H )),bind(B,$thf( P )),bind(C,$thf( Q )),bind(D,$thf( R )),bind(E,$thf( H @ ( R @ ( Q @ equivalent ) @ ( P @ ( Q @ equivalent ) @ ( R @ equivalent ) @ equivalent ) @ ( P @ equivalent ) @ equivalent ) )),bind(F,$thf( H ))]]) ).
thf(141,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( true @ ( true @ ( A @ ( A @ ( D @ ( C @ equivalent ) @ ( B @ ( C @ equivalent ) @ ( D @ equivalent ) @ equivalent ) @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[124]) ).
thf(748,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ equivalent ) @ ( C @ ( B @ equivalent ) @ ( D @ ( B @ equivalent ) @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
!= ( a @ ( b @ equivalent ) @ ( c @ ( c @ ( b @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[674,7]) ).
thf(749,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( D @ equivalent ) @ ( C @ ( B @ equivalent ) @ ( D @ ( B @ equivalent ) @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
!= ( a @ ( b @ equivalent ) @ ( c @ ( c @ ( b @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[748]) ).
thf(750,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( D @ equivalent ) @ ( C @ ( B @ equivalent ) @ ( D @ ( B @ equivalent ) @ ( C @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) )
!= ( a @ ( b @ equivalent ) @ ( c @ ( c @ ( b @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) ) ),
inference(simp,[status(thm)],[749]) ).
thf(1123,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ equivalent ) @ is_a_theorem )
!= ( C @ ( B @ equivalent ) @ is_a_theorem ) )
| ( true != true )
| ( ( true @ ( C @ is_a_theorem @ ( true @ ( B @ is_a_theorem @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[1099,22]) ).
thf(1124,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ equivalent ) @ is_a_theorem )
!= ( C @ ( B @ equivalent ) @ is_a_theorem ) )
| ( ( true @ ( C @ is_a_theorem @ ( true @ ( B @ is_a_theorem @ ifeq ) ) ) )
= true ) ),
inference(simp,[status(thm)],[1123]) ).
thf(1125,plain,
! [A: $i] :
( ( true @ ( A @ is_a_theorem @ ( true @ ( A @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[1124:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(50,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ equivalent ) @ ( A @ ( C @ equivalent ) @ ( B @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ is_a_theorem )
!= ( F @ ( E @ equivalent ) @ ( D @ ( E @ equivalent ) @ ( F @ equivalent ) @ equivalent ) @ is_a_theorem ) )
| ( ( true @ ( true @ ( true @ ( D @ is_a_theorem @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[13,41]) ).
thf(54,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ equivalent ) @ ( A @ ( C @ equivalent ) @ ( B @ equivalent ) @ equivalent ) @ ( A @ equivalent ) )
!= ( F @ ( E @ equivalent ) @ ( D @ ( E @ equivalent ) @ ( F @ equivalent ) @ equivalent ) ) )
| ( ( true @ ( true @ ( true @ ( D @ is_a_theorem @ ifeq ) ) ) )
= true ) ),
inference(simp,[status(thm)],[50]) ).
thf(854,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( a @ ( b @ equivalent ) ) )
| ( ( A @ ( D @ equivalent ) @ ( C @ ( B @ equivalent ) @ ( D @ ( B @ equivalent ) @ ( C @ equivalent ) @ equivalent ) @ equivalent ) )
!= ( c @ ( c @ ( b @ equivalent ) @ ( a @ equivalent ) @ equivalent ) ) ) ),
inference(simp,[status(thm)],[750]) ).
thf(855,plain,
! [C: $i,B: $i,A: $i] :
( ( a @ ( b @ equivalent ) @ ( C @ equivalent ) @ ( B @ ( A @ equivalent ) @ ( C @ ( A @ equivalent ) @ ( B @ equivalent ) @ equivalent ) @ equivalent ) )
!= ( c @ ( c @ ( b @ equivalent ) @ ( a @ equivalent ) @ equivalent ) ) ),
inference(simp,[status(thm)],[854]) ).
thf(1251,plain,
! [C: $i,B: $i,A: $i] :
( ( ( true @ ( A @ is_a_theorem @ ( true @ ( A @ is_a_theorem @ ifeq ) ) ) )
!= ( true @ ( C @ is_a_theorem @ ( true @ ( B @ is_a_theorem @ ifeq ) ) ) ) )
| ( ( true @ ( true @ ( true @ ( C @ ( B @ equivalent ) @ is_a_theorem @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[1125,11]) ).
thf(1252,plain,
! [A: $i] :
( ( true @ ( true @ ( true @ ( A @ ( A @ equivalent ) @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[1251:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(3848,plain,
$false,
inference(e,[status(thm)],[88,228,591,778,674,108,473,11,40,8,564,592,1401,5,10,538,1222,24,37,25,317,9,593,141,1099,1192,13,41,750,34,22,1125,12,54,7,39,855,1400,1252]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL024-10 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.08 % 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
% 0.20/10.68 % Computer : n008.cluster.edu
% 0.20/10.68 % Model : x86_64 x86_64
% 0.20/10.68 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/10.68 % Memory : 8046.5625MB
% 0.20/10.68 % OS : Linux 6.8.0-71-generic
% 0.20/10.68 % CPULimit : 300
% 0.20/10.68 % WCLimit : 300
% 0.20/10.68 % DateTime : Fri Sep 25 21:45:08 UTC 2026
% 0.20/10.69 % CPUTime :
% 0.20/10.69 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
% 1.39/11.52 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.75/11.78 % [INFO] Parsing done (251ms).
% 1.93/11.80 % [INFO] Running in sequential loop mode.
% 2.80/12.41 % [INFO] eprover registered as external prover.
% 2.80/12.42 % [INFO] Scanning for conjecture ...
% 3.00/12.54 % [INFO] Found a conjecture (or negated_conjecture) and 3 axioms. Running axiom selection ...
% 3.00/12.59 % [INFO] Axiom selection finished. Selected 3 axioms (removed 0 axioms).
% 3.15/12.60 % [INFO] Problem is propositional (TPTP CNF).
% 3.15/12.61 % [INFO] Type checking passed.
% 3.15/12.62 % [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 ...
% 49.48/22.63 % External prover 'e' found a proof!
% 49.48/22.63 % [INFO] Killing All external provers ...
% 49.48/22.63 % Time passed: 11737ms (effective reasoning time: 10821ms)
% 49.48/22.63 % Axioms used in derivation (3): xgk, condensed_detachment, ifeq_axiom
% 49.48/22.63 % No. of inferences in proof: 101
% 49.48/22.63 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 11737 ms resp. 10821 ms w/o parsing
% 40.80/22.78 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 40.80/22.78 % [INFO] Killing All external provers ...
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