%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL130-1 : TPTP v9.3.1. Released v1.0.0.
% 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 : 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 07:50:56 AM UTC 2026
% Result : Unsatisfiable 11.11s 4.10s
% Output : Refutation 10.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 3
% Syntax : Number of formulae : 98 ( 37 unt; 0 typ; 0 def)
% Number of atoms : 279 ( 101 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 2491 ( 140 ~; 97 |; 0 &;2254 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 6 con; 0-2 aty)
% Number of variables : 458 ( 0 ^; 458 !; 0 ?; 458 :)
% Comments :
%------------------------------------------------------------------------------
thf(is_a_theorem_decl,type,
is_a_theorem: $i > $o ).
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(e_decl,type,
e: $i ).
thf(3,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( D @ ( C @ equivalent ) @ ( D @ ( B @ equivalent ) @ equivalent ) @ ( C @ ( B @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p_4) ).
thf(8,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( D @ ( C @ equivalent ) @ ( D @ ( B @ equivalent ) @ equivalent ) @ ( C @ ( B @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(2,axiom,
! [B: $i,A: $i] :
( ( B @ is_a_theorem )
| ~ ( A @ is_a_theorem )
| ~ ( B @ ( A @ equivalent ) @ is_a_theorem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',condensed_detachment) ).
thf(6,plain,
! [B: $i,A: $i] :
( ( B @ is_a_theorem )
| ~ ( A @ is_a_theorem )
| ~ ( B @ ( A @ equivalent ) @ is_a_theorem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(7,plain,
! [B: $i,A: $i] :
( ( B @ is_a_theorem )
| ~ ( A @ is_a_theorem )
| ~ ( B @ ( A @ equivalent ) @ is_a_theorem ) ),
inference(cnf,[status(esa)],[6]) ).
thf(14,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ equivalent ) @ ( D @ ( B @ equivalent ) @ equivalent ) @ ( C @ ( B @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
!= ( F @ ( E @ equivalent ) @ is_a_theorem ) )
| ( F @ is_a_theorem )
| ~ ( E @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8,7]) ).
thf(15,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ equivalent ) @ ( D @ ( B @ equivalent ) @ equivalent ) @ ( C @ ( B @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
!= ( F @ ( E @ equivalent ) @ is_a_theorem ) )
| ( F @ is_a_theorem )
| ~ ( E @ is_a_theorem ) ),
inference(simp,[status(thm)],[14]) ).
thf(16,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ is_a_theorem )
| ~ ( D @ ( C @ equivalent ) @ ( D @ ( B @ equivalent ) @ equivalent ) @ ( C @ ( B @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[15:[bind(A,$thf( G )),bind(B,$thf( O )),bind(C,$thf( Q )),bind(D,$thf( R )),bind(E,$thf( R @ ( Q @ equivalent ) @ ( R @ ( O @ equivalent ) @ equivalent ) @ ( Q @ ( O @ equivalent ) @ equivalent ) @ ( G @ equivalent ) )),bind(F,$thf( G ))]]) ).
thf(23,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ is_a_theorem )
| ~ ( D @ ( C @ equivalent ) @ ( D @ ( B @ equivalent ) @ equivalent ) @ ( C @ ( B @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[16]) ).
thf(29,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ equivalent ) @ ( D @ ( B @ equivalent ) @ equivalent ) @ ( C @ ( B @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
!= ( H @ ( G @ equivalent ) @ ( H @ ( F @ equivalent ) @ equivalent ) @ ( G @ ( F @ equivalent ) @ equivalent ) @ ( E @ equivalent ) @ is_a_theorem ) )
| ( E @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8,23]) ).
thf(30,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ equivalent ) @ ( D @ ( B @ equivalent ) @ equivalent ) @ ( C @ ( B @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
!= ( H @ ( G @ equivalent ) @ ( H @ ( F @ equivalent ) @ equivalent ) @ ( G @ ( F @ equivalent ) @ equivalent ) @ ( E @ equivalent ) @ is_a_theorem ) )
| ( E @ is_a_theorem ) ),
inference(simp,[status(thm)],[29]) ).
thf(31,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( C @ ( B @ equivalent ) @ ( C @ ( A @ equivalent ) @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ ( F @ ( E @ equivalent ) @ ( F @ ( D @ equivalent ) @ equivalent ) @ ( E @ ( D @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[30:[bind(A,$thf( ZD @ ( ZC @ equivalent ) @ ( ZD @ ( ZA @ equivalent ) @ equivalent ) @ ( ZC @ ( ZA @ equivalent ) @ equivalent ) )),bind(B,$thf( Q )),bind(C,$thf( S )),bind(D,$thf( T )),bind(E,$thf( T @ ( S @ equivalent ) @ ( T @ ( Q @ equivalent ) @ equivalent ) @ ( S @ ( Q @ equivalent ) @ equivalent ) @ ( ZD @ ( ZC @ equivalent ) @ ( ZD @ ( ZA @ equivalent ) @ equivalent ) @ ( ZC @ ( ZA @ equivalent ) @ equivalent ) @ equivalent ) )),bind(F,$thf( ZA )),bind(G,$thf( ZC )),bind(H,$thf( ZD ))]]) ).
thf(32,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( C @ ( B @ equivalent ) @ ( C @ ( A @ equivalent ) @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ ( F @ ( E @ equivalent ) @ ( F @ ( D @ equivalent ) @ equivalent ) @ ( E @ ( D @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
inference(simp,[status(thm)],[31]) ).
thf(64,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ equivalent ) @ ( C @ ( A @ equivalent ) @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ ( F @ ( E @ equivalent ) @ ( F @ ( D @ equivalent ) @ equivalent ) @ ( E @ ( D @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
!= ( J @ ( I @ equivalent ) @ ( J @ ( H @ equivalent ) @ equivalent ) @ ( I @ ( H @ equivalent ) @ equivalent ) @ ( G @ equivalent ) @ is_a_theorem ) )
| ( G @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[32,23]) ).
thf(65,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ equivalent ) @ ( C @ ( A @ equivalent ) @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ ( F @ ( E @ equivalent ) @ ( F @ ( D @ equivalent ) @ equivalent ) @ ( E @ ( D @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
!= ( J @ ( I @ equivalent ) @ ( J @ ( H @ equivalent ) @ equivalent ) @ ( I @ ( H @ equivalent ) @ equivalent ) @ ( G @ equivalent ) @ is_a_theorem ) )
| ( G @ is_a_theorem ) ),
inference(simp,[status(thm)],[64]) ).
thf(66,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ equivalent ) @ ( C @ ( A @ equivalent ) @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[65:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( Q )),bind(E,$thf( S )),bind(F,$thf( T )),bind(G,$thf( T @ ( S @ equivalent ) @ ( T @ ( Q @ equivalent ) @ equivalent ) @ ( S @ ( Q @ equivalent ) @ equivalent ) )),bind(H,$thf( A )),bind(I,$thf( B )),bind(J,$thf( C ))]]) ).
thf(75,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ equivalent ) @ ( C @ ( A @ equivalent ) @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem ),
inference(simp,[status(thm)],[66]) ).
thf(17,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ equivalent ) @ ( D @ ( B @ equivalent ) @ equivalent ) @ ( C @ ( B @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( F @ is_a_theorem )
| ~ $true
| ~ ( F @ ( E @ equivalent ) @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[8,7]) ).
thf(18,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ equivalent ) @ ( D @ ( B @ equivalent ) @ equivalent ) @ ( C @ ( B @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( F @ is_a_theorem )
| ~ ( F @ ( E @ equivalent ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[17]) ).
thf(19,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ is_a_theorem )
| ~ ( A @ ( B @ ( E @ ( D @ equivalent ) @ ( E @ ( C @ equivalent ) @ equivalent ) @ ( D @ ( C @ equivalent ) @ equivalent ) @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[18:[bind(A,$thf( H )),bind(B,$thf( Q )),bind(C,$thf( S )),bind(D,$thf( T )),bind(E,$thf( H @ ( T @ ( S @ equivalent ) @ ( T @ ( Q @ equivalent ) @ equivalent ) @ ( S @ ( Q @ equivalent ) @ equivalent ) @ ( H @ equivalent ) @ equivalent ) )),bind(F,$thf( F ))]]) ).
thf(24,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ is_a_theorem )
| ~ ( A @ ( B @ ( E @ ( D @ equivalent ) @ ( E @ ( C @ equivalent ) @ equivalent ) @ ( D @ ( C @ equivalent ) @ equivalent ) @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[19]) ).
thf(83,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ equivalent ) @ ( C @ ( A @ equivalent ) @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
!= ( D @ ( E @ ( H @ ( G @ equivalent ) @ ( H @ ( F @ equivalent ) @ equivalent ) @ ( G @ ( F @ equivalent ) @ equivalent ) @ ( E @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
| ( D @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[75,24]) ).
thf(84,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ equivalent ) @ ( C @ ( A @ equivalent ) @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
!= ( D @ ( E @ ( H @ ( G @ equivalent ) @ ( H @ ( F @ equivalent ) @ equivalent ) @ ( G @ ( F @ equivalent ) @ equivalent ) @ ( E @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
| ( D @ is_a_theorem ) ),
inference(simp,[status(thm)],[83]) ).
thf(85,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( E @ ( D @ equivalent ) @ ( E @ ( C @ ( B @ equivalent ) @ ( C @ ( A @ equivalent ) @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ ( D @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[84:[bind(A,$thf( ZJ @ ( ZI @ equivalent ) @ ( ZJ @ ( ZG @ equivalent ) @ equivalent ) @ ( ZI @ ( ZG @ equivalent ) @ equivalent ) @ ( ZK @ equivalent ) )),bind(B,$thf( ZK )),bind(C,$thf( ZL )),bind(D,$thf( ZL @ ( ZK @ equivalent ) @ ( ZL @ ( ZJ @ ( ZI @ equivalent ) @ ( ZJ @ ( ZG @ equivalent ) @ equivalent ) @ ( ZI @ ( ZG @ equivalent ) @ equivalent ) @ ( ZK @ equivalent ) @ equivalent ) @ equivalent ) )),bind(E,$thf( ZK )),bind(F,$thf( ZG )),bind(G,$thf( ZI )),bind(H,$thf( ZJ ))]]) ).
thf(106,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( E @ ( D @ equivalent ) @ ( E @ ( C @ ( B @ equivalent ) @ ( C @ ( A @ equivalent ) @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ ( D @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
inference(simp,[status(thm)],[85]) ).
thf(114,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( D @ equivalent ) @ ( E @ ( C @ ( B @ equivalent ) @ ( C @ ( A @ equivalent ) @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ ( D @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
!= ( F @ ( G @ ( J @ ( I @ equivalent ) @ ( J @ ( H @ equivalent ) @ equivalent ) @ ( I @ ( H @ equivalent ) @ equivalent ) @ ( G @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
| ( F @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,24]) ).
thf(115,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( D @ equivalent ) @ ( E @ ( C @ ( B @ equivalent ) @ ( C @ ( A @ equivalent ) @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ ( D @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
!= ( F @ ( G @ ( J @ ( I @ equivalent ) @ ( J @ ( H @ equivalent ) @ equivalent ) @ ( I @ ( H @ equivalent ) @ equivalent ) @ ( G @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
| ( F @ is_a_theorem ) ),
inference(simp,[status(thm)],[114]) ).
thf(116,plain,
! [A: $i] : ( A @ ( A @ equivalent ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[115:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( L )),bind(E,$thf( L )),bind(F,$thf( L @ ( L @ equivalent ) )),bind(G,$thf( L )),bind(H,$thf( A )),bind(I,$thf( B )),bind(J,$thf( C ))]]) ).
thf(138,plain,
! [A: $i] : ( A @ ( A @ equivalent ) @ is_a_theorem ),
inference(simp,[status(thm)],[116]) ).
thf(1,negated_conjecture,
~ ( e @ ( c @ equivalent ) @ ( e @ ( b @ equivalent ) @ equivalent ) @ ( c @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ ( a @ equivalent ) @ is_a_theorem ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_lg_2) ).
thf(4,plain,
~ ( e @ ( c @ equivalent ) @ ( e @ ( b @ equivalent ) @ equivalent ) @ ( c @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ ( a @ equivalent ) @ is_a_theorem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(5,plain,
~ ( e @ ( c @ equivalent ) @ ( e @ ( b @ equivalent ) @ equivalent ) @ ( c @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ ( a @ equivalent ) @ is_a_theorem ),
inference(polarity_switch,[status(thm)],[4]) ).
thf(9,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ equivalent ) @ ( D @ ( B @ equivalent ) @ equivalent ) @ ( C @ ( B @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
!= ( e @ ( c @ equivalent ) @ ( e @ ( b @ equivalent ) @ equivalent ) @ ( c @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ ( a @ equivalent ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8,5]) ).
thf(10,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( C @ equivalent ) @ ( D @ ( B @ equivalent ) @ equivalent ) @ ( C @ ( B @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
!= ( e @ ( c @ equivalent ) @ ( e @ ( b @ equivalent ) @ equivalent ) @ ( c @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ ( a @ equivalent ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[9]) ).
thf(11,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( C @ equivalent ) @ ( D @ ( B @ equivalent ) @ equivalent ) @ ( C @ ( B @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ equivalent ) )
!= ( e @ ( c @ equivalent ) @ ( e @ ( b @ equivalent ) @ equivalent ) @ ( c @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ ( a @ equivalent ) ) ),
inference(simp,[status(thm)],[10]) ).
thf(12,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( e @ ( c @ equivalent ) @ ( e @ ( b @ equivalent ) @ equivalent ) @ ( c @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) ) )
| ( ( D @ ( C @ equivalent ) @ ( D @ ( B @ equivalent ) @ equivalent ) @ ( C @ ( B @ equivalent ) @ equivalent ) @ ( A @ equivalent ) )
!= a ) ),
inference(simp,[status(thm)],[11]) ).
thf(13,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ equivalent ) @ ( C @ ( A @ equivalent ) @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ ( e @ ( c @ equivalent ) @ ( e @ ( b @ equivalent ) @ equivalent ) @ ( c @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) )
!= a ),
inference(simp,[status(thm)],[12]) ).
thf(51,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ equivalent ) @ ( C @ ( A @ equivalent ) @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ ( F @ ( E @ equivalent ) @ ( F @ ( D @ equivalent ) @ equivalent ) @ ( E @ ( D @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
!= ( e @ ( c @ equivalent ) @ ( e @ ( b @ equivalent ) @ equivalent ) @ ( c @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ ( a @ equivalent ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[32,5]) ).
thf(52,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ equivalent ) @ ( C @ ( A @ equivalent ) @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ ( F @ ( E @ equivalent ) @ ( F @ ( D @ equivalent ) @ equivalent ) @ ( E @ ( D @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
!= ( e @ ( c @ equivalent ) @ ( e @ ( b @ equivalent ) @ equivalent ) @ ( c @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ ( a @ equivalent ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[51]) ).
thf(73,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ equivalent ) @ ( C @ ( A @ equivalent ) @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ ( F @ ( E @ equivalent ) @ ( F @ ( D @ equivalent ) @ equivalent ) @ ( E @ ( D @ equivalent ) @ equivalent ) @ equivalent ) )
!= ( e @ ( c @ equivalent ) @ ( e @ ( b @ equivalent ) @ equivalent ) @ ( c @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ ( a @ equivalent ) ) ),
inference(simp,[status(thm)],[52]) ).
thf(20,plain,
! [B: $i,A: $i] :
( ~ $true
| ( ( B @ ( A @ equivalent ) @ is_a_theorem )
!= ( A @ is_a_theorem ) )
| ( B @ is_a_theorem )
| ~ ( A @ is_a_theorem ) ),
inference(eqfactor_ordered,[status(thm)],[7]) ).
thf(22,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ equivalent ) )
!= A )
| ~ ( A @ is_a_theorem )
| ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[20]) ).
thf(81,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ equivalent ) @ ( C @ ( A @ equivalent ) @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
!= ( e @ ( c @ equivalent ) @ ( e @ ( b @ equivalent ) @ equivalent ) @ ( c @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ ( a @ equivalent ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[75,5]) ).
thf(82,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ equivalent ) @ ( C @ ( A @ equivalent ) @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
!= ( e @ ( c @ equivalent ) @ ( e @ ( b @ equivalent ) @ equivalent ) @ ( c @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ ( a @ equivalent ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[81]) ).
thf(104,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ equivalent ) @ ( C @ ( A @ equivalent ) @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) )
!= ( e @ ( c @ equivalent ) @ ( e @ ( b @ equivalent ) @ equivalent ) @ ( c @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ ( a @ equivalent ) ) ),
inference(simp,[status(thm)],[82]) ).
thf(111,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ equivalent ) @ ( C @ ( A @ equivalent ) @ equivalent ) )
!= ( e @ ( c @ equivalent ) @ ( e @ ( b @ equivalent ) @ equivalent ) @ ( c @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) ) )
| ( ( B @ ( A @ equivalent ) )
!= a ) ),
inference(simp,[status(thm)],[104]) ).
thf(143,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ equivalent ) )
!= ( e @ ( c @ equivalent ) @ ( e @ ( b @ equivalent ) @ equivalent ) @ ( c @ ( b @ equivalent ) @ equivalent ) ) )
| ( ( C @ ( A @ equivalent ) )
!= a )
| ( ( B @ ( A @ equivalent ) )
!= a ) ),
inference(simp,[status(thm)],[111]) ).
thf(144,plain,
! [C: $i,B: $i,A: $i] :
( ( C
!= ( e @ ( c @ equivalent ) @ ( e @ ( b @ equivalent ) @ equivalent ) ) )
| ( B
!= ( c @ ( b @ equivalent ) ) )
| ( ( C @ ( A @ equivalent ) )
!= a )
| ( ( B @ ( A @ equivalent ) )
!= a ) ),
inference(simp,[status(thm)],[143]) ).
thf(147,plain,
! [A: $i] :
( ( ( e @ ( c @ equivalent ) @ ( e @ ( b @ equivalent ) @ equivalent ) @ ( A @ equivalent ) )
!= a )
| ( ( c @ ( b @ equivalent ) @ ( A @ equivalent ) )
!= a ) ),
inference(simp,[status(thm)],[144]) ).
thf(178,plain,
! [A: $i] :
( ( a != a )
| ( ( e @ ( c @ equivalent ) @ ( e @ ( b @ equivalent ) @ equivalent ) @ ( A @ equivalent ) )
!= ( c @ ( b @ equivalent ) @ ( A @ equivalent ) ) )
| ( ( c @ ( b @ equivalent ) @ ( A @ equivalent ) )
!= a ) ),
inference(eqfactor_ordered,[status(thm)],[147]) ).
thf(180,plain,
! [A: $i] :
( ( ( e @ ( c @ equivalent ) @ ( e @ ( b @ equivalent ) @ equivalent ) )
!= ( c @ ( b @ equivalent ) ) )
| ( A != A )
| ( ( c @ ( b @ equivalent ) @ ( A @ equivalent ) )
!= a ) ),
inference(simp,[status(thm)],[178]) ).
thf(181,plain,
! [A: $i] :
( ( ( e @ ( c @ equivalent ) @ ( e @ ( b @ equivalent ) @ equivalent ) )
!= ( c @ ( b @ equivalent ) ) )
| ( ( c @ ( b @ equivalent ) @ ( A @ equivalent ) )
!= a ) ),
inference(simp,[status(thm)],[180]) ).
thf(112,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( D @ equivalent ) @ ( E @ ( C @ ( B @ equivalent ) @ ( C @ ( A @ equivalent ) @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ ( D @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
!= ( e @ ( c @ equivalent ) @ ( e @ ( b @ equivalent ) @ equivalent ) @ ( c @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ ( a @ equivalent ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,5]) ).
thf(113,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ equivalent ) @ ( E @ ( C @ ( B @ equivalent ) @ ( C @ ( A @ equivalent ) @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ ( D @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
!= ( e @ ( c @ equivalent ) @ ( e @ ( b @ equivalent ) @ equivalent ) @ ( c @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ ( a @ equivalent ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[112]) ).
thf(135,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ equivalent ) @ ( E @ ( C @ ( B @ equivalent ) @ ( C @ ( A @ equivalent ) @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ ( D @ equivalent ) @ equivalent ) @ equivalent ) )
!= ( e @ ( c @ equivalent ) @ ( e @ ( b @ equivalent ) @ equivalent ) @ ( c @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ ( a @ equivalent ) ) ),
inference(simp,[status(thm)],[113]) ).
thf(149,plain,
! [A: $i] :
( ( ( A @ ( A @ equivalent ) @ is_a_theorem )
!= ( e @ ( c @ equivalent ) @ ( e @ ( b @ equivalent ) @ equivalent ) @ ( c @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ ( a @ equivalent ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[138,5]) ).
thf(150,plain,
! [A: $i] :
( ( A @ ( A @ equivalent ) @ is_a_theorem )
!= ( e @ ( c @ equivalent ) @ ( e @ ( b @ equivalent ) @ equivalent ) @ ( c @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ ( a @ equivalent ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[149]) ).
thf(172,plain,
! [A: $i] :
( ( A @ ( A @ equivalent ) )
!= ( e @ ( c @ equivalent ) @ ( e @ ( b @ equivalent ) @ equivalent ) @ ( c @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ ( a @ equivalent ) ) ),
inference(simp,[status(thm)],[150]) ).
thf(199,plain,
! [A: $i] :
( ( A
!= ( e @ ( c @ equivalent ) @ ( e @ ( b @ equivalent ) @ equivalent ) @ ( c @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) ) )
| ( A != a ) ),
inference(simp,[status(thm)],[172]) ).
thf(200,plain,
( ( e @ ( c @ equivalent ) @ ( e @ ( b @ equivalent ) @ equivalent ) @ ( c @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) )
!= a ),
inference(simp,[status(thm)],[199]) ).
thf(179,plain,
! [A: $i] :
( ( ( e @ ( c @ equivalent ) @ ( e @ ( b @ equivalent ) @ equivalent ) @ ( A @ equivalent ) )
!= ( c @ ( b @ equivalent ) @ ( A @ equivalent ) ) )
| ( ( c @ ( b @ equivalent ) @ ( A @ equivalent ) )
!= a ) ),
inference(simp,[status(thm)],[178]) ).
thf(126,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( D @ equivalent ) @ ( E @ ( C @ ( B @ equivalent ) @ ( C @ ( A @ equivalent ) @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ ( D @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
!= ( I @ ( H @ equivalent ) @ ( I @ ( G @ equivalent ) @ equivalent ) @ ( H @ ( G @ equivalent ) @ equivalent ) @ ( F @ equivalent ) @ is_a_theorem ) )
| ( F @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,23]) ).
thf(127,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( D @ equivalent ) @ ( E @ ( C @ ( B @ equivalent ) @ ( C @ ( A @ equivalent ) @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ ( D @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
!= ( I @ ( H @ equivalent ) @ ( I @ ( G @ equivalent ) @ equivalent ) @ ( H @ ( G @ equivalent ) @ equivalent ) @ ( F @ equivalent ) @ is_a_theorem ) )
| ( F @ is_a_theorem ) ),
inference(simp,[status(thm)],[126]) ).
thf(128,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( F @ ( E @ equivalent ) @ ( F @ ( D @ equivalent ) @ equivalent ) @ ( C @ ( B @ equivalent ) @ ( C @ ( A @ equivalent ) @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ ( E @ ( D @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[127:[bind(A,$thf( T )),bind(B,$thf( V )),bind(C,$thf( W )),bind(D,$thf( ZD @ ( ZB @ equivalent ) )),bind(E,$thf( ZE @ ( ZD @ equivalent ) @ ( ZE @ ( ZB @ equivalent ) @ equivalent ) )),bind(F,$thf( ZE @ ( ZD @ equivalent ) @ ( ZE @ ( ZB @ equivalent ) @ equivalent ) @ ( W @ ( V @ equivalent ) @ ( W @ ( T @ equivalent ) @ equivalent ) @ ( V @ ( T @ equivalent ) @ equivalent ) @ ( ZD @ ( ZB @ equivalent ) @ equivalent ) @ equivalent ) )),bind(G,$thf( ZB )),bind(H,$thf( ZD )),bind(I,$thf( ZE ))]]) ).
thf(136,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( F @ ( E @ equivalent ) @ ( F @ ( D @ equivalent ) @ equivalent ) @ ( C @ ( B @ equivalent ) @ ( C @ ( A @ equivalent ) @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ ( E @ ( D @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
inference(simp,[status(thm)],[128]) ).
thf(204,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( F @ ( E @ equivalent ) @ ( F @ ( D @ equivalent ) @ equivalent ) @ ( C @ ( B @ equivalent ) @ ( C @ ( A @ equivalent ) @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ ( E @ ( D @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
!= ( G @ ( H @ ( K @ ( J @ equivalent ) @ ( K @ ( I @ equivalent ) @ equivalent ) @ ( J @ ( I @ equivalent ) @ equivalent ) @ ( H @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
| ( G @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[136,24]) ).
thf(205,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( F @ ( E @ equivalent ) @ ( F @ ( D @ equivalent ) @ equivalent ) @ ( C @ ( B @ equivalent ) @ ( C @ ( A @ equivalent ) @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ ( E @ ( D @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
!= ( G @ ( H @ ( K @ ( J @ equivalent ) @ ( K @ ( I @ equivalent ) @ equivalent ) @ ( J @ ( I @ equivalent ) @ equivalent ) @ ( H @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ) )
| ( G @ is_a_theorem ) ),
inference(simp,[status(thm)],[204]) ).
thf(206,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( D @ ( G @ ( F @ equivalent ) @ ( G @ ( E @ equivalent ) @ equivalent ) @ ( F @ ( E @ equivalent ) @ equivalent ) @ equivalent ) @ ( D @ ( C @ ( B @ equivalent ) @ ( C @ ( A @ equivalent ) @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[205:[bind(A,$thf( ZP )),bind(B,$thf( ZR )),bind(C,$thf( ZS )),bind(D,$thf( ZS @ ( ZR @ equivalent ) @ ( ZS @ ( ZP @ equivalent ) @ equivalent ) @ ( ZR @ ( ZP @ equivalent ) @ equivalent ) )),bind(E,$thf( ZZE @ ( ZZD @ equivalent ) @ ( ZZE @ ( ZZB @ equivalent ) @ equivalent ) @ ( ZZD @ ( ZZB @ equivalent ) @ equivalent ) )),bind(F,$thf( ZU )),bind(G,$thf( ZU @ ( ZZE @ ( ZZD @ equivalent ) @ ( ZZE @ ( ZZB @ equivalent ) @ equivalent ) @ ( ZZD @ ( ZZB @ equivalent ) @ equivalent ) @ equivalent ) @ ( ZU @ ( ZS @ ( ZR @ equivalent ) @ ( ZS @ ( ZP @ equivalent ) @ equivalent ) @ ( ZR @ ( ZP @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) )),bind(H,$thf( ZS @ ( ZR @ equivalent ) @ ( ZS @ ( ZP @ equivalent ) @ equivalent ) @ ( ZR @ ( ZP @ equivalent ) @ equivalent ) )),bind(I,$thf( ZZB )),bind(J,$thf( ZZD )),bind(K,$thf( ZZE ))]]) ).
thf(233,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( D @ ( G @ ( F @ equivalent ) @ ( G @ ( E @ equivalent ) @ equivalent ) @ ( F @ ( E @ equivalent ) @ equivalent ) @ equivalent ) @ ( D @ ( C @ ( B @ equivalent ) @ ( C @ ( A @ equivalent ) @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
inference(simp,[status(thm)],[206]) ).
thf(244,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( G @ ( F @ equivalent ) @ ( G @ ( E @ equivalent ) @ equivalent ) @ ( F @ ( E @ equivalent ) @ equivalent ) @ equivalent ) @ ( D @ ( C @ ( B @ equivalent ) @ ( C @ ( A @ equivalent ) @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
!= ( K @ ( J @ equivalent ) @ ( K @ ( I @ equivalent ) @ equivalent ) @ ( J @ ( I @ equivalent ) @ equivalent ) @ ( H @ equivalent ) @ is_a_theorem ) )
| ( H @ is_a_theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[233,23]) ).
thf(245,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( G @ ( F @ equivalent ) @ ( G @ ( E @ equivalent ) @ equivalent ) @ ( F @ ( E @ equivalent ) @ equivalent ) @ equivalent ) @ ( D @ ( C @ ( B @ equivalent ) @ ( C @ ( A @ equivalent ) @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
!= ( K @ ( J @ equivalent ) @ ( K @ ( I @ equivalent ) @ equivalent ) @ ( J @ ( I @ equivalent ) @ equivalent ) @ ( H @ equivalent ) @ is_a_theorem ) )
| ( H @ is_a_theorem ) ),
inference(simp,[status(thm)],[244]) ).
thf(246,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( D @ ( G @ ( F @ equivalent ) @ ( G @ ( E @ equivalent ) @ equivalent ) @ equivalent ) @ ( D @ ( F @ ( E @ equivalent ) @ equivalent ) @ equivalent ) @ ( C @ ( B @ equivalent ) @ ( C @ ( A @ equivalent ) @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
inference(pattern_uni,[status(thm)],[245:[bind(A,$thf( T )),bind(B,$thf( V )),bind(C,$thf( W )),bind(D,$thf( ZM @ ( ZS @ ( ZR @ equivalent ) @ ( ZS @ ( ZP @ equivalent ) @ equivalent ) @ equivalent ) @ ( ZM @ ( ZR @ ( ZP @ equivalent ) @ equivalent ) @ equivalent ) )),bind(E,$thf( ZP )),bind(F,$thf( ZR )),bind(G,$thf( ZS )),bind(H,$thf( ZM @ ( ZS @ ( ZR @ equivalent ) @ ( ZS @ ( ZP @ equivalent ) @ equivalent ) @ equivalent ) @ ( ZM @ ( ZR @ ( ZP @ equivalent ) @ equivalent ) @ equivalent ) @ ( W @ ( V @ equivalent ) @ ( W @ ( T @ equivalent ) @ equivalent ) @ ( V @ ( T @ equivalent ) @ equivalent ) @ equivalent ) )),bind(I,$thf( ZR @ ( ZP @ equivalent ) )),bind(J,$thf( ZS @ ( ZR @ equivalent ) @ ( ZS @ ( ZP @ equivalent ) @ equivalent ) )),bind(K,$thf( ZM ))]]) ).
thf(265,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( D @ ( G @ ( F @ equivalent ) @ ( G @ ( E @ equivalent ) @ equivalent ) @ equivalent ) @ ( D @ ( F @ ( E @ equivalent ) @ equivalent ) @ equivalent ) @ ( C @ ( B @ equivalent ) @ ( C @ ( A @ equivalent ) @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem ),
inference(simp,[status(thm)],[246]) ).
thf(237,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( G @ ( F @ equivalent ) @ ( G @ ( E @ equivalent ) @ equivalent ) @ ( F @ ( E @ equivalent ) @ equivalent ) @ equivalent ) @ ( D @ ( C @ ( B @ equivalent ) @ ( C @ ( A @ equivalent ) @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
!= ( e @ ( c @ equivalent ) @ ( e @ ( b @ equivalent ) @ equivalent ) @ ( c @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ ( a @ equivalent ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[233,5]) ).
thf(238,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( G @ ( F @ equivalent ) @ ( G @ ( E @ equivalent ) @ equivalent ) @ ( F @ ( E @ equivalent ) @ equivalent ) @ equivalent ) @ ( D @ ( C @ ( B @ equivalent ) @ ( C @ ( A @ equivalent ) @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
!= ( e @ ( c @ equivalent ) @ ( e @ ( b @ equivalent ) @ equivalent ) @ ( c @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ ( a @ equivalent ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[237]) ).
thf(260,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( G @ ( F @ equivalent ) @ ( G @ ( E @ equivalent ) @ equivalent ) @ ( F @ ( E @ equivalent ) @ equivalent ) @ equivalent ) @ ( D @ ( C @ ( B @ equivalent ) @ ( C @ ( A @ equivalent ) @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) )
!= ( e @ ( c @ equivalent ) @ ( e @ ( b @ equivalent ) @ equivalent ) @ ( c @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ ( a @ equivalent ) ) ),
inference(simp,[status(thm)],[238]) ).
thf(25,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ equivalent ) @ ( D @ ( B @ equivalent ) @ equivalent ) @ ( C @ ( B @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( F @ ( E @ equivalent ) )
!= E )
| ~ $true
| ( F @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[8,22]) ).
thf(26,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ equivalent ) @ ( D @ ( B @ equivalent ) @ equivalent ) @ ( C @ ( B @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( F @ ( E @ equivalent ) )
!= E )
| ( F @ is_a_theorem ) ),
inference(simp,[status(thm)],[25]) ).
thf(27,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( E @ ( D @ equivalent ) @ ( E @ ( C @ equivalent ) @ equivalent ) @ ( D @ ( C @ equivalent ) @ equivalent ) @ ( B @ equivalent ) @ equivalent ) @ equivalent ) )
!= ( B @ ( E @ ( D @ equivalent ) @ ( E @ ( C @ equivalent ) @ equivalent ) @ ( D @ ( C @ equivalent ) @ equivalent ) @ ( B @ equivalent ) @ equivalent ) ) )
| ( A @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[26:[bind(A,$thf( H )),bind(B,$thf( Q )),bind(C,$thf( S )),bind(D,$thf( T )),bind(E,$thf( H @ ( T @ ( S @ equivalent ) @ ( T @ ( Q @ equivalent ) @ equivalent ) @ ( S @ ( Q @ equivalent ) @ equivalent ) @ ( H @ equivalent ) @ equivalent ) )),bind(F,$thf( F ))]]) ).
thf(28,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( E @ ( D @ equivalent ) @ ( E @ ( C @ equivalent ) @ equivalent ) @ ( D @ ( C @ equivalent ) @ equivalent ) @ ( B @ equivalent ) @ equivalent ) @ equivalent ) )
!= ( B @ ( E @ ( D @ equivalent ) @ ( E @ ( C @ equivalent ) @ equivalent ) @ ( D @ ( C @ equivalent ) @ equivalent ) @ ( B @ equivalent ) @ equivalent ) ) )
| ( A @ is_a_theorem ) ),
inference(simp,[status(thm)],[27]) ).
thf(21,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ equivalent ) @ is_a_theorem )
!= ( A @ is_a_theorem ) )
| ~ ( A @ is_a_theorem )
| ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[20]) ).
thf(145,plain,
! [C: $i,B: $i,A: $i] :
( ( a != a )
| ( ( C @ ( A @ equivalent ) )
!= ( B @ ( A @ equivalent ) ) )
| ( ( C @ ( B @ equivalent ) )
!= ( e @ ( c @ equivalent ) @ ( e @ ( b @ equivalent ) @ equivalent ) @ ( c @ ( b @ equivalent ) @ equivalent ) ) )
| ( ( B @ ( A @ equivalent ) )
!= a ) ),
inference(eqfactor_ordered,[status(thm)],[143]) ).
thf(146,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ equivalent ) )
!= ( e @ ( c @ equivalent ) @ ( e @ ( b @ equivalent ) @ equivalent ) @ ( c @ ( b @ equivalent ) @ equivalent ) ) )
| ( ( B @ ( A @ equivalent ) )
!= a ) ),
inference(pattern_uni,[status(thm)],[145:[bind(A,$thf( A )),bind(B,$thf( C ))]]) ).
thf(148,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ equivalent ) )
!= ( e @ ( c @ equivalent ) @ ( e @ ( b @ equivalent ) @ equivalent ) @ ( c @ ( b @ equivalent ) @ equivalent ) ) )
| ( ( B @ ( A @ equivalent ) )
!= a ) ),
inference(simp,[status(thm)],[146]) ).
thf(271,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( D @ equivalent ) )
!= ( e @ ( c @ equivalent ) @ ( e @ ( b @ equivalent ) @ equivalent ) @ ( c @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) ) )
| ( ( E @ ( C @ ( B @ equivalent ) @ ( C @ ( A @ equivalent ) @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ ( D @ equivalent ) @ equivalent ) )
!= a ) ),
inference(simp,[status(thm)],[135]) ).
thf(49,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A != B )
| ( ( B @ ( E @ ( D @ equivalent ) @ ( E @ ( C @ equivalent ) @ equivalent ) @ ( D @ ( C @ equivalent ) @ equivalent ) @ ( B @ equivalent ) @ equivalent ) )
!= ( E @ ( D @ equivalent ) @ ( E @ ( C @ equivalent ) @ equivalent ) @ ( D @ ( C @ equivalent ) @ equivalent ) @ ( B @ equivalent ) ) )
| ( A @ is_a_theorem ) ),
inference(simp,[status(thm)],[28]) ).
thf(50,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ equivalent ) @ ( D @ ( B @ equivalent ) @ equivalent ) @ ( C @ ( B @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ equivalent ) )
!= ( D @ ( C @ equivalent ) @ ( D @ ( B @ equivalent ) @ equivalent ) @ ( C @ ( B @ equivalent ) @ equivalent ) @ ( A @ equivalent ) ) )
| ( A @ is_a_theorem ) ),
inference(simp,[status(thm)],[49]) ).
thf(182,plain,
! [A: $i] :
( ( ( e @ ( c @ equivalent ) )
!= c )
| ( ( e @ ( b @ equivalent ) )
!= b )
| ( ( c @ ( b @ equivalent ) @ ( A @ equivalent ) )
!= a ) ),
inference(simp,[status(thm)],[181]) ).
thf(36,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ equivalent ) @ ( D @ ( B @ equivalent ) @ equivalent ) @ ( C @ ( B @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( F @ ( E @ equivalent ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ~ $true
| ( F @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[8,21]) ).
thf(37,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ equivalent ) @ ( D @ ( B @ equivalent ) @ equivalent ) @ ( C @ ( B @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ equivalent ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( ( F @ ( E @ equivalent ) @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ( F @ is_a_theorem ) ),
inference(simp,[status(thm)],[36]) ).
thf(38,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( E @ ( D @ equivalent ) @ ( E @ ( C @ equivalent ) @ equivalent ) @ ( D @ ( C @ equivalent ) @ equivalent ) @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
!= ( B @ ( E @ ( D @ equivalent ) @ ( E @ ( C @ equivalent ) @ equivalent ) @ ( D @ ( C @ equivalent ) @ equivalent ) @ ( B @ equivalent ) @ equivalent ) @ is_a_theorem ) )
| ( A @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[37:[bind(A,$thf( H )),bind(B,$thf( Q )),bind(C,$thf( S )),bind(D,$thf( T )),bind(E,$thf( H @ ( T @ ( S @ equivalent ) @ ( T @ ( Q @ equivalent ) @ equivalent ) @ ( S @ ( Q @ equivalent ) @ equivalent ) @ ( H @ equivalent ) @ equivalent ) )),bind(F,$thf( F ))]]) ).
thf(43,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( E @ ( D @ equivalent ) @ ( E @ ( C @ equivalent ) @ equivalent ) @ ( D @ ( C @ equivalent ) @ equivalent ) @ ( B @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
!= ( B @ ( E @ ( D @ equivalent ) @ ( E @ ( C @ equivalent ) @ equivalent ) @ ( D @ ( C @ equivalent ) @ equivalent ) @ ( B @ equivalent ) @ equivalent ) @ is_a_theorem ) )
| ( A @ is_a_theorem ) ),
inference(simp,[status(thm)],[38]) ).
thf(202,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( F @ ( E @ equivalent ) @ ( F @ ( D @ equivalent ) @ equivalent ) @ ( C @ ( B @ equivalent ) @ ( C @ ( A @ equivalent ) @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ ( E @ ( D @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
!= ( e @ ( c @ equivalent ) @ ( e @ ( b @ equivalent ) @ equivalent ) @ ( c @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ ( a @ equivalent ) @ is_a_theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[136,5]) ).
thf(203,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ equivalent ) @ ( F @ ( D @ equivalent ) @ equivalent ) @ ( C @ ( B @ equivalent ) @ ( C @ ( A @ equivalent ) @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ ( E @ ( D @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
!= ( e @ ( c @ equivalent ) @ ( e @ ( b @ equivalent ) @ equivalent ) @ ( c @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ ( a @ equivalent ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[202]) ).
thf(227,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ equivalent ) @ ( F @ ( D @ equivalent ) @ equivalent ) @ ( C @ ( B @ equivalent ) @ ( C @ ( A @ equivalent ) @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ ( E @ ( D @ equivalent ) @ equivalent ) @ equivalent ) )
!= ( e @ ( c @ equivalent ) @ ( e @ ( b @ equivalent ) @ equivalent ) @ ( c @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ ( a @ equivalent ) ) ),
inference(simp,[status(thm)],[203]) ).
thf(308,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E
!= ( e @ ( c @ equivalent ) @ ( e @ ( b @ equivalent ) @ equivalent ) @ ( c @ ( b @ equivalent ) @ equivalent ) ) )
| ( D != a )
| ( ( E @ ( C @ ( B @ equivalent ) @ ( C @ ( A @ equivalent ) @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ ( D @ equivalent ) @ equivalent ) )
!= a ) ),
inference(simp,[status(thm)],[271]) ).
thf(309,plain,
! [C: $i,B: $i,A: $i] :
( ( e @ ( c @ equivalent ) @ ( e @ ( b @ equivalent ) @ equivalent ) @ ( c @ ( b @ equivalent ) @ equivalent ) @ ( C @ ( B @ equivalent ) @ ( C @ ( A @ equivalent ) @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) )
!= a ),
inference(simp,[status(thm)],[308]) ).
thf(352,plain,
$false,
inference(e,[status(thm)],[138,5,24,13,73,22,181,135,104,23,200,179,106,147,265,233,6,260,28,21,32,148,172,7,271,50,182,11,143,43,8,75,4,136,111,227,309]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL130-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.14/0.61 % Computer : n008.cluster.edu
% 0.14/0.61 % Model : x86_64 x86_64
% 0.14/0.61 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.61 % Memory : 8046.5625MB
% 0.14/0.61 % OS : Linux 6.8.0-71-generic
% 0.14/0.61 % CPULimit : 300
% 0.14/0.61 % WCLimit : 300
% 0.14/0.61 % DateTime : Fri Sep 25 21:54:43 UTC 2026
% 0.14/0.61 % CPUTime :
% 0.14/0.61 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
% 1.00/1.21 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.18/1.38 % [INFO] Parsing done (172ms).
% 1.18/1.39 % [INFO] Running in sequential loop mode.
% 1.91/1.80 % [INFO] eprover registered as external prover.
% 1.91/1.81 % [INFO] Scanning for conjecture ...
% 1.91/1.90 % [INFO] Found a conjecture (or negated_conjecture) and 2 axioms. Running axiom selection ...
% 2.06/1.93 % [INFO] Axiom selection finished. Selected 2 axioms (removed 0 axioms).
% 2.06/1.94 % [INFO] Problem is propositional (TPTP CNF).
% 2.06/1.94 % [INFO] Type checking passed.
% 2.06/1.94 % [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 ...
% 11.11/4.10 % External prover 'e' found a proof!
% 11.11/4.10 % [INFO] Killing All external provers ...
% 11.11/4.10 % Time passed: 3342ms (effective reasoning time: 2699ms)
% 11.11/4.10 % Axioms used in derivation (2): p_4, condensed_detachment
% 11.11/4.10 % No. of inferences in proof: 98
% 11.11/4.10 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 3342 ms resp. 2699 ms w/o parsing
% 10.25/4.21 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 10.25/4.21 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------