%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUN075+2 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n018.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 08:18:40 AM UTC 2026
% Result : Theorem 41.65s 10.74s
% Output : Refutation 35.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 28
% Syntax : Number of formulae : 128 ( 47 unt; 0 typ; 16 def)
% Number of atoms : 735 ( 147 equ; 0 cnn)
% Maximal formula atoms : 23 ( 5 avg)
% Number of connectives : 2250 ( 430 ~; 385 |; 164 &;1271 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 48 ( 11 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 23 ( 20 usr; 3 con; 0-3 aty)
% Number of variables : 629 ( 24 ^; 472 !; 117 ?; 629 :)
% ( 0 !>; 0 ?*; 0 @-; 16 @+)
% Comments :
%------------------------------------------------------------------------------
thf(r2_decl,type,
r2: $i > $i > $o ).
thf(r1_decl,type,
r1: $i > $o ).
thf(r3_decl,type,
r3: $i > $i > $i > $o ).
thf(r4_decl,type,
r4: $i > $i > $i > $o ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i > $i ).
thf(sk3_decl,type,
sk3: $i > $i > $i ).
thf(sk5_decl,type,
sk5: $i > $i > $i ).
thf(sk6_decl,type,
sk6: $i > $i > $i ).
thf(sk7_decl,type,
sk7: $i > $i > $i ).
thf(sk8_decl,type,
sk8: $i > $i > $i ).
thf(sk9_decl,type,
sk9: $i > $i > $i ).
thf(sk10_decl,type,
sk10: $i > $i > $i ).
thf(sk11_decl,type,
sk11: $i > $i > $i ).
thf(sk12_decl,type,
sk12: $i > $i > $i ).
thf(sk13_decl,type,
sk13: $i > $i ).
thf(sk14_decl,type,
sk14: $i > $i ).
thf(sk15_decl,type,
sk15: $i > $i ).
thf(sk16_decl,type,
sk16: $i > $i ).
thf(sk17_decl,type,
sk17: $i > $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
! [B: $i] :
( ( ( B = A )
& ( B @ r1 ) )
| ( ( B != A )
& ~ ( B @ r1 ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( ^ [A: $i] :
@+[B: $i] :
! [C: $i] :
( ( ( C = B )
& ( C @ ( A @ r2 ) ) )
| ( ( C != B )
& ~ ( C @ ( A @ r2 ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
! [D: $i] :
( ( ( D = C )
& ( D @ ( A @ ( B @ r3 ) ) ) )
| ( ( D != C )
& ~ ( D @ ( A @ ( B @ r3 ) ) ) ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
( ? [D: $i] :
( ( D @ ( A @ ( B @ r3 ) ) )
& ( C @ ( D @ r2 ) ) )
& ? [D: $i] :
( ( D = C )
& ? [E: $i] :
( ( D @ ( E @ ( B @ r3 ) ) )
& ( E @ ( A @ r2 ) ) ) ) ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
( ( C
= ( B @ ( A @ sk5 ) ) )
& ? [D: $i] :
( ( C @ ( D @ ( B @ r3 ) ) )
& ( D @ ( A @ r2 ) ) ) ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
( ( B @ ( A @ sk6 ) @ ( C @ ( B @ r3 ) ) )
& ( C @ ( A @ r2 ) ) ) ) ) ).
thf(sk8_def,definition,
( sk8
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
( ( C @ ( A @ ( B @ r3 ) ) )
& ( B @ ( A @ sk5 ) @ ( C @ r2 ) ) ) ) ) ).
thf(sk9_def,definition,
( sk9
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
( ? [D: $i] :
( ( D @ ( A @ ( B @ r4 ) ) )
& ( C @ ( B @ ( D @ r3 ) ) ) )
& ? [D: $i] :
( ( D = C )
& ? [E: $i] :
( ( D @ ( E @ ( B @ r4 ) ) )
& ( E @ ( A @ r2 ) ) ) ) ) ) ) ).
thf(sk10_def,definition,
( sk10
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
( ( C
= ( B @ ( A @ sk9 ) ) )
& ? [D: $i] :
( ( C @ ( D @ ( B @ r4 ) ) )
& ( D @ ( A @ r2 ) ) ) ) ) ) ).
thf(sk11_def,definition,
( sk11
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
( ( B @ ( A @ sk10 ) @ ( C @ ( B @ r4 ) ) )
& ( C @ ( A @ r2 ) ) ) ) ) ).
thf(sk12_def,definition,
( sk12
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
( ( C @ ( A @ ( B @ r4 ) ) )
& ( B @ ( A @ sk9 ) @ ( B @ ( C @ r3 ) ) ) ) ) ) ).
thf(sk13_def,definition,
( sk13
= ( ^ [A: $i] :
@+[B: $i] :
( ( B = A )
& ? [C: $i] :
( ( B @ ( C @ ( A @ r3 ) ) )
& ( C @ r1 ) ) ) ) ) ).
thf(sk14_def,definition,
( sk14
= ( ^ [A: $i] :
@+[B: $i] :
( ( A @ sk13 @ ( B @ ( A @ r3 ) ) )
& ( B @ r1 ) ) ) ) ).
thf(sk15_def,definition,
( sk15
= ( ^ [A: $i] :
@+[B: $i] :
( ? [C: $i] :
( ( B = C )
& ( C @ r1 ) )
& ? [C: $i] :
( ( B @ ( C @ ( A @ r4 ) ) )
& ( C @ r1 ) ) ) ) ) ).
thf(sk16_def,definition,
( sk16
= ( ^ [A: $i] :
@+[B: $i] :
( ( A @ sk15 @ ( B @ ( A @ r4 ) ) )
& ( B @ r1 ) ) ) ) ).
thf(sk17_def,definition,
( sk17
= ( ^ [A: $i] :
@+[B: $i] :
( ( ( A @ sk15 )
= B )
& ( B @ r1 ) ) ) ) ).
thf(11,axiom,
! [A: $i] :
? [B: $i] :
( ? [C: $i] :
( ( B = C )
& ( C @ r1 ) )
& ? [C: $i] :
( ( B @ ( C @ ( A @ r4 ) ) )
& ( C @ r1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_5a) ).
thf(88,plain,
! [A: $i] :
? [B: $i] :
( ? [C: $i] :
( ( B = C )
& ( C @ r1 ) )
& ? [C: $i] :
( ( B @ ( C @ ( A @ r4 ) ) )
& ( C @ r1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(1,conjecture,
? [A: $i] :
( ? [B: $i] :
( ? [C: $i] :
( ? [D: $i] :
( ? [E: $i] :
( ? [F: $i] :
( ? [G: $i] :
( ? [H: $i] :
( ? [I: $i] :
( ( H @ ( I @ r2 ) )
& ( I @ r1 ) )
& ( G @ ( H @ r2 ) ) )
& ( F @ ( G @ r2 ) ) )
& ( E @ ( F @ r2 ) ) )
& ( D @ ( E @ r2 ) ) )
& ( C @ ( D @ r2 ) ) )
& ( B @ ( C @ r2 ) ) )
& ? [C: $i] :
( ? [D: $i] :
( ? [E: $i] :
( ( D @ ( E @ r2 ) )
& ( E @ r1 ) )
& ( C @ ( D @ r2 ) ) )
& ( A @ ( C @ ( B @ r3 ) ) ) ) )
& ? [B: $i] :
( ? [C: $i] :
( ? [D: $i] :
( ? [E: $i] :
( ? [F: $i] :
( ? [G: $i] :
( ? [H: $i] :
( ? [I: $i] :
( ? [J: $i] :
( ? [K: $i] :
( ( J @ ( K @ r2 ) )
& ( K @ r1 ) )
& ( I @ ( J @ r2 ) ) )
& ( H @ ( I @ r2 ) ) )
& ( G @ ( H @ r2 ) ) )
& ( F @ ( G @ r2 ) ) )
& ( E @ ( F @ r2 ) ) )
& ( D @ ( E @ r2 ) ) )
& ( C @ ( D @ r2 ) ) )
& ( B @ ( C @ r2 ) ) )
& ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sevenplustwoeqnine) ).
thf(2,negated_conjecture,
~ ? [A: $i] :
( ? [B: $i] :
( ? [C: $i] :
( ? [D: $i] :
( ? [E: $i] :
( ? [F: $i] :
( ? [G: $i] :
( ? [H: $i] :
( ? [I: $i] :
( ( H @ ( I @ r2 ) )
& ( I @ r1 ) )
& ( G @ ( H @ r2 ) ) )
& ( F @ ( G @ r2 ) ) )
& ( E @ ( F @ r2 ) ) )
& ( D @ ( E @ r2 ) ) )
& ( C @ ( D @ r2 ) ) )
& ( B @ ( C @ r2 ) ) )
& ? [C: $i] :
( ? [D: $i] :
( ? [E: $i] :
( ( D @ ( E @ r2 ) )
& ( E @ r1 ) )
& ( C @ ( D @ r2 ) ) )
& ( A @ ( C @ ( B @ r3 ) ) ) ) )
& ? [B: $i] :
( ? [C: $i] :
( ? [D: $i] :
( ? [E: $i] :
( ? [F: $i] :
( ? [G: $i] :
( ? [H: $i] :
( ? [I: $i] :
( ? [J: $i] :
( ? [K: $i] :
( ( J @ ( K @ r2 ) )
& ( K @ r1 ) )
& ( I @ ( J @ r2 ) ) )
& ( H @ ( I @ r2 ) ) )
& ( G @ ( H @ r2 ) ) )
& ( F @ ( G @ r2 ) ) )
& ( E @ ( F @ r2 ) ) )
& ( D @ ( E @ r2 ) ) )
& ( C @ ( D @ r2 ) ) )
& ( B @ ( C @ r2 ) ) )
& ( A = B ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(14,plain,
~ ? [A: $i] :
( ? [B: $i] :
( ? [C: $i] :
( ? [D: $i] :
( ? [E: $i] :
( ? [F: $i] :
( ? [G: $i] :
( ? [H: $i] :
( ? [I: $i] :
( ( H @ ( I @ r2 ) )
& ( I @ r1 ) )
& ( G @ ( H @ r2 ) ) )
& ( F @ ( G @ r2 ) ) )
& ( E @ ( F @ r2 ) ) )
& ( D @ ( E @ r2 ) ) )
& ( C @ ( D @ r2 ) ) )
& ( B @ ( C @ r2 ) ) )
& ? [C: $i] :
( ? [D: $i] :
( ? [E: $i] :
( ( D @ ( E @ r2 ) )
& ( E @ r1 ) )
& ( C @ ( D @ r2 ) ) )
& ( A @ ( C @ ( B @ r3 ) ) ) ) )
& ? [B: $i] :
( ? [C: $i] :
( ? [D: $i] :
( ? [E: $i] :
( ? [F: $i] :
( ? [G: $i] :
( ? [H: $i] :
( ? [I: $i] :
( ? [J: $i] :
( ? [K: $i] :
( ( J @ ( K @ r2 ) )
& ( K @ r1 ) )
& ( I @ ( J @ r2 ) ) )
& ( H @ ( I @ r2 ) ) )
& ( G @ ( H @ r2 ) ) )
& ( F @ ( G @ r2 ) ) )
& ( E @ ( F @ r2 ) ) )
& ( D @ ( E @ r2 ) ) )
& ( C @ ( D @ r2 ) ) )
& ( B @ ( C @ r2 ) ) )
& ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(15,plain,
! [V: $i,U: $i,T: $i,S: $i,R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( U @ ( V @ r2 ) )
| ~ ( V @ r1 )
| ~ ( T @ ( U @ r2 ) )
| ~ ( S @ ( T @ r2 ) )
| ~ ( R @ ( S @ r2 ) )
| ~ ( Q @ ( R @ r2 ) )
| ~ ( P @ ( Q @ r2 ) )
| ~ ( L @ ( P @ r2 ) )
| ~ ( N @ ( O @ r2 ) )
| ~ ( O @ r1 )
| ~ ( M @ ( N @ r2 ) )
| ~ ( A @ ( M @ ( L @ r3 ) ) )
| ~ ( J @ ( K @ r2 ) )
| ~ ( K @ r1 )
| ~ ( I @ ( J @ r2 ) )
| ~ ( H @ ( I @ r2 ) )
| ~ ( G @ ( H @ r2 ) )
| ~ ( F @ ( G @ r2 ) )
| ~ ( E @ ( F @ r2 ) )
| ~ ( D @ ( E @ r2 ) )
| ~ ( C @ ( D @ r2 ) )
| ~ ( B @ ( C @ r2 ) )
| ( A != B ) ),
inference(cnf,[status(esa)],[14]) ).
thf(16,plain,
! [V: $i,U: $i,T: $i,S: $i,R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( U @ ( V @ r2 ) )
| ~ ( V @ r1 )
| ~ ( T @ ( U @ r2 ) )
| ~ ( S @ ( T @ r2 ) )
| ~ ( R @ ( S @ r2 ) )
| ~ ( Q @ ( R @ r2 ) )
| ~ ( P @ ( Q @ r2 ) )
| ~ ( L @ ( P @ r2 ) )
| ~ ( N @ ( O @ r2 ) )
| ~ ( O @ r1 )
| ~ ( M @ ( N @ r2 ) )
| ~ ( A @ ( M @ ( L @ r3 ) ) )
| ~ ( J @ ( K @ r2 ) )
| ~ ( K @ r1 )
| ~ ( I @ ( J @ r2 ) )
| ~ ( H @ ( I @ r2 ) )
| ~ ( G @ ( H @ r2 ) )
| ~ ( F @ ( G @ r2 ) )
| ~ ( E @ ( F @ r2 ) )
| ~ ( D @ ( E @ r2 ) )
| ~ ( C @ ( D @ r2 ) )
| ~ ( B @ ( C @ r2 ) )
| ( A != B ) ),
inference(lifteq,[status(thm)],[15]) ).
thf(17,plain,
! [U: $i,T: $i,S: $i,R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( T @ ( U @ r2 ) )
| ~ ( U @ r1 )
| ~ ( S @ ( T @ r2 ) )
| ~ ( R @ ( S @ r2 ) )
| ~ ( Q @ ( R @ r2 ) )
| ~ ( P @ ( Q @ r2 ) )
| ~ ( O @ ( P @ r2 ) )
| ~ ( K @ ( O @ r2 ) )
| ~ ( M @ ( N @ r2 ) )
| ~ ( N @ r1 )
| ~ ( L @ ( M @ r2 ) )
| ~ ( A @ ( L @ ( K @ r3 ) ) )
| ~ ( I @ ( J @ r2 ) )
| ~ ( J @ r1 )
| ~ ( H @ ( I @ r2 ) )
| ~ ( G @ ( H @ r2 ) )
| ~ ( F @ ( G @ r2 ) )
| ~ ( E @ ( F @ r2 ) )
| ~ ( D @ ( E @ r2 ) )
| ~ ( C @ ( D @ r2 ) )
| ~ ( B @ ( C @ r2 ) )
| ~ ( A @ ( B @ r2 ) ) ),
inference(simp,[status(thm)],[16]) ).
thf(212,plain,
! [U: $i,T: $i,S: $i,R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ $true
| ( ( M @ ( N @ r2 ) )
!= ( I @ ( J @ r2 ) ) )
| ~ ( T @ ( U @ r2 ) )
| ~ ( U @ r1 )
| ~ ( S @ ( T @ r2 ) )
| ~ ( R @ ( S @ r2 ) )
| ~ ( Q @ ( R @ r2 ) )
| ~ ( P @ ( Q @ r2 ) )
| ~ ( O @ ( P @ r2 ) )
| ~ ( K @ ( O @ r2 ) )
| ~ ( N @ r1 )
| ~ ( L @ ( M @ r2 ) )
| ~ ( A @ ( L @ ( K @ r3 ) ) )
| ~ ( I @ ( J @ r2 ) )
| ~ ( J @ r1 )
| ~ ( H @ ( I @ r2 ) )
| ~ ( G @ ( H @ r2 ) )
| ~ ( F @ ( G @ r2 ) )
| ~ ( E @ ( F @ r2 ) )
| ~ ( D @ ( E @ r2 ) )
| ~ ( C @ ( D @ r2 ) )
| ~ ( B @ ( C @ r2 ) )
| ~ ( A @ ( B @ r2 ) ) ),
inference(eqfactor_ordered,[status(thm)],[17]) ).
thf(370,plain,
! [S: $i,R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( R @ ( S @ r2 ) )
| ~ ( S @ r1 )
| ~ ( Q @ ( R @ r2 ) )
| ~ ( P @ ( Q @ r2 ) )
| ~ ( O @ ( P @ r2 ) )
| ~ ( N @ ( O @ r2 ) )
| ~ ( M @ ( N @ r2 ) )
| ~ ( I @ ( M @ r2 ) )
| ~ ( L @ r1 )
| ~ ( J @ ( K @ r2 ) )
| ~ ( A @ ( J @ ( I @ r3 ) ) )
| ~ ( K @ ( L @ r2 ) )
| ~ ( L @ r1 )
| ~ ( H @ ( K @ r2 ) )
| ~ ( G @ ( H @ r2 ) )
| ~ ( F @ ( G @ r2 ) )
| ~ ( E @ ( F @ r2 ) )
| ~ ( D @ ( E @ r2 ) )
| ~ ( C @ ( D @ r2 ) )
| ~ ( B @ ( C @ r2 ) )
| ~ ( A @ ( B @ r2 ) ) ),
inference(pattern_uni,[status(thm)],[212:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( F )),bind(G,$thf( G )),bind(H,$thf( H )),bind(I,$thf( M )),bind(J,$thf( N ))]]) ).
thf(523,plain,
! [S: $i,R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( R @ ( S @ r2 ) )
| ~ ( S @ r1 )
| ~ ( Q @ ( R @ r2 ) )
| ~ ( P @ ( Q @ r2 ) )
| ~ ( O @ ( P @ r2 ) )
| ~ ( N @ ( O @ r2 ) )
| ~ ( M @ ( N @ r2 ) )
| ~ ( I @ ( M @ r2 ) )
| ~ ( J @ ( K @ r2 ) )
| ~ ( A @ ( J @ ( I @ r3 ) ) )
| ~ ( K @ ( L @ r2 ) )
| ~ ( L @ r1 )
| ~ ( H @ ( K @ r2 ) )
| ~ ( G @ ( H @ r2 ) )
| ~ ( F @ ( G @ r2 ) )
| ~ ( E @ ( F @ r2 ) )
| ~ ( D @ ( E @ r2 ) )
| ~ ( C @ ( D @ r2 ) )
| ~ ( B @ ( C @ r2 ) )
| ~ ( A @ ( B @ r2 ) ) ),
inference(simp,[status(thm)],[370]) ).
thf(781,plain,
! [S: $i,R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ $true
| ( ( R @ ( S @ r2 ) )
!= ( K @ ( L @ r2 ) ) )
| ~ ( S @ r1 )
| ~ ( Q @ ( R @ r2 ) )
| ~ ( P @ ( Q @ r2 ) )
| ~ ( O @ ( P @ r2 ) )
| ~ ( N @ ( O @ r2 ) )
| ~ ( M @ ( N @ r2 ) )
| ~ ( I @ ( M @ r2 ) )
| ~ ( J @ ( K @ r2 ) )
| ~ ( A @ ( J @ ( I @ r3 ) ) )
| ~ ( K @ ( L @ r2 ) )
| ~ ( L @ r1 )
| ~ ( H @ ( K @ r2 ) )
| ~ ( G @ ( H @ r2 ) )
| ~ ( F @ ( G @ r2 ) )
| ~ ( E @ ( F @ r2 ) )
| ~ ( D @ ( E @ r2 ) )
| ~ ( C @ ( D @ r2 ) )
| ~ ( B @ ( C @ r2 ) )
| ~ ( A @ ( B @ r2 ) ) ),
inference(eqfactor_ordered,[status(thm)],[523]) ).
thf(903,plain,
! [Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( Q @ r1 )
| ~ ( O @ ( P @ r2 ) )
| ~ ( N @ ( O @ r2 ) )
| ~ ( M @ ( N @ r2 ) )
| ~ ( L @ ( M @ r2 ) )
| ~ ( K @ ( L @ r2 ) )
| ~ ( I @ ( K @ r2 ) )
| ~ ( J @ ( P @ r2 ) )
| ~ ( A @ ( J @ ( I @ r3 ) ) )
| ~ ( P @ ( Q @ r2 ) )
| ~ ( Q @ r1 )
| ~ ( H @ ( P @ r2 ) )
| ~ ( G @ ( H @ r2 ) )
| ~ ( F @ ( G @ r2 ) )
| ~ ( E @ ( F @ r2 ) )
| ~ ( D @ ( E @ r2 ) )
| ~ ( C @ ( D @ r2 ) )
| ~ ( B @ ( C @ r2 ) )
| ~ ( A @ ( B @ r2 ) ) ),
inference(pattern_uni,[status(thm)],[781:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( F )),bind(G,$thf( G )),bind(H,$thf( H )),bind(I,$thf( I )),bind(J,$thf( J )),bind(K,$thf( R )),bind(L,$thf( S ))]]) ).
thf(1044,plain,
! [Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( O @ ( P @ r2 ) )
| ~ ( N @ ( O @ r2 ) )
| ~ ( M @ ( N @ r2 ) )
| ~ ( L @ ( M @ r2 ) )
| ~ ( K @ ( L @ r2 ) )
| ~ ( I @ ( K @ r2 ) )
| ~ ( J @ ( P @ r2 ) )
| ~ ( A @ ( J @ ( I @ r3 ) ) )
| ~ ( P @ ( Q @ r2 ) )
| ~ ( Q @ r1 )
| ~ ( H @ ( P @ r2 ) )
| ~ ( G @ ( H @ r2 ) )
| ~ ( F @ ( G @ r2 ) )
| ~ ( E @ ( F @ r2 ) )
| ~ ( D @ ( E @ r2 ) )
| ~ ( C @ ( D @ r2 ) )
| ~ ( B @ ( C @ r2 ) )
| ~ ( A @ ( B @ r2 ) ) ),
inference(simp,[status(thm)],[903]) ).
thf(1429,plain,
! [Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ $true
| ( ( N @ ( O @ r2 ) )
!= ( G @ ( H @ r2 ) ) )
| ~ ( O @ ( P @ r2 ) )
| ~ ( M @ ( N @ r2 ) )
| ~ ( L @ ( M @ r2 ) )
| ~ ( K @ ( L @ r2 ) )
| ~ ( I @ ( K @ r2 ) )
| ~ ( J @ ( P @ r2 ) )
| ~ ( A @ ( J @ ( I @ r3 ) ) )
| ~ ( P @ ( Q @ r2 ) )
| ~ ( Q @ r1 )
| ~ ( H @ ( P @ r2 ) )
| ~ ( G @ ( H @ r2 ) )
| ~ ( F @ ( G @ r2 ) )
| ~ ( E @ ( F @ r2 ) )
| ~ ( D @ ( E @ r2 ) )
| ~ ( C @ ( D @ r2 ) )
| ~ ( B @ ( C @ r2 ) )
| ~ ( A @ ( B @ r2 ) ) ),
inference(eqfactor_ordered,[status(thm)],[1044]) ).
thf(1510,plain,
! [O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( M @ ( N @ r2 ) )
| ~ ( K @ ( L @ r2 ) )
| ~ ( J @ ( K @ r2 ) )
| ~ ( I @ ( J @ r2 ) )
| ~ ( G @ ( I @ r2 ) )
| ~ ( H @ ( N @ r2 ) )
| ~ ( A @ ( H @ ( G @ r3 ) ) )
| ~ ( N @ ( O @ r2 ) )
| ~ ( O @ r1 )
| ~ ( M @ ( N @ r2 ) )
| ~ ( L @ ( M @ r2 ) )
| ~ ( F @ ( L @ r2 ) )
| ~ ( E @ ( F @ r2 ) )
| ~ ( D @ ( E @ r2 ) )
| ~ ( C @ ( D @ r2 ) )
| ~ ( B @ ( C @ r2 ) )
| ~ ( A @ ( B @ r2 ) ) ),
inference(pattern_uni,[status(thm)],[1429:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( F )),bind(G,$thf( N )),bind(H,$thf( O ))]]) ).
thf(1677,plain,
! [O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( K @ ( L @ r2 ) )
| ~ ( J @ ( K @ r2 ) )
| ~ ( I @ ( J @ r2 ) )
| ~ ( G @ ( I @ r2 ) )
| ~ ( H @ ( N @ r2 ) )
| ~ ( A @ ( H @ ( G @ r3 ) ) )
| ~ ( N @ ( O @ r2 ) )
| ~ ( O @ r1 )
| ~ ( M @ ( N @ r2 ) )
| ~ ( L @ ( M @ r2 ) )
| ~ ( F @ ( L @ r2 ) )
| ~ ( E @ ( F @ r2 ) )
| ~ ( D @ ( E @ r2 ) )
| ~ ( C @ ( D @ r2 ) )
| ~ ( B @ ( C @ r2 ) )
| ~ ( A @ ( B @ r2 ) ) ),
inference(simp,[status(thm)],[1510]) ).
thf(3,axiom,
? [A: $i] :
! [B: $i] :
( ( ( B = A )
& ( B @ r1 ) )
| ( ( B != A )
& ~ ( B @ r1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1) ).
thf(18,plain,
? [A: $i] :
! [B: $i] :
( ( ( B = A )
& ( B @ r1 ) )
| ( ( B != A )
& ~ ( B @ r1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(19,plain,
! [A: $i] :
( ( ( A = sk1 )
| ( A != sk1 ) )
& ( ( A @ r1 )
| ( A != sk1 ) )
& ( ( A = sk1 )
| ~ ( A @ r1 ) )
& ( ( A @ r1 )
| ~ ( A @ r1 ) ) ),
inference(cnf,[status(esa)],[18]) ).
thf(22,plain,
! [A: $i] :
( ( A @ r1 )
| ( A != sk1 ) ),
inference(cnfConj,[status(thm)],[19]) ).
thf(25,plain,
! [A: $i] :
( ( A @ r1 )
| ( A != sk1 ) ),
inference(lifteq,[status(thm)],[22]) ).
thf(26,plain,
sk1 @ r1,
inference(simp,[status(thm)],[25]) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ~ ( B @ ( A @ r2 ) )
| ! [C: $i] :
( ( C != B )
| ~ ( C @ r1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_7a) ).
thf(104,plain,
! [A: $i,B: $i] :
( ~ ( B @ ( A @ r2 ) )
| ! [C: $i] :
( ( C != B )
| ~ ( C @ r1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(105,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ r2 ) )
| ( C != B )
| ~ ( C @ r1 ) ),
inference(cnf,[status(esa)],[104]) ).
thf(106,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ r2 ) )
| ~ ( C @ r1 )
| ( C != B ) ),
inference(lifteq,[status(thm)],[105]) ).
thf(107,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ r2 ) )
| ~ ( B @ r1 ) ),
inference(simp,[status(thm)],[106]) ).
thf(114,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ r1 )
!= ( B @ r1 ) )
| ~ ( B @ ( A @ r2 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[26,107]) ).
thf(115,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ r1 )
!= ( B @ r1 ) )
| ~ ( B @ ( A @ r2 ) ) ),
inference(simp,[status(thm)],[114]) ).
thf(116,plain,
! [A: $i] :
~ ( sk1 @ ( A @ r2 ) ),
inference(pattern_uni,[status(thm)],[115:[bind(A,$thf( A )),bind(B,$thf( sk1 ))]]) ).
thf(10,axiom,
! [A: $i] :
? [B: $i] :
( ( B = A )
& ? [C: $i] :
( ( B @ ( C @ ( A @ r3 ) ) )
& ( C @ r1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4a) ).
thf(82,plain,
! [A: $i] :
? [B: $i] :
( ( B = A )
& ? [C: $i] :
( ( B @ ( C @ ( A @ r3 ) ) )
& ( C @ r1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(83,plain,
! [A: $i] :
( ( ( A @ sk13 )
= A )
& ( A @ sk13 @ ( A @ sk14 @ ( A @ r3 ) ) )
& ( A @ sk14 @ r1 ) ),
inference(cnf,[status(esa)],[82]) ).
thf(84,plain,
! [A: $i] : ( A @ sk14 @ r1 ),
inference(cnfConj,[status(thm)],[83]) ).
thf(21,plain,
! [A: $i] :
( ( A = sk1 )
| ~ ( A @ r1 ) ),
inference(cnfConj,[status(thm)],[19]) ).
thf(24,plain,
! [A: $i] :
( ~ ( A @ r1 )
| ( A = sk1 ) ),
inference(lifteq,[status(thm)],[21]) ).
thf(1070,plain,
! [B: $i,A: $i] :
( ( ( A @ sk14 @ r1 )
!= ( B @ r1 ) )
| ~ $true
| ( B = sk1 ) ),
inference(paramod_ordered,[status(thm)],[84,24]) ).
thf(1071,plain,
! [B: $i,A: $i] :
( ( ( A @ sk14 @ r1 )
!= ( B @ r1 ) )
| ( B = sk1 ) ),
inference(simp,[status(thm)],[1070]) ).
thf(1072,plain,
! [A: $i] :
( ( A @ sk14 )
= sk1 ),
inference(pattern_uni,[status(thm)],[1071:[bind(A,$thf( C )),bind(B,$thf( C @ sk14 ))]]) ).
thf(1096,plain,
! [A: $i] :
( ( A @ sk14 )
= sk1 ),
inference(simp,[status(thm)],[1072]) ).
thf(89,plain,
! [A: $i] :
( ( ( A @ sk15 )
= ( A @ sk17 ) )
& ( A @ sk17 @ r1 )
& ( A @ sk15 @ ( A @ sk16 @ ( A @ r4 ) ) )
& ( A @ sk16 @ r1 ) ),
inference(cnf,[status(esa)],[88]) ).
thf(93,plain,
! [A: $i] :
( ( A @ sk15 )
= ( A @ sk17 ) ),
inference(cnfConj,[status(thm)],[89]) ).
thf(94,plain,
! [A: $i] :
( ( A @ sk17 )
= ( A @ sk15 ) ),
inference(lifteq,[status(thm)],[93]) ).
thf(92,plain,
! [A: $i] : ( A @ sk17 @ r1 ),
inference(cnfConj,[status(thm)],[89]) ).
thf(1079,plain,
! [B: $i,A: $i] :
( ( ( A @ sk17 @ r1 )
!= ( B @ r1 ) )
| ~ $true
| ( B = sk1 ) ),
inference(paramod_ordered,[status(thm)],[92,24]) ).
thf(1080,plain,
! [B: $i,A: $i] :
( ( ( A @ sk17 @ r1 )
!= ( B @ r1 ) )
| ( B = sk1 ) ),
inference(simp,[status(thm)],[1079]) ).
thf(1081,plain,
! [A: $i] :
( ( A @ sk17 )
= sk1 ),
inference(pattern_uni,[status(thm)],[1080:[bind(A,$thf( C )),bind(B,$thf( C @ sk17 ))]]) ).
thf(1101,plain,
! [A: $i] :
( ( A @ sk17 )
= sk1 ),
inference(simp,[status(thm)],[1081]) ).
thf(1277,plain,
! [A: $i] :
( ( A @ sk15 )
= sk1 ),
inference(rewrite,[status(thm)],[94,1101]) ).
thf(4,axiom,
! [A: $i] :
? [B: $i] :
! [C: $i] :
( ( ( C = B )
& ( C @ ( A @ r2 ) ) )
| ( ( C != B )
& ~ ( C @ ( A @ r2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2) ).
thf(29,plain,
! [A: $i] :
? [B: $i] :
! [C: $i] :
( ( ( C = B )
& ( C @ ( A @ r2 ) ) )
| ( ( C != B )
& ~ ( C @ ( A @ r2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(30,plain,
! [B: $i,A: $i] :
( ( ( B
= ( A @ sk2 ) )
| ( B
!= ( A @ sk2 ) ) )
& ( ( B @ ( A @ r2 ) )
| ( B
!= ( A @ sk2 ) ) )
& ( ( B
= ( A @ sk2 ) )
| ~ ( B @ ( A @ r2 ) ) )
& ( ( B @ ( A @ r2 ) )
| ~ ( B @ ( A @ r2 ) ) ) ),
inference(cnf,[status(esa)],[29]) ).
thf(33,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ r2 ) )
| ( B
!= ( A @ sk2 ) ) ),
inference(cnfConj,[status(thm)],[30]) ).
thf(36,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ r2 ) )
| ( B
!= ( A @ sk2 ) ) ),
inference(lifteq,[status(thm)],[33]) ).
thf(37,plain,
! [A: $i] : ( A @ sk2 @ ( A @ r2 ) ),
inference(simp,[status(thm)],[36]) ).
thf(1223,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk2 @ ( A @ r2 ) )
!= ( C @ ( B @ r2 ) ) )
| ~ $true
| ~ ( C @ r1 ) ),
inference(paramod_ordered,[status(thm)],[37,107]) ).
thf(1224,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk2 @ ( A @ r2 ) )
!= ( C @ ( B @ r2 ) ) )
| ~ ( C @ r1 ) ),
inference(simp,[status(thm)],[1223]) ).
thf(1225,plain,
! [A: $i] :
~ ( A @ sk2 @ r1 ),
inference(pattern_uni,[status(thm)],[1224:[bind(A,$thf( D )),bind(B,$thf( D )),bind(C,$thf( D @ sk2 ))]]) ).
thf(1235,plain,
! [A: $i] :
~ ( A @ sk2 @ r1 ),
inference(simp,[status(thm)],[1225]) ).
thf(7,axiom,
! [A: $i,B: $i] :
? [C: $i] :
( ? [D: $i] :
( ( D @ ( B @ ( A @ r3 ) ) )
& ( C @ ( D @ r2 ) ) )
& ? [D: $i] :
( ( D = C )
& ? [E: $i] :
( ( D @ ( E @ ( A @ r3 ) ) )
& ( E @ ( B @ r2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1a) ).
thf(62,plain,
! [A: $i,B: $i] :
? [C: $i] :
( ? [D: $i] :
( ( D @ ( B @ ( A @ r3 ) ) )
& ( C @ ( D @ r2 ) ) )
& ? [D: $i] :
( ( D = C )
& ? [E: $i] :
( ( D @ ( E @ ( A @ r3 ) ) )
& ( E @ ( B @ r2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(5,axiom,
! [A: $i,B: $i] :
? [C: $i] :
! [D: $i] :
( ( ( D = C )
& ( D @ ( B @ ( A @ r3 ) ) ) )
| ( ( D != C )
& ~ ( D @ ( B @ ( A @ r3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_3) ).
thf(40,plain,
! [A: $i,B: $i] :
? [C: $i] :
! [D: $i] :
( ( ( D = C )
& ( D @ ( B @ ( A @ r3 ) ) ) )
| ( ( D != C )
& ~ ( D @ ( B @ ( A @ r3 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(41,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C
= ( A @ ( B @ sk3 ) ) )
| ( C
!= ( A @ ( B @ sk3 ) ) ) )
& ( ( C @ ( B @ ( A @ r3 ) ) )
| ( C
!= ( A @ ( B @ sk3 ) ) ) )
& ( ( C
= ( A @ ( B @ sk3 ) ) )
| ~ ( C @ ( B @ ( A @ r3 ) ) ) )
& ( ( C @ ( B @ ( A @ r3 ) ) )
| ~ ( C @ ( B @ ( A @ r3 ) ) ) ) ),
inference(cnf,[status(esa)],[40]) ).
thf(43,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ ( B @ sk3 ) ) )
| ~ ( C @ ( B @ ( A @ r3 ) ) ) ),
inference(cnfConj,[status(thm)],[41]) ).
thf(46,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ r3 ) ) )
| ( C
= ( A @ ( B @ sk3 ) ) ) ),
inference(lifteq,[status(thm)],[43]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( A = B )
| ! [C: $i] :
( ~ ( C @ ( B @ r2 ) )
| ! [D: $i] :
( ( D != C )
| ~ ( D @ ( A @ r2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_3a) ).
thf(78,plain,
! [A: $i,B: $i] :
( ( A = B )
| ! [C: $i] :
( ~ ( C @ ( B @ r2 ) )
| ! [D: $i] :
( ( D != C )
| ~ ( D @ ( A @ r2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(90,plain,
! [A: $i] : ( A @ sk16 @ r1 ),
inference(cnfConj,[status(thm)],[89]) ).
thf(1093,plain,
! [B: $i,A: $i] :
( ( ( A @ sk16 @ r1 )
!= ( B @ r1 ) )
| ~ $true
| ( B = sk1 ) ),
inference(paramod_ordered,[status(thm)],[90,24]) ).
thf(1094,plain,
! [B: $i,A: $i] :
( ( ( A @ sk16 @ r1 )
!= ( B @ r1 ) )
| ( B = sk1 ) ),
inference(simp,[status(thm)],[1093]) ).
thf(1095,plain,
! [A: $i] :
( ( A @ sk16 )
= sk1 ),
inference(pattern_uni,[status(thm)],[1094:[bind(A,$thf( C )),bind(B,$thf( C @ sk16 ))]]) ).
thf(1100,plain,
! [A: $i] :
( ( A @ sk16 )
= sk1 ),
inference(simp,[status(thm)],[1095]) ).
thf(8,axiom,
! [A: $i,B: $i] :
? [C: $i] :
( ? [D: $i] :
( ( D @ ( B @ ( A @ r4 ) ) )
& ( C @ ( A @ ( D @ r3 ) ) ) )
& ? [D: $i] :
( ( D = C )
& ? [E: $i] :
( ( D @ ( E @ ( A @ r4 ) ) )
& ( E @ ( B @ r2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2a) ).
thf(70,plain,
! [A: $i,B: $i] :
? [C: $i] :
( ? [D: $i] :
( ( D @ ( B @ ( A @ r4 ) ) )
& ( C @ ( A @ ( D @ r3 ) ) ) )
& ? [D: $i] :
( ( D = C )
& ? [E: $i] :
( ( D @ ( E @ ( A @ r4 ) ) )
& ( E @ ( B @ r2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(1167,plain,
! [B: $i,A: $i] :
( ( ( A @ sk2 @ ( A @ r2 ) )
!= ( sk1 @ ( B @ r2 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[37,116]) ).
thf(1168,plain,
! [B: $i,A: $i] :
( ( A @ sk2 @ ( A @ r2 ) )
!= ( sk1 @ ( B @ r2 ) ) ),
inference(simp,[status(thm)],[1167]) ).
thf(1228,plain,
! [B: $i,A: $i] :
( ( ( A @ sk2 )
!= sk1 )
| ( A != B ) ),
inference(simp,[status(thm)],[1168]) ).
thf(1238,plain,
! [A: $i] :
( ( A @ sk2 )
!= sk1 ),
inference(simp,[status(thm)],[1228]) ).
thf(71,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ sk12 ) @ ( B @ ( A @ r4 ) ) )
& ( A @ ( B @ sk9 ) @ ( A @ ( A @ ( B @ sk12 ) @ r3 ) ) )
& ( ( A @ ( B @ sk10 ) )
= ( A @ ( B @ sk9 ) ) )
& ( A @ ( B @ sk10 ) @ ( A @ ( B @ sk11 ) @ ( A @ r4 ) ) )
& ( A @ ( B @ sk11 ) @ ( B @ r2 ) ) ),
inference(cnf,[status(esa)],[70]) ).
thf(72,plain,
! [B: $i,A: $i] : ( A @ ( B @ sk11 ) @ ( B @ r2 ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(32,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ sk2 ) )
| ~ ( B @ ( A @ r2 ) ) ),
inference(cnfConj,[status(thm)],[30]) ).
thf(35,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ r2 ) )
| ( B
= ( A @ sk2 ) ) ),
inference(lifteq,[status(thm)],[32]) ).
thf(3172,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk11 ) @ ( B @ r2 ) )
!= ( D @ ( C @ r2 ) ) )
| ~ $true
| ( D
= ( C @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[72,35]) ).
thf(3173,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk11 ) @ ( B @ r2 ) )
!= ( D @ ( C @ r2 ) ) )
| ( D
= ( C @ sk2 ) ) ),
inference(simp,[status(thm)],[3172]) ).
thf(3174,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ sk11 ) )
= ( A @ sk2 ) ),
inference(pattern_uni,[status(thm)],[3173:[bind(A,$thf( F )),bind(B,$thf( E )),bind(C,$thf( E )),bind(D,$thf( F @ ( E @ sk11 ) ))]]) ).
thf(3283,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ sk11 ) )
= ( A @ sk2 ) ),
inference(simp,[status(thm)],[3174]) ).
thf(85,plain,
! [A: $i] : ( A @ sk13 @ ( A @ sk14 @ ( A @ r3 ) ) ),
inference(cnfConj,[status(thm)],[83]) ).
thf(86,plain,
! [A: $i] :
( ( A @ sk13 )
= A ),
inference(cnfConj,[status(thm)],[83]) ).
thf(87,plain,
! [A: $i] :
( ( A @ sk13 )
= A ),
inference(lifteq,[status(thm)],[86]) ).
thf(3404,plain,
! [A: $i] : ( A @ ( sk1 @ ( A @ r3 ) ) ),
inference(rewrite,[status(thm)],[85,87,1096]) ).
thf(44,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ r3 ) ) )
| ( C
!= ( A @ ( B @ sk3 ) ) ) ),
inference(cnfConj,[status(thm)],[41]) ).
thf(47,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ r3 ) ) )
| ( C
!= ( A @ ( B @ sk3 ) ) ) ),
inference(lifteq,[status(thm)],[44]) ).
thf(48,plain,
! [B: $i,A: $i] : ( A @ ( B @ sk3 ) @ ( B @ ( A @ r3 ) ) ),
inference(simp,[status(thm)],[47]) ).
thf(12,axiom,
! [A: $i] :
( ? [B: $i,C: $i] :
( ( A = C )
& ( C @ ( B @ r2 ) ) )
| ? [B: $i] :
( ( A = B )
& ( B @ r1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_6a) ).
thf(95,plain,
! [A: $i] :
( ? [B: $i,C: $i] :
( ( A = C )
& ( C @ ( B @ r2 ) ) )
| ? [B: $i] :
( ( A = B )
& ( B @ r1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(63,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ sk8 ) @ ( B @ ( A @ r3 ) ) )
& ( A @ ( B @ sk5 ) @ ( A @ ( B @ sk8 ) @ r2 ) )
& ( ( A @ ( B @ sk6 ) )
= ( A @ ( B @ sk5 ) ) )
& ( A @ ( B @ sk6 ) @ ( A @ ( B @ sk7 ) @ ( A @ r3 ) ) )
& ( A @ ( B @ sk7 ) @ ( B @ r2 ) ) ),
inference(cnf,[status(esa)],[62]) ).
thf(65,plain,
! [B: $i,A: $i] : ( A @ ( B @ sk7 ) @ ( B @ r2 ) ),
inference(cnfConj,[status(thm)],[63]) ).
thf(2277,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk7 ) @ ( B @ r2 ) )
!= ( D @ ( C @ r2 ) ) )
| ~ $true
| ( D
= ( C @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[65,35]) ).
thf(2278,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk7 ) @ ( B @ r2 ) )
!= ( D @ ( C @ r2 ) ) )
| ( D
= ( C @ sk2 ) ) ),
inference(simp,[status(thm)],[2277]) ).
thf(2279,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ sk7 ) )
= ( A @ sk2 ) ),
inference(pattern_uni,[status(thm)],[2278:[bind(A,$thf( F )),bind(B,$thf( E )),bind(C,$thf( E )),bind(D,$thf( F @ ( E @ sk7 ) ))]]) ).
thf(2342,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ sk7 ) )
= ( A @ sk2 ) ),
inference(simp,[status(thm)],[2279]) ).
thf(6,axiom,
! [A: $i,B: $i] :
? [C: $i] :
! [D: $i] :
( ( ( D = C )
& ( D @ ( B @ ( A @ r4 ) ) ) )
| ( ( D != C )
& ~ ( D @ ( B @ ( A @ r4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4) ).
thf(51,plain,
! [A: $i,B: $i] :
? [C: $i] :
! [D: $i] :
( ( ( D = C )
& ( D @ ( B @ ( A @ r4 ) ) ) )
| ( ( D != C )
& ~ ( D @ ( B @ ( A @ r4 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(1816,plain,
! [O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ $true
| ( ( J @ ( K @ r2 ) )
!= ( E @ ( F @ r2 ) ) )
| ~ ( K @ ( L @ r2 ) )
| ~ ( I @ ( J @ r2 ) )
| ~ ( G @ ( I @ r2 ) )
| ~ ( H @ ( N @ r2 ) )
| ~ ( A @ ( H @ ( G @ r3 ) ) )
| ~ ( N @ ( O @ r2 ) )
| ~ ( O @ r1 )
| ~ ( M @ ( N @ r2 ) )
| ~ ( L @ ( M @ r2 ) )
| ~ ( F @ ( L @ r2 ) )
| ~ ( E @ ( F @ r2 ) )
| ~ ( D @ ( E @ r2 ) )
| ~ ( C @ ( D @ r2 ) )
| ~ ( B @ ( C @ r2 ) )
| ~ ( A @ ( B @ r2 ) ) ),
inference(eqfactor_ordered,[status(thm)],[1677]) ).
thf(1922,plain,
! [M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( J @ r2 ) )
| ~ ( G @ ( H @ r2 ) )
| ~ ( E @ ( G @ r2 ) )
| ~ ( F @ ( L @ r2 ) )
| ~ ( A @ ( F @ ( E @ r3 ) ) )
| ~ ( L @ ( M @ r2 ) )
| ~ ( M @ r1 )
| ~ ( K @ ( L @ r2 ) )
| ~ ( J @ ( K @ r2 ) )
| ~ ( I @ ( J @ r2 ) )
| ~ ( H @ ( I @ r2 ) )
| ~ ( D @ ( H @ r2 ) )
| ~ ( C @ ( D @ r2 ) )
| ~ ( B @ ( C @ r2 ) )
| ~ ( A @ ( B @ r2 ) ) ),
inference(pattern_uni,[status(thm)],[1816:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( J )),bind(F,$thf( K ))]]) ).
thf(2008,plain,
! [M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( G @ ( H @ r2 ) )
| ~ ( E @ ( G @ r2 ) )
| ~ ( F @ ( L @ r2 ) )
| ~ ( A @ ( F @ ( E @ r3 ) ) )
| ~ ( L @ ( M @ r2 ) )
| ~ ( M @ r1 )
| ~ ( K @ ( L @ r2 ) )
| ~ ( J @ ( K @ r2 ) )
| ~ ( I @ ( J @ r2 ) )
| ~ ( H @ ( I @ r2 ) )
| ~ ( D @ ( H @ r2 ) )
| ~ ( C @ ( D @ r2 ) )
| ~ ( B @ ( C @ r2 ) )
| ~ ( A @ ( B @ r2 ) ) ),
inference(simp,[status(thm)],[1922]) ).
thf(2475,plain,
! [M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ $true
| ( ( E @ ( G @ r2 ) )
!= ( C @ ( D @ r2 ) ) )
| ~ ( G @ ( H @ r2 ) )
| ~ ( F @ ( L @ r2 ) )
| ~ ( A @ ( F @ ( E @ r3 ) ) )
| ~ ( L @ ( M @ r2 ) )
| ~ ( M @ r1 )
| ~ ( K @ ( L @ r2 ) )
| ~ ( J @ ( K @ r2 ) )
| ~ ( I @ ( J @ r2 ) )
| ~ ( H @ ( I @ r2 ) )
| ~ ( D @ ( H @ r2 ) )
| ~ ( C @ ( D @ r2 ) )
| ~ ( B @ ( C @ r2 ) )
| ~ ( A @ ( B @ r2 ) ) ),
inference(eqfactor_ordered,[status(thm)],[2008]) ).
thf(2550,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( F @ r2 ) )
| ~ ( D @ ( J @ r2 ) )
| ~ ( A @ ( D @ ( C @ r3 ) ) )
| ~ ( J @ ( K @ r2 ) )
| ~ ( K @ r1 )
| ~ ( I @ ( J @ r2 ) )
| ~ ( H @ ( I @ r2 ) )
| ~ ( G @ ( H @ r2 ) )
| ~ ( F @ ( G @ r2 ) )
| ~ ( E @ ( F @ r2 ) )
| ~ ( C @ ( E @ r2 ) )
| ~ ( B @ ( C @ r2 ) )
| ~ ( A @ ( B @ r2 ) ) ),
inference(pattern_uni,[status(thm)],[2475:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( E )),bind(D,$thf( G ))]]) ).
thf(2636,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( J @ r2 ) )
| ~ ( A @ ( D @ ( C @ r3 ) ) )
| ~ ( J @ ( K @ r2 ) )
| ~ ( K @ r1 )
| ~ ( I @ ( J @ r2 ) )
| ~ ( H @ ( I @ r2 ) )
| ~ ( G @ ( H @ r2 ) )
| ~ ( F @ ( G @ r2 ) )
| ~ ( E @ ( F @ r2 ) )
| ~ ( C @ ( E @ r2 ) )
| ~ ( B @ ( C @ r2 ) )
| ~ ( A @ ( B @ r2 ) ) ),
inference(simp,[status(thm)],[2550]) ).
thf(3637,plain,
$false,
inference(e,[status(thm)],[88,523,14,1677,116,1096,17,1277,1235,82,62,24,37,46,78,1100,29,70,1238,3283,3404,1044,35,48,18,95,87,104,2342,40,26,1101,51,2008,2636,107]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUN075+2 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.11 % 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
% 0.23/0.49 % Computer : n018.cluster.edu
% 0.23/0.49 % Model : x86_64 x86_64
% 0.23/0.49 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.23/0.49 % Memory : 8046.5625MB
% 0.23/0.49 % OS : Linux 6.8.0-71-generic
% 0.23/0.49 % CPULimit : 300
% 0.23/0.49 % WCLimit : 300
% 0.23/0.49 % DateTime : Sat Sep 26 04:32:36 UTC 2026
% 0.27/0.49 % CPUTime :
% 0.27/0.49 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.96/0.99 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.45/1.25 % [INFO] Parsing done (256ms).
% 1.45/1.27 % [INFO] Running in sequential loop mode.
% 2.46/1.87 % [INFO] eprover registered as external prover.
% 2.46/1.88 % [INFO] Scanning for conjecture ...
% 2.66/2.04 % [INFO] Found a conjecture (or negated_conjecture) and 11 axioms. Running axiom selection ...
% 2.96/2.09 % [INFO] Axiom selection finished. Selected 11 axioms (removed 0 axioms).
% 2.96/2.14 % [INFO] Problem is first-order (TPTP FOF).
% 3.21/2.16 % [INFO] Type checking passed.
% 3.21/2.16 % [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 ...
% 41.65/10.74 % External prover 'e' found a proof!
% 41.65/10.74 % [INFO] Killing All external provers ...
% 41.65/10.74 % Time passed: 10106ms (effective reasoning time: 9457ms)
% 41.65/10.74 % 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)>
% 41.65/10.74 % Axioms used in derivation (11): axiom_1a, axiom_4a, axiom_2, axiom_3, axiom_7a, axiom_6a, axiom_3a, axiom_4, axiom_1, axiom_2a, axiom_5a
% 41.65/10.74 % No. of inferences in proof: 112
% 41.65/10.74 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 10106 ms resp. 9457 ms w/o parsing
% 35.08/10.94 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 35.08/10.95 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------