%------------------------------------------------------------------------------
% File : Leo-III---1.7.19
% Problem : LCL473+1 : TPTP v9.2.0. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 1 12:41:11 PM UTC 2025
% Result : Theorem 221.11s 147.31s
% Output : Refutation 221.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 42
% Syntax : Number of formulae : 178 ( 44 unt; 0 typ; 0 def)
% Number of atoms : 664 ( 128 equ; 0 cnn)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 3438 ( 293 ~; 291 |; 29 &;2731 @)
% ( 26 <=>; 68 =>; 0 <=; 0 <~>)
% Maximal formula depth : 35 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 47 ( 44 usr; 40 con; 0-2 aty)
% Number of variables : 575 ( 0 ^; 575 !; 0 ?; 575 :)
% Comments :
%------------------------------------------------------------------------------
thf(equivalence_2_type,type,
equivalence_2: $o ).
thf(op_or_type,type,
op_or: $o ).
thf(op_implies_and_type,type,
op_implies_and: $o ).
thf(op_equiv_type,type,
op_equiv: $o ).
thf(substitution_of_equivalents_type,type,
substitution_of_equivalents: $o ).
thf(cn3_type,type,
cn3: $o ).
thf(cn1_type,type,
cn1: $o ).
thf(modus_ponens_type,type,
modus_ponens: $o ).
thf(or_type,type,
or: $i > $i > $i ).
thf(not_type,type,
not: $i > $i ).
thf(and_type,type,
and: $i > $i > $i ).
thf(cn2_type,type,
cn2: $o ).
thf(op_and_type,type,
op_and: $o ).
thf(implies_type,type,
implies: $i > $i > $i ).
thf(equiv_type,type,
equiv: $i > $i > $i ).
thf(and_2_type,type,
and_2: $o ).
thf(is_a_theorem_type,type,
is_a_theorem: $i > $o ).
thf(modus_tollens_type,type,
modus_tollens: $o ).
thf(kn2_type,type,
kn2: $o ).
thf(or_3_type,type,
or_3: $o ).
thf(and_3_type,type,
and_3: $o ).
thf(r2_type,type,
r2: $o ).
thf(kn1_type,type,
kn1: $o ).
thf(implies_3_type,type,
implies_3: $o ).
thf(and_1_type,type,
and_1: $o ).
thf(implies_2_type,type,
implies_2: $o ).
thf(r1_type,type,
r1: $o ).
thf(r3_type,type,
r3: $o ).
thf(op_implies_or_type,type,
op_implies_or: $o ).
thf(equivalence_3_type,type,
equivalence_3: $o ).
thf(equivalence_1_type,type,
equivalence_1: $o ).
thf(implies_1_type,type,
implies_1: $o ).
thf(or_2_type,type,
or_2: $o ).
thf(kn3_type,type,
kn3: $o ).
thf(or_1_type,type,
or_1: $o ).
thf(r4_type,type,
r4: $o ).
thf(r5_type,type,
r5: $o ).
thf(sk18_type,type,
sk18: $i ).
thf(sk19_type,type,
sk19: $i ).
thf(sk22_type,type,
sk22: $i ).
thf(sk34_type,type,
sk34: $i ).
thf(sk35_type,type,
sk35: $i ).
thf(sk41_type,type,
sk41: $i ).
thf(sk42_type,type,
sk42: $i ).
thf(12,axiom,
cn2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',luka_cn2) ).
thf(56,plain,
cn2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(29,axiom,
( r3
<=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ ( or @ A @ B ) @ ( or @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r3) ).
thf(106,plain,
( ( r3
=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ ( or @ A @ B ) @ ( or @ B @ A ) ) ) )
& ( ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ ( or @ A @ B ) @ ( or @ B @ A ) ) )
=> r3 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(18,axiom,
( modus_tollens
<=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ ( implies @ ( not @ B ) @ ( not @ A ) ) @ ( implies @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',modus_tollens) ).
thf(70,plain,
( ( modus_tollens
=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ ( implies @ ( not @ B ) @ ( not @ A ) ) @ ( implies @ A @ B ) ) ) )
& ( ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ ( implies @ ( not @ B ) @ ( not @ A ) ) @ ( implies @ A @ B ) ) )
=> modus_tollens ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(36,axiom,
( cn1
<=> ! [A: $i,B: $i,C: $i] : ( is_a_theorem @ ( implies @ ( implies @ A @ B ) @ ( implies @ ( implies @ B @ C ) @ ( implies @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cn1) ).
thf(129,plain,
( ( cn1
=> ! [A: $i,B: $i,C: $i] : ( is_a_theorem @ ( implies @ ( implies @ A @ B ) @ ( implies @ ( implies @ B @ C ) @ ( implies @ A @ C ) ) ) ) )
& ( ! [A: $i,B: $i,C: $i] : ( is_a_theorem @ ( implies @ ( implies @ A @ B ) @ ( implies @ ( implies @ B @ C ) @ ( implies @ A @ C ) ) ) )
=> cn1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(19,axiom,
( kn2
<=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ ( and @ A @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kn2) ).
thf(73,plain,
( ( kn2
=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ ( and @ A @ B ) @ A ) ) )
& ( ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ ( and @ A @ B ) @ A ) )
=> kn2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(34,axiom,
( equivalence_1
<=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ ( equiv @ A @ B ) @ ( implies @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equivalence_1) ).
thf(123,plain,
( ( equivalence_1
=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ ( equiv @ A @ B ) @ ( implies @ A @ B ) ) ) )
& ( ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ ( equiv @ A @ B ) @ ( implies @ A @ B ) ) )
=> equivalence_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(16,axiom,
( op_equiv
=> ! [A: $i,B: $i] :
( ( equiv @ A @ B )
= ( and @ ( implies @ A @ B ) @ ( implies @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_equiv) ).
thf(64,plain,
( op_equiv
=> ! [A: $i,B: $i] :
( ( equiv @ A @ B )
= ( and @ ( implies @ A @ B ) @ ( implies @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(65,plain,
! [B: $i,A: $i] :
( ~ op_equiv
| ( ( equiv @ A @ B )
= ( and @ ( implies @ A @ B ) @ ( implies @ B @ A ) ) ) ),
inference(cnf,[status(esa)],[64]) ).
thf(66,plain,
! [B: $i,A: $i] :
( ( ( equiv @ A @ B )
= ( and @ ( implies @ A @ B ) @ ( implies @ B @ A ) ) )
| ~ op_equiv ),
inference(lifteq,[status(thm)],[65]) ).
thf(6,axiom,
op_equiv,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_op_equiv) ).
thf(48,plain,
op_equiv,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(15,axiom,
( op_implies_and
=> ! [A: $i,B: $i] :
( ( implies @ A @ B )
= ( not @ ( and @ A @ ( not @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_implies_and) ).
thf(61,plain,
( op_implies_and
=> ! [A: $i,B: $i] :
( ( implies @ A @ B )
= ( not @ ( and @ A @ ( not @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(62,plain,
! [B: $i,A: $i] :
( ~ op_implies_and
| ( ( implies @ A @ B )
= ( not @ ( and @ A @ ( not @ B ) ) ) ) ),
inference(cnf,[status(esa)],[61]) ).
thf(63,plain,
! [B: $i,A: $i] :
( ( ( implies @ A @ B )
= ( not @ ( and @ A @ ( not @ B ) ) ) )
| ~ op_implies_and ),
inference(lifteq,[status(thm)],[62]) ).
thf(4,axiom,
op_implies_and,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_op_implies_and) ).
thf(46,plain,
op_implies_and,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(2667,plain,
! [B: $i,A: $i] :
( ( ( implies @ A @ B )
= ( not @ ( and @ A @ ( not @ B ) ) ) )
| ~ $true ),
inference(rewrite,[status(thm)],[63,46]) ).
thf(2668,plain,
! [B: $i,A: $i] :
( ( implies @ A @ B )
= ( not @ ( and @ A @ ( not @ B ) ) ) ),
inference(simp,[status(thm)],[2667]) ).
thf(4142,plain,
! [B: $i,A: $i] :
( ( ( equiv @ A @ B )
= ( and @ ( not @ ( and @ A @ ( not @ B ) ) ) @ ( not @ ( and @ B @ ( not @ A ) ) ) ) )
| ~ $true ),
inference(rewrite,[status(thm)],[66,48,2668]) ).
thf(4143,plain,
! [B: $i,A: $i] :
( ( equiv @ A @ B )
= ( and @ ( not @ ( and @ A @ ( not @ B ) ) ) @ ( not @ ( and @ B @ ( not @ A ) ) ) ) ),
inference(simp,[status(thm)],[4142]) ).
thf(31,axiom,
( op_implies_or
=> ! [A: $i,B: $i] :
( ( implies @ A @ B )
= ( or @ ( not @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_implies_or) ).
thf(114,plain,
( op_implies_or
=> ! [A: $i,B: $i] :
( ( implies @ A @ B )
= ( or @ ( not @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(9,axiom,
cn1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',luka_cn1) ).
thf(51,plain,
cn1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(5,axiom,
op_or,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_op_or) ).
thf(47,plain,
op_or,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(28,axiom,
( substitution_of_equivalents
<=> ! [A: $i,B: $i] :
( ( is_a_theorem @ ( equiv @ A @ B ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',substitution_of_equivalents) ).
thf(100,plain,
( ( substitution_of_equivalents
=> ! [A: $i,B: $i] :
( ( is_a_theorem @ ( equiv @ A @ B ) )
=> ( A = B ) ) )
& ( ! [A: $i,B: $i] :
( ( is_a_theorem @ ( equiv @ A @ B ) )
=> ( A = B ) )
=> substitution_of_equivalents ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(39,axiom,
( kn3
<=> ! [A: $i,B: $i,C: $i] : ( is_a_theorem @ ( implies @ ( implies @ A @ B ) @ ( implies @ ( not @ ( and @ B @ C ) ) @ ( not @ ( and @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kn3) ).
thf(138,plain,
( ( kn3
=> ! [A: $i,B: $i,C: $i] : ( is_a_theorem @ ( implies @ ( implies @ A @ B ) @ ( implies @ ( not @ ( and @ B @ C ) ) @ ( not @ ( and @ C @ A ) ) ) ) ) )
& ( ! [A: $i,B: $i,C: $i] : ( is_a_theorem @ ( implies @ ( implies @ A @ B ) @ ( implies @ ( not @ ( and @ B @ C ) ) @ ( not @ ( and @ C @ A ) ) ) ) )
=> kn3 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(24,axiom,
( implies_3
<=> ! [A: $i,B: $i,C: $i] : ( is_a_theorem @ ( implies @ ( implies @ A @ B ) @ ( implies @ ( implies @ B @ C ) @ ( implies @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',implies_3) ).
thf(88,plain,
( ( implies_3
=> ! [A: $i,B: $i,C: $i] : ( is_a_theorem @ ( implies @ ( implies @ A @ B ) @ ( implies @ ( implies @ B @ C ) @ ( implies @ A @ C ) ) ) ) )
& ( ! [A: $i,B: $i,C: $i] : ( is_a_theorem @ ( implies @ ( implies @ A @ B ) @ ( implies @ ( implies @ B @ C ) @ ( implies @ A @ C ) ) ) )
=> implies_3 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(33,axiom,
( cn3
<=> ! [A: $i] : ( is_a_theorem @ ( implies @ ( implies @ ( not @ A ) @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cn3) ).
thf(120,plain,
( ( cn3
=> ! [A: $i] : ( is_a_theorem @ ( implies @ ( implies @ ( not @ A ) @ A ) @ A ) ) )
& ( ! [A: $i] : ( is_a_theorem @ ( implies @ ( implies @ ( not @ A ) @ A ) @ A ) )
=> cn3 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(11,axiom,
( op_or
=> ! [A: $i,B: $i] :
( ( or @ A @ B )
= ( not @ ( and @ ( not @ A ) @ ( not @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_or) ).
thf(53,plain,
( op_or
=> ! [A: $i,B: $i] :
( ( or @ A @ B )
= ( not @ ( and @ ( not @ A ) @ ( not @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(54,plain,
! [B: $i,A: $i] :
( ~ op_or
| ( ( or @ A @ B )
= ( not @ ( and @ ( not @ A ) @ ( not @ B ) ) ) ) ),
inference(cnf,[status(esa)],[53]) ).
thf(55,plain,
! [B: $i,A: $i] :
( ( ( or @ A @ B )
= ( not @ ( and @ ( not @ A ) @ ( not @ B ) ) ) )
| ~ op_or ),
inference(lifteq,[status(thm)],[54]) ).
thf(3,axiom,
op_or,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',luka_op_or) ).
thf(45,plain,
op_or,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(186,plain,
! [B: $i,A: $i] :
( ( ( or @ A @ B )
= ( not @ ( and @ ( not @ A ) @ ( not @ B ) ) ) )
| ~ $true ),
inference(rewrite,[status(thm)],[55,45]) ).
thf(187,plain,
! [B: $i,A: $i] :
( ( or @ A @ B )
= ( not @ ( and @ ( not @ A ) @ ( not @ B ) ) ) ),
inference(simp,[status(thm)],[186]) ).
thf(208,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( not @ ( and @ ( or @ A @ B ) @ ( not @ D ) ) )
= ( or @ C @ D ) )
| ( ( not @ ( and @ ( not @ A ) @ ( not @ B ) ) )
!= ( not @ C ) ) ),
inference(paramod_ordered,[status(thm)],[187,187]) ).
thf(209,plain,
! [C: $i,B: $i,A: $i] :
( ( not @ ( and @ ( or @ B @ C ) @ ( not @ A ) ) )
= ( or @ ( and @ ( not @ B ) @ ( not @ C ) ) @ A ) ),
inference(pattern_uni,[status(thm)],[208:[bind(A,$thf( G )),bind(B,$thf( H )),bind(C,$thf( and @ ( not @ G ) @ ( not @ H ) )),bind(D,$thf( D ))]]) ).
thf(220,plain,
! [C: $i,B: $i,A: $i] :
( ( not @ ( and @ ( or @ B @ C ) @ ( not @ A ) ) )
= ( or @ ( and @ ( not @ B ) @ ( not @ C ) ) @ A ) ),
inference(simp,[status(thm)],[209]) ).
thf(271,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not @ ( and @ ( not @ ( and @ ( not @ A ) @ ( not @ B ) ) ) @ ( not @ C ) ) )
= ( or @ ( and @ ( not @ D ) @ ( not @ E ) ) @ C ) )
| ( ( or @ A @ B )
!= ( or @ D @ E ) ) ),
inference(paramod_ordered,[status(thm)],[187,220]) ).
thf(272,plain,
! [C: $i,B: $i,A: $i] :
( ( not @ ( and @ ( not @ ( and @ ( not @ A ) @ ( not @ B ) ) ) @ ( not @ C ) ) )
= ( or @ ( and @ ( not @ A ) @ ( not @ B ) ) @ C ) ),
inference(pattern_uni,[status(thm)],[271:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( A )),bind(E,$thf( B ))]]) ).
thf(510,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not @ ( and @ ( not @ ( and @ ( not @ A ) @ ( not @ B ) ) ) @ ( not @ C ) ) )
= ( not @ ( and @ ( or @ E @ F ) @ ( not @ D ) ) ) )
| ( ( or @ ( and @ ( not @ A ) @ ( not @ B ) ) @ C )
!= ( or @ ( and @ ( not @ E ) @ ( not @ F ) ) @ D ) ) ),
inference(paramod_ordered,[status(thm)],[272,220]) ).
thf(511,plain,
! [C: $i,B: $i,A: $i] :
( ( not @ ( and @ ( not @ ( and @ ( not @ A ) @ ( not @ B ) ) ) @ ( not @ C ) ) )
= ( not @ ( and @ ( or @ A @ B ) @ ( not @ C ) ) ) ),
inference(pattern_uni,[status(thm)],[510:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( C )),bind(E,$thf( A )),bind(F,$thf( B ))]]) ).
thf(10,axiom,
modus_ponens,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',luka_modus_ponens) ).
thf(52,plain,
modus_ponens,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(38,axiom,
( or_2
<=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ B @ ( or @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',or_2) ).
thf(135,plain,
( ( or_2
=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ B @ ( or @ A @ B ) ) ) )
& ( ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ B @ ( or @ A @ B ) ) )
=> or_2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(136,plain,
( ~ ( is_a_theorem @ ( implies @ sk42 @ ( or @ sk41 @ sk42 ) ) )
| or_2 ),
inference(cnf,[status(esa)],[135]) ).
thf(8919,plain,
( ~ ( is_a_theorem @ ( not @ ( and @ sk42 @ ( not @ ( or @ sk41 @ sk42 ) ) ) ) )
| or_2 ),
inference(rewrite,[status(thm)],[136,2668]) ).
thf(210,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( not @ ( and @ ( not @ C ) @ ( or @ A @ B ) ) )
= ( or @ C @ D ) )
| ( ( not @ ( and @ ( not @ A ) @ ( not @ B ) ) )
!= ( not @ D ) ) ),
inference(paramod_ordered,[status(thm)],[187,187]) ).
thf(211,plain,
! [C: $i,B: $i,A: $i] :
( ( not @ ( and @ ( not @ A ) @ ( or @ B @ C ) ) )
= ( or @ A @ ( and @ ( not @ B ) @ ( not @ C ) ) ) ),
inference(pattern_uni,[status(thm)],[210:[bind(A,$thf( G )),bind(B,$thf( H )),bind(C,$thf( C )),bind(D,$thf( and @ ( not @ G ) @ ( not @ H ) ))]]) ).
thf(221,plain,
! [C: $i,B: $i,A: $i] :
( ( not @ ( and @ ( not @ A ) @ ( or @ B @ C ) ) )
= ( or @ A @ ( and @ ( not @ B ) @ ( not @ C ) ) ) ),
inference(simp,[status(thm)],[211]) ).
thf(380,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not @ ( and @ ( not @ C ) @ ( not @ ( and @ ( not @ A ) @ ( not @ B ) ) ) ) )
= ( or @ C @ ( and @ ( not @ D ) @ ( not @ E ) ) ) )
| ( ( or @ A @ B )
!= ( or @ D @ E ) ) ),
inference(paramod_ordered,[status(thm)],[187,221]) ).
thf(381,plain,
! [C: $i,B: $i,A: $i] :
( ( not @ ( and @ ( not @ C ) @ ( not @ ( and @ ( not @ A ) @ ( not @ B ) ) ) ) )
= ( or @ C @ ( and @ ( not @ A ) @ ( not @ B ) ) ) ),
inference(pattern_uni,[status(thm)],[380:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( A )),bind(E,$thf( B ))]]) ).
thf(1378,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not @ ( and @ ( not @ C ) @ ( not @ ( and @ ( not @ A ) @ ( not @ B ) ) ) ) )
= ( not @ ( and @ ( not @ D ) @ ( or @ E @ F ) ) ) )
| ( ( or @ C @ ( and @ ( not @ A ) @ ( not @ B ) ) )
!= ( or @ D @ ( and @ ( not @ E ) @ ( not @ F ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[381,221]) ).
thf(1379,plain,
! [C: $i,B: $i,A: $i] :
( ( not @ ( and @ ( not @ C ) @ ( not @ ( and @ ( not @ A ) @ ( not @ B ) ) ) ) )
= ( not @ ( and @ ( not @ C ) @ ( or @ A @ B ) ) ) ),
inference(pattern_uni,[status(thm)],[1378:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( C )),bind(E,$thf( A )),bind(F,$thf( B ))]]) ).
thf(13,axiom,
op_equiv,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',luka_op_equiv) ).
thf(57,plain,
op_equiv,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(42,axiom,
( r5
<=> ! [A: $i,B: $i,C: $i] : ( is_a_theorem @ ( implies @ ( implies @ B @ C ) @ ( implies @ ( or @ A @ B ) @ ( or @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r5) ).
thf(147,plain,
( ( r5
=> ! [A: $i,B: $i,C: $i] : ( is_a_theorem @ ( implies @ ( implies @ B @ C ) @ ( implies @ ( or @ A @ B ) @ ( or @ A @ C ) ) ) ) )
& ( ! [A: $i,B: $i,C: $i] : ( is_a_theorem @ ( implies @ ( implies @ B @ C ) @ ( implies @ ( or @ A @ B ) @ ( or @ A @ C ) ) ) )
=> r5 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(37,axiom,
( cn2
<=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ A @ ( implies @ ( not @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cn2) ).
thf(132,plain,
( ( cn2
=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ A @ ( implies @ ( not @ A ) @ B ) ) ) )
& ( ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ A @ ( implies @ ( not @ A ) @ B ) ) )
=> cn2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(378,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not @ ( and @ ( not @ A ) @ ( or @ B @ C ) ) )
= ( not @ ( and @ ( not @ D ) @ ( not @ E ) ) ) )
| ( ( or @ A @ ( and @ ( not @ B ) @ ( not @ C ) ) )
!= ( or @ D @ E ) ) ),
inference(paramod_ordered,[status(thm)],[221,187]) ).
thf(379,plain,
! [C: $i,B: $i,A: $i] :
( ( not @ ( and @ ( not @ A ) @ ( or @ B @ C ) ) )
= ( not @ ( and @ ( not @ A ) @ ( not @ ( and @ ( not @ B ) @ ( not @ C ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[378:[bind(A,$thf( A )),bind(B,$thf( H )),bind(C,$thf( I )),bind(D,$thf( A )),bind(E,$thf( and @ ( not @ H ) @ ( not @ I ) ))]]) ).
thf(428,plain,
! [C: $i,B: $i,A: $i] :
( ( not @ ( and @ ( not @ A ) @ ( or @ B @ C ) ) )
= ( not @ ( and @ ( not @ A ) @ ( not @ ( and @ ( not @ B ) @ ( not @ C ) ) ) ) ) ),
inference(simp,[status(thm)],[379]) ).
thf(23,axiom,
( kn1
<=> ! [A: $i] : ( is_a_theorem @ ( implies @ A @ ( and @ A @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kn1) ).
thf(85,plain,
( ( kn1
=> ! [A: $i] : ( is_a_theorem @ ( implies @ A @ ( and @ A @ A ) ) ) )
& ( ! [A: $i] : ( is_a_theorem @ ( implies @ A @ ( and @ A @ A ) ) )
=> kn1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(14,axiom,
( op_and
=> ! [A: $i,B: $i] :
( ( and @ A @ B )
= ( not @ ( or @ ( not @ A ) @ ( not @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_and) ).
thf(58,plain,
( op_and
=> ! [A: $i,B: $i] :
( ( and @ A @ B )
= ( not @ ( or @ ( not @ A ) @ ( not @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(59,plain,
! [B: $i,A: $i] :
( ~ op_and
| ( ( and @ A @ B )
= ( not @ ( or @ ( not @ A ) @ ( not @ B ) ) ) ) ),
inference(cnf,[status(esa)],[58]) ).
thf(60,plain,
! [B: $i,A: $i] :
( ( ( and @ A @ B )
= ( not @ ( or @ ( not @ A ) @ ( not @ B ) ) ) )
| ~ op_and ),
inference(lifteq,[status(thm)],[59]) ).
thf(32,axiom,
( equivalence_3
<=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ ( implies @ A @ B ) @ ( implies @ ( implies @ B @ A ) @ ( equiv @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equivalence_3) ).
thf(117,plain,
( ( equivalence_3
=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ ( implies @ A @ B ) @ ( implies @ ( implies @ B @ A ) @ ( equiv @ A @ B ) ) ) ) )
& ( ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ ( implies @ A @ B ) @ ( implies @ ( implies @ B @ A ) @ ( equiv @ A @ B ) ) ) )
=> equivalence_3 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(27,axiom,
( r1
<=> ! [A: $i] : ( is_a_theorem @ ( implies @ ( or @ A @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r1) ).
thf(97,plain,
( ( r1
=> ! [A: $i] : ( is_a_theorem @ ( implies @ ( or @ A @ A ) @ A ) ) )
& ( ! [A: $i] : ( is_a_theorem @ ( implies @ ( or @ A @ A ) @ A ) )
=> r1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(1361,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not @ ( and @ ( not @ E ) @ ( or @ A @ B ) ) )
= ( or @ E @ ( and @ ( not @ C ) @ ( not @ D ) ) ) )
| ( ( not @ ( and @ ( not @ A ) @ ( not @ B ) ) )
!= ( not @ ( and @ ( not @ C ) @ ( not @ D ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[187,381]) ).
thf(1362,plain,
! [C: $i,B: $i,A: $i] :
( ( not @ ( and @ ( not @ C ) @ ( or @ A @ B ) ) )
= ( or @ C @ ( and @ ( not @ A ) @ ( not @ B ) ) ) ),
inference(pattern_uni,[status(thm)],[1361:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(1573,plain,
! [C: $i,B: $i,A: $i] :
( ( not @ ( and @ ( not @ C ) @ ( or @ A @ B ) ) )
= ( or @ C @ ( and @ ( not @ A ) @ ( not @ B ) ) ) ),
inference(simp,[status(thm)],[1362]) ).
thf(40,axiom,
( or_1
<=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ A @ ( or @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',or_1) ).
thf(141,plain,
( ( or_1
=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ A @ ( or @ A @ B ) ) ) )
& ( ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ A @ ( or @ A @ B ) ) )
=> or_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(30,axiom,
( modus_ponens
<=> ! [A: $i,B: $i] :
( ( ( is_a_theorem @ A )
& ( is_a_theorem @ ( implies @ A @ B ) ) )
=> ( is_a_theorem @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',modus_ponens) ).
thf(109,plain,
( ( modus_ponens
=> ! [A: $i,B: $i] :
( ( ( is_a_theorem @ A )
& ( is_a_theorem @ ( implies @ A @ B ) ) )
=> ( is_a_theorem @ B ) ) )
& ( ! [A: $i,B: $i] :
( ( ( is_a_theorem @ A )
& ( is_a_theorem @ ( implies @ A @ B ) ) )
=> ( is_a_theorem @ B ) )
=> modus_ponens ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(269,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not @ ( and @ ( or @ B @ C ) @ ( not @ A ) ) )
= ( not @ ( and @ ( not @ D ) @ ( not @ E ) ) ) )
| ( ( or @ ( and @ ( not @ B ) @ ( not @ C ) ) @ A )
!= ( or @ D @ E ) ) ),
inference(paramod_ordered,[status(thm)],[220,187]) ).
thf(270,plain,
! [C: $i,B: $i,A: $i] :
( ( not @ ( and @ ( or @ B @ C ) @ ( not @ A ) ) )
= ( not @ ( and @ ( not @ ( and @ ( not @ B ) @ ( not @ C ) ) ) @ ( not @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[269:[bind(A,$thf( A )),bind(B,$thf( H )),bind(C,$thf( I )),bind(D,$thf( and @ ( not @ H ) @ ( not @ I ) )),bind(E,$thf( A ))]]) ).
thf(290,plain,
! [C: $i,B: $i,A: $i] :
( ( not @ ( and @ ( or @ B @ C ) @ ( not @ A ) ) )
= ( not @ ( and @ ( not @ ( and @ ( not @ B ) @ ( not @ C ) ) ) @ ( not @ A ) ) ) ),
inference(simp,[status(thm)],[270]) ).
thf(1074,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not @ ( and @ ( not @ ( and @ ( not @ B ) @ ( not @ C ) ) ) @ ( not @ A ) ) )
= ( or @ ( and @ ( not @ E ) @ ( not @ F ) ) @ D ) )
| ( ( not @ ( and @ ( or @ B @ C ) @ ( not @ A ) ) )
!= ( not @ ( and @ ( or @ E @ F ) @ ( not @ D ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[290,220]) ).
thf(1075,plain,
! [C: $i,B: $i,A: $i] :
( ( not @ ( and @ ( not @ ( and @ ( not @ B ) @ ( not @ C ) ) ) @ ( not @ A ) ) )
= ( or @ ( and @ ( not @ B ) @ ( not @ C ) ) @ A ) ),
inference(pattern_uni,[status(thm)],[1074:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( A )),bind(E,$thf( B )),bind(F,$thf( C ))]]) ).
thf(1,conjecture,
equivalence_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_equivalence_2) ).
thf(2,negated_conjecture,
~ equivalence_2,
inference(neg_conjecture,[status(cth)],[1]) ).
thf(44,plain,
~ equivalence_2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(542,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( not @ ( and @ ( or @ A @ B ) @ ( not @ E ) ) )
= ( or @ ( and @ ( not @ C ) @ ( not @ D ) ) @ E ) )
| ( ( not @ ( and @ ( not @ A ) @ ( not @ B ) ) )
!= ( not @ ( and @ ( not @ C ) @ ( not @ D ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[187,272]) ).
thf(543,plain,
! [C: $i,B: $i,A: $i] :
( ( not @ ( and @ ( or @ A @ B ) @ ( not @ C ) ) )
= ( or @ ( and @ ( not @ A ) @ ( not @ B ) ) @ C ) ),
inference(pattern_uni,[status(thm)],[542:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(577,plain,
! [C: $i,B: $i,A: $i] :
( ( not @ ( and @ ( or @ A @ B ) @ ( not @ C ) ) )
= ( or @ ( and @ ( not @ A ) @ ( not @ B ) ) @ C ) ),
inference(simp,[status(thm)],[543]) ).
thf(98,plain,
( ~ ( is_a_theorem @ ( implies @ ( or @ sk22 @ sk22 ) @ sk22 ) )
| r1 ),
inference(cnf,[status(esa)],[97]) ).
thf(4032,plain,
( ~ ( is_a_theorem @ ( not @ ( and @ ( or @ sk22 @ sk22 ) @ ( not @ sk22 ) ) ) )
| r1 ),
inference(rewrite,[status(thm)],[98,2668]) ).
thf(41,axiom,
( r4
<=> ! [A: $i,B: $i,C: $i] : ( is_a_theorem @ ( implies @ ( or @ A @ ( or @ B @ C ) ) @ ( or @ B @ ( or @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r4) ).
thf(144,plain,
( ( r4
=> ! [A: $i,B: $i,C: $i] : ( is_a_theorem @ ( implies @ ( or @ A @ ( or @ B @ C ) ) @ ( or @ B @ ( or @ A @ C ) ) ) ) )
& ( ! [A: $i,B: $i,C: $i] : ( is_a_theorem @ ( implies @ ( or @ A @ ( or @ B @ C ) ) @ ( or @ B @ ( or @ A @ C ) ) ) )
=> r4 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(7,axiom,
substitution_of_equivalents,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',use_substitution_of_equivalents) ).
thf(49,plain,
substitution_of_equivalents,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(20,axiom,
( or_3
<=> ! [A: $i,B: $i,C: $i] : ( is_a_theorem @ ( implies @ ( implies @ A @ C ) @ ( implies @ ( implies @ B @ C ) @ ( implies @ ( or @ A @ B ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',or_3) ).
thf(76,plain,
( ( or_3
=> ! [A: $i,B: $i,C: $i] : ( is_a_theorem @ ( implies @ ( implies @ A @ C ) @ ( implies @ ( implies @ B @ C ) @ ( implies @ ( or @ A @ B ) @ C ) ) ) ) )
& ( ! [A: $i,B: $i,C: $i] : ( is_a_theorem @ ( implies @ ( implies @ A @ C ) @ ( implies @ ( implies @ B @ C ) @ ( implies @ ( or @ A @ B ) @ C ) ) ) )
=> or_3 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(103,plain,
! [B: $i,A: $i] :
( ~ substitution_of_equivalents
| ~ ( is_a_theorem @ ( equiv @ A @ B ) )
| ( A = B ) ),
inference(cnf,[status(esa)],[100]) ).
thf(105,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ substitution_of_equivalents
| ~ ( is_a_theorem @ ( equiv @ A @ B ) ) ),
inference(lifteq,[status(thm)],[103]) ).
thf(169,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ $true
| ~ ( is_a_theorem @ ( equiv @ A @ B ) ) ),
inference(rewrite,[status(thm)],[105,49]) ).
thf(170,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( is_a_theorem @ ( equiv @ A @ B ) ) ),
inference(simp,[status(thm)],[169]) ).
thf(113,plain,
! [B: $i,A: $i] :
( ~ modus_ponens
| ~ ( is_a_theorem @ A )
| ~ ( is_a_theorem @ ( implies @ A @ B ) )
| ( is_a_theorem @ B ) ),
inference(cnf,[status(esa)],[109]) ).
thf(154,plain,
! [B: $i,A: $i] :
( ~ modus_ponens
| ~ ( is_a_theorem @ A )
| ( is_a_theorem @ B )
| ( ( is_a_theorem @ ( implies @ A @ B ) )
!= ( is_a_theorem @ A ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[113]) ).
thf(155,plain,
! [B: $i,A: $i] :
( ( is_a_theorem @ B )
| ~ modus_ponens
| ~ ( is_a_theorem @ A )
| ( ( is_a_theorem @ ( implies @ A @ B ) )
!= ( is_a_theorem @ A ) ) ),
inference(simp,[status(thm)],[154]) ).
thf(163,plain,
! [B: $i,A: $i] :
( ( is_a_theorem @ B )
| ~ $true
| ~ ( is_a_theorem @ A )
| ( ( is_a_theorem @ ( implies @ A @ B ) )
!= ( is_a_theorem @ A ) ) ),
inference(rewrite,[status(thm)],[155,52]) ).
thf(164,plain,
! [B: $i,A: $i] :
( ( is_a_theorem @ B )
| ~ ( is_a_theorem @ A )
| ( ( is_a_theorem @ ( implies @ A @ B ) )
!= ( is_a_theorem @ A ) ) ),
inference(simp,[status(thm)],[163]) ).
thf(175,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( is_a_theorem @ ( equiv @ A @ B ) )
| ( is_a_theorem @ D )
| ~ ( is_a_theorem @ C )
| ( ( is_a_theorem @ B )
!= ( is_a_theorem @ C ) )
| ( A
!= ( implies @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[170,164]) ).
thf(176,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( is_a_theorem @ ( equiv @ ( implies @ B @ C ) @ A ) )
| ( is_a_theorem @ C )
| ~ ( is_a_theorem @ B )
| ( ( is_a_theorem @ A )
!= ( is_a_theorem @ B ) ) ),
inference(pattern_uni,[status(thm)],[175:[bind(A,$thf( implies @ E @ F )),bind(B,$thf( B )),bind(C,$thf( E )),bind(D,$thf( F ))]]) ).
thf(179,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( is_a_theorem @ ( equiv @ ( implies @ B @ C ) @ A ) )
| ( is_a_theorem @ C )
| ~ ( is_a_theorem @ B )
| ( ( is_a_theorem @ A )
!= ( is_a_theorem @ B ) ) ),
inference(simp,[status(thm)],[176]) ).
thf(819,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( is_a_theorem @ ( equiv @ A @ B ) )
| ~ ( is_a_theorem @ B )
| ( is_a_theorem @ E )
| ~ ( is_a_theorem @ D )
| ( ( is_a_theorem @ C )
!= ( is_a_theorem @ D ) )
| ( A
!= ( equiv @ ( implies @ D @ E ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[170,179]) ).
thf(820,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( is_a_theorem @ ( equiv @ ( equiv @ ( implies @ C @ D ) @ B ) @ A ) )
| ~ ( is_a_theorem @ A )
| ( is_a_theorem @ D )
| ~ ( is_a_theorem @ C )
| ( ( is_a_theorem @ B )
!= ( is_a_theorem @ C ) ) ),
inference(pattern_uni,[status(thm)],[819:[bind(A,$thf( equiv @ ( implies @ H @ I ) @ G )),bind(B,$thf( B )),bind(C,$thf( G )),bind(D,$thf( H )),bind(E,$thf( I ))]]) ).
thf(834,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( is_a_theorem @ ( equiv @ ( equiv @ ( implies @ C @ D ) @ B ) @ A ) )
| ~ ( is_a_theorem @ A )
| ( is_a_theorem @ D )
| ~ ( is_a_theorem @ C )
| ( ( is_a_theorem @ B )
!= ( is_a_theorem @ C ) ) ),
inference(simp,[status(thm)],[820]) ).
thf(845,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( is_a_theorem @ ( equiv @ A @ B ) )
| ~ ( is_a_theorem @ B )
| ~ ( is_a_theorem @ C )
| ( is_a_theorem @ F )
| ~ ( is_a_theorem @ E )
| ( ( is_a_theorem @ D )
!= ( is_a_theorem @ E ) )
| ( A
!= ( equiv @ ( equiv @ ( implies @ E @ F ) @ D ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[170,834]) ).
thf(846,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( is_a_theorem @ ( equiv @ ( equiv @ ( equiv @ ( implies @ D @ E ) @ C ) @ B ) @ A ) )
| ~ ( is_a_theorem @ A )
| ~ ( is_a_theorem @ B )
| ( is_a_theorem @ E )
| ~ ( is_a_theorem @ D )
| ( ( is_a_theorem @ C )
!= ( is_a_theorem @ D ) ) ),
inference(pattern_uni,[status(thm)],[845:[bind(A,$thf( equiv @ ( equiv @ ( implies @ K @ L ) @ J ) @ H )),bind(B,$thf( B )),bind(C,$thf( H )),bind(D,$thf( J )),bind(E,$thf( K )),bind(F,$thf( L ))]]) ).
thf(872,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( is_a_theorem @ ( equiv @ ( equiv @ ( equiv @ ( implies @ D @ E ) @ C ) @ B ) @ A ) )
| ~ ( is_a_theorem @ A )
| ~ ( is_a_theorem @ B )
| ( is_a_theorem @ E )
| ~ ( is_a_theorem @ D )
| ( ( is_a_theorem @ C )
!= ( is_a_theorem @ D ) ) ),
inference(simp,[status(thm)],[846]) ).
thf(1963,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( is_a_theorem @ ( equiv @ A @ B ) )
| ~ ( is_a_theorem @ ( equiv @ ( equiv @ B @ D ) @ C ) )
| ~ ( is_a_theorem @ C )
| ~ ( is_a_theorem @ D )
| ( is_a_theorem @ G )
| ~ ( is_a_theorem @ F )
| ( ( is_a_theorem @ E )
!= ( is_a_theorem @ F ) )
| ( A
!= ( equiv @ ( implies @ F @ G ) @ E ) ) ),
inference(paramod_ordered,[status(thm)],[170,872]) ).
thf(1964,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( is_a_theorem @ ( equiv @ ( equiv @ ( implies @ E @ F ) @ D ) @ A ) )
| ~ ( is_a_theorem @ ( equiv @ ( equiv @ A @ C ) @ B ) )
| ~ ( is_a_theorem @ B )
| ~ ( is_a_theorem @ C )
| ( is_a_theorem @ F )
| ~ ( is_a_theorem @ E )
| ( ( is_a_theorem @ D )
!= ( is_a_theorem @ E ) ) ),
inference(pattern_uni,[status(thm)],[1963:[bind(A,$thf( equiv @ ( implies @ J @ K ) @ I )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( I )),bind(F,$thf( J )),bind(G,$thf( K ))]]) ).
thf(2002,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( is_a_theorem @ ( equiv @ ( equiv @ ( implies @ E @ F ) @ D ) @ A ) )
| ~ ( is_a_theorem @ ( equiv @ ( equiv @ A @ C ) @ B ) )
| ~ ( is_a_theorem @ B )
| ~ ( is_a_theorem @ C )
| ( is_a_theorem @ F )
| ~ ( is_a_theorem @ E )
| ( ( is_a_theorem @ D )
!= ( is_a_theorem @ E ) ) ),
inference(simp,[status(thm)],[1964]) ).
thf(2015,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( is_a_theorem @ ( equiv @ A @ B ) )
| ~ ( is_a_theorem @ B )
| ~ ( is_a_theorem @ ( equiv @ ( equiv @ C @ E ) @ D ) )
| ~ ( is_a_theorem @ D )
| ~ ( is_a_theorem @ E )
| ( is_a_theorem @ H )
| ~ ( is_a_theorem @ G )
| ( ( is_a_theorem @ F )
!= ( is_a_theorem @ G ) )
| ( A
!= ( equiv @ ( equiv @ ( implies @ G @ H ) @ F ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[170,2002]) ).
thf(2016,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( is_a_theorem @ ( equiv @ ( equiv @ ( equiv @ ( implies @ F @ G ) @ E ) @ D ) @ A ) )
| ~ ( is_a_theorem @ A )
| ~ ( is_a_theorem @ ( equiv @ ( equiv @ D @ C ) @ B ) )
| ~ ( is_a_theorem @ B )
| ~ ( is_a_theorem @ C )
| ( is_a_theorem @ G )
| ~ ( is_a_theorem @ F )
| ( ( is_a_theorem @ E )
!= ( is_a_theorem @ F ) ) ),
inference(pattern_uni,[status(thm)],[2015:[bind(A,$thf( equiv @ ( equiv @ ( implies @ M @ N ) @ L ) @ J )),bind(B,$thf( B )),bind(C,$thf( J )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( L )),bind(G,$thf( M )),bind(H,$thf( N ))]]) ).
thf(2072,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( is_a_theorem @ ( equiv @ ( equiv @ ( equiv @ ( implies @ F @ G ) @ E ) @ D ) @ A ) )
| ~ ( is_a_theorem @ A )
| ~ ( is_a_theorem @ ( equiv @ ( equiv @ D @ C ) @ B ) )
| ~ ( is_a_theorem @ B )
| ~ ( is_a_theorem @ C )
| ( is_a_theorem @ G )
| ~ ( is_a_theorem @ F )
| ( ( is_a_theorem @ E )
!= ( is_a_theorem @ F ) ) ),
inference(simp,[status(thm)],[2016]) ).
thf(3268,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( is_a_theorem @ ( equiv @ ( equiv @ ( equiv @ ( not @ ( and @ F @ ( not @ G ) ) ) @ E ) @ D ) @ A ) )
| ~ ( is_a_theorem @ A )
| ~ ( is_a_theorem @ ( equiv @ ( equiv @ D @ C ) @ B ) )
| ~ ( is_a_theorem @ B )
| ~ ( is_a_theorem @ C )
| ( is_a_theorem @ G )
| ~ ( is_a_theorem @ F )
| ( ( is_a_theorem @ E )
!= ( is_a_theorem @ F ) ) ),
inference(rewrite,[status(thm)],[2072,2668]) ).
thf(3330,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ op_and
| ~ ( is_a_theorem @ ( equiv @ ( equiv @ ( equiv @ ( not @ ( not @ ( or @ ( not @ A ) @ ( not @ B ) ) ) ) @ G ) @ F ) @ C ) )
| ~ ( is_a_theorem @ C )
| ~ ( is_a_theorem @ ( equiv @ ( equiv @ F @ E ) @ D ) )
| ~ ( is_a_theorem @ D )
| ~ ( is_a_theorem @ E )
| ( is_a_theorem @ I )
| ~ ( is_a_theorem @ H )
| ( ( is_a_theorem @ G )
!= ( is_a_theorem @ H ) )
| ( ( and @ A @ B )
!= ( and @ H @ ( not @ I ) ) ) ),
inference(paramod_ordered,[status(thm)],[60,3268]) ).
thf(3331,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ op_and
| ~ ( is_a_theorem @ ( equiv @ ( equiv @ ( equiv @ ( not @ ( not @ ( or @ ( not @ A ) @ ( not @ ( not @ G ) ) ) ) ) @ F ) @ E ) @ B ) )
| ~ ( is_a_theorem @ B )
| ~ ( is_a_theorem @ ( equiv @ ( equiv @ E @ D ) @ C ) )
| ~ ( is_a_theorem @ C )
| ~ ( is_a_theorem @ D )
| ( is_a_theorem @ G )
| ~ ( is_a_theorem @ A )
| ( ( is_a_theorem @ F )
!= ( is_a_theorem @ A ) ) ),
inference(pattern_uni,[status(thm)],[3330:[bind(A,$thf( A )),bind(B,$thf( not @ J )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( F )),bind(G,$thf( G )),bind(H,$thf( A )),bind(I,$thf( J ))]]) ).
thf(3401,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ op_and
| ~ ( is_a_theorem @ ( equiv @ ( equiv @ ( equiv @ ( not @ ( not @ ( or @ ( not @ A ) @ ( not @ ( not @ G ) ) ) ) ) @ F ) @ E ) @ B ) )
| ~ ( is_a_theorem @ B )
| ~ ( is_a_theorem @ ( equiv @ ( equiv @ E @ D ) @ C ) )
| ~ ( is_a_theorem @ C )
| ~ ( is_a_theorem @ D )
| ( is_a_theorem @ G )
| ~ ( is_a_theorem @ A )
| ( ( is_a_theorem @ F )
!= ( is_a_theorem @ A ) ) ),
inference(simp,[status(thm)],[3331]) ).
thf(3483,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( is_a_theorem @ ( equiv @ A @ B ) )
| ~ op_and
| ~ ( is_a_theorem @ ( equiv @ ( equiv @ ( equiv @ ( not @ B ) @ H ) @ G ) @ D ) )
| ~ ( is_a_theorem @ D )
| ~ ( is_a_theorem @ ( equiv @ ( equiv @ G @ F ) @ E ) )
| ~ ( is_a_theorem @ E )
| ~ ( is_a_theorem @ F )
| ( is_a_theorem @ I )
| ~ ( is_a_theorem @ C )
| ( ( is_a_theorem @ H )
!= ( is_a_theorem @ C ) )
| ( A
!= ( not @ ( or @ ( not @ C ) @ ( not @ ( not @ I ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[170,3401]) ).
thf(3484,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( is_a_theorem @ ( equiv @ ( not @ ( or @ ( not @ G ) @ ( not @ ( not @ H ) ) ) ) @ A ) )
| ~ op_and
| ~ ( is_a_theorem @ ( equiv @ ( equiv @ ( equiv @ ( not @ A ) @ F ) @ E ) @ B ) )
| ~ ( is_a_theorem @ B )
| ~ ( is_a_theorem @ ( equiv @ ( equiv @ E @ D ) @ C ) )
| ~ ( is_a_theorem @ C )
| ~ ( is_a_theorem @ D )
| ( is_a_theorem @ H )
| ~ ( is_a_theorem @ G )
| ( ( is_a_theorem @ F )
!= ( is_a_theorem @ G ) ) ),
inference(pattern_uni,[status(thm)],[3483:[bind(A,$thf( not @ ( or @ ( not @ M ) @ ( not @ ( not @ O ) ) ) )),bind(B,$thf( B )),bind(C,$thf( M )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( F )),bind(G,$thf( G )),bind(H,$thf( H )),bind(I,$thf( O ))]]) ).
thf(3902,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( is_a_theorem @ ( equiv @ ( not @ ( or @ ( not @ G ) @ ( not @ ( not @ H ) ) ) ) @ A ) )
| ~ op_and
| ~ ( is_a_theorem @ ( equiv @ ( equiv @ ( equiv @ ( not @ A ) @ F ) @ E ) @ B ) )
| ~ ( is_a_theorem @ B )
| ~ ( is_a_theorem @ ( equiv @ ( equiv @ E @ D ) @ C ) )
| ~ ( is_a_theorem @ C )
| ~ ( is_a_theorem @ D )
| ( is_a_theorem @ H )
| ~ ( is_a_theorem @ G )
| ( ( is_a_theorem @ F )
!= ( is_a_theorem @ G ) ) ),
inference(simp,[status(thm)],[3484]) ).
thf(4635,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( is_a_theorem @ ( and @ ( not @ ( and @ ( not @ ( or @ ( not @ G ) @ ( not @ ( not @ H ) ) ) ) @ ( not @ A ) ) ) @ ( not @ ( and @ A @ ( not @ ( not @ ( or @ ( not @ G ) @ ( not @ ( not @ H ) ) ) ) ) ) ) ) )
| ~ op_and
| ~ ( is_a_theorem @ ( and @ ( not @ ( and @ ( equiv @ ( equiv @ ( not @ A ) @ F ) @ E ) @ ( not @ B ) ) ) @ ( not @ ( and @ B @ ( not @ ( equiv @ ( equiv @ ( not @ A ) @ F ) @ E ) ) ) ) ) )
| ~ ( is_a_theorem @ B )
| ~ ( is_a_theorem @ ( and @ ( not @ ( and @ ( equiv @ E @ D ) @ ( not @ C ) ) ) @ ( not @ ( and @ C @ ( not @ ( equiv @ E @ D ) ) ) ) ) )
| ~ ( is_a_theorem @ C )
| ~ ( is_a_theorem @ D )
| ( is_a_theorem @ H )
| ~ ( is_a_theorem @ G )
| ( ( is_a_theorem @ F )
!= ( is_a_theorem @ G ) ) ),
inference(rewrite,[status(thm)],[3902,4143]) ).
thf(25,axiom,
( and_1
<=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ ( and @ A @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_1) ).
thf(91,plain,
( ( and_1
=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ ( and @ A @ B ) @ A ) ) )
& ( ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ ( and @ A @ B ) @ A ) )
=> and_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(17,axiom,
( and_2
<=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ ( and @ A @ B ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_2) ).
thf(67,plain,
( ( and_2
=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ ( and @ A @ B ) @ B ) ) )
& ( ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ ( and @ A @ B ) @ B ) )
=> and_2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(69,plain,
! [B: $i,A: $i] :
( ~ and_2
| ( is_a_theorem @ ( implies @ ( and @ A @ B ) @ B ) ) ),
inference(cnf,[status(esa)],[67]) ).
thf(9001,plain,
! [B: $i,A: $i] :
( ~ and_2
| ( is_a_theorem @ ( not @ ( and @ ( and @ A @ B ) @ ( not @ B ) ) ) ) ),
inference(rewrite,[status(thm)],[69,2668]) ).
thf(4783,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( is_a_theorem @ ( and @ ( not @ ( and @ ( not @ ( or @ ( not @ I ) @ ( not @ ( not @ J ) ) ) ) @ ( not @ C ) ) ) @ ( not @ ( and @ C @ ( not @ ( not @ ( or @ ( not @ I ) @ ( or @ A @ B ) ) ) ) ) ) ) )
| ~ op_and
| ~ ( is_a_theorem @ ( and @ ( not @ ( and @ ( equiv @ ( equiv @ ( not @ C ) @ H ) @ G ) @ ( not @ D ) ) ) @ ( not @ ( and @ D @ ( not @ ( equiv @ ( equiv @ ( not @ C ) @ H ) @ G ) ) ) ) ) )
| ~ ( is_a_theorem @ D )
| ~ ( is_a_theorem @ ( and @ ( not @ ( and @ ( equiv @ G @ F ) @ ( not @ E ) ) ) @ ( not @ ( and @ E @ ( not @ ( equiv @ G @ F ) ) ) ) ) )
| ~ ( is_a_theorem @ E )
| ~ ( is_a_theorem @ F )
| ( is_a_theorem @ J )
| ~ ( is_a_theorem @ I )
| ( ( is_a_theorem @ H )
!= ( is_a_theorem @ I ) )
| ( ( not @ ( and @ ( not @ A ) @ ( not @ B ) ) )
!= ( not @ ( not @ J ) ) ) ),
inference(paramod_ordered,[status(thm)],[187,4635]) ).
thf(5260,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( is_a_theorem @ J )
| ~ ( is_a_theorem @ ( and @ ( not @ ( and @ ( not @ ( or @ ( not @ I ) @ ( not @ ( not @ J ) ) ) ) @ ( not @ C ) ) ) @ ( not @ ( and @ C @ ( not @ ( not @ ( or @ ( not @ I ) @ ( or @ A @ B ) ) ) ) ) ) ) )
| ~ op_and
| ~ ( is_a_theorem @ ( and @ ( not @ ( and @ ( equiv @ ( equiv @ ( not @ C ) @ H ) @ G ) @ ( not @ D ) ) ) @ ( not @ ( and @ D @ ( not @ ( equiv @ ( equiv @ ( not @ C ) @ H ) @ G ) ) ) ) ) )
| ~ ( is_a_theorem @ D )
| ~ ( is_a_theorem @ ( and @ ( not @ ( and @ ( equiv @ G @ F ) @ ( not @ E ) ) ) @ ( not @ ( and @ E @ ( not @ ( equiv @ G @ F ) ) ) ) ) )
| ~ ( is_a_theorem @ E )
| ~ ( is_a_theorem @ F )
| ~ ( is_a_theorem @ I )
| ( ( is_a_theorem @ H )
!= ( is_a_theorem @ I ) )
| ( ( and @ ( not @ A ) @ ( not @ B ) )
!= ( not @ J ) ) ),
inference(simp,[status(thm)],[4783]) ).
thf(6249,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( is_a_theorem @ J )
| ~ ( is_a_theorem @ ( and @ ( not @ ( and @ ( not @ ( or @ ( not @ I ) @ ( not @ ( not @ J ) ) ) ) @ ( not @ C ) ) ) @ ( not @ ( and @ C @ ( not @ ( not @ ( or @ ( not @ I ) @ ( or @ A @ B ) ) ) ) ) ) ) )
| ~ op_and
| ~ ( is_a_theorem @ ( and @ ( not @ ( and @ ( and @ ( not @ ( and @ ( equiv @ ( not @ C ) @ H ) @ ( not @ G ) ) ) @ ( not @ ( and @ G @ ( not @ ( equiv @ ( not @ C ) @ H ) ) ) ) ) @ ( not @ D ) ) ) @ ( not @ ( and @ D @ ( not @ ( and @ ( not @ ( and @ ( equiv @ ( not @ C ) @ H ) @ ( not @ G ) ) ) @ ( not @ ( and @ G @ ( not @ ( equiv @ ( not @ C ) @ H ) ) ) ) ) ) ) ) ) )
| ~ ( is_a_theorem @ D )
| ~ ( is_a_theorem @ ( and @ ( not @ ( and @ ( and @ ( not @ ( and @ G @ ( not @ F ) ) ) @ ( not @ ( and @ F @ ( not @ G ) ) ) ) @ ( not @ E ) ) ) @ ( not @ ( and @ E @ ( not @ ( and @ ( not @ ( and @ G @ ( not @ F ) ) ) @ ( not @ ( and @ F @ ( not @ G ) ) ) ) ) ) ) ) )
| ~ ( is_a_theorem @ E )
| ~ ( is_a_theorem @ F )
| ~ ( is_a_theorem @ I )
| ( ( is_a_theorem @ H )
!= ( is_a_theorem @ I ) )
| ( ( and @ ( not @ A ) @ ( not @ B ) )
!= ( not @ J ) ) ),
inference(rewrite,[status(thm)],[5260,4143]) ).
thf(9056,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ and_2
| ( is_a_theorem @ L )
| ~ op_and
| ~ ( is_a_theorem @ ( and @ ( not @ ( and @ ( and @ ( not @ ( and @ ( equiv @ ( not @ E ) @ J ) @ ( not @ I ) ) ) @ ( not @ ( and @ I @ ( not @ ( equiv @ ( not @ E ) @ J ) ) ) ) ) @ ( not @ F ) ) ) @ ( not @ ( and @ F @ ( not @ ( and @ ( not @ ( and @ ( equiv @ ( not @ E ) @ J ) @ ( not @ I ) ) ) @ ( not @ ( and @ I @ ( not @ ( equiv @ ( not @ E ) @ J ) ) ) ) ) ) ) ) ) )
| ~ ( is_a_theorem @ F )
| ~ ( is_a_theorem @ ( and @ ( not @ ( and @ ( and @ ( not @ ( and @ I @ ( not @ H ) ) ) @ ( not @ ( and @ H @ ( not @ I ) ) ) ) @ ( not @ G ) ) ) @ ( not @ ( and @ G @ ( not @ ( and @ ( not @ ( and @ I @ ( not @ H ) ) ) @ ( not @ ( and @ H @ ( not @ I ) ) ) ) ) ) ) ) )
| ~ ( is_a_theorem @ G )
| ~ ( is_a_theorem @ H )
| ~ ( is_a_theorem @ K )
| ( ( is_a_theorem @ J )
!= ( is_a_theorem @ K ) )
| ( ( and @ ( not @ C ) @ ( not @ D ) )
!= ( not @ L ) )
| ( ( is_a_theorem @ ( not @ ( and @ ( and @ A @ B ) @ ( not @ B ) ) ) )
!= ( is_a_theorem @ ( and @ ( not @ ( and @ ( not @ ( or @ ( not @ K ) @ ( not @ ( not @ L ) ) ) ) @ ( not @ E ) ) ) @ ( not @ ( and @ E @ ( not @ ( not @ ( or @ ( not @ K ) @ ( or @ C @ D ) ) ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[9001,6249]) ).
thf(9084,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( is_a_theorem @ L )
| ~ and_2
| ~ op_and
| ~ ( is_a_theorem @ ( and @ ( not @ ( and @ ( and @ ( not @ ( and @ ( equiv @ ( not @ E ) @ J ) @ ( not @ I ) ) ) @ ( not @ ( and @ I @ ( not @ ( equiv @ ( not @ E ) @ J ) ) ) ) ) @ ( not @ F ) ) ) @ ( not @ ( and @ F @ ( not @ ( and @ ( not @ ( and @ ( equiv @ ( not @ E ) @ J ) @ ( not @ I ) ) ) @ ( not @ ( and @ I @ ( not @ ( equiv @ ( not @ E ) @ J ) ) ) ) ) ) ) ) ) )
| ~ ( is_a_theorem @ F )
| ~ ( is_a_theorem @ ( and @ ( not @ ( and @ ( and @ ( not @ ( and @ I @ ( not @ H ) ) ) @ ( not @ ( and @ H @ ( not @ I ) ) ) ) @ ( not @ G ) ) ) @ ( not @ ( and @ G @ ( not @ ( and @ ( not @ ( and @ I @ ( not @ H ) ) ) @ ( not @ ( and @ H @ ( not @ I ) ) ) ) ) ) ) ) )
| ~ ( is_a_theorem @ G )
| ~ ( is_a_theorem @ H )
| ~ ( is_a_theorem @ K )
| ( ( is_a_theorem @ J )
!= ( is_a_theorem @ K ) )
| ( ( and @ ( not @ C ) @ ( not @ D ) )
!= ( not @ L ) )
| ( ( not @ ( and @ ( and @ A @ B ) @ ( not @ B ) ) )
!= ( and @ ( not @ ( and @ ( not @ ( or @ ( not @ K ) @ ( not @ ( not @ L ) ) ) ) @ ( not @ E ) ) ) @ ( not @ ( and @ E @ ( not @ ( not @ ( or @ ( not @ K ) @ ( or @ C @ D ) ) ) ) ) ) ) ) ),
inference(simp,[status(thm)],[9056]) ).
thf(10412,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( is_a_theorem @ L )
| ~ and_2
| ~ op_and
| ~ ( is_a_theorem @ ( and @ ( not @ ( and @ ( and @ ( not @ ( and @ ( and @ ( not @ ( and @ ( not @ E ) @ ( not @ J ) ) ) @ ( not @ ( and @ J @ ( not @ ( not @ E ) ) ) ) ) @ ( not @ I ) ) ) @ ( not @ ( and @ I @ ( not @ ( and @ ( not @ ( and @ ( not @ E ) @ ( not @ J ) ) ) @ ( not @ ( and @ J @ ( not @ ( not @ E ) ) ) ) ) ) ) ) ) @ ( not @ F ) ) ) @ ( not @ ( and @ F @ ( not @ ( and @ ( not @ ( and @ ( and @ ( not @ ( and @ ( not @ E ) @ ( not @ J ) ) ) @ ( not @ ( and @ J @ ( not @ ( not @ E ) ) ) ) ) @ ( not @ I ) ) ) @ ( not @ ( and @ I @ ( not @ ( and @ ( not @ ( and @ ( not @ E ) @ ( not @ J ) ) ) @ ( not @ ( and @ J @ ( not @ ( not @ E ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( is_a_theorem @ F )
| ~ ( is_a_theorem @ ( and @ ( not @ ( and @ ( and @ ( not @ ( and @ I @ ( not @ H ) ) ) @ ( not @ ( and @ H @ ( not @ I ) ) ) ) @ ( not @ G ) ) ) @ ( not @ ( and @ G @ ( not @ ( and @ ( not @ ( and @ I @ ( not @ H ) ) ) @ ( not @ ( and @ H @ ( not @ I ) ) ) ) ) ) ) ) )
| ~ ( is_a_theorem @ G )
| ~ ( is_a_theorem @ H )
| ~ ( is_a_theorem @ K )
| ( ( is_a_theorem @ J )
!= ( is_a_theorem @ K ) )
| ( ( and @ ( not @ C ) @ ( not @ D ) )
!= ( not @ L ) )
| ( ( not @ ( and @ ( and @ A @ B ) @ ( not @ B ) ) )
!= ( and @ ( not @ ( and @ ( not @ ( or @ ( not @ K ) @ ( not @ ( not @ L ) ) ) ) @ ( not @ E ) ) ) @ ( not @ ( and @ E @ ( not @ ( not @ ( or @ ( not @ K ) @ ( or @ C @ D ) ) ) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[9084,4143]) ).
thf(43,axiom,
( equivalence_2
<=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ ( equiv @ A @ B ) @ ( implies @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equivalence_2) ).
thf(150,plain,
( ( equivalence_2
=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ ( equiv @ A @ B ) @ ( implies @ B @ A ) ) ) )
& ( ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ ( equiv @ A @ B ) @ ( implies @ B @ A ) ) )
=> equivalence_2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(8,axiom,
cn3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',luka_cn3) ).
thf(50,plain,
cn3,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(92,plain,
( ~ ( is_a_theorem @ ( implies @ ( and @ sk18 @ sk19 ) @ sk18 ) )
| and_1 ),
inference(cnf,[status(esa)],[91]) ).
thf(3940,plain,
( ~ ( is_a_theorem @ ( not @ ( and @ ( and @ sk18 @ sk19 ) @ ( not @ sk18 ) ) ) )
| and_1 ),
inference(rewrite,[status(thm)],[92,2668]) ).
thf(35,axiom,
( implies_1
<=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ A @ ( implies @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',implies_1) ).
thf(126,plain,
( ( implies_1
=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ A @ ( implies @ B @ A ) ) ) )
& ( ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ A @ ( implies @ B @ A ) ) )
=> implies_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(127,plain,
( ~ ( is_a_theorem @ ( implies @ sk34 @ ( implies @ sk35 @ sk34 ) ) )
| implies_1 ),
inference(cnf,[status(esa)],[126]) ).
thf(8858,plain,
( ~ ( is_a_theorem @ ( not @ ( and @ sk34 @ ( not @ ( implies @ sk35 @ sk34 ) ) ) ) )
| implies_1 ),
inference(rewrite,[status(thm)],[127,2668]) ).
thf(22,axiom,
( r2
<=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ B @ ( or @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r2) ).
thf(82,plain,
( ( r2
=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ B @ ( or @ A @ B ) ) ) )
& ( ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ B @ ( or @ A @ B ) ) )
=> r2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(21,axiom,
( and_3
<=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ A @ ( implies @ B @ ( and @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_3) ).
thf(79,plain,
( ( and_3
=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ A @ ( implies @ B @ ( and @ A @ B ) ) ) ) )
& ( ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ A @ ( implies @ B @ ( and @ A @ B ) ) ) )
=> and_3 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(12206,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( is_a_theorem @ L )
| ~ and_2
| ~ op_and
| ~ ( is_a_theorem @ ( and @ ( not @ ( and @ ( and @ ( not @ ( and @ ( and @ ( not @ ( and @ ( not @ E ) @ ( not @ J ) ) ) @ ( not @ ( and @ J @ ( not @ ( not @ E ) ) ) ) ) @ ( not @ I ) ) ) @ ( not @ ( and @ I @ ( not @ ( and @ ( not @ ( and @ ( not @ E ) @ ( not @ J ) ) ) @ ( not @ ( and @ J @ ( not @ ( not @ E ) ) ) ) ) ) ) ) ) @ ( not @ F ) ) ) @ ( not @ ( and @ F @ ( not @ ( and @ ( not @ ( and @ ( and @ ( not @ ( and @ ( not @ E ) @ ( not @ J ) ) ) @ ( not @ ( and @ J @ ( not @ ( not @ E ) ) ) ) ) @ ( not @ I ) ) ) @ ( not @ ( and @ I @ ( not @ ( and @ ( not @ ( and @ ( not @ E ) @ ( not @ J ) ) ) @ ( not @ ( and @ J @ ( not @ ( not @ E ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( is_a_theorem @ F )
| ~ ( is_a_theorem @ ( and @ ( not @ ( and @ ( and @ ( not @ ( and @ I @ ( not @ H ) ) ) @ ( not @ ( and @ H @ ( not @ I ) ) ) ) @ ( not @ G ) ) ) @ ( not @ ( and @ G @ ( not @ ( and @ ( not @ ( and @ I @ ( not @ H ) ) ) @ ( not @ ( and @ H @ ( not @ I ) ) ) ) ) ) ) ) )
| ~ ( is_a_theorem @ G )
| ~ ( is_a_theorem @ H )
| ~ ( is_a_theorem @ K )
| ( ( is_a_theorem @ J )
!= ( is_a_theorem @ K ) )
| ( ( and @ ( not @ C ) @ ( not @ D ) )
!= ( not @ L ) )
| ( ( not @ ( and @ ( and @ A @ B ) @ ( not @ B ) ) )
!= ( not @ L ) )
| ( ( and @ ( not @ ( and @ ( not @ ( or @ ( not @ K ) @ ( not @ ( not @ L ) ) ) ) @ ( not @ E ) ) ) @ ( not @ ( and @ E @ ( not @ ( not @ ( or @ ( not @ K ) @ ( or @ C @ D ) ) ) ) ) ) )
!= ( and @ ( not @ C ) @ ( not @ D ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[10412]) ).
thf(12707,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( is_a_theorem @ L )
| ~ and_2
| ~ op_and
| ~ ( is_a_theorem @ ( and @ ( not @ ( and @ ( and @ ( not @ ( and @ ( and @ ( not @ ( and @ ( not @ E ) @ ( not @ J ) ) ) @ ( not @ ( and @ J @ ( not @ ( not @ E ) ) ) ) ) @ ( not @ I ) ) ) @ ( not @ ( and @ I @ ( not @ ( and @ ( not @ ( and @ ( not @ E ) @ ( not @ J ) ) ) @ ( not @ ( and @ J @ ( not @ ( not @ E ) ) ) ) ) ) ) ) ) @ ( not @ F ) ) ) @ ( not @ ( and @ F @ ( not @ ( and @ ( not @ ( and @ ( and @ ( not @ ( and @ ( not @ E ) @ ( not @ J ) ) ) @ ( not @ ( and @ J @ ( not @ ( not @ E ) ) ) ) ) @ ( not @ I ) ) ) @ ( not @ ( and @ I @ ( not @ ( and @ ( not @ ( and @ ( not @ E ) @ ( not @ J ) ) ) @ ( not @ ( and @ J @ ( not @ ( not @ E ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( is_a_theorem @ F )
| ~ ( is_a_theorem @ ( and @ ( not @ ( and @ ( and @ ( not @ ( and @ I @ ( not @ H ) ) ) @ ( not @ ( and @ H @ ( not @ I ) ) ) ) @ ( not @ G ) ) ) @ ( not @ ( and @ G @ ( not @ ( and @ ( not @ ( and @ I @ ( not @ H ) ) ) @ ( not @ ( and @ H @ ( not @ I ) ) ) ) ) ) ) ) )
| ~ ( is_a_theorem @ G )
| ~ ( is_a_theorem @ H )
| ~ ( is_a_theorem @ K )
| ( ( is_a_theorem @ J )
!= ( is_a_theorem @ K ) )
| ( ( and @ ( not @ C ) @ ( not @ D ) )
!= ( not @ L ) )
| ( ( not @ ( and @ ( and @ A @ B ) @ ( not @ B ) ) )
!= ( not @ L ) )
| ( ( not @ ( and @ ( not @ ( or @ ( not @ K ) @ ( not @ ( not @ L ) ) ) ) @ ( not @ E ) ) )
!= ( not @ C ) )
| ( ( not @ ( and @ E @ ( not @ ( not @ ( or @ ( not @ K ) @ ( or @ C @ D ) ) ) ) ) )
!= ( not @ D ) ) ),
inference(simp,[status(thm)],[12206]) ).
thf(26,axiom,
( implies_2
<=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ ( implies @ A @ ( implies @ A @ B ) ) @ ( implies @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',implies_2) ).
thf(94,plain,
( ( implies_2
=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ ( implies @ A @ ( implies @ A @ B ) ) @ ( implies @ A @ B ) ) ) )
& ( ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ ( implies @ A @ ( implies @ A @ B ) ) @ ( implies @ A @ B ) ) )
=> implies_2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(42158,plain,
$false,
inference(e,[status(thm)],[56,106,70,129,73,123,4143,114,51,47,100,138,88,120,511,52,8919,1379,46,57,147,61,221,132,428,85,381,220,60,117,97,1573,53,141,109,1075,45,64,44,577,4032,144,49,187,76,4635,91,10412,135,9001,48,6249,150,50,67,3940,8858,272,82,290,58,126,79,12707,2668,94]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : LCL473+1 : TPTP v9.2.0. Bugfixed v9.2.0.
% 0.07/0.13 % Command : run_Leo-III %s %d THM
% 0.14/0.34 % Computer : n013.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Tue Sep 30 13:22:39 EDT 2025
% 0.14/0.35 % CPUTime :
% 1.07/0.94 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.30/1.09 % [INFO] Parsing done (148ms).
% 1.52/1.10 % [INFO] Running in sequential loop mode.
% 1.96/1.31 % [INFO] eprover registered as external prover.
% 1.96/1.32 % [INFO] Scanning for conjecture ...
% 1.96/1.37 % [INFO] Found a conjecture (or negated_conjecture) and 42 axioms. Running axiom selection ...
% 2.13/1.41 % [INFO] Axiom selection finished. Selected 41 axioms (removed 1 axioms).
% 2.13/1.47 % [INFO] Problem is first-order (TPTP FOF).
% 2.47/1.47 % [INFO] Type checking passed.
% 2.47/1.47 % [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 ...
% 221.11/147.31 % External prover 'e' found a proof!
% 221.11/147.31 % [INFO] Killing All external provers ...
% 221.11/147.31 % Time passed: 146770ms (effective reasoning time: 146200ms)
% 221.11/147.31 % 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)>
% 221.11/147.31 % Axioms used in derivation (41): or_3, and_1, equivalence_2, luka_op_or, cn1, op_equiv, kn1, implies_3, op_implies_and, cn3, luka_cn3, substitution_of_equivalents, luka_cn2, kn2, cn2, hilbert_op_implies_and, equivalence_3, modus_tollens, luka_cn1, op_and, luka_modus_ponens, r5, or_1, kn3, luka_op_equiv, and_3, use_substitution_of_equivalents, r4, modus_ponens, hilbert_op_or, r1, r2, equivalence_1, or_2, implies_1, r3, and_2, op_or, op_implies_or, hilbert_op_equiv, implies_2
% 221.11/147.31 % No. of inferences in proof: 178
% 221.11/147.31 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 146770 ms resp. 146200 ms w/o parsing
% 221.31/147.37 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 221.31/147.37 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------