%------------------------------------------------------------------------------
% File : Leo-III---1.7.19
% Problem : LCL501+1 : TPTP v9.2.0. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n002.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 12:41:14 PM UTC 2025
% Result : Theorem 13.76s 3.61s
% Output : Refutation 13.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 45
% Syntax : Number of formulae : 130 ( 31 unt; 0 typ; 0 def)
% Number of atoms : 379 ( 41 equ; 0 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 1232 ( 94 ~; 92 |; 29 &; 923 @)
% ( 26 <=>; 68 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 62 ( 59 usr; 55 con; 0-2 aty)
% Number of variables : 261 ( 0 ^; 261 !; 0 ?; 261 :)
% Comments :
%------------------------------------------------------------------------------
thf(kn3_type,type,
kn3: $o ).
thf(r3_type,type,
r3: $o ).
thf(r4_type,type,
r4: $o ).
thf(r2_type,type,
r2: $o ).
thf(op_equiv_type,type,
op_equiv: $o ).
thf(r5_type,type,
r5: $o ).
thf(op_or_type,type,
op_or: $o ).
thf(r1_type,type,
r1: $o ).
thf(modus_ponens_type,type,
modus_ponens: $o ).
thf(op_implies_or_type,type,
op_implies_or: $o ).
thf(op_and_type,type,
op_and: $o ).
thf(substitution_of_equivalents_type,type,
substitution_of_equivalents: $o ).
thf(op_implies_and_type,type,
op_implies_and: $o ).
thf(equiv_type,type,
equiv: $i > $i > $i ).
thf(and_type,type,
and: $i > $i > $i ).
thf(implies_type,type,
implies: $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(not_type,type,
not: $i > $i ).
thf(kn2_type,type,
kn2: $o ).
thf(or_3_type,type,
or_3: $o ).
thf(or_type,type,
or: $i > $i > $i ).
thf(and_3_type,type,
and_3: $o ).
thf(kn1_type,type,
kn1: $o ).
thf(implies_3_type,type,
implies_3: $o ).
thf(equivalence_2_type,type,
equivalence_2: $o ).
thf(and_1_type,type,
and_1: $o ).
thf(implies_2_type,type,
implies_2: $o ).
thf(equivalence_3_type,type,
equivalence_3: $o ).
thf(cn3_type,type,
cn3: $o ).
thf(equivalence_1_type,type,
equivalence_1: $o ).
thf(implies_1_type,type,
implies_1: $o ).
thf(cn1_type,type,
cn1: $o ).
thf(cn2_type,type,
cn2: $o ).
thf(or_2_type,type,
or_2: $o ).
thf(or_1_type,type,
or_1: $o ).
thf(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: $i ).
thf(sk3_type,type,
sk3: $i ).
thf(sk4_type,type,
sk4: $i ).
thf(sk5_type,type,
sk5: $i ).
thf(sk6_type,type,
sk6: $i ).
thf(sk10_type,type,
sk10: $i ).
thf(sk11_type,type,
sk11: $i ).
thf(sk14_type,type,
sk14: $i ).
thf(sk18_type,type,
sk18: $i ).
thf(sk19_type,type,
sk19: $i ).
thf(sk20_type,type,
sk20: $i ).
thf(sk21_type,type,
sk21: $i ).
thf(sk33_type,type,
sk33: $i ).
thf(sk36_type,type,
sk36: $i ).
thf(sk37_type,type,
sk37: $i ).
thf(sk41_type,type,
sk41: $i ).
thf(sk42_type,type,
sk42: $i ).
thf(sk43_type,type,
sk43: $i ).
thf(sk44_type,type,
sk44: $i ).
thf(sk45_type,type,
sk45: $i ).
thf(sk46_type,type,
sk46: $i ).
thf(34,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)],[34]) ).
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(64,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(66,plain,
! [B: $i,A: $i] :
( ~ and_2
| ( is_a_theorem @ ( implies @ ( and @ A @ B ) @ B ) ) ),
inference(cnf,[status(esa)],[64]) ).
thf(29,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)],[29]) ).
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(31,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)],[31]) ).
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(159,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(160,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)],[159]) ).
thf(11,axiom,
modus_ponens,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_modus_ponens) ).
thf(56,plain,
modus_ponens,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(167,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)],[160,56]) ).
thf(168,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)],[167]) ).
thf(179,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ substitution_of_equivalents
| ~ ( is_a_theorem @ ( equiv @ A @ B ) )
| ( is_a_theorem @ D )
| ~ ( is_a_theorem @ C )
| ( ( is_a_theorem @ A )
!= ( is_a_theorem @ C ) )
| ( B
!= ( implies @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[105,168]) ).
thf(180,plain,
! [C: $i,B: $i,A: $i] :
( ~ substitution_of_equivalents
| ~ ( is_a_theorem @ ( equiv @ A @ ( implies @ B @ C ) ) )
| ( is_a_theorem @ C )
| ~ ( is_a_theorem @ B )
| ( ( is_a_theorem @ A )
!= ( is_a_theorem @ B ) ) ),
inference(pattern_uni,[status(thm)],[179:[bind(A,$thf( A )),bind(B,$thf( implies @ E @ F )),bind(C,$thf( E )),bind(D,$thf( F ))]]) ).
thf(183,plain,
! [C: $i,B: $i,A: $i] :
( ~ substitution_of_equivalents
| ~ ( is_a_theorem @ ( equiv @ A @ ( implies @ B @ C ) ) )
| ( is_a_theorem @ C )
| ~ ( is_a_theorem @ B )
| ( ( is_a_theorem @ A )
!= ( is_a_theorem @ B ) ) ),
inference(simp,[status(thm)],[180]) ).
thf(14,axiom,
substitution_of_equivalents,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',use_substitution_of_equivalents) ).
thf(59,plain,
substitution_of_equivalents,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(210,plain,
! [C: $i,B: $i,A: $i] :
( ~ $true
| ~ ( is_a_theorem @ ( equiv @ A @ ( implies @ B @ C ) ) )
| ( is_a_theorem @ C )
| ~ ( is_a_theorem @ B )
| ( ( is_a_theorem @ A )
!= ( is_a_theorem @ B ) ) ),
inference(rewrite,[status(thm)],[183,59]) ).
thf(211,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( is_a_theorem @ ( equiv @ A @ ( implies @ B @ C ) ) )
| ( is_a_theorem @ C )
| ~ ( is_a_theorem @ B )
| ( ( is_a_theorem @ A )
!= ( is_a_theorem @ B ) ) ),
inference(simp,[status(thm)],[210]) ).
thf(231,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ and_2
| ( is_a_theorem @ E )
| ~ ( is_a_theorem @ D )
| ( ( is_a_theorem @ C )
!= ( is_a_theorem @ D ) )
| ( ( is_a_theorem @ ( implies @ ( and @ A @ B ) @ B ) )
!= ( is_a_theorem @ ( equiv @ C @ ( implies @ D @ E ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[66,211]) ).
thf(256,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( is_a_theorem @ E )
| ~ and_2
| ~ ( is_a_theorem @ D )
| ( ( is_a_theorem @ C )
!= ( is_a_theorem @ D ) )
| ( ( implies @ ( and @ A @ B ) @ B )
!= ( equiv @ C @ ( implies @ D @ E ) ) ) ),
inference(simp,[status(thm)],[231]) ).
thf(286,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( is_a_theorem @ E )
| ~ and_2
| ~ ( is_a_theorem @ D )
| ( ( implies @ ( and @ A @ B ) @ B )
!= ( equiv @ C @ ( implies @ D @ E ) ) )
| ~ ( is_a_theorem @ C )
| ~ ( is_a_theorem @ D ) ),
inference(bool_ext,[status(thm)],[256]) ).
thf(301,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( is_a_theorem @ E )
| ~ and_2
| ~ ( is_a_theorem @ D )
| ( ( implies @ ( and @ A @ B ) @ B )
!= ( equiv @ C @ ( implies @ D @ E ) ) )
| ~ ( is_a_theorem @ C ) ),
inference(simp,[status(thm)],[286]) ).
thf(7,axiom,
op_equiv,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rosser_op_equiv) ).
thf(52,plain,
op_equiv,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
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(70,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(37,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)],[37]) ).
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(73,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(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(76,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(39,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)],[39]) ).
thf(35,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)],[35]) ).
thf(40,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(138,plain,
( op_or
=> ! [A: $i,B: $i] :
( ( or @ A @ B )
= ( not @ ( and @ ( not @ A ) @ ( not @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(25,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(88,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)],[25]) ).
thf(41,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)],[41]) ).
thf(142,plain,
( ~ ( is_a_theorem @ ( implies @ sk45 @ ( or @ sk45 @ sk46 ) ) )
| or_1 ),
inference(cnf,[status(esa)],[141]) ).
thf(45,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(153,plain,
( op_implies_and
=> ! [A: $i,B: $i] :
( ( implies @ A @ B )
= ( not @ ( and @ A @ ( not @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
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(61,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(62,plain,
! [B: $i,A: $i] :
( ~ op_equiv
| ( ( equiv @ A @ B )
= ( and @ ( implies @ A @ B ) @ ( implies @ B @ A ) ) ) ),
inference(cnf,[status(esa)],[61]) ).
thf(63,plain,
! [B: $i,A: $i] :
( ( ( and @ ( implies @ A @ B ) @ ( implies @ B @ A ) )
= ( equiv @ A @ B ) )
| ~ op_equiv ),
inference(lifteq,[status(thm)],[62]) ).
thf(6,axiom,
op_equiv,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_op_equiv) ).
thf(51,plain,
op_equiv,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(188,plain,
! [B: $i,A: $i] :
( ( ( and @ ( implies @ A @ B ) @ ( implies @ B @ A ) )
= ( equiv @ A @ B ) )
| ~ $true ),
inference(rewrite,[status(thm)],[63,51]) ).
thf(189,plain,
! [B: $i,A: $i] :
( ( and @ ( implies @ A @ B ) @ ( implies @ B @ A ) )
= ( equiv @ A @ B ) ),
inference(simp,[status(thm)],[188]) ).
thf(12,axiom,
op_implies_or,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_op_implies_or) ).
thf(57,plain,
op_implies_or,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(30,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)],[30]) ).
thf(121,plain,
( ~ ( is_a_theorem @ ( implies @ ( implies @ ( not @ sk33 ) @ sk33 ) @ sk33 ) )
| cn3 ),
inference(cnf,[status(esa)],[120]) ).
thf(43,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(147,plain,
( op_and
=> ! [A: $i,B: $i] :
( ( and @ A @ B )
= ( not @ ( or @ ( not @ A ) @ ( not @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(38,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)],[38]) ).
thf(89,plain,
( ~ ( is_a_theorem @ ( implies @ ( equiv @ sk18 @ sk19 ) @ ( implies @ sk19 @ sk18 ) ) )
| equivalence_2 ),
inference(cnf,[status(esa)],[88]) ).
thf(133,plain,
( ~ ( is_a_theorem @ ( implies @ sk41 @ ( implies @ ( not @ sk41 ) @ sk42 ) ) )
| cn2 ),
inference(cnf,[status(esa)],[132]) ).
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(85,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(15,axiom,
op_implies_and,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rosser_op_implies_and) ).
thf(60,plain,
op_implies_and,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(33,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)],[33]) ).
thf(26,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)],[26]) ).
thf(92,plain,
( ~ ( is_a_theorem @ ( implies @ ( and @ sk20 @ sk21 ) @ sk20 ) )
| and_1 ),
inference(cnf,[status(esa)],[91]) ).
thf(65,plain,
( ~ ( is_a_theorem @ ( implies @ ( and @ sk1 @ sk2 ) @ sk2 ) )
| and_2 ),
inference(cnf,[status(esa)],[64]) ).
thf(28,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)],[28]) ).
thf(46,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(156,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)],[46]) ).
thf(8,axiom,
r5,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_r5) ).
thf(53,plain,
r5,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(77,plain,
( ~ ( is_a_theorem @ ( implies @ sk10 @ ( implies @ sk11 @ ( and @ sk10 @ sk11 ) ) ) )
| and_3 ),
inference(cnf,[status(esa)],[76]) ).
thf(71,plain,
( ~ ( is_a_theorem @ ( implies @ ( and @ sk5 @ sk6 ) @ sk5 ) )
| kn2 ),
inference(cnf,[status(esa)],[70]) ).
thf(9,axiom,
op_or,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rosser_op_or) ).
thf(54,plain,
op_or,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(42,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)],[42]) ).
thf(4,axiom,
r4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_r4) ).
thf(49,plain,
r4,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(3,axiom,
r3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_r3) ).
thf(48,plain,
r3,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(44,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(150,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)],[44]) ).
thf(5,axiom,
r2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_r2) ).
thf(50,plain,
r2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
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(67,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,
( 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)],[36]) ).
thf(127,plain,
( ~ ( is_a_theorem @ ( implies @ sk36 @ ( implies @ sk37 @ sk36 ) ) )
| implies_1 ),
inference(cnf,[status(esa)],[126]) ).
thf(10,axiom,
r1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_r1) ).
thf(55,plain,
r1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(32,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)],[32]) ).
thf(13,axiom,
op_and,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_op_and) ).
thf(58,plain,
op_and,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(23,axiom,
( kn1
<=> ! [A: $i] : ( is_a_theorem @ ( implies @ A @ ( and @ A @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kn1) ).
thf(82,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(22,axiom,
( r2
<=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ B @ ( or @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r2) ).
thf(79,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(177,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ substitution_of_equivalents
| ~ ( 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)],[105,168]) ).
thf(178,plain,
! [C: $i,B: $i,A: $i] :
( ~ substitution_of_equivalents
| ~ ( is_a_theorem @ ( equiv @ ( implies @ B @ C ) @ A ) )
| ( is_a_theorem @ C )
| ~ ( is_a_theorem @ B )
| ( ( is_a_theorem @ A )
!= ( is_a_theorem @ B ) ) ),
inference(pattern_uni,[status(thm)],[177:[bind(A,$thf( implies @ E @ F )),bind(B,$thf( B )),bind(C,$thf( E )),bind(D,$thf( F ))]]) ).
thf(182,plain,
! [C: $i,B: $i,A: $i] :
( ~ substitution_of_equivalents
| ~ ( 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)],[178]) ).
thf(194,plain,
! [C: $i,B: $i,A: $i] :
( ~ $true
| ~ ( 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(rewrite,[status(thm)],[182,59]) ).
thf(195,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)],[194]) ).
thf(27,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)],[27]) ).
thf(136,plain,
( ~ ( is_a_theorem @ ( implies @ sk44 @ ( or @ sk43 @ sk44 ) ) )
| or_2 ),
inference(cnf,[status(esa)],[135]) ).
thf(1,conjecture,
kn3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rosser_kn3) ).
thf(2,negated_conjecture,
~ kn3,
inference(neg_conjecture,[status(cth)],[1]) ).
thf(47,plain,
~ kn3,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(68,plain,
( ~ ( is_a_theorem @ ( implies @ ( implies @ ( not @ sk4 ) @ ( not @ sk3 ) ) @ ( implies @ sk3 @ sk4 ) ) )
| modus_tollens ),
inference(cnf,[status(esa)],[67]) ).
thf(83,plain,
( ~ ( is_a_theorem @ ( implies @ sk14 @ ( and @ sk14 @ sk14 ) ) )
| kn1 ),
inference(cnf,[status(esa)],[82]) ).
thf(2041,plain,
$false,
inference(e,[status(thm)],[120,301,52,70,129,73,64,59,76,135,123,138,88,56,142,153,189,57,211,106,121,147,61,132,89,133,85,60,117,92,65,97,156,53,141,77,109,256,71,54,144,49,91,66,48,150,50,67,127,55,114,58,82,168,51,79,195,94,126,136,47,68,83,100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : LCL501+1 : TPTP v9.2.0. Bugfixed v9.2.0.
% 0.06/0.12 % Command : run_Leo-III %s %d THM
% 0.11/0.32 % Computer : n002.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Tue Sep 30 13:34:24 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.94/0.90 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.23/1.04 % [INFO] Parsing done (146ms).
% 1.50/1.05 % [INFO] Running in sequential loop mode.
% 1.91/1.26 % [INFO] eprover registered as external prover.
% 1.91/1.27 % [INFO] Scanning for conjecture ...
% 1.91/1.32 % [INFO] Found a conjecture (or negated_conjecture) and 44 axioms. Running axiom selection ...
% 2.14/1.36 % [INFO] Axiom selection finished. Selected 44 axioms (removed 0 axioms).
% 2.27/1.41 % [INFO] Problem is first-order (TPTP FOF).
% 2.27/1.41 % [INFO] Type checking passed.
% 2.27/1.42 % [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 ...
% 13.76/3.61 % External prover 'e' found a proof!
% 13.76/3.61 % [INFO] Killing All external provers ...
% 13.76/3.61 % Time passed: 3096ms (effective reasoning time: 2552ms)
% 13.76/3.61 % 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)>
% 13.76/3.61 % Axioms used in derivation (44): or_3, and_1, op_equiv, cn2, kn1, op_and, r5, principia_r5, r1, implies_3, principia_r4, op_implies_and, cn3, principia_r2, principia_op_and, principia_r3, equivalence_2, cn1, rosser_op_or, principia_modus_ponens, kn2, rosser_op_implies_and, equivalence_3, modus_tollens, kn3, and_3, or_1, principia_op_equiv, use_substitution_of_equivalents, r4, modus_ponens, r2, equivalence_1, or_2, implies_1, r3, and_2, substitution_of_equivalents, rosser_op_equiv, principia_r1, op_or, op_implies_or, implies_2, principia_op_implies_or
% 13.76/3.61 % No. of inferences in proof: 130
% 13.76/3.61 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 3096 ms resp. 2552 ms w/o parsing
% 13.78/3.66 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 13.78/3.66 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------