TSTP Solution File: NUM636^2 by Leo-III---1.7.10
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : NUM636^2 : TPTP v8.1.2. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n023.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 : Tue May 7 08:00:17 EDT 2024
% Result : Theorem 32.20s 7.41s
% Output : Refutation 32.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 10
% Syntax : Number of formulae : 100 ( 36 unt; 5 typ; 0 def)
% Number of atoms : 316 ( 310 equ; 80 cnn)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 1106 ( 252 ~; 199 |; 2 &; 647 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 64 ( 64 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 5 usr; 5 con; 0-2 aty)
% Number of variables : 244 ( 75 ^ 167 !; 2 ?; 244 :)
% Comments :
%------------------------------------------------------------------------------
thf(one_type,type,
one: $i ).
thf(succ_type,type,
succ: $i > $i ).
thf(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: $i > $i ).
thf(sk3_type,type,
sk3: ( $i > $o ) > $i ).
thf(1,conjecture,
! [A: $i] :
( ( succ @ A )
!= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz2) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( succ @ A )
!= A ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(6,plain,
~ ! [A: $i] :
( ( succ @ A )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(7,plain,
~ ~ ? [A: $i] :
( ( succ @ A )
= A ),
inference(miniscope,[status(thm)],[6]) ).
thf(8,plain,
( ( succ @ sk1 )
= sk1 ),
inference(cnf,[status(esa)],[7]) ).
thf(9,plain,
( ( succ @ sk1 )
= sk1 ),
inference(lifteq,[status(thm)],[8]) ).
thf(5,axiom,
! [A: $i > $o] :
( ( ( A @ one )
& ! [B: $i] :
( ( A @ B )
=> ( A @ ( succ @ B ) ) ) )
=> ! [B: $i] : ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',induction) ).
thf(18,plain,
! [A: $i > $o] :
( ( ( A @ one )
& ! [B: $i] :
( ( A @ B )
=> ( A @ ( succ @ B ) ) ) )
=> ! [B: $i] : ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(19,plain,
! [B: $i,A: $i > $o] :
( ~ ( A @ one )
| ~ ( A @ ( succ @ ( sk3 @ A ) ) )
| ( A @ B ) ),
inference(cnf,[status(esa)],[18]) ).
thf(36,plain,
! [B: $i,A: $i > $o] :
( ~ ( A @ one )
| ~ ( A @ ( succ @ ( sk3 @ A ) ) )
| ( ( A @ B )
!= ( ~ ( A @ one ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[19]) ).
thf(57,plain,
! [B: $i,A: $i > $o] :
( ~ ( A @ one )
| ~ ( A @ ( succ @ ( sk3 @ A ) ) )
| ( ( A @ B )
!= ( ~ ( A @ one ) ) ) ),
inference(simp,[status(thm)],[36]) ).
thf(88,plain,
! [B: $i,A: $i > $o] :
( ~ ( A @ one )
| ~ ( A @ sk1 )
| ( ( A @ B )
!= ( ~ ( A @ one ) ) )
| ( ( succ @ ( sk3 @ A ) )
!= ( succ @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[9,57]) ).
thf(113,plain,
! [B: $i,A: $i > $o] :
( ~ ( A @ one )
| ~ ( A @ sk1 )
| ( ( A @ B )
!= ( ~ ( A @ one ) ) )
| ( ( sk3 @ A )
!= sk1 ) ),
inference(simp,[status(thm)],[88]) ).
thf(238,plain,
! [B: $i,A: $i > $o] :
( ~ ( A @ one )
| ( ( A @ B )
!= ( ~ ( A @ one ) ) )
| ( ( sk3 @ A )
!= sk1 )
| ( ( A @ sk1 )
!= ( A @ one ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[113]) ).
thf(253,plain,
! [B: $i,A: $i > $o] :
( ~ ( A @ one )
| ( ( A @ B )
!= ( ~ ( A @ one ) ) )
| ( ( sk3 @ A )
!= sk1 )
| ( ( A @ sk1 )
!= ( A @ one ) ) ),
inference(pre_uni,[status(thm)],[238:[]]) ).
thf(38,plain,
! [B: $i > $o,A: $i] :
( ~ ~ ( B @ one )
| ~ ~ ( B
@ ( succ
@ ( sk3
@ ^ [C: $i] :
~ ( B @ C ) ) ) )
| ~ ( B @ A ) ),
inference(prim_subst,[status(thm)],[19:[bind(A,$thf( ^ [D: $i] : ~ ( C @ D ) ))]]) ).
thf(64,plain,
! [B: $i > $o,A: $i] :
( ~ ( B @ A )
| ( B
@ ( succ
@ ( sk3
@ ^ [C: $i] :
~ ( B @ C ) ) ) )
| ( B @ one ) ),
inference(cnf,[status(esa)],[38]) ).
thf(65,plain,
! [B: $i > $o,A: $i] :
( ~ ( B @ A )
| ( B
@ ( succ
@ ( sk3
@ ^ [C: $i] :
~ ( B @ C ) ) ) )
| ( B @ one ) ),
inference(simp,[status(thm)],[64]) ).
thf(20,plain,
! [B: $i,A: $i > $o] :
( ~ ( A @ one )
| ( A @ ( sk3 @ A ) )
| ( A @ B ) ),
inference(cnf,[status(esa)],[18]) ).
thf(22,plain,
! [A: $i] :
( ( one != one )
| ( one
= ( sk3 @ ( (=) @ $i @ one ) ) )
| ( one = A ) ),
inference(replace_leibeq,[status(thm)],[20:[bind(A,$thf( (=) @ $i @ one ))]]) ).
thf(25,plain,
! [A: $i] :
( ( one != one )
| ( ( sk3 @ ( (=) @ $i @ one ) )
= one )
| ( one = A ) ),
inference(lifteq,[status(thm)],[22]) ).
thf(26,plain,
! [A: $i] :
( ( ( sk3 @ ( (=) @ $i @ one ) )
= one )
| ( one = A ) ),
inference(simp,[status(thm)],[25]) ).
thf(3,axiom,
! [A: $i] :
( ( succ @ A )
!= one ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',one_is_first) ).
thf(10,plain,
! [A: $i] :
( ( succ @ A )
!= one ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(11,plain,
~ ? [A: $i] :
( ( succ @ A )
= one ),
inference(miniscope,[status(thm)],[10]) ).
thf(12,plain,
! [A: $i] :
( ( succ @ A )
!= one ),
inference(cnf,[status(esa)],[11]) ).
thf(13,plain,
! [A: $i] :
( ( succ @ A )
!= one ),
inference(lifteq,[status(thm)],[12]) ).
thf(166,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( (=) @ $i @ one ) )
= one )
| ( A
!= ( succ @ B ) ) ),
inference(paramod_ordered,[status(thm)],[26,13]) ).
thf(167,plain,
( ( sk3 @ ( (=) @ $i @ one ) )
= one ),
inference(pattern_uni,[status(thm)],[166:[bind(A,$thf( succ @ C )),bind(B,$thf( C ))]]) ).
thf(352,plain,
! [D: $i,C: $i > $o,B: $i,A: $i > $o] :
( ~ ( A @ one )
| ( A @ B )
| ( C @ ( sk3 @ C ) )
| ( C @ D )
| ( ( A @ ( sk3 @ A ) )
!= ( C @ one ) ) ),
inference(paramod_ordered,[status(thm)],[20,20]) ).
thf(394,plain,
! [C: $i,B: $i > $o,A: $i] :
( ( one != one )
| ( one = A )
| ( B @ ( sk3 @ B ) )
| ( B @ C )
| ( ( one
= ( sk3 @ ( (=) @ $i @ one ) ) )
!= ( B @ one ) ) ),
inference(replace_leibeq,[status(thm)],[352:[bind(A,$thf( (=) @ $i @ one ))]]) ).
thf(430,plain,
! [C: $i,B: $i > $o,A: $i] :
( ( one != one )
| ( one = A )
| ( B @ ( sk3 @ B ) )
| ( B @ C )
| ( ( one
= ( sk3 @ ( (=) @ $i @ one ) ) )
!= ( B @ one ) ) ),
inference(lifteq,[status(thm)],[394]) ).
thf(460,plain,
! [B: $i,A: $i] :
( ( one
= ( sk3 @ ( (=) @ $i @ B ) ) )
| ( one
= ( sk3
@ ( (=) @ $i
@ ( sk3
@ ^ [C: $i] :
( one
= ( sk3 @ ( (=) @ $i @ C ) ) ) ) ) ) )
| ( one = A ) ),
inference(pre_uni,[status(thm)],[430:[bind(A,$thf( A )),bind(B,$thf( ^ [D: $i] : ( one = ( sk3 @ ( (=) @ $i @ D ) ) ) )),bind(C,$thf( C ))]]) ).
thf(529,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( (=) @ $i @ B ) )
= one )
| ( ( sk3
@ ( (=) @ $i
@ ( sk3
@ ^ [C: $i] :
( one
= ( sk3 @ ( (=) @ $i @ C ) ) ) ) ) )
= one )
| ( one = A ) ),
inference(lifteq,[status(thm)],[460]) ).
thf(530,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( (=) @ $i @ B ) )
= one )
| ( ( sk3
@ ( (=) @ $i
@ ( sk3
@ ^ [C: $i] :
( one
= ( sk3 @ ( (=) @ $i @ C ) ) ) ) ) )
= one )
| ( one = A ) ),
inference(simp,[status(thm)],[529]) ).
thf(1653,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( (=) @ $i @ B ) )
= one )
| ( one = A )
| ( ( sk3
@ ( (=) @ $i
@ ( sk3
@ ^ [C: $i] :
( one
= ( sk3 @ ( (=) @ $i @ C ) ) ) ) ) )
!= ( sk3 @ ( (=) @ $i @ B ) ) )
| ( one != one ) ),
inference(eqfactor_ordered,[status(thm)],[530]) ).
thf(1726,plain,
! [A: $i] :
( ( ( sk3
@ ( (=) @ $i
@ ( sk3
@ ^ [B: $i] :
( one
= ( sk3 @ ( (=) @ $i @ B ) ) ) ) ) )
= one )
| ( one = A ) ),
inference(pattern_uni,[status(thm)],[1653:[bind(A,$thf( A )),bind(B,$thf( sk3 @ ^ [C: $i] : ( one = ( sk3 @ ( (=) @ $i @ C ) ) ) ))]]) ).
thf(2376,plain,
! [B: $i,A: $i] :
( ( ( sk3
@ ( (=) @ $i
@ ( sk3
@ ^ [C: $i] :
( one
= ( sk3 @ ( (=) @ $i @ C ) ) ) ) ) )
= one )
| ( A
!= ( succ @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1726,13]) ).
thf(2377,plain,
( ( sk3
@ ( (=) @ $i
@ ( sk3
@ ^ [A: $i] :
( one
= ( sk3 @ ( (=) @ $i @ A ) ) ) ) ) )
= one ),
inference(pattern_uni,[status(thm)],[2376:[bind(A,$thf( succ @ C )),bind(B,$thf( C ))]]) ).
thf(2920,plain,
! [B: $i,A: $i > $o] :
( ~ ( A @ one )
| ~ ( A @ ( succ @ one ) )
| ( ( A @ B )
!= ( ~ ( A @ one ) ) )
| ( ( sk3
@ ( (=) @ $i
@ ( sk3
@ ^ [C: $i] :
( one
= ( sk3 @ ( (=) @ $i @ C ) ) ) ) ) )
!= ( sk3 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2377,57]) ).
thf(2921,plain,
! [A: $i] :
( ( ( sk3
@ ^ [B: $i] :
( one
= ( sk3 @ ( (=) @ $i @ B ) ) ) )
!= one )
| ( ( sk3
@ ^ [B: $i] :
( one
= ( sk3 @ ( (=) @ $i @ B ) ) ) )
!= ( succ @ one ) )
| ( ( ( sk3
@ ^ [B: $i] :
( one
= ( sk3 @ ( (=) @ $i @ B ) ) ) )
= A )
!= ( ( sk3
@ ^ [B: $i] :
( one
= ( sk3 @ ( (=) @ $i @ B ) ) ) )
!= one ) ) ),
inference(pattern_uni,[status(thm)],[2920:[bind(A,$thf( (=) @ $i @ ( sk3 @ ^ [C: $i] : ( one = ( sk3 @ ( (=) @ $i @ C ) ) ) ) )),bind(B,$thf( B ))]]) ).
thf(2934,plain,
! [A: $i] :
( ( ( sk3
@ ^ [B: $i] :
( one
= ( sk3 @ ( (=) @ $i @ B ) ) ) )
!= one )
| ( ( sk3
@ ^ [B: $i] :
( one
= ( sk3 @ ( (=) @ $i @ B ) ) ) )
!= ( succ @ one ) )
| ( ( ( sk3
@ ^ [B: $i] :
( one
= ( sk3 @ ( (=) @ $i @ B ) ) ) )
= A )
!= ( ( sk3
@ ^ [B: $i] :
( one
= ( sk3 @ ( (=) @ $i @ B ) ) ) )
!= one ) ) ),
inference(lifteq,[status(thm)],[2921]) ).
thf(2956,plain,
! [A: $i] :
( ( ( sk3
@ ^ [B: $i] :
( one
= ( sk3 @ ( (=) @ $i @ B ) ) ) )
!= one )
| ( ( sk3
@ ^ [B: $i] :
( one
= ( sk3 @ ( (=) @ $i @ B ) ) ) )
!= ( succ @ one ) )
| ( ( ( sk3
@ ^ [B: $i] :
( one
= ( sk3 @ ( (=) @ $i @ B ) ) ) )
= A )
!= ( ( sk3
@ ^ [B: $i] :
( one
= ( sk3 @ ( (=) @ $i @ B ) ) ) )
!= one ) ) ),
inference(simp,[status(thm)],[2934]) ).
thf(2978,plain,
! [A: $i] :
( ( ( sk3
@ ^ [B: $i] :
( one
= ( sk3 @ ( (=) @ $i @ B ) ) ) )
!= ( succ @ one ) )
| ( ( ( sk3
@ ^ [B: $i] :
( one
= ( sk3 @ ( (=) @ $i @ B ) ) ) )
= A )
!= ( ( sk3
@ ^ [B: $i] :
( one
= ( sk3 @ ( (=) @ $i @ B ) ) ) )
!= one ) )
| ( ( sk3 @ ( (=) @ $i @ one ) )
!= ( sk3
@ ^ [B: $i] :
( one
= ( sk3 @ ( (=) @ $i @ B ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[167,2956]) ).
thf(3036,plain,
! [A: $i] :
( ( ( sk3
@ ^ [B: $i] :
( one
= ( sk3 @ ( (=) @ $i @ B ) ) ) )
!= ( succ @ one ) )
| ( ( ( sk3
@ ^ [B: $i] :
( one
= ( sk3 @ ( (=) @ $i @ B ) ) ) )
= A )
!= ( ( sk3
@ ^ [B: $i] :
( one
= ( sk3 @ ( (=) @ $i @ B ) ) ) )
!= one ) )
| ( ( (=) @ $i @ one )
!= ( ^ [B: $i] :
( one
= ( sk3 @ ( (=) @ $i @ B ) ) ) ) ) ),
inference(simp,[status(thm)],[2978]) ).
thf(3053,plain,
! [A: $i] :
( ( ( sk3
@ ^ [B: $i] :
( one
= ( sk3 @ ( (=) @ $i @ B ) ) ) )
!= ( succ @ one ) )
| ( ( ( sk3
@ ^ [B: $i] :
( one
= ( sk3 @ ( (=) @ $i @ B ) ) ) )
= A )
!= ( ( sk3
@ ^ [B: $i] :
( one
= ( sk3 @ ( (=) @ $i @ B ) ) ) )
!= one ) )
| ( ( ^ [B: $i] : one )
!= ( ^ [B: $i] : one ) )
| ( ( ^ [B: $i] : B )
!= ( ^ [B: $i] : ( sk3 @ ( (=) @ $i @ B ) ) ) ) ),
inference(simp,[status(thm)],[3036]) ).
thf(3143,plain,
! [A: $i] :
( ( ( sk3
@ ^ [B: $i] :
( one
= ( sk3 @ ( (=) @ $i @ B ) ) ) )
!= ( succ @ one ) )
| ( ( ( sk3
@ ^ [B: $i] :
( one
= ( sk3 @ ( (=) @ $i @ B ) ) ) )
= A )
!= ( ( sk3
@ ^ [B: $i] :
( one
= ( sk3 @ ( (=) @ $i @ B ) ) ) )
!= one ) )
| ( ( ^ [B: $i] : B )
!= ( ^ [B: $i] : ( sk3 @ ( (=) @ $i @ B ) ) ) ) ),
inference(simp,[status(thm)],[3053]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( ( succ @ A )
= ( succ @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',succ_injective) ).
thf(14,plain,
! [A: $i,B: $i] :
( ( ( succ @ A )
= ( succ @ B ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(15,plain,
! [B: $i,A: $i] :
( ( ( succ @ A )
!= ( succ @ B ) )
| ( A = B ) ),
inference(cnf,[status(esa)],[14]) ).
thf(16,plain,
! [B: $i,A: $i] :
( ( ( succ @ A )
!= ( succ @ B ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[15]) ).
thf(17,plain,
! [A: $i] :
( ( sk2 @ ( succ @ A ) )
= A ),
introduced(tautology,[new_symbols(inverse(succ),[sk2])]) ).
thf(33,plain,
! [D: $i,C: $i > $o,B: $i,A: $i > $o] :
( ~ ( A @ one )
| ~ ( A @ ( succ @ ( sk3 @ A ) ) )
| ~ ( C @ one )
| ( C @ D )
| ( ( A @ B )
!= ( C @ ( succ @ ( sk3 @ C ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[19,19]) ).
thf(58,plain,
! [D: $i,C: $i > $o,B: $i,A: $i > $o] :
( ~ ( A @ one )
| ~ ( A @ ( succ @ ( sk3 @ A ) ) )
| ~ ( C @ one )
| ( C @ D )
| ( ( A @ B )
!= ( C @ ( succ @ ( sk3 @ C ) ) ) ) ),
inference(pre_uni,[status(thm)],[33:[]]) ).
thf(59,plain,
! [D: $i,C: $i > $o,B: $i,A: $i > $o] :
( ( C @ D )
| ~ ( C @ one )
| ~ ( A @ ( succ @ ( sk3 @ A ) ) )
| ~ ( A @ one )
| ( ( A @ B )
!= ( C @ ( succ @ ( sk3 @ C ) ) ) ) ),
inference(pre_uni,[status(thm)],[58:[]]) ).
thf(41,plain,
! [C: $i > $o,B: $i > $o,A: $i] :
( ~ ( ( B @ one )
| ( C @ one ) )
| ~ ( ( B
@ ( succ
@ ( sk3
@ ^ [D: $i] :
( ( B @ D )
| ( C @ D ) ) ) ) )
| ( C
@ ( succ
@ ( sk3
@ ^ [D: $i] :
( ( B @ D )
| ( C @ D ) ) ) ) ) )
| ( B @ A )
| ( C @ A ) ),
inference(prim_subst,[status(thm)],[19:[bind(A,$thf( ^ [E: $i] : ( ( C @ E ) | ( D @ E ) ) ))]]) ).
thf(67,plain,
! [C: $i > $o,B: $i > $o,A: $i] :
( ( B @ A )
| ( C @ A )
| ~ ( B
@ ( succ
@ ( sk3
@ ^ [D: $i] :
( ( B @ D )
| ( C @ D ) ) ) ) )
| ~ ( B @ one ) ),
inference(cnf,[status(esa)],[41]) ).
thf(71,plain,
! [C: $i > $o,B: $i > $o,A: $i] :
( ( B @ A )
| ( C @ A )
| ~ ( B
@ ( succ
@ ( sk3
@ ^ [D: $i] :
( ( B @ D )
| ( C @ D ) ) ) ) )
| ~ ( B @ one ) ),
inference(simp,[status(thm)],[67]) ).
thf(29,plain,
! [A: $i] :
( ( ( sk2 @ sk1 )
= A )
| ( ( succ @ sk1 )
!= ( succ @ A ) ) ),
inference(paramod_ordered,[status(thm)],[9,17]) ).
thf(30,plain,
( ( sk2 @ sk1 )
= sk1 ),
inference(pattern_uni,[status(thm)],[29:[bind(A,$thf( sk1 ))]]) ).
thf(138,plain,
! [A: $i] :
( ( sk1 = A )
| ( ( sk2 @ ( succ @ A ) )
!= ( sk2 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[30,17]) ).
thf(140,plain,
! [A: $i] :
( ( sk1 = A )
| ( ( succ @ A )
!= sk1 ) ),
inference(simp,[status(thm)],[138]) ).
thf(31,plain,
! [B: $i,A: $i > $o] :
( ~ ( A @ one )
| ~ ( A @ sk1 )
| ( A @ B )
| ( ( succ @ ( sk3 @ A ) )
!= ( succ @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[9,19]) ).
thf(56,plain,
! [B: $i,A: $i > $o] :
( ( A @ B )
| ~ ( A @ one )
| ~ ( A @ sk1 )
| ( ( sk3 @ A )
!= sk1 ) ),
inference(simp,[status(thm)],[31]) ).
thf(37,plain,
! [B: $i,A: $i > $o] :
( ~ ( A @ one )
| ~ ( A @ ( succ @ ( sk3 @ A ) ) )
| ( ( A @ B )
!= ( ~ ( A @ ( succ @ ( sk3 @ A ) ) ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[19]) ).
thf(50,plain,
! [B: $i,A: $i > $o] :
( ~ ( A @ one )
| ~ ( A @ ( succ @ ( sk3 @ A ) ) )
| ( ( A @ B )
!= ( ~ ( A @ ( succ @ ( sk3 @ A ) ) ) ) ) ),
inference(simp,[status(thm)],[37]) ).
thf(284,plain,
! [B: $i,A: $i > $o] :
( ~ ( A @ one )
| ~ ( A @ ( succ @ ( sk3 @ A ) ) )
| ( ( ~ ( A @ sk1 ) )
!= ( A @ B ) )
| ( ( succ @ ( sk3 @ A ) )
!= ( succ @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[9,50]) ).
thf(311,plain,
! [B: $i,A: $i > $o] :
( ~ ( A @ one )
| ~ ( A @ ( succ @ ( sk3 @ A ) ) )
| ( ( ~ ( A @ sk1 ) )
!= ( A @ B ) )
| ( ( sk3 @ A )
!= sk1 ) ),
inference(simp,[status(thm)],[284]) ).
thf(1352,plain,
! [B: $i,A: $i > $o] :
( ~ ( A @ one )
| ~ ( A @ sk1 )
| ( ( ~ ( A @ sk1 ) )
!= ( A @ B ) )
| ( ( sk3 @ A )
!= sk1 )
| ( ( succ @ ( sk3 @ A ) )
!= ( succ @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[9,311]) ).
thf(1440,plain,
! [B: $i,A: $i > $o] :
( ~ ( A @ one )
| ~ ( A @ sk1 )
| ( ( ~ ( A @ sk1 ) )
!= ( A @ B ) )
| ( ( sk3 @ A )
!= sk1 )
| ( ( sk3 @ A )
!= sk1 ) ),
inference(simp,[status(thm)],[1352]) ).
thf(1462,plain,
! [B: $i,A: $i > $o] :
( ~ ( A @ one )
| ~ ( A @ sk1 )
| ( ( ~ ( A @ sk1 ) )
!= ( A @ B ) )
| ( ( sk3 @ A )
!= sk1 ) ),
inference(simp,[status(thm)],[1440]) ).
thf(32,plain,
! [D: $i,C: $i > $o,B: $i,A: $i > $o] :
( ~ ( A @ one )
| ~ ( A @ ( succ @ ( sk3 @ A ) ) )
| ~ ( C @ ( succ @ ( sk3 @ C ) ) )
| ( C @ D )
| ( ( A @ B )
!= ( C @ one ) ) ),
inference(paramod_ordered,[status(thm)],[19,19]) ).
thf(60,plain,
! [D: $i,C: $i > $o,B: $i,A: $i > $o] :
( ~ ( A @ one )
| ~ ( A @ ( succ @ ( sk3 @ A ) ) )
| ~ ( C @ ( succ @ ( sk3 @ C ) ) )
| ( C @ D )
| ( ( A @ B )
!= ( C @ one ) ) ),
inference(pre_uni,[status(thm)],[32:[]]) ).
thf(61,plain,
! [D: $i,C: $i > $o,B: $i,A: $i > $o] :
( ( C @ D )
| ~ ( C @ ( succ @ ( sk3 @ C ) ) )
| ~ ( A @ ( succ @ ( sk3 @ A ) ) )
| ~ ( A @ one )
| ( ( A @ B )
!= ( C @ one ) ) ),
inference(pre_uni,[status(thm)],[60:[]]) ).
thf(94,plain,
! [B: $i,A: $i > $o] :
( ~ ( A @ one )
| ( ( A @ B )
!= ( ~ ( A @ one ) ) )
| ( ( A @ ( succ @ ( sk3 @ A ) ) )
!= ( A @ one ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[57]) ).
thf(116,plain,
! [B: $i,A: $i > $o] :
( ~ ( A @ one )
| ( ( A @ B )
!= ( ~ ( A @ one ) ) )
| ( ( A @ ( succ @ ( sk3 @ A ) ) )
!= ( A @ one ) ) ),
inference(pre_uni,[status(thm)],[94:[]]) ).
thf(27,plain,
! [A: $i] :
( ( sk1 != one )
| ( ( succ @ sk1 )
!= ( succ @ A ) ) ),
inference(paramod_ordered,[status(thm)],[9,13]) ).
thf(28,plain,
sk1 != one,
inference(pattern_uni,[status(thm)],[27:[bind(A,$thf( sk1 ))]]) ).
thf(66,plain,
! [C: $i > $o,B: $i > $o,A: $i] :
( ( B @ A )
| ( C @ A )
| ~ ( B
@ ( succ
@ ( sk3
@ ^ [D: $i] :
( ( B @ D )
| ( C @ D ) ) ) ) )
| ~ ( C @ one ) ),
inference(cnf,[status(esa)],[41]) ).
thf(70,plain,
! [C: $i > $o,B: $i > $o,A: $i] :
( ( B @ A )
| ( C @ A )
| ~ ( B
@ ( succ
@ ( sk3
@ ^ [D: $i] :
( ( B @ D )
| ( C @ D ) ) ) ) )
| ~ ( C @ one ) ),
inference(simp,[status(thm)],[66]) ).
thf(3064,plain,
! [A: $i] :
( ( ( sk3
@ ^ [B: $i] :
( one
= ( sk3 @ ( (=) @ $i @ B ) ) ) )
!= ( succ @ one ) )
| ( ( one = A )
!= ( ( sk3
@ ^ [B: $i] :
( one
= ( sk3 @ ( (=) @ $i @ B ) ) ) )
!= one ) )
| ( ( (=) @ $i @ one )
!= ( ^ [B: $i] :
( one
= ( sk3 @ ( (=) @ $i @ B ) ) ) ) )
| ( ( sk3 @ ( (=) @ $i @ one ) )
!= ( sk3
@ ^ [B: $i] :
( one
= ( sk3 @ ( (=) @ $i @ B ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[167,3036]) ).
thf(3119,plain,
! [A: $i] :
( ( ( sk3
@ ^ [B: $i] :
( one
= ( sk3 @ ( (=) @ $i @ B ) ) ) )
!= ( succ @ one ) )
| ( ( one = A )
!= ( ( sk3
@ ^ [B: $i] :
( one
= ( sk3 @ ( (=) @ $i @ B ) ) ) )
!= one ) )
| ( ( (=) @ $i @ one )
!= ( ^ [B: $i] :
( one
= ( sk3 @ ( (=) @ $i @ B ) ) ) ) )
| ( ( (=) @ $i @ one )
!= ( ^ [B: $i] :
( one
= ( sk3 @ ( (=) @ $i @ B ) ) ) ) ) ),
inference(simp,[status(thm)],[3064]) ).
thf(3146,plain,
! [A: $i] :
( ( ( sk3
@ ^ [B: $i] :
( one
= ( sk3 @ ( (=) @ $i @ B ) ) ) )
!= ( succ @ one ) )
| ( ( one = A )
!= ( ( sk3
@ ^ [B: $i] :
( one
= ( sk3 @ ( (=) @ $i @ B ) ) ) )
!= one ) )
| ( ( (=) @ $i @ one )
!= ( ^ [B: $i] :
( one
= ( sk3 @ ( (=) @ $i @ B ) ) ) ) ) ),
inference(simp,[status(thm)],[3119]) ).
thf(3963,plain,
! [A: $i] :
( ( ( sk3
@ ^ [B: $i] :
( one
= ( sk3 @ ( (=) @ $i @ B ) ) ) )
!= ( succ @ one ) )
| ( ( one = A )
!= ( ( sk3
@ ^ [B: $i] :
( one
= ( sk3 @ ( (=) @ $i @ B ) ) ) )
!= one ) )
| ( ( ^ [B: $i] : one )
!= ( ^ [B: $i] : one ) )
| ( ( ^ [B: $i] : B )
!= ( ^ [B: $i] : ( sk3 @ ( (=) @ $i @ B ) ) ) ) ),
inference(simp,[status(thm)],[3146]) ).
thf(4081,plain,
! [A: $i] :
( ( ( sk3
@ ^ [B: $i] :
( one
= ( sk3 @ ( (=) @ $i @ B ) ) ) )
!= ( succ @ one ) )
| ( ( one = A )
!= ( ( sk3
@ ^ [B: $i] :
( one
= ( sk3 @ ( (=) @ $i @ B ) ) ) )
!= one ) )
| ( ( ^ [B: $i] : B )
!= ( ^ [B: $i] : ( sk3 @ ( (=) @ $i @ B ) ) ) ) ),
inference(simp,[status(thm)],[3963]) ).
thf(604,plain,
! [B: $i > $o,A: $i] :
( ~ ( B @ A )
| ~ ~ ( B @ one )
| ~ ~ ( B @ sk1 )
| ( ( sk3
@ ^ [C: $i] :
~ ( B @ C ) )
!= sk1 ) ),
inference(prim_subst,[status(thm)],[56:[bind(A,$thf( ^ [D: $i] : ~ ( C @ D ) ))]]) ).
thf(679,plain,
! [B: $i > $o,A: $i] :
( ( ( sk3
@ ^ [C: $i] :
~ ( B @ C ) )
!= sk1 )
| ( B @ sk1 )
| ( B @ one )
| ~ ( B @ A ) ),
inference(cnf,[status(esa)],[604]) ).
thf(680,plain,
! [B: $i > $o,A: $i] :
( ( ( sk3
@ ^ [C: $i] :
~ ( B @ C ) )
!= sk1 )
| ( B @ sk1 )
| ( B @ one )
| ~ ( B @ A ) ),
inference(simp,[status(thm)],[679]) ).
thf(3220,plain,
! [B: $i > $o,A: $i] :
( ( ( sk3
@ ^ [C: $i] :
~ ~ ( B @ C ) )
!= sk1 )
| ~ ( B @ sk1 )
| ~ ( B @ one )
| ~ ~ ( B @ A ) ),
inference(prim_subst,[status(thm)],[680:[bind(A,$thf( A )),bind(B,$thf( ^ [D: $i] : ~ ( C @ D ) ))]]) ).
thf(3422,plain,
! [B: $i > $o,A: $i] :
( ( B @ A )
| ~ ( B @ one )
| ~ ( B @ sk1 )
| ( ( sk3
@ ^ [C: $i] :
~ ~ ( B @ C ) )
!= sk1 ) ),
inference(cnf,[status(esa)],[3220]) ).
thf(3423,plain,
! [B: $i > $o,A: $i] :
( ( B @ A )
| ~ ( B @ one )
| ~ ( B @ sk1 )
| ( ( sk3 @ B )
!= sk1 ) ),
inference(simp,[status(thm)],[3422]) ).
thf(34,plain,
! [B: $i,A: $i > $o] :
( ~ ( A @ one )
| ( A @ B )
| ( ( A @ ( succ @ ( sk3 @ A ) ) )
!= ( A @ one ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[19]) ).
thf(62,plain,
! [B: $i,A: $i > $o] :
( ~ ( A @ one )
| ( A @ B )
| ( ( A @ ( succ @ ( sk3 @ A ) ) )
!= ( A @ one ) ) ),
inference(pre_uni,[status(thm)],[34:[]]) ).
thf(63,plain,
! [B: $i,A: $i > $o] :
( ( A @ B )
| ~ ( A @ one )
| ( ( A @ ( succ @ ( sk3 @ A ) ) )
!= ( A @ one ) ) ),
inference(pre_uni,[status(thm)],[62:[]]) ).
thf(6283,plain,
$false,
inference(e,[status(thm)],[253,6,65,3143,13,17,59,71,113,140,2956,10,56,14,1462,20,57,61,3036,116,28,70,2377,9,4081,311,3423,167,680,3146,63,18,50,16,30,19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM636^2 : TPTP v8.1.2. Released v3.7.0.
% 0.07/0.16 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n023.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Mon May 6 12:08:54 EDT 2024
% 0.16/0.37 % CPUTime :
% 0.98/0.87 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.17/0.98 % [INFO] Parsing done (113ms).
% 1.30/0.99 % [INFO] Running in sequential loop mode.
% 1.65/1.21 % [INFO] eprover registered as external prover.
% 1.65/1.21 % [INFO] cvc4 registered as external prover.
% 1.65/1.22 % [INFO] Scanning for conjecture ...
% 1.86/1.27 % [INFO] Found a conjecture and 3 axioms. Running axiom selection ...
% 1.86/1.29 % [INFO] Axiom selection finished. Selected 3 axioms (removed 0 axioms).
% 1.86/1.29 % [INFO] Problem is higher-order (TPTP THF).
% 1.86/1.30 % [INFO] Type checking passed.
% 1.86/1.30 % [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 ...
% 32.20/7.40 % External prover 'e' found a proof!
% 32.20/7.40 % [INFO] Killing All external provers ...
% 32.20/7.41 % Time passed: 6869ms (effective reasoning time: 6412ms)
% 32.20/7.41 % 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)>
% 32.20/7.41 % Axioms used in derivation (3): induction, one_is_first, succ_injective
% 32.20/7.41 % No. of inferences in proof: 95
% 32.20/7.41 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 6869 ms resp. 6412 ms w/o parsing
% 32.44/7.49 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 32.44/7.49 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------