TSTP Solution File: SEV248^5 by Leo-III-SAT---1.7.15
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.15
% Problem : SEV248^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d SAT
% Computer : n025.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 : Mon Jun 24 15:59:51 EDT 2024
% Result : Theorem 80.62s 13.57s
% Output : Refutation 80.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 58
% Number of leaves : 1
% Syntax : Number of formulae : 76 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 593 ( 566 equ; 73 cnn)
% Maximal formula atoms : 7 ( 7 avg)
% Number of connectives : 555 ( 74 ~; 258 |; 7 &; 216 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 20 ( 20 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 147 ( 33 ^ 114 !; 0 ?; 147 :)
% Comments :
%------------------------------------------------------------------------------
thf(a_type,type,
a: $tType ).
thf(sk1_type,type,
sk1: a ).
thf(sk2_type,type,
sk2: a ).
thf(sk3_type,type,
sk3: a ).
thf(sk4_type,type,
sk4: a ).
thf(sk5_type,type,
sk5: a > $o ).
thf(sk6_type,type,
sk6: ( a > $o ) > a ).
thf(sk7_type,type,
sk7: a > ( a > $o ) > a ).
thf(1,conjecture,
! [A: a,B: a,C: a,D: a] :
( ( ! [E: a > $o] :
( ( ( E
= ( (=) @ a @ A ) )
| ! [F: a] :
( ( E @ F )
= ( ( F = A )
| ( F = B ) ) ) )
= ( ( E
= ( (=) @ a @ C ) )
| ! [F: a] :
( ( E @ F )
= ( ( F = C )
| ( F = D ) ) ) ) ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM103_pme) ).
thf(2,negated_conjecture,
~ ! [A: a,B: a,C: a,D: a] :
( ( ! [E: a > $o] :
( ( ( E
= ( (=) @ a @ A ) )
| ! [F: a] :
( ( E @ F )
= ( ( F = A )
| ( F = B ) ) ) )
= ( ( E
= ( (=) @ a @ C ) )
| ! [F: a] :
( ( E @ F )
= ( ( F = C )
| ( F = D ) ) ) ) ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: a,B: a,C: a,D: a] :
( ( ! [E: a > $o] :
( ( ( E
= ( (=) @ a @ A ) )
| ! [F: a] :
( ( E @ F )
= ( ( F = A )
| ( F = B ) ) ) )
= ( ( E
= ( (=) @ a @ C ) )
| ! [F: a] :
( ( E @ F )
= ( ( F = C )
| ( F = D ) ) ) ) ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
( ( ! [A: a > $o] :
( ( ( A
= ( (=) @ a @ sk1 ) )
| ! [B: a] :
( ( A @ B )
= ( ( B = sk1 )
| ( B = sk2 ) ) ) )
= ( ( A
= ( (=) @ a @ sk3 ) )
| ! [B: a] :
( ( A @ B )
= ( ( B = sk3 )
| ( B = sk4 ) ) ) ) ) )
!= ( ( sk1 = sk3 )
& ( sk2 = sk4 ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(5,plain,
( ( ( sk1 = sk3 )
& ( sk2 = sk4 ) )
!= ( ! [A: a > $o] :
( ( ( A
= ( (=) @ a @ sk1 ) )
| ! [B: a] :
( ( A @ B )
= ( ( B = sk1 )
| ( B = sk2 ) ) ) )
= ( ( A
= ( (=) @ a @ sk3 ) )
| ! [B: a] :
( ( A @ B )
= ( ( B = sk3 )
| ( B = sk4 ) ) ) ) ) ) ),
inference(lifteq,[status(thm)],[4]) ).
thf(7,plain,
( ( ( sk1 = sk3 )
& ( sk2 = sk4 ) )
| ! [A: a > $o] :
( ( ( A
= ( (=) @ a @ sk1 ) )
| ! [B: a] :
( ( A @ B )
= ( ( B = sk1 )
| ( B = sk2 ) ) ) )
= ( ( A
= ( (=) @ a @ sk3 ) )
| ! [B: a] :
( ( A @ B )
= ( ( B = sk3 )
| ( B = sk4 ) ) ) ) ) ),
inference(bool_ext,[status(thm)],[5]) ).
thf(10,plain,
! [A: a > $o] :
( ( ( ( A
= ( (=) @ a @ sk1 ) )
| ! [B: a] :
( ( A @ B )
= ( ( B = sk1 )
| ( B = sk2 ) ) ) )
= ( ( A
= ( (=) @ a @ sk3 ) )
| ! [B: a] :
( ( A @ B )
= ( ( B = sk3 )
| ( B = sk4 ) ) ) ) )
| ( sk2 = sk4 ) ),
inference(cnf,[status(esa)],[7]) ).
thf(12,plain,
! [A: a > $o] :
( ( ( ( A
= ( (=) @ a @ sk3 ) )
| ! [B: a] :
( ( A @ B )
= ( ( B = sk3 )
| ( B = sk4 ) ) ) )
= ( ( A
= ( (=) @ a @ sk1 ) )
| ! [B: a] :
( ( A @ B )
= ( ( B = sk1 )
| ( B = sk2 ) ) ) ) )
| ( sk4 = sk2 ) ),
inference(lifteq,[status(thm)],[10]) ).
thf(15,plain,
! [A: a > $o] :
( ( sk4 = sk2 )
| ( A
= ( (=) @ a @ sk3 ) )
| ! [B: a] :
( ( A @ B )
= ( ( B = sk3 )
| ( B = sk4 ) ) )
| ~ ( ( A
= ( (=) @ a @ sk1 ) )
| ! [B: a] :
( ( A @ B )
= ( ( B = sk1 )
| ( B = sk2 ) ) ) ) ),
inference(bool_ext,[status(thm)],[12]) ).
thf(25,plain,
! [B: a,A: a > $o] :
( ( ( A @ ( sk7 @ B @ A ) )
!= ( ( ( sk7 @ B @ A )
= sk1 )
| ( ( sk7 @ B @ A )
= sk2 ) ) )
| ( A
= ( (=) @ a @ sk3 ) )
| ( ( A @ B )
= ( ( B = sk3 )
| ( B = sk4 ) ) )
| ( sk4 = sk2 ) ),
inference(cnf,[status(esa)],[15]) ).
thf(27,plain,
! [B: a,A: a > $o] :
( ( ( A @ ( sk7 @ B @ A ) )
!= ( ( ( sk7 @ B @ A )
= sk1 )
| ( ( sk7 @ B @ A )
= sk2 ) ) )
| ( A
= ( (=) @ a @ sk3 ) )
| ( ( A @ B )
= ( ( B = sk3 )
| ( B = sk4 ) ) )
| ( sk4 = sk2 ) ),
inference(lifteq,[status(thm)],[25]) ).
thf(1432,plain,
! [A: a] :
( ( sk4 = sk2 )
| ( ( ( A = sk3 )
| ( A = sk4 ) )
= ( ( A = sk1 )
| ( A = sk2 ) ) )
| ( ( ^ [B: a] :
( ( B = sk1 )
| ( B = sk2 ) ) )
= ( (=) @ a @ sk3 ) ) ),
inference(pre_uni,[status(thm)],[27:[bind(A,$thf( ^ [C: a] : ( ( C = sk1 ) | ( C = sk2 ) ) )),bind(B,$thf( B ))]]) ).
thf(1631,plain,
! [A: a] :
( ( sk4 = sk2 )
| ( ( ( A = sk3 )
| ( A = sk4 ) )
= ( ( A = sk1 )
| ( A = sk2 ) ) )
| ( ( ^ [B: a] :
( ( B = sk1 )
| ( B = sk2 ) ) )
= ( (=) @ a @ sk3 ) ) ),
inference(simp,[status(thm)],[1432]) ).
thf(11,plain,
! [A: a > $o] :
( ( ( ( A
= ( (=) @ a @ sk1 ) )
| ! [B: a] :
( ( A @ B )
= ( ( B = sk1 )
| ( B = sk2 ) ) ) )
= ( ( A
= ( (=) @ a @ sk3 ) )
| ! [B: a] :
( ( A @ B )
= ( ( B = sk3 )
| ( B = sk4 ) ) ) ) )
| ( sk1 = sk3 ) ),
inference(cnf,[status(esa)],[7]) ).
thf(13,plain,
! [A: a > $o] :
( ( ( ( A
= ( (=) @ a @ sk3 ) )
| ! [B: a] :
( ( A @ B )
= ( ( B = sk3 )
| ( B = sk4 ) ) ) )
= ( ( A
= ( (=) @ a @ sk1 ) )
| ! [B: a] :
( ( A @ B )
= ( ( B = sk1 )
| ( B = sk2 ) ) ) ) )
| ( sk3 = sk1 ) ),
inference(lifteq,[status(thm)],[11]) ).
thf(30,plain,
! [A: a > $o] :
( ( sk3 = sk1 )
| ~ ( ( A
= ( (=) @ a @ sk3 ) )
| ! [B: a] :
( ( A @ B )
= ( ( B = sk3 )
| ( B = sk4 ) ) ) )
| ( A
= ( (=) @ a @ sk1 ) )
| ! [B: a] :
( ( A @ B )
= ( ( B = sk1 )
| ( B = sk2 ) ) ) ),
inference(bool_ext,[status(thm)],[13]) ).
thf(48,plain,
! [B: a,A: a > $o] :
( ( A
= ( (=) @ a @ sk1 ) )
| ( ( A @ B )
= ( ( B = sk1 )
| ( B = sk2 ) ) )
| ( A
!= ( (=) @ a @ sk3 ) )
| ( sk3 = sk1 ) ),
inference(cnf,[status(esa)],[30]) ).
thf(50,plain,
! [B: a,A: a > $o] :
( ( A
= ( (=) @ a @ sk1 ) )
| ( ( A @ B )
= ( ( B = sk1 )
| ( B = sk2 ) ) )
| ( A
!= ( (=) @ a @ sk3 ) )
| ( sk3 = sk1 ) ),
inference(lifteq,[status(thm)],[48]) ).
thf(51,plain,
! [A: a] :
( ( ( (=) @ a @ sk3 )
= ( (=) @ a @ sk1 ) )
| ( ( ( A = sk1 )
| ( A = sk2 ) )
= ( sk3 = A ) )
| ( sk3 = sk1 ) ),
inference(simp,[status(thm)],[50]) ).
thf(3215,plain,
! [A: a] :
( ( ( (=) @ a @ sk3 )
= ( (=) @ a @ sk1 ) )
| ( sk3 = sk1 )
| ~ ( ( A = sk1 )
| ( A = sk2 ) )
| ( sk3 = A ) ),
inference(bool_ext,[status(thm)],[51]) ).
thf(3430,plain,
! [A: a] :
( ( sk3 = A )
| ( ( (=) @ a @ sk3 )
= ( (=) @ a @ sk1 ) )
| ( sk3 = sk1 )
| ~ ( ( A = sk1 )
| ( A = sk2 ) ) ),
inference(lifteq,[status(thm)],[3215]) ).
thf(3492,plain,
! [A: a] :
( ( A != sk1 )
| ( sk3 = sk1 )
| ( ( (=) @ a @ sk3 )
= ( (=) @ a @ sk1 ) )
| ( sk3 = A ) ),
inference(cnf,[status(esa)],[3430]) ).
thf(3495,plain,
! [A: a] :
( ( A != sk1 )
| ( sk3 = sk1 )
| ( ( (=) @ a @ sk3 )
= ( (=) @ a @ sk1 ) )
| ( sk3 = A ) ),
inference(lifteq,[status(thm)],[3492]) ).
thf(3496,plain,
( ( sk3 = sk1 )
| ( ( (=) @ a @ sk3 )
= ( (=) @ a @ sk1 ) ) ),
inference(simp,[status(thm)],[3495]) ).
thf(3585,plain,
! [A: a] :
( ( ( sk3 = A )
= ( sk1 = A ) )
| ( sk3 = sk1 ) ),
inference(func_ext,[status(esa)],[3496]) ).
thf(3837,plain,
! [A: a] :
( ( sk3 = sk1 )
| ( sk3 != A )
| ( sk1 = A ) ),
inference(bool_ext,[status(thm)],[3585]) ).
thf(4017,plain,
! [A: a] :
( ( sk3 != A )
| ( sk1 = A )
| ( sk3 = sk1 ) ),
inference(lifteq,[status(thm)],[3837]) ).
thf(4053,plain,
sk3 = sk1,
inference(simp,[status(thm)],[4017]) ).
thf(14,plain,
! [A: a > $o] :
( ( sk4 = sk2 )
| ~ ( ( A
= ( (=) @ a @ sk3 ) )
| ! [B: a] :
( ( A @ B )
= ( ( B = sk3 )
| ( B = sk4 ) ) ) )
| ( A
= ( (=) @ a @ sk1 ) )
| ! [B: a] :
( ( A @ B )
= ( ( B = sk1 )
| ( B = sk2 ) ) ) ),
inference(bool_ext,[status(thm)],[12]) ).
thf(21,plain,
! [B: a,A: a > $o] :
( ( A
= ( (=) @ a @ sk1 ) )
| ( ( A @ B )
= ( ( B = sk1 )
| ( B = sk2 ) ) )
| ( ( A @ ( sk6 @ A ) )
!= ( ( ( sk6 @ A )
= sk3 )
| ( ( sk6 @ A )
= sk4 ) ) )
| ( sk4 = sk2 ) ),
inference(cnf,[status(esa)],[14]) ).
thf(24,plain,
! [B: a,A: a > $o] :
( ( A
= ( (=) @ a @ sk1 ) )
| ( ( A @ B )
= ( ( B = sk1 )
| ( B = sk2 ) ) )
| ( ( A @ ( sk6 @ A ) )
!= ( ( ( sk6 @ A )
= sk3 )
| ( ( sk6 @ A )
= sk4 ) ) )
| ( sk4 = sk2 ) ),
inference(lifteq,[status(thm)],[21]) ).
thf(556,plain,
! [A: a] :
( ( sk4 = sk2 )
| ( ( ( A = sk3 )
| ( A = sk4 ) )
= ( ( A = sk1 )
| ( A = sk2 ) ) )
| ( ( ^ [B: a] :
( ( B = sk3 )
| ( B = sk4 ) ) )
= ( (=) @ a @ sk1 ) ) ),
inference(pre_uni,[status(thm)],[24:[bind(A,$thf( ^ [C: a] : ( ( C = sk3 ) | ( C = sk4 ) ) )),bind(B,$thf( B ))]]) ).
thf(866,plain,
! [A: a] :
( ( sk4 = sk2 )
| ( ( ( A = sk3 )
| ( A = sk4 ) )
= ( ( A = sk1 )
| ( A = sk2 ) ) )
| ( ( ^ [B: a] :
( ( B = sk3 )
| ( B = sk4 ) ) )
= ( (=) @ a @ sk1 ) ) ),
inference(simp,[status(thm)],[556]) ).
thf(5085,plain,
! [A: a] :
( ( sk4 = sk2 )
| ( ( ( A = sk1 )
| ( A = sk4 ) )
= ( ( A = sk1 )
| ( A = sk2 ) ) )
| ( ( ^ [B: a] :
( ( B = sk1 )
| ( B = sk4 ) ) )
= ( (=) @ a @ sk1 ) ) ),
inference(rewrite,[status(thm)],[866,4053]) ).
thf(6,plain,
( ~ ( ( sk1 = sk3 )
& ( sk2 = sk4 ) )
| ~ ! [A: a > $o] :
( ( ( A
= ( (=) @ a @ sk1 ) )
| ! [B: a] :
( ( A @ B )
= ( ( B = sk1 )
| ( B = sk2 ) ) ) )
= ( ( A
= ( (=) @ a @ sk3 ) )
| ! [B: a] :
( ( A @ B )
= ( ( B = sk3 )
| ( B = sk4 ) ) ) ) ) ),
inference(bool_ext,[status(thm)],[5]) ).
thf(8,plain,
( ( ( ( sk5
= ( (=) @ a @ sk1 ) )
| ! [A: a] :
( ( sk5 @ A )
= ( ( A = sk1 )
| ( A = sk2 ) ) ) )
!= ( ( sk5
= ( (=) @ a @ sk3 ) )
| ! [A: a] :
( ( sk5 @ A )
= ( ( A = sk3 )
| ( A = sk4 ) ) ) ) )
| ( sk1 != sk3 )
| ( sk2 != sk4 ) ),
inference(cnf,[status(esa)],[6]) ).
thf(9,plain,
( ( ( ( sk5
= ( (=) @ a @ sk3 ) )
| ! [A: a] :
( ( sk5 @ A )
= ( ( A = sk3 )
| ( A = sk4 ) ) ) )
!= ( ( sk5
= ( (=) @ a @ sk1 ) )
| ! [A: a] :
( ( sk5 @ A )
= ( ( A = sk1 )
| ( A = sk2 ) ) ) ) )
| ( sk3 != sk1 )
| ( sk4 != sk2 ) ),
inference(lifteq,[status(thm)],[8]) ).
thf(4135,plain,
( ( ( ( sk5
= ( (=) @ a @ sk1 ) )
| ! [A: a] :
( ( sk5 @ A )
= ( ( A = sk1 )
| ( A = sk4 ) ) ) )
!= ( ( sk5
= ( (=) @ a @ sk1 ) )
| ! [A: a] :
( ( sk5 @ A )
= ( ( A = sk1 )
| ( A = sk2 ) ) ) ) )
| ( sk1 != sk1 )
| ( sk4 != sk2 ) ),
inference(rewrite,[status(thm)],[9,4053]) ).
thf(4136,plain,
( ( ( ( sk5
= ( (=) @ a @ sk1 ) )
| ! [A: a] :
( ( sk5 @ A )
= ( ( A = sk1 )
| ( A = sk4 ) ) ) )
!= ( ( sk5
= ( (=) @ a @ sk1 ) )
| ! [A: a] :
( ( sk5 @ A )
= ( ( A = sk1 )
| ( A = sk2 ) ) ) ) )
| ( sk4 != sk2 ) ),
inference(simp,[status(thm)],[4135]) ).
thf(4193,plain,
( ( ( sk5
= ( (=) @ a @ sk1 ) )
!= ( sk5
= ( (=) @ a @ sk1 ) ) )
| ( ( ! [A: a] :
( ( sk5 @ A )
= ( ( A = sk1 )
| ( A = sk4 ) ) ) )
!= ( ! [A: a] :
( ( sk5 @ A )
= ( ( A = sk1 )
| ( A = sk2 ) ) ) ) )
| ( sk4 != sk2 ) ),
inference(simp,[status(thm)],[4136]) ).
thf(4196,plain,
( ( ( ! [A: a] :
( ( sk5 @ A )
= ( ( A = sk1 )
| ( A = sk4 ) ) ) )
!= ( ! [A: a] :
( ( sk5 @ A )
= ( ( A = sk1 )
| ( A = sk2 ) ) ) ) )
| ( sk4 != sk2 ) ),
inference(simp,[status(thm)],[4193]) ).
thf(4209,plain,
( ( ( ^ [A: a] :
( ( sk5 @ A )
= ( ( A = sk1 )
| ( A = sk4 ) ) ) )
!= ( ^ [A: a] :
( ( sk5 @ A )
= ( ( A = sk1 )
| ( A = sk2 ) ) ) ) )
| ( sk4 != sk2 ) ),
inference(simp,[status(thm)],[4196]) ).
thf(4258,plain,
( ( sk5 != sk5 )
| ( ( ^ [A: a] :
( ( A = sk1 )
| ( A = sk4 ) ) )
!= ( ^ [A: a] :
( ( A = sk1 )
| ( A = sk2 ) ) ) )
| ( sk4 != sk2 ) ),
inference(simp,[status(thm)],[4209]) ).
thf(4260,plain,
( ( ( ^ [A: a] :
( ( A = sk1 )
| ( A = sk4 ) ) )
!= ( ^ [A: a] :
( ( A = sk1 )
| ( A = sk2 ) ) ) )
| ( sk4 != sk2 ) ),
inference(simp,[status(thm)],[4258]) ).
thf(4261,plain,
( ( ( ^ [A: a] : ( A = sk1 ) )
!= ( ^ [A: a] : ( A = sk1 ) ) )
| ( ( ^ [A: a] : ( A = sk4 ) )
!= ( ^ [A: a] : ( A = sk2 ) ) )
| ( sk4 != sk2 ) ),
inference(simp,[status(thm)],[4260]) ).
thf(4263,plain,
( ( ( ^ [A: a] : ( A = sk4 ) )
!= ( ^ [A: a] : ( A = sk2 ) ) )
| ( sk4 != sk2 ) ),
inference(simp,[status(thm)],[4261]) ).
thf(4264,plain,
( ( ( ^ [A: a] : A )
!= ( ^ [A: a] : A ) )
| ( ( ^ [A: a] : sk4 )
!= ( ^ [A: a] : sk2 ) )
| ( sk4 != sk2 ) ),
inference(simp,[status(thm)],[4263]) ).
thf(4266,plain,
( ( ( ^ [A: a] : sk4 )
!= ( ^ [A: a] : sk2 ) )
| ( sk4 != sk2 ) ),
inference(simp,[status(thm)],[4264]) ).
thf(4267,plain,
( ( sk4 != sk2 )
| ( sk4 != sk2 ) ),
inference(func_ext,[status(esa)],[4266]) ).
thf(4268,plain,
sk4 != sk2,
inference(simp,[status(thm)],[4267]) ).
thf(5086,plain,
! [A: a] :
( ( ( ( A = sk1 )
| ( A = sk4 ) )
= ( ( A = sk1 )
| ( A = sk2 ) ) )
| ( ( ^ [B: a] :
( ( B = sk1 )
| ( B = sk4 ) ) )
= ( (=) @ a @ sk1 ) ) ),
inference(simplifyReflect,[status(thm)],[5085,4268]) ).
thf(5087,plain,
! [B: a,A: a] :
( ( ( ( B = sk1 )
| ( B = sk4 ) )
= ( sk1 = B ) )
| ( ( ( A = sk1 )
| ( A = sk4 ) )
= ( ( A = sk1 )
| ( A = sk2 ) ) ) ),
inference(func_ext,[status(esa)],[5086]) ).
thf(5106,plain,
! [B: a,A: a] :
( ~ ( ( B = sk1 )
| ( B = sk4 ) )
| ( sk1 = B )
| ~ ( ( A = sk1 )
| ( A = sk4 ) )
| ( A = sk1 )
| ( A = sk2 ) ),
inference(bool_ext,[status(thm)],[5087]) ).
thf(5145,plain,
! [B: a,A: a] :
( ( sk1 = B )
| ~ ( ( B = sk1 )
| ( B = sk4 ) )
| ~ ( ( A = sk1 )
| ( A = sk4 ) )
| ( A = sk1 )
| ( A = sk2 ) ),
inference(lifteq,[status(thm)],[5106]) ).
thf(5212,plain,
! [B: a,A: a] :
( ( A = sk1 )
| ( A = sk2 )
| ( A != sk4 )
| ( B != sk4 )
| ( sk1 = B ) ),
inference(cnf,[status(esa)],[5145]) ).
thf(5218,plain,
! [B: a,A: a] :
( ( A = sk1 )
| ( A = sk2 )
| ( A != sk4 )
| ( B != sk4 )
| ( sk1 = B ) ),
inference(lifteq,[status(thm)],[5212]) ).
thf(5219,plain,
( ( sk4 = sk1 )
| ( sk4 = sk2 )
| ( sk4 = sk1 ) ),
inference(simp,[status(thm)],[5218]) ).
thf(5285,plain,
( ( sk4 = sk1 )
| ( sk4 = sk2 ) ),
inference(simp,[status(thm)],[5219]) ).
thf(5286,plain,
sk4 = sk1,
inference(simplifyReflect,[status(thm)],[5285,4268]) ).
thf(5758,plain,
! [A: a] :
( ( sk2 = sk1 )
| ( ( ( A = sk1 )
| ( A = sk2 ) )
= ( ( A = sk1 )
| ( A = sk1 ) ) )
| ( ( ^ [B: a] :
( ( B = sk1 )
| ( B = sk2 ) ) )
= ( (=) @ a @ sk1 ) ) ),
inference(rewrite,[status(thm)],[1631,4053,5286]) ).
thf(5759,plain,
! [A: a] :
( ( sk2 = sk1 )
| ( ( ( A = sk1 )
| ( A = sk2 ) )
= ( A = sk1 ) )
| ( ( ^ [B: a] :
( ( B = sk1 )
| ( B = sk2 ) ) )
= ( (=) @ a @ sk1 ) ) ),
inference(simp,[status(thm)],[5758]) ).
thf(5289,plain,
sk2 != sk1,
inference(rewrite,[status(thm)],[4268,5286]) ).
thf(5760,plain,
! [A: a] :
( ( ( ( A = sk1 )
| ( A = sk2 ) )
= ( A = sk1 ) )
| ( ( ^ [B: a] :
( ( B = sk1 )
| ( B = sk2 ) ) )
= ( (=) @ a @ sk1 ) ) ),
inference(simplifyReflect,[status(thm)],[5759,5289]) ).
thf(5762,plain,
! [A: a] :
( ( ( ^ [B: a] :
( ( B = sk1 )
| ( B = sk2 ) ) )
= ( (=) @ a @ sk1 ) )
| ~ ( ( A = sk1 )
| ( A = sk2 ) )
| ( A = sk1 ) ),
inference(bool_ext,[status(thm)],[5760]) ).
thf(5766,plain,
! [A: a] :
( ( A = sk1 )
| ( ( ^ [B: a] :
( ( B = sk1 )
| ( B = sk2 ) ) )
= ( (=) @ a @ sk1 ) )
| ~ ( ( A = sk1 )
| ( A = sk2 ) ) ),
inference(lifteq,[status(thm)],[5762]) ).
thf(5768,plain,
! [A: a] :
( ( A != sk2 )
| ( ( ^ [B: a] :
( ( B = sk1 )
| ( B = sk2 ) ) )
= ( (=) @ a @ sk1 ) )
| ( A = sk1 ) ),
inference(cnf,[status(esa)],[5766]) ).
thf(5770,plain,
! [A: a] :
( ( A != sk2 )
| ( ( ^ [B: a] :
( ( B = sk1 )
| ( B = sk2 ) ) )
= ( (=) @ a @ sk1 ) )
| ( A = sk1 ) ),
inference(lifteq,[status(thm)],[5768]) ).
thf(5771,plain,
( ( ( ^ [A: a] :
( ( A = sk1 )
| ( A = sk2 ) ) )
= ( (=) @ a @ sk1 ) )
| ( sk2 = sk1 ) ),
inference(simp,[status(thm)],[5770]) ).
thf(5777,plain,
( ( ^ [A: a] :
( ( A = sk1 )
| ( A = sk2 ) ) )
= ( (=) @ a @ sk1 ) ),
inference(simplifyReflect,[status(thm)],[5771,5289]) ).
thf(5778,plain,
! [A: a] :
( ( ( A = sk1 )
| ( A = sk2 ) )
= ( sk1 = A ) ),
inference(func_ext,[status(esa)],[5777]) ).
thf(5784,plain,
! [A: a] :
( ~ ( ( A = sk1 )
| ( A = sk2 ) )
| ( sk1 = A ) ),
inference(bool_ext,[status(thm)],[5778]) ).
thf(5798,plain,
! [A: a] :
( ( sk1 = A )
| ~ ( ( A = sk1 )
| ( A = sk2 ) ) ),
inference(lifteq,[status(thm)],[5784]) ).
thf(5810,plain,
! [A: a] :
( ( A != sk2 )
| ( sk1 = A ) ),
inference(cnf,[status(esa)],[5798]) ).
thf(5812,plain,
! [A: a] :
( ( A != sk2 )
| ( sk1 = A ) ),
inference(lifteq,[status(thm)],[5810]) ).
thf(5813,plain,
sk2 = sk1,
inference(simp,[status(thm)],[5812]) ).
thf(5830,plain,
$false,
inference(simplifyReflect,[status(thm)],[5813,5289]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SEV248^5 : TPTP v8.2.0. Released v4.0.0.
% 0.06/0.11 % Command : run_Leo-III %s %d SAT
% 0.10/0.31 % Computer : n025.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Fri Jun 21 18:44:10 EDT 2024
% 0.10/0.31 % CPUTime :
% 0.99/0.95 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.26/1.11 % [INFO] Parsing done (154ms).
% 1.26/1.12 % [INFO] Running in sequential loop mode.
% 1.85/1.48 % [INFO] nitpick registered as external prover.
% 1.85/1.48 % [INFO] Scanning for conjecture ...
% 2.04/1.57 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.04/1.61 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.04/1.61 % [INFO] Problem is higher-order (TPTP THF).
% 2.04/1.62 % [INFO] Type checking passed.
% 2.04/1.62 % [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 ...
% 80.62/13.55 % [INFO] Killing All external provers ...
% 80.62/13.57 % Time passed: 13067ms (effective reasoning time: 12426ms)
% 80.62/13.57 % 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)>
% 80.62/13.57 % Axioms used in derivation (0):
% 80.62/13.57 % No. of inferences in proof: 76
% 80.62/13.57 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 13067 ms resp. 12426 ms w/o parsing
% 80.75/13.64 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 80.75/13.64 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------