TSTP Solution File: SEV119^5 by Leo-III---1.7.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : SEV119^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n018.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 21 04:09:59 EDT 2024
% Result : Theorem 130.13s 35.24s
% Output : Refutation 130.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 28
% Syntax : Number of formulae : 82 ( 25 unt; 27 typ; 0 def)
% Number of atoms : 365 ( 39 equ; 0 cnn)
% Maximal formula atoms : 14 ( 6 avg)
% Number of connectives : 1387 ( 67 ~; 98 |; 102 &; 898 @)
% ( 0 <=>; 222 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 274 ( 274 >; 0 *; 0 +; 0 <<)
% Number of symbols : 30 ( 28 usr; 18 con; 0-4 aty)
% Number of variables : 475 ( 140 ^ 335 !; 0 ?; 475 :)
% Comments :
%------------------------------------------------------------------------------
thf(a_type,type,
a: $tType ).
thf(sk1_type,type,
sk1: ( a > a > $o ) > $o ).
thf(sk2_type,type,
sk2: a > a > $o ).
thf(sk3_type,type,
sk3: a > a > $o ).
thf(sk6_type,type,
sk6: a ).
thf(sk7_type,type,
sk7: a ).
thf(sk8_type,type,
sk8: a > a > $o ).
thf(sk11_type,type,
sk11: a > a > $o ).
thf(sk14_type,type,
sk14: a > a > $o ).
thf(sk17_type,type,
sk17: a > a > $o ).
thf(sk18_type,type,
sk18: a ).
thf(sk27_type,type,
sk27: a ).
thf(sk28_type,type,
sk28: a ).
thf(sk32_type,type,
sk32: a ).
thf(sk33_type,type,
sk33: a ).
thf(sk37_type,type,
sk37: a ).
thf(sk38_type,type,
sk38: a ).
thf(sk51_type,type,
sk51: a > a > $o ).
thf(sk52_type,type,
sk52: a > a > a > a > $o ).
thf(sk63_type,type,
sk63: a > a > $o ).
thf(sk64_type,type,
sk64: a > a > $o ).
thf(sk69_type,type,
sk69: a ).
thf(sk70_type,type,
sk70: a ).
thf(sk71_type,type,
sk71: a ).
thf(sk72_type,type,
sk72: a ).
thf(sk89_type,type,
sk89: a ).
thf(sk90_type,type,
sk90: a ).
thf(1,conjecture,
! [A: ( a > a > $o ) > $o,B: a > a > $o,C: a > a > $o] :
( ( ^ [D: a,E: a] :
! [F: a > a > $o] :
( ( ! [G: a,H: a] :
( ( ( B @ G @ H )
| ( C @ G @ H ) )
=> ( F @ G @ H ) )
& ( A @ F ) )
=> ( F @ D @ E ) ) )
= ( ^ [D: a,E: a] :
! [F: a > a > $o] :
( ( ! [G: a,H: a] :
( ( ! [I: a > a > $o] :
( ( ! [J: a,K: a] :
( ( B @ J @ K )
=> ( I @ J @ K ) )
& ( A @ I ) )
=> ( I @ G @ H ) )
| ! [I: a > a > $o] :
( ( ! [J: a,K: a] :
( ( C @ J @ K )
=> ( I @ J @ K ) )
& ( A @ I ) )
=> ( I @ G @ H ) ) )
=> ( F @ G @ H ) )
& ( A @ F ) )
=> ( F @ D @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM252_pme) ).
thf(2,negated_conjecture,
~ ! [A: ( a > a > $o ) > $o,B: a > a > $o,C: a > a > $o] :
( ( ^ [D: a,E: a] :
! [F: a > a > $o] :
( ( ! [G: a,H: a] :
( ( ( B @ G @ H )
| ( C @ G @ H ) )
=> ( F @ G @ H ) )
& ( A @ F ) )
=> ( F @ D @ E ) ) )
= ( ^ [D: a,E: a] :
! [F: a > a > $o] :
( ( ! [G: a,H: a] :
( ( ! [I: a > a > $o] :
( ( ! [J: a,K: a] :
( ( B @ J @ K )
=> ( I @ J @ K ) )
& ( A @ I ) )
=> ( I @ G @ H ) )
| ! [I: a > a > $o] :
( ( ! [J: a,K: a] :
( ( C @ J @ K )
=> ( I @ J @ K ) )
& ( A @ I ) )
=> ( I @ G @ H ) ) )
=> ( F @ G @ H ) )
& ( A @ F ) )
=> ( F @ D @ E ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: ( a > a > $o ) > $o,B: a > a > $o,C: a > a > $o] :
( ( ^ [D: a,E: a] :
! [F: a > a > $o] :
( ( ! [G: a,H: a] :
( ( ( B @ G @ H )
| ( C @ G @ H ) )
=> ( F @ G @ H ) )
& ( A @ F ) )
=> ( F @ D @ E ) ) )
= ( ^ [D: a,E: a] :
! [F: a > a > $o] :
( ( ! [G: a,H: a] :
( ( ! [I: a > a > $o] :
( ( ! [J: a,K: a] :
( ( B @ J @ K )
=> ( I @ J @ K ) )
& ( A @ I ) )
=> ( I @ G @ H ) )
| ! [I: a > a > $o] :
( ( ! [J: a,K: a] :
( ( C @ J @ K )
=> ( I @ J @ K ) )
& ( A @ I ) )
=> ( I @ G @ H ) ) )
=> ( F @ G @ H ) )
& ( A @ F ) )
=> ( F @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
( ( ^ [A: a,B: a] :
! [C: a > a > $o] :
( ( ! [D: a,E: a] :
( ( ( sk2 @ D @ E )
| ( sk3 @ D @ E ) )
=> ( C @ D @ E ) )
& ( sk1 @ C ) )
=> ( C @ A @ B ) ) )
!= ( ^ [A: a,B: a] :
! [C: a > a > $o] :
( ( ! [D: a,E: a] :
( ( ! [F: a > a > $o] :
( ( ! [G: a,H: a] :
( ( sk2 @ G @ H )
=> ( F @ G @ H ) )
& ( sk1 @ F ) )
=> ( F @ D @ E ) )
| ! [F: a > a > $o] :
( ( ! [G: a,H: a] :
( ( sk3 @ G @ H )
=> ( F @ G @ H ) )
& ( sk1 @ F ) )
=> ( F @ D @ E ) ) )
=> ( C @ D @ E ) )
& ( sk1 @ C ) )
=> ( C @ A @ B ) ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(5,plain,
( ( ^ [A: a,B: a] :
! [C: a > a > $o] :
( ( ! [D: a,E: a] :
( ( ( sk2 @ D @ E )
| ( sk3 @ D @ E ) )
=> ( C @ D @ E ) )
& ( sk1 @ C ) )
=> ( C @ A @ B ) ) )
!= ( ^ [A: a,B: a] :
! [C: a > a > $o] :
( ( ! [D: a,E: a] :
( ( ! [F: a > a > $o] :
( ( ! [G: a,H: a] :
( ( sk2 @ G @ H )
=> ( F @ G @ H ) )
& ( sk1 @ F ) )
=> ( F @ D @ E ) )
| ! [F: a > a > $o] :
( ( ! [G: a,H: a] :
( ( sk3 @ G @ H )
=> ( F @ G @ H ) )
& ( sk1 @ F ) )
=> ( F @ D @ E ) ) )
=> ( C @ D @ E ) )
& ( sk1 @ C ) )
=> ( C @ A @ B ) ) ) ),
inference(lifteq,[status(thm)],[4]) ).
thf(6,plain,
( ( ^ [A: a,B: a,C: a > a > $o] :
( ( ! [D: a,E: a] :
( ( ( sk2 @ D @ E )
| ( sk3 @ D @ E ) )
=> ( C @ D @ E ) )
& ( sk1 @ C ) )
=> ( C @ A @ B ) ) )
!= ( ^ [A: a,B: a,C: a > a > $o] :
( ( ! [D: a,E: a] :
( ( ! [F: a > a > $o] :
( ( ! [G: a,H: a] :
( ( sk2 @ G @ H )
=> ( F @ G @ H ) )
& ( sk1 @ F ) )
=> ( F @ D @ E ) )
| ! [F: a > a > $o] :
( ( ! [G: a,H: a] :
( ( sk3 @ G @ H )
=> ( F @ G @ H ) )
& ( sk1 @ F ) )
=> ( F @ D @ E ) ) )
=> ( C @ D @ E ) )
& ( sk1 @ C ) )
=> ( C @ A @ B ) ) ) ),
inference(simp,[status(thm)],[5]) ).
thf(8,plain,
( ( ( ^ [A: a,B: a,C: a > a > $o] :
( ! [D: a,E: a] :
( ( ( sk2 @ D @ E )
| ( sk3 @ D @ E ) )
=> ( C @ D @ E ) )
& ( sk1 @ C ) ) )
!= ( ^ [A: a,B: a,C: a > a > $o] :
( ! [D: a,E: a] :
( ( ! [F: a > a > $o] :
( ( ! [G: a,H: a] :
( ( sk2 @ G @ H )
=> ( F @ G @ H ) )
& ( sk1 @ F ) )
=> ( F @ D @ E ) )
| ! [F: a > a > $o] :
( ( ! [G: a,H: a] :
( ( sk3 @ G @ H )
=> ( F @ G @ H ) )
& ( sk1 @ F ) )
=> ( F @ D @ E ) ) )
=> ( C @ D @ E ) )
& ( sk1 @ C ) ) ) )
| ( ( ^ [A: a,B: a,C: a > a > $o] : ( C @ A @ B ) )
!= ( ^ [A: a,B: a,C: a > a > $o] : ( C @ A @ B ) ) ) ),
inference(simp,[status(thm)],[6]) ).
thf(10,plain,
( ( ^ [A: a,B: a,C: a > a > $o] :
( ! [D: a,E: a] :
( ( ( sk2 @ D @ E )
| ( sk3 @ D @ E ) )
=> ( C @ D @ E ) )
& ( sk1 @ C ) ) )
!= ( ^ [A: a,B: a,C: a > a > $o] :
( ! [D: a,E: a] :
( ( ! [F: a > a > $o] :
( ( ! [G: a,H: a] :
( ( sk2 @ G @ H )
=> ( F @ G @ H ) )
& ( sk1 @ F ) )
=> ( F @ D @ E ) )
| ! [F: a > a > $o] :
( ( ! [G: a,H: a] :
( ( sk3 @ G @ H )
=> ( F @ G @ H ) )
& ( sk1 @ F ) )
=> ( F @ D @ E ) ) )
=> ( C @ D @ E ) )
& ( sk1 @ C ) ) ) ),
inference(simp,[status(thm)],[8]) ).
thf(11,plain,
( ( ( ^ [A: a,B: a,C: a > a > $o] :
! [D: a,E: a] :
( ( ( sk2 @ D @ E )
| ( sk3 @ D @ E ) )
=> ( C @ D @ E ) ) )
!= ( ^ [A: a,B: a,C: a > a > $o] :
! [D: a,E: a] :
( ( ! [F: a > a > $o] :
( ( ! [G: a,H: a] :
( ( sk2 @ G @ H )
=> ( F @ G @ H ) )
& ( sk1 @ F ) )
=> ( F @ D @ E ) )
| ! [F: a > a > $o] :
( ( ! [G: a,H: a] :
( ( sk3 @ G @ H )
=> ( F @ G @ H ) )
& ( sk1 @ F ) )
=> ( F @ D @ E ) ) )
=> ( C @ D @ E ) ) ) )
| ( ( ^ [A: a,B: a] : sk1 )
!= ( ^ [A: a,B: a] : sk1 ) ) ),
inference(simp,[status(thm)],[10]) ).
thf(13,plain,
( ( ^ [A: a,B: a,C: a > a > $o] :
! [D: a,E: a] :
( ( ( sk2 @ D @ E )
| ( sk3 @ D @ E ) )
=> ( C @ D @ E ) ) )
!= ( ^ [A: a,B: a,C: a > a > $o] :
! [D: a,E: a] :
( ( ! [F: a > a > $o] :
( ( ! [G: a,H: a] :
( ( sk2 @ G @ H )
=> ( F @ G @ H ) )
& ( sk1 @ F ) )
=> ( F @ D @ E ) )
| ! [F: a > a > $o] :
( ( ! [G: a,H: a] :
( ( sk3 @ G @ H )
=> ( F @ G @ H ) )
& ( sk1 @ F ) )
=> ( F @ D @ E ) ) )
=> ( C @ D @ E ) ) ) ),
inference(simp,[status(thm)],[11]) ).
thf(14,plain,
( ( ^ [A: a,B: a,C: a > a > $o,D: a] :
! [E: a] :
( ( ( sk2 @ D @ E )
| ( sk3 @ D @ E ) )
=> ( C @ D @ E ) ) )
!= ( ^ [A: a,B: a,C: a > a > $o,D: a] :
! [E: a] :
( ( ! [F: a > a > $o] :
( ( ! [G: a,H: a] :
( ( sk2 @ G @ H )
=> ( F @ G @ H ) )
& ( sk1 @ F ) )
=> ( F @ D @ E ) )
| ! [F: a > a > $o] :
( ( ! [G: a,H: a] :
( ( sk3 @ G @ H )
=> ( F @ G @ H ) )
& ( sk1 @ F ) )
=> ( F @ D @ E ) ) )
=> ( C @ D @ E ) ) ) ),
inference(simp,[status(thm)],[13]) ).
thf(16,plain,
( ( ^ [A: a,B: a,C: a > a > $o,D: a,E: a] :
( ( ( sk2 @ D @ E )
| ( sk3 @ D @ E ) )
=> ( C @ D @ E ) ) )
!= ( ^ [A: a,B: a,C: a > a > $o,D: a,E: a] :
( ( ! [F: a > a > $o] :
( ( ! [G: a,H: a] :
( ( sk2 @ G @ H )
=> ( F @ G @ H ) )
& ( sk1 @ F ) )
=> ( F @ D @ E ) )
| ! [F: a > a > $o] :
( ( ! [G: a,H: a] :
( ( sk3 @ G @ H )
=> ( F @ G @ H ) )
& ( sk1 @ F ) )
=> ( F @ D @ E ) ) )
=> ( C @ D @ E ) ) ) ),
inference(simp,[status(thm)],[14]) ).
thf(18,plain,
( ( ( ^ [A: a,B: a,C: a > a > $o,D: a,E: a] :
( ( sk2 @ D @ E )
| ( sk3 @ D @ E ) ) )
!= ( ^ [A: a,B: a,C: a > a > $o,D: a,E: a] :
( ! [F: a > a > $o] :
( ( ! [G: a,H: a] :
( ( sk2 @ G @ H )
=> ( F @ G @ H ) )
& ( sk1 @ F ) )
=> ( F @ D @ E ) )
| ! [F: a > a > $o] :
( ( ! [G: a,H: a] :
( ( sk3 @ G @ H )
=> ( F @ G @ H ) )
& ( sk1 @ F ) )
=> ( F @ D @ E ) ) ) ) )
| ( ( ^ [A: a,B: a,C: a > a > $o] : C )
!= ( ^ [A: a,B: a,C: a > a > $o] : C ) ) ),
inference(simp,[status(thm)],[16]) ).
thf(20,plain,
( ( ^ [A: a,B: a,C: a > a > $o,D: a,E: a] :
( ( sk2 @ D @ E )
| ( sk3 @ D @ E ) ) )
!= ( ^ [A: a,B: a,C: a > a > $o,D: a,E: a] :
( ! [F: a > a > $o] :
( ( ! [G: a,H: a] :
( ( sk2 @ G @ H )
=> ( F @ G @ H ) )
& ( sk1 @ F ) )
=> ( F @ D @ E ) )
| ! [F: a > a > $o] :
( ( ! [G: a,H: a] :
( ( sk3 @ G @ H )
=> ( F @ G @ H ) )
& ( sk1 @ F ) )
=> ( F @ D @ E ) ) ) ) ),
inference(simp,[status(thm)],[18]) ).
thf(22,plain,
( ( ( sk2 @ sk27 @ sk28 )
| ( sk3 @ sk27 @ sk28 ) )
!= ( ! [A: a > a > $o] :
( ( ! [B: a,C: a] :
( ( sk2 @ B @ C )
=> ( A @ B @ C ) )
& ( sk1 @ A ) )
=> ( A @ sk27 @ sk28 ) )
| ! [A: a > a > $o] :
( ( ! [B: a,C: a] :
( ( sk3 @ B @ C )
=> ( A @ B @ C ) )
& ( sk1 @ A ) )
=> ( A @ sk27 @ sk28 ) ) ) ),
inference(func_ext,[status(esa)],[20]) ).
thf(103,plain,
( ~ ( ( sk2 @ sk27 @ sk28 )
| ( sk3 @ sk27 @ sk28 ) )
| ~ ( ! [A: a > a > $o] :
( ( ! [B: a,C: a] :
( ( sk2 @ B @ C )
=> ( A @ B @ C ) )
& ( sk1 @ A ) )
=> ( A @ sk27 @ sk28 ) )
| ! [A: a > a > $o] :
( ( ! [B: a,C: a] :
( ( sk3 @ B @ C )
=> ( A @ B @ C ) )
& ( sk1 @ A ) )
=> ( A @ sk27 @ sk28 ) ) ) ),
inference(bool_ext,[status(thm)],[22]) ).
thf(106,plain,
( ( sk1 @ sk63 )
| ~ ( sk2 @ sk27 @ sk28 ) ),
inference(cnf,[status(esa)],[103]) ).
thf(21,plain,
( ( ( ^ [A: a,B: a,C: a > a > $o] : sk2 )
!= ( ^ [A: a,B: a,C: a > a > $o,D: a,E: a] :
! [F: a > a > $o] :
( ( ! [G: a,H: a] :
( ( sk2 @ G @ H )
=> ( F @ G @ H ) )
& ( sk1 @ F ) )
=> ( F @ D @ E ) ) ) )
| ( ( ^ [A: a,B: a,C: a > a > $o] : sk3 )
!= ( ^ [A: a,B: a,C: a > a > $o,D: a,E: a] :
! [F: a > a > $o] :
( ( ! [G: a,H: a] :
( ( sk3 @ G @ H )
=> ( F @ G @ H ) )
& ( sk1 @ F ) )
=> ( F @ D @ E ) ) ) ) ),
inference(simp,[status(thm)],[20]) ).
thf(9,plain,
( ( ( ! [A: a,B: a] :
( ( ( sk2 @ A @ B )
| ( sk3 @ A @ B ) )
=> ( sk8 @ A @ B ) )
& ( sk1 @ sk8 ) )
=> ( sk8 @ sk6 @ sk7 ) )
!= ( ( ! [A: a,B: a] :
( ( ! [C: a > a > $o] :
( ( ! [D: a,E: a] :
( ( sk2 @ D @ E )
=> ( C @ D @ E ) )
& ( sk1 @ C ) )
=> ( C @ A @ B ) )
| ! [C: a > a > $o] :
( ( ! [D: a,E: a] :
( ( sk3 @ D @ E )
=> ( C @ D @ E ) )
& ( sk1 @ C ) )
=> ( C @ A @ B ) ) )
=> ( sk8 @ A @ B ) )
& ( sk1 @ sk8 ) )
=> ( sk8 @ sk6 @ sk7 ) ) ),
inference(func_ext,[status(esa)],[6]) ).
thf(157,plain,
( ~ ( ( ! [A: a,B: a] :
( ( ( sk2 @ A @ B )
| ( sk3 @ A @ B ) )
=> ( sk8 @ A @ B ) )
& ( sk1 @ sk8 ) )
=> ( sk8 @ sk6 @ sk7 ) )
| ~ ( ( ! [A: a,B: a] :
( ( ! [C: a > a > $o] :
( ( ! [D: a,E: a] :
( ( sk2 @ D @ E )
=> ( C @ D @ E ) )
& ( sk1 @ C ) )
=> ( C @ A @ B ) )
| ! [C: a > a > $o] :
( ( ! [D: a,E: a] :
( ( sk3 @ D @ E )
=> ( C @ D @ E ) )
& ( sk1 @ C ) )
=> ( C @ A @ B ) ) )
=> ( sk8 @ A @ B ) )
& ( sk1 @ sk8 ) )
=> ( sk8 @ sk6 @ sk7 ) ) ),
inference(bool_ext,[status(thm)],[9]) ).
thf(197,plain,
( ~ ( sk8 @ sk6 @ sk7 )
| ~ ( sk8 @ sk6 @ sk7 ) ),
inference(cnf,[status(esa)],[157]) ).
thf(229,plain,
~ ( sk8 @ sk6 @ sk7 ),
inference(simp,[status(thm)],[197]) ).
thf(17,plain,
( ( ! [A: a] :
( ( ( sk2 @ sk18 @ A )
| ( sk3 @ sk18 @ A ) )
=> ( sk17 @ sk18 @ A ) ) )
!= ( ! [A: a] :
( ( ! [B: a > a > $o] :
( ( ! [C: a,D: a] :
( ( sk2 @ C @ D )
=> ( B @ C @ D ) )
& ( sk1 @ B ) )
=> ( B @ sk18 @ A ) )
| ! [B: a > a > $o] :
( ( ! [C: a,D: a] :
( ( sk3 @ C @ D )
=> ( B @ C @ D ) )
& ( sk1 @ B ) )
=> ( B @ sk18 @ A ) ) )
=> ( sk17 @ sk18 @ A ) ) ) ),
inference(func_ext,[status(esa)],[14]) ).
thf(108,plain,
( ~ ( sk63 @ sk27 @ sk28 )
| ~ ( sk3 @ sk27 @ sk28 ) ),
inference(cnf,[status(esa)],[103]) ).
thf(15,plain,
( ( ! [A: a,B: a] :
( ( ( sk2 @ A @ B )
| ( sk3 @ A @ B ) )
=> ( sk14 @ A @ B ) ) )
!= ( ! [A: a,B: a] :
( ( ! [C: a > a > $o] :
( ( ! [D: a,E: a] :
( ( sk2 @ D @ E )
=> ( C @ D @ E ) )
& ( sk1 @ C ) )
=> ( C @ A @ B ) )
| ! [C: a > a > $o] :
( ( ! [D: a,E: a] :
( ( sk3 @ D @ E )
=> ( C @ D @ E ) )
& ( sk1 @ C ) )
=> ( C @ A @ B ) ) )
=> ( sk14 @ A @ B ) ) ) ),
inference(func_ext,[status(esa)],[13]) ).
thf(123,plain,
( ( ^ [A: a] :
! [B: a] :
( ( ( sk2 @ A @ B )
| ( sk3 @ A @ B ) )
=> ( sk14 @ A @ B ) ) )
!= ( ^ [A: a] :
! [B: a] :
( ( ! [C: a > a > $o] :
( ( ! [D: a,E: a] :
( ( sk2 @ D @ E )
=> ( C @ D @ E ) )
& ( sk1 @ C ) )
=> ( C @ A @ B ) )
| ! [C: a > a > $o] :
( ( ! [D: a,E: a] :
( ( sk3 @ D @ E )
=> ( C @ D @ E ) )
& ( sk1 @ C ) )
=> ( C @ A @ B ) ) )
=> ( sk14 @ A @ B ) ) ) ),
inference(simp,[status(thm)],[15]) ).
thf(150,plain,
( ( ^ [A: a,B: a] :
( ( ( sk2 @ A @ B )
| ( sk3 @ A @ B ) )
=> ( sk14 @ A @ B ) ) )
!= ( ^ [A: a,B: a] :
( ( ! [C: a > a > $o] :
( ( ! [D: a,E: a] :
( ( sk2 @ D @ E )
=> ( C @ D @ E ) )
& ( sk1 @ C ) )
=> ( C @ A @ B ) )
| ! [C: a > a > $o] :
( ( ! [D: a,E: a] :
( ( sk3 @ D @ E )
=> ( C @ D @ E ) )
& ( sk1 @ C ) )
=> ( C @ A @ B ) ) )
=> ( sk14 @ A @ B ) ) ) ),
inference(simp,[status(thm)],[123]) ).
thf(107,plain,
( ~ ( sk63 @ sk27 @ sk28 )
| ~ ( sk2 @ sk27 @ sk28 ) ),
inference(cnf,[status(esa)],[103]) ).
thf(209,plain,
( ( sk1 @ sk8 )
| ( sk1 @ sk8 ) ),
inference(cnf,[status(esa)],[157]) ).
thf(227,plain,
sk1 @ sk8,
inference(simp,[status(thm)],[209]) ).
thf(151,plain,
( ( ( ^ [A: a,B: a] :
( ( sk2 @ A @ B )
| ( sk3 @ A @ B ) ) )
!= ( ^ [A: a,B: a] :
( ! [C: a > a > $o] :
( ( ! [D: a,E: a] :
( ( sk2 @ D @ E )
=> ( C @ D @ E ) )
& ( sk1 @ C ) )
=> ( C @ A @ B ) )
| ! [C: a > a > $o] :
( ( ! [D: a,E: a] :
( ( sk3 @ D @ E )
=> ( C @ D @ E ) )
& ( sk1 @ C ) )
=> ( C @ A @ B ) ) ) ) )
| ( sk14 != sk14 ) ),
inference(simp,[status(thm)],[150]) ).
thf(152,plain,
( ( ^ [A: a,B: a] :
( ( sk2 @ A @ B )
| ( sk3 @ A @ B ) ) )
!= ( ^ [A: a,B: a] :
( ! [C: a > a > $o] :
( ( ! [D: a,E: a] :
( ( sk2 @ D @ E )
=> ( C @ D @ E ) )
& ( sk1 @ C ) )
=> ( C @ A @ B ) )
| ! [C: a > a > $o] :
( ( ! [D: a,E: a] :
( ( sk3 @ D @ E )
=> ( C @ D @ E ) )
& ( sk1 @ C ) )
=> ( C @ A @ B ) ) ) ) ),
inference(simp,[status(thm)],[151]) ).
thf(116,plain,
( ( sk1 @ sk64 )
| ~ ( sk3 @ sk27 @ sk28 ) ),
inference(cnf,[status(esa)],[103]) ).
thf(257,plain,
( ~ ! [A: a] :
( ( ( sk2 @ sk18 @ A )
| ( sk3 @ sk18 @ A ) )
=> ( sk17 @ sk18 @ A ) )
| ~ ! [A: a] :
( ( ! [B: a > a > $o] :
( ( ! [C: a,D: a] :
( ( sk2 @ C @ D )
=> ( B @ C @ D ) )
& ( sk1 @ B ) )
=> ( B @ sk18 @ A ) )
| ! [B: a > a > $o] :
( ( ! [C: a,D: a] :
( ( sk3 @ C @ D )
=> ( B @ C @ D ) )
& ( sk1 @ B ) )
=> ( B @ sk18 @ A ) ) )
=> ( sk17 @ sk18 @ A ) ) ),
inference(bool_ext,[status(thm)],[17]) ).
thf(265,plain,
( ~ ( sk17 @ sk18 @ sk90 )
| ~ ( sk17 @ sk18 @ sk89 ) ),
inference(cnf,[status(esa)],[257]) ).
thf(109,plain,
( ~ ( sk64 @ sk27 @ sk28 )
| ~ ( sk2 @ sk27 @ sk28 ) ),
inference(cnf,[status(esa)],[103]) ).
thf(256,plain,
( ( ^ [A: a] :
( ( ( sk2 @ sk18 @ A )
| ( sk3 @ sk18 @ A ) )
=> ( sk17 @ sk18 @ A ) ) )
!= ( ^ [A: a] :
( ( ! [B: a > a > $o] :
( ( ! [C: a,D: a] :
( ( sk2 @ C @ D )
=> ( B @ C @ D ) )
& ( sk1 @ B ) )
=> ( B @ sk18 @ A ) )
| ! [B: a > a > $o] :
( ( ! [C: a,D: a] :
( ( sk3 @ C @ D )
=> ( B @ C @ D ) )
& ( sk1 @ B ) )
=> ( B @ sk18 @ A ) ) )
=> ( sk17 @ sk18 @ A ) ) ) ),
inference(simp,[status(thm)],[17]) ).
thf(124,plain,
( ~ ! [A: a,B: a] :
( ( ( sk2 @ A @ B )
| ( sk3 @ A @ B ) )
=> ( sk14 @ A @ B ) )
| ~ ! [A: a,B: a] :
( ( ! [C: a > a > $o] :
( ( ! [D: a,E: a] :
( ( sk2 @ D @ E )
=> ( C @ D @ E ) )
& ( sk1 @ C ) )
=> ( C @ A @ B ) )
| ! [C: a > a > $o] :
( ( ! [D: a,E: a] :
( ( sk3 @ D @ E )
=> ( C @ D @ E ) )
& ( sk1 @ C ) )
=> ( C @ A @ B ) ) )
=> ( sk14 @ A @ B ) ) ),
inference(bool_ext,[status(thm)],[15]) ).
thf(128,plain,
( ~ ( sk14 @ sk71 @ sk72 )
| ~ ( sk14 @ sk69 @ sk70 ) ),
inference(cnf,[status(esa)],[124]) ).
thf(105,plain,
( ( sk1 @ sk64 )
| ~ ( sk2 @ sk27 @ sk28 ) ),
inference(cnf,[status(esa)],[103]) ).
thf(359,plain,
( ( ( ^ [A: a] :
( ( sk2 @ sk18 @ A )
| ( sk3 @ sk18 @ A ) ) )
!= ( ^ [A: a] :
( ! [B: a > a > $o] :
( ( ! [C: a,D: a] :
( ( sk2 @ C @ D )
=> ( B @ C @ D ) )
& ( sk1 @ B ) )
=> ( B @ sk18 @ A ) )
| ! [B: a > a > $o] :
( ( ! [C: a,D: a] :
( ( sk3 @ C @ D )
=> ( B @ C @ D ) )
& ( sk1 @ B ) )
=> ( B @ sk18 @ A ) ) ) ) )
| ( ( sk17 @ sk18 )
!= ( sk17 @ sk18 ) ) ),
inference(simp,[status(thm)],[256]) ).
thf(360,plain,
( ( ^ [A: a] :
( ( sk2 @ sk18 @ A )
| ( sk3 @ sk18 @ A ) ) )
!= ( ^ [A: a] :
( ! [B: a > a > $o] :
( ( ! [C: a,D: a] :
( ( sk2 @ C @ D )
=> ( B @ C @ D ) )
& ( sk1 @ B ) )
=> ( B @ sk18 @ A ) )
| ! [B: a > a > $o] :
( ( ! [C: a,D: a] :
( ( sk3 @ C @ D )
=> ( B @ C @ D ) )
& ( sk1 @ B ) )
=> ( B @ sk18 @ A ) ) ) ) ),
inference(simp,[status(thm)],[359]) ).
thf(12,plain,
( ( ! [A: a,B: a] :
( ( ( sk2 @ A @ B )
| ( sk3 @ A @ B ) )
=> ( sk11 @ A @ B ) )
& ( sk1 @ sk11 ) )
!= ( ! [A: a,B: a] :
( ( ! [C: a > a > $o] :
( ( ! [D: a,E: a] :
( ( sk2 @ D @ E )
=> ( C @ D @ E ) )
& ( sk1 @ C ) )
=> ( C @ A @ B ) )
| ! [C: a > a > $o] :
( ( ! [D: a,E: a] :
( ( sk3 @ D @ E )
=> ( C @ D @ E ) )
& ( sk1 @ C ) )
=> ( C @ A @ B ) ) )
=> ( sk11 @ A @ B ) )
& ( sk1 @ sk11 ) ) ),
inference(func_ext,[status(esa)],[10]) ).
thf(284,plain,
( ( ( ! [A: a,B: a] :
( ( ( sk2 @ A @ B )
| ( sk3 @ A @ B ) )
=> ( sk11 @ A @ B ) ) )
!= ( ! [A: a,B: a] :
( ( ! [C: a > a > $o] :
( ( ! [D: a,E: a] :
( ( sk2 @ D @ E )
=> ( C @ D @ E ) )
& ( sk1 @ C ) )
=> ( C @ A @ B ) )
| ! [C: a > a > $o] :
( ( ! [D: a,E: a] :
( ( sk3 @ D @ E )
=> ( C @ D @ E ) )
& ( sk1 @ C ) )
=> ( C @ A @ B ) ) )
=> ( sk11 @ A @ B ) ) ) )
| ( ( sk1 @ sk11 )
!= ( sk1 @ sk11 ) ) ),
inference(simp,[status(thm)],[12]) ).
thf(311,plain,
( ( ! [A: a,B: a] :
( ( ( sk2 @ A @ B )
| ( sk3 @ A @ B ) )
=> ( sk11 @ A @ B ) ) )
!= ( ! [A: a,B: a] :
( ( ! [C: a > a > $o] :
( ( ! [D: a,E: a] :
( ( sk2 @ D @ E )
=> ( C @ D @ E ) )
& ( sk1 @ C ) )
=> ( C @ A @ B ) )
| ! [C: a > a > $o] :
( ( ! [D: a,E: a] :
( ( sk3 @ D @ E )
=> ( C @ D @ E ) )
& ( sk1 @ C ) )
=> ( C @ A @ B ) ) )
=> ( sk11 @ A @ B ) ) ) ),
inference(simp,[status(thm)],[284]) ).
thf(7,plain,
( ( ! [A: a > a > $o] :
( ( ! [B: a,C: a] :
( ( ( sk2 @ B @ C )
| ( sk3 @ B @ C ) )
=> ( A @ B @ C ) )
& ( sk1 @ A ) )
=> ( A @ sk4 @ sk5 ) ) )
!= ( ! [A: a > a > $o] :
( ( ! [B: a,C: a] :
( ( ! [D: a > a > $o] :
( ( ! [E: a,F: a] :
( ( sk2 @ E @ F )
=> ( D @ E @ F ) )
& ( sk1 @ D ) )
=> ( D @ B @ C ) )
| ! [D: a > a > $o] :
( ( ! [E: a,F: a] :
( ( sk3 @ E @ F )
=> ( D @ E @ F ) )
& ( sk1 @ D ) )
=> ( D @ B @ C ) ) )
=> ( A @ B @ C ) )
& ( sk1 @ A ) )
=> ( A @ sk4 @ sk5 ) ) ) ),
inference(func_ext,[status(esa)],[5]) ).
thf(54,plain,
( ~ ! [A: a > a > $o] :
( ( ! [B: a,C: a] :
( ( ( sk2 @ B @ C )
| ( sk3 @ B @ C ) )
=> ( A @ B @ C ) )
& ( sk1 @ A ) )
=> ( A @ sk4 @ sk5 ) )
| ~ ! [A: a > a > $o] :
( ( ! [B: a,C: a] :
( ( ! [D: a > a > $o] :
( ( ! [E: a,F: a] :
( ( sk2 @ E @ F )
=> ( D @ E @ F ) )
& ( sk1 @ D ) )
=> ( D @ B @ C ) )
| ! [D: a > a > $o] :
( ( ! [E: a,F: a] :
( ( sk3 @ E @ F )
=> ( D @ E @ F ) )
& ( sk1 @ D ) )
=> ( D @ B @ C ) ) )
=> ( A @ B @ C ) )
& ( sk1 @ A ) )
=> ( A @ sk4 @ sk5 ) ) ),
inference(bool_ext,[status(thm)],[7]) ).
thf(81,plain,
! [B: a,A: a] :
( ( sk1 @ ( sk52 @ B @ A ) )
| ( sk1 @ sk51 ) ),
inference(cnf,[status(esa)],[54]) ).
thf(112,plain,
( ~ ( sk64 @ sk27 @ sk28 )
| ~ ( sk3 @ sk27 @ sk28 ) ),
inference(cnf,[status(esa)],[103]) ).
thf(286,plain,
( ( ! [A: a,B: a] :
( ( ( sk2 @ A @ B )
| ( sk3 @ A @ B ) )
=> ( sk11 @ A @ B ) )
& ( sk1 @ sk11 ) )
| ( ! [A: a,B: a] :
( ( ! [C: a > a > $o] :
( ( ! [D: a,E: a] :
( ( sk2 @ D @ E )
=> ( C @ D @ E ) )
& ( sk1 @ C ) )
=> ( C @ A @ B ) )
| ! [C: a > a > $o] :
( ( ! [D: a,E: a] :
( ( sk3 @ D @ E )
=> ( C @ D @ E ) )
& ( sk1 @ C ) )
=> ( C @ A @ B ) ) )
=> ( sk11 @ A @ B ) )
& ( sk1 @ sk11 ) ) ),
inference(bool_ext,[status(thm)],[12]) ).
thf(332,plain,
( ( sk1 @ sk11 )
| ( sk1 @ sk11 ) ),
inference(cnf,[status(esa)],[286]) ).
thf(355,plain,
sk1 @ sk11,
inference(simp,[status(thm)],[332]) ).
thf(114,plain,
( ( sk1 @ sk63 )
| ~ ( sk3 @ sk27 @ sk28 ) ),
inference(cnf,[status(esa)],[103]) ).
thf(23,plain,
( ( ( sk2 @ sk32 @ sk33 )
!= ( ! [A: a > a > $o] :
( ( ! [B: a,C: a] :
( ( sk2 @ B @ C )
=> ( A @ B @ C ) )
& ( sk1 @ A ) )
=> ( A @ sk32 @ sk33 ) ) ) )
| ( ( sk3 @ sk37 @ sk38 )
!= ( ! [A: a > a > $o] :
( ( ! [B: a,C: a] :
( ( sk3 @ B @ C )
=> ( A @ B @ C ) )
& ( sk1 @ A ) )
=> ( A @ sk37 @ sk38 ) ) ) ) ),
inference(func_ext,[status(esa)],[21]) ).
thf(2396,plain,
$false,
inference(cvc4,[status(thm)],[5,10,14,106,6,21,229,13,17,22,108,3,150,16,107,15,227,20,152,116,265,109,256,128,105,360,311,81,7,112,123,355,114,23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEV119^5 : TPTP v8.2.0. Released v4.0.0.
% 0.15/0.15 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n018.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
% 0.23/0.37 % CPULimit : 300
% 0.23/0.37 % WCLimit : 300
% 0.23/0.37 % DateTime : Sun May 19 18:42:39 EDT 2024
% 0.23/0.37 % CPUTime :
% 0.94/0.86 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.20/0.97 % [INFO] Parsing done (103ms).
% 1.30/0.98 % [INFO] Running in sequential loop mode.
% 1.62/1.18 % [INFO] eprover registered as external prover.
% 1.72/1.19 % [INFO] cvc4 registered as external prover.
% 1.72/1.19 % [INFO] Scanning for conjecture ...
% 1.91/1.25 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.91/1.28 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.91/1.28 % [INFO] Problem is higher-order (TPTP THF).
% 1.91/1.28 % [INFO] Type checking passed.
% 1.91/1.29 % [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 ...
% 130.13/35.24 % External prover 'cvc4' found a proof!
% 130.13/35.24 % [INFO] Killing All external provers ...
% 130.13/35.24 % Time passed: 34714ms (effective reasoning time: 34258ms)
% 130.13/35.24 % 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)>
% 130.13/35.24 % Axioms used in derivation (0):
% 130.13/35.24 % No. of inferences in proof: 55
% 130.13/35.24 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 34714 ms resp. 34258 ms w/o parsing
% 130.13/35.29 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 130.13/35.30 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------