TSTP Solution File: SEV085^5 by Leo-III-SAT---1.7.15
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.15
% Problem : SEV085^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d SAT
% Computer : n026.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 15:59:29 EDT 2024
% Result : Theorem 40.43s 7.60s
% Output : Refutation 40.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 1
% Syntax : Number of formulae : 31 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 184 ( 85 equ; 40 cnn)
% Maximal formula atoms : 7 ( 5 avg)
% Number of connectives : 560 ( 68 ~; 57 |; 16 &; 415 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 276 ( 276 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 196 ( 76 ^ 102 !; 18 ?; 196 :)
% Comments :
%------------------------------------------------------------------------------
thf(sk1_type,type,
sk1: ( ( $i > $o ) > ( $i > $o ) > $o ) > $i > $o ).
thf(sk2_type,type,
sk2: ( ( $i > $o ) > ( $i > $o ) > $o ) > $i > $o ).
thf(sk3_type,type,
sk3: ( ( $i > $o ) > ( $i > $o ) > $o ) > $i > $o ).
thf(sk4_type,type,
sk4: ( ( $i > $o ) > ( $i > $o ) > $o ) > $i > $o ).
thf(1,conjecture,
? [A: ( $i > $o ) > ( $i > $o ) > $o] :
( ? [B: $i > $o,C: $i > $o] : ( A @ B @ C )
& ? [B: $i > $o,C: $i > $o] :
~ ( A @ B @ C )
& ! [B: $i > $o] : ( A @ B @ B )
& ! [B: $i > $o,C: $i > $o,D: $i > $o] :
( ( ( A @ B @ C )
& ( A @ C @ D ) )
=> ( A @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM120_2_pme) ).
thf(2,negated_conjecture,
~ ? [A: ( $i > $o ) > ( $i > $o ) > $o] :
( ? [B: $i > $o,C: $i > $o] : ( A @ B @ C )
& ? [B: $i > $o,C: $i > $o] :
~ ( A @ B @ C )
& ! [B: $i > $o] : ( A @ B @ B )
& ! [B: $i > $o,C: $i > $o,D: $i > $o] :
( ( ( A @ B @ C )
& ( A @ C @ D ) )
=> ( A @ B @ D ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ? [A: ( $i > $o ) > ( $i > $o ) > $o] :
( ? [B: $i > $o,C: $i > $o] : ( A @ B @ C )
& ? [B: $i > $o,C: $i > $o] :
~ ( A @ B @ C )
& ! [B: $i > $o] : ( A @ B @ B )
& ! [B: $i > $o,C: $i > $o,D: $i > $o] :
( ( ( A @ B @ C )
& ( A @ C @ D ) )
=> ( A @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
~ ? [A: ( $i > $o ) > ( $i > $o ) > $o] :
( ? [B: $i > $o,C: $i > $o] : ( A @ B @ C )
& ~ ! [B: $i > $o,C: $i > $o] : ( A @ B @ C )
& ! [B: $i > $o] : ( A @ B @ B )
& ! [B: $i > $o,C: $i > $o,D: $i > $o] :
( ( ( A @ B @ C )
& ( A @ C @ D ) )
=> ( A @ B @ D ) ) ),
inference(miniscope,[status(thm)],[3]) ).
thf(7,plain,
! [E: $i > $o,D: $i > $o,C: $i > $o,B: $i > $o,A: ( $i > $o ) > ( $i > $o ) > $o] :
( ~ ( A @ B @ C )
| ( A @ D @ E )
| ~ ( A @ ( sk1 @ A ) @ ( sk1 @ A ) )
| ~ ( A @ ( sk2 @ A ) @ ( sk4 @ A ) ) ),
inference(cnf,[status(esa)],[4]) ).
thf(60,plain,
! [E: $i > $o,D: $i > $o,C: $i > $o,B: $i > $o,A: ( $i > $o ) > ( $i > $o ) > $o] :
( ~ ( A @ B @ C )
| ~ ( A @ ( sk1 @ A ) @ ( sk1 @ A ) )
| ~ ( A @ ( sk2 @ A ) @ ( sk4 @ A ) )
| ( ( A @ D @ E )
!= ( ~ ( A @ B @ C ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[7]) ).
thf(100,plain,
! [E: $i > $o,D: ( $i > $o ) > ( $i > $o ) > $i,C: $i > $o,B: $i > $o,A: $i > $o] :
( ~ ( A @ ( D @ A @ B ) )
| ~ ( sk1
@ ^ [F: $i > $o,G: $i > $o] : ( F @ ( D @ F @ G ) )
@ ( D
@ ( sk1
@ ^ [F: $i > $o,G: $i > $o] : ( F @ ( D @ F @ G ) ) )
@ ( sk1
@ ^ [F: $i > $o,G: $i > $o] : ( F @ ( D @ F @ G ) ) ) ) )
| ~ ( sk2
@ ^ [F: $i > $o,G: $i > $o] : ( F @ ( D @ F @ G ) )
@ ( D
@ ( sk2
@ ^ [F: $i > $o,G: $i > $o] : ( F @ ( D @ F @ G ) ) )
@ ( sk4
@ ^ [F: $i > $o,G: $i > $o] : ( F @ ( D @ F @ G ) ) ) ) )
| ( ( E
@ ( D
@ ^ [F: $i] :
~ ( E @ F )
@ C ) )
!= ( A @ ( D @ A @ B ) ) ) ),
inference(pre_uni,[status(thm)],[60:[bind(A,$thf( ^ [G: $i > $o] : ^ [H: $i > $o] : ( G @ ( G @ G @ H ) ) )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( ^ [G: $i] : ~ ( L @ G ) ))]]) ).
thf(104,plain,
! [E: $i > $o,D: ( $i > $o ) > ( $i > $o ) > $i,C: $i > $o,B: $i > $o,A: $i > $o] :
( ~ ( sk2
@ ^ [F: $i > $o,G: $i > $o] : ( F @ ( D @ F @ G ) )
@ ( D
@ ( sk2
@ ^ [F: $i > $o,G: $i > $o] : ( F @ ( D @ F @ G ) ) )
@ ( sk4
@ ^ [F: $i > $o,G: $i > $o] : ( F @ ( D @ F @ G ) ) ) ) )
| ~ ( sk1
@ ^ [F: $i > $o,G: $i > $o] : ( F @ ( D @ F @ G ) )
@ ( D
@ ( sk1
@ ^ [F: $i > $o,G: $i > $o] : ( F @ ( D @ F @ G ) ) )
@ ( sk1
@ ^ [F: $i > $o,G: $i > $o] : ( F @ ( D @ F @ G ) ) ) ) )
| ~ ( A @ ( D @ A @ B ) )
| ( ( E
@ ( D
@ ^ [F: $i] :
~ ( E @ F )
@ C ) )
!= ( A @ ( D @ A @ B ) ) ) ),
inference(pre_uni,[status(thm)],[100:[]]) ).
thf(169,plain,
! [E: $i > $o,D: ( $i > $o ) > ( $i > $o ) > $i,C: $i > $o,B: $i > $o,A: $i > $o] :
( ~ ( sk2
@ ^ [F: $i > $o,G: $i > $o] : ( F @ ( D @ F @ G ) )
@ ( D
@ ( sk2
@ ^ [F: $i > $o,G: $i > $o] : ( F @ ( D @ F @ G ) ) )
@ ( sk4
@ ^ [F: $i > $o,G: $i > $o] : ( F @ ( D @ F @ G ) ) ) ) )
| ~ ( sk1
@ ^ [F: $i > $o,G: $i > $o] : ( F @ ( D @ F @ G ) )
@ ( D
@ ( sk1
@ ^ [F: $i > $o,G: $i > $o] : ( F @ ( D @ F @ G ) ) )
@ ( sk1
@ ^ [F: $i > $o,G: $i > $o] : ( F @ ( D @ F @ G ) ) ) ) )
| ~ ( A @ ( D @ A @ B ) )
| ( ( E
@ ( D
@ ^ [F: $i] :
~ ( E @ F )
@ C ) )
!= ( A @ ( D @ A @ B ) ) ) ),
inference(simp,[status(thm)],[104]) ).
thf(194,plain,
! [E: $i > $o,D: ( $i > $o ) > ( $i > $o ) > $i,C: $i > $o,B: $i > $o,A: $i > $o] :
( ~ ( sk2
@ ^ [F: $i > $o,G: $i > $o] : ( F @ ( D @ F @ G ) )
@ ( D
@ ( sk2
@ ^ [F: $i > $o,G: $i > $o] : ( F @ ( D @ F @ G ) ) )
@ ( sk4
@ ^ [F: $i > $o,G: $i > $o] : ( F @ ( D @ F @ G ) ) ) ) )
| ~ ( sk1
@ ^ [F: $i > $o,G: $i > $o] : ( F @ ( D @ F @ G ) )
@ ( D
@ ( sk1
@ ^ [F: $i > $o,G: $i > $o] : ( F @ ( D @ F @ G ) ) )
@ ( sk1
@ ^ [F: $i > $o,G: $i > $o] : ( F @ ( D @ F @ G ) ) ) ) )
| ~ ( A @ ( D @ A @ B ) )
| ( ( E
@ ( D
@ ^ [F: $i] :
~ ( E @ F )
@ C ) )
!= ( A @ ( D @ A @ B ) ) )
| ~ ( A @ ( D @ A @ B ) ) ),
inference(eqfactor_ordered,[status(thm)],[169]) ).
thf(234,plain,
! [A: ( $i > $o ) > ( $i > $o ) > $i] :
( ~ ( sk2
@ ^ [B: $i > $o,C: $i > $o] : ( B @ ( A @ B @ C ) )
@ ( A
@ ( sk2
@ ^ [B: $i > $o,C: $i > $o] : ( B @ ( A @ B @ C ) ) )
@ ( sk4
@ ^ [B: $i > $o,C: $i > $o] : ( B @ ( A @ B @ C ) ) ) ) )
| ~ ( sk1
@ ^ [B: $i > $o,C: $i > $o] : ( B @ ( A @ B @ C ) )
@ ( A
@ ( sk1
@ ^ [B: $i > $o,C: $i > $o] : ( B @ ( A @ B @ C ) ) )
@ ( sk1
@ ^ [B: $i > $o,C: $i > $o] : ( B @ ( A @ B @ C ) ) ) ) )
| ~ $true ),
inference(pre_uni,[status(thm)],[194:[bind(A,$thf( ^ [F: $i] : $true )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( ^ [F: $i] : $true ))]]) ).
thf(263,plain,
! [A: ( $i > $o ) > ( $i > $o ) > $i] :
( ~ ( sk2
@ ^ [B: $i > $o,C: $i > $o] : ( B @ ( A @ B @ C ) )
@ ( A
@ ( sk2
@ ^ [B: $i > $o,C: $i > $o] : ( B @ ( A @ B @ C ) ) )
@ ( sk4
@ ^ [B: $i > $o,C: $i > $o] : ( B @ ( A @ B @ C ) ) ) ) )
| ~ ( sk1
@ ^ [B: $i > $o,C: $i > $o] : ( B @ ( A @ B @ C ) )
@ ( A
@ ( sk1
@ ^ [B: $i > $o,C: $i > $o] : ( B @ ( A @ B @ C ) ) )
@ ( sk1
@ ^ [B: $i > $o,C: $i > $o] : ( B @ ( A @ B @ C ) ) ) ) ) ),
inference(simp,[status(thm)],[234]) ).
thf(6,plain,
! [E: $i > $o,D: $i > $o,C: $i > $o,B: $i > $o,A: ( $i > $o ) > ( $i > $o ) > $o] :
( ~ ( A @ B @ C )
| ( A @ D @ E )
| ~ ( A @ ( sk1 @ A ) @ ( sk1 @ A ) )
| ( A @ ( sk3 @ A ) @ ( sk4 @ A ) ) ),
inference(cnf,[status(esa)],[4]) ).
thf(9,plain,
! [D: $i > $o,C: $i > $o,B: $i > $o,A: $i > $o] :
( ( A != B )
| ( C = D )
| ( ( sk1 @ ( (=) @ ( $i > $o ) ) )
!= ( sk1 @ ( (=) @ ( $i > $o ) ) ) )
| ( ( sk3 @ ( (=) @ ( $i > $o ) ) )
= ( sk4 @ ( (=) @ ( $i > $o ) ) ) ) ),
inference(replace_andrewseq,[status(thm)],[6:[bind(A,$thf( (=) @ ( $i > $o ) ))]]) ).
thf(13,plain,
! [D: $i > $o,C: $i > $o,B: $i > $o,A: $i > $o] :
( ( A != B )
| ( C = D )
| ( ( sk1 @ ( (=) @ ( $i > $o ) ) )
!= ( sk1 @ ( (=) @ ( $i > $o ) ) ) )
| ( ( sk4 @ ( (=) @ ( $i > $o ) ) )
= ( sk3 @ ( (=) @ ( $i > $o ) ) ) ) ),
inference(lifteq,[status(thm)],[9]) ).
thf(14,plain,
! [B: $i > $o,A: $i > $o] :
( ( A = B )
| ( ( sk4 @ ( (=) @ ( $i > $o ) ) )
= ( sk3 @ ( (=) @ ( $i > $o ) ) ) ) ),
inference(simp,[status(thm)],[13]) ).
thf(39,plain,
! [B: $i > $o,A: $i > $o] :
( ( A = B )
| ( ( sk4 @ ( (=) @ ( $i > $o ) ) )
!= A )
| ( ( sk3 @ ( (=) @ ( $i > $o ) ) )
!= B ) ),
inference(eqfactor_ordered,[status(thm)],[14]) ).
thf(41,plain,
( ( sk4 @ ( (=) @ ( $i > $o ) ) )
= ( sk3 @ ( (=) @ ( $i > $o ) ) ) ),
inference(pattern_uni,[status(thm)],[39:[bind(A,$thf( sk4 @ ( (=) @ ( $i > $o ) ) )),bind(B,$thf( sk3 @ ( (=) @ ( $i > $o ) ) ))]]) ).
thf(5,plain,
! [E: $i > $o,D: $i > $o,C: $i > $o,B: $i > $o,A: ( $i > $o ) > ( $i > $o ) > $o] :
( ~ ( A @ B @ C )
| ( A @ D @ E )
| ~ ( A @ ( sk1 @ A ) @ ( sk1 @ A ) )
| ( A @ ( sk2 @ A ) @ ( sk3 @ A ) ) ),
inference(cnf,[status(esa)],[4]) ).
thf(8,plain,
! [D: $i > $o,C: $i > $o,B: $i > $o,A: $i > $o] :
( ( A != B )
| ( C = D )
| ( ( sk1 @ ( (=) @ ( $i > $o ) ) )
!= ( sk1 @ ( (=) @ ( $i > $o ) ) ) )
| ( ( sk2 @ ( (=) @ ( $i > $o ) ) )
= ( sk3 @ ( (=) @ ( $i > $o ) ) ) ) ),
inference(replace_andrewseq,[status(thm)],[5:[bind(A,$thf( (=) @ ( $i > $o ) ))]]) ).
thf(15,plain,
! [D: $i > $o,C: $i > $o,B: $i > $o,A: $i > $o] :
( ( A != B )
| ( C = D )
| ( ( sk1 @ ( (=) @ ( $i > $o ) ) )
!= ( sk1 @ ( (=) @ ( $i > $o ) ) ) )
| ( ( sk3 @ ( (=) @ ( $i > $o ) ) )
= ( sk2 @ ( (=) @ ( $i > $o ) ) ) ) ),
inference(lifteq,[status(thm)],[8]) ).
thf(16,plain,
! [B: $i > $o,A: $i > $o] :
( ( A = B )
| ( ( sk3 @ ( (=) @ ( $i > $o ) ) )
= ( sk2 @ ( (=) @ ( $i > $o ) ) ) ) ),
inference(simp,[status(thm)],[15]) ).
thf(308,plain,
! [B: $i > $o,A: $i > $o] :
( ( A = B )
| ( ( sk3 @ ( (=) @ ( $i > $o ) ) )
!= B )
| ( ( sk2 @ ( (=) @ ( $i > $o ) ) )
!= A ) ),
inference(eqfactor_ordered,[status(thm)],[16]) ).
thf(319,plain,
( ( sk3 @ ( (=) @ ( $i > $o ) ) )
= ( sk2 @ ( (=) @ ( $i > $o ) ) ) ),
inference(pattern_uni,[status(thm)],[308:[bind(A,$thf( sk2 @ ( (=) @ ( $i > $o ) ) )),bind(B,$thf( sk3 @ ( (=) @ ( $i > $o ) ) ))]]) ).
thf(346,plain,
( ( sk4 @ ( (=) @ ( $i > $o ) ) )
= ( sk2 @ ( (=) @ ( $i > $o ) ) ) ),
inference(rewrite,[status(thm)],[41,319]) ).
thf(582,plain,
! [E: $i > $o,D: $i > $o,C: $i > $o,B: $i > $o,A: ( $i > $o ) > ( $i > $o ) > $o] :
( ~ ( A @ B @ C )
| ( A @ D @ E )
| ~ ( A @ ( sk1 @ A ) @ ( sk1 @ A ) )
| ~ ( A @ ( sk2 @ A ) @ ( sk2 @ ( (=) @ ( $i > $o ) ) ) )
| ( ( sk4 @ ( (=) @ ( $i > $o ) ) )
!= ( sk4 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[346,7]) ).
thf(583,plain,
! [D: $i > $o,C: $i > $o,B: $i > $o,A: $i > $o] :
( ( A != B )
| ( C = D )
| ( ( sk1 @ ( (=) @ ( $i > $o ) ) )
!= ( sk1 @ ( (=) @ ( $i > $o ) ) ) )
| ( ( sk2 @ ( (=) @ ( $i > $o ) ) )
!= ( sk2 @ ( (=) @ ( $i > $o ) ) ) ) ),
inference(pattern_uni,[status(thm)],[582:[bind(A,$thf( (=) @ ( $i > $o ) )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( E ))]]) ).
thf(584,plain,
! [D: $i > $o,C: $i > $o,B: $i > $o,A: $i > $o] :
( ( A != B )
| ( C = D )
| ( ( sk1 @ ( (=) @ ( $i > $o ) ) )
!= ( sk1 @ ( (=) @ ( $i > $o ) ) ) )
| ( ( sk2 @ ( (=) @ ( $i > $o ) ) )
!= ( sk2 @ ( (=) @ ( $i > $o ) ) ) ) ),
inference(lifteq,[status(thm)],[583]) ).
thf(586,plain,
! [B: $i > $o,A: $i > $o] : ( A = B ),
inference(simp,[status(thm)],[584]) ).
thf(588,plain,
! [C: $i,B: $i > $o,A: $i > $o] :
( ( A @ C )
= ( B @ C ) ),
inference(func_ext,[status(esa)],[586]) ).
thf(2868,plain,
$false,
inference(simplifyReflect,[status(thm)],[263,588]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEV085^5 : TPTP v8.2.0. Released v4.0.0.
% 0.11/0.12 % Command : run_Leo-III %s %d SAT
% 0.12/0.32 % Computer : n026.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Fri Jun 21 19:08:55 EDT 2024
% 0.17/0.32 % CPUTime :
% 0.84/0.85 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.12/0.95 % [INFO] Parsing done (96ms).
% 1.12/0.96 % [INFO] Running in sequential loop mode.
% 1.41/1.15 % [INFO] nitpick registered as external prover.
% 1.41/1.16 % [INFO] Scanning for conjecture ...
% 1.66/1.21 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.77/1.23 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.77/1.23 % [INFO] Problem is higher-order (TPTP THF).
% 1.77/1.23 % [INFO] Type checking passed.
% 1.77/1.24 % [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 ...
% 40.43/7.60 % [INFO] Killing All external provers ...
% 40.43/7.60 % Time passed: 7083ms (effective reasoning time: 6638ms)
% 40.43/7.60 % 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)>
% 40.43/7.60 % Axioms used in derivation (0):
% 40.43/7.60 % No. of inferences in proof: 31
% 40.43/7.60 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 7083 ms resp. 6638 ms w/o parsing
% 40.54/7.67 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 40.54/7.67 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------