TSTP Solution File: SEV292^5 by Leo-III---1.7.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : SEV292^5 : TPTP v8.2.0. Bugfixed v6.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% 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 : Tue May 21 04:10:18 EDT 2024
% Result : Theorem 58.93s 15.60s
% Output : Refutation 58.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 13
% Syntax : Number of formulae : 40 ( 5 unt; 8 typ; 4 def)
% Number of atoms : 158 ( 61 equ; 0 cnn)
% Maximal formula atoms : 8 ( 4 avg)
% Number of connectives : 508 ( 120 ~; 42 |; 106 &; 231 @)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 150 ( 150 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 165 ( 63 ^ 30 !; 72 ?; 165 :)
% Comments :
%------------------------------------------------------------------------------
thf(cP_type,type,
cP: ( ( $i > $o ) > $o ) > $o ).
thf(cONE_type,type,
cONE: ( $i > $o ) > $o ).
thf(cONE_def,definition,
( cONE
= ( cSUCC @ cZERO ) ) ).
thf(cSUCC_type,type,
cSUCC: ( ( $i > $o ) > $o ) > ( $i > $o ) > $o ).
thf(cSUCC_def,definition,
( cSUCC
= ( ^ [A: ( $i > $o ) > $o,B: $i > $o] :
? [C: $i] :
( ( B @ C )
& ( A
@ ^ [D: $i] :
( ( D != C )
& ( B @ D ) ) ) ) ) ) ).
thf(cZERO_type,type,
cZERO: ( $i > $o ) > $o ).
thf(cZERO_def,definition,
( cZERO
= ( ^ [A: $i > $o] :
~ ? [B: $i] : ( A @ B ) ) ) ).
thf(c_less__eq__type,type,
c_less__eq_: ( ( $i > $o ) > $o ) > ( ( $i > $o ) > $o ) > $o ).
thf(c_less__eq__def,definition,
( c_less__eq_
= ( ^ [A: ( $i > $o ) > $o,B: ( $i > $o ) > $o] :
! [C: ( ( $i > $o ) > $o ) > $o] :
( ( ( C @ A )
& ! [D: ( $i > $o ) > $o] :
( ( C @ D )
=> ( C @ ( cSUCC @ D ) ) ) )
=> ( C @ B ) ) ) ) ).
thf(sk1_type,type,
sk1: ( ( $i > $o ) > $o ) > $o ).
thf(sk2_type,type,
sk2: ( ( $i > $o ) > $o ) > ( ( $i > $o ) > $o ) > $o ).
thf(sk3_type,type,
sk3: ( ( $i > $o ) > $o ) > ( ( $i > $o ) > $o ) > $o ).
thf(1,conjecture,
( ( cP @ cONE )
=> ? [A: ( $i > $o ) > $o] :
( ( c_less__eq_ @ cZERO @ A )
& ( c_less__eq_ @ A @ ( cSUCC @ cONE ) )
& ( cP @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cBLEDSOE7A) ).
thf(2,negated_conjecture,
~ ( ( cP @ cONE )
=> ? [A: ( $i > $o ) > $o] :
( ( c_less__eq_ @ cZERO @ A )
& ( c_less__eq_ @ A @ ( cSUCC @ cONE ) )
& ( cP @ A ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ( cP
@ ^ [A: $i > $o] :
? [B: $i] :
( ( A @ B )
& ~ ? [C: $i] :
( ( C != B )
& ( A @ C ) ) ) )
=> ? [A: ( $i > $o ) > $o] :
( ! [B: ( ( $i > $o ) > $o ) > $o] :
( ( ( B
@ ^ [C: $i > $o] :
~ ? [D: $i] : ( C @ D ) )
& ! [C: ( $i > $o ) > $o] :
( ( B @ C )
=> ( B
@ ^ [D: $i > $o] :
? [E: $i] :
( ( D @ E )
& ( C
@ ^ [F: $i] :
( ( F != E )
& ( D @ F ) ) ) ) ) ) )
=> ( B @ A ) )
& ! [B: ( ( $i > $o ) > $o ) > $o] :
( ( ( B @ A )
& ! [C: ( $i > $o ) > $o] :
( ( B @ C )
=> ( B
@ ^ [D: $i > $o] :
? [E: $i] :
( ( D @ E )
& ( C
@ ^ [F: $i] :
( ( F != E )
& ( D @ F ) ) ) ) ) ) )
=> ( B
@ ^ [C: $i > $o] :
? [D: $i] :
( ( C @ D )
& ? [E: $i] :
( ( E != D )
& ( C @ E )
& ~ ? [F: $i] :
( ( F != E )
& ( F != D )
& ( C @ F ) ) ) ) ) )
& ( cP @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(5,plain,
! [A: ( $i > $o ) > $o] :
( ( sk1 @ A )
| ( sk3 @ A @ A )
| ~ ( cP @ A ) ),
inference(cnf,[status(esa)],[3]) ).
thf(4,plain,
! [B: ( $i > $o ) > $o,A: ( $i > $o ) > $o] :
( ( sk1 @ A )
| ~ ( sk3 @ A @ B )
| ( sk3 @ A
@ ^ [C: $i > $o] :
? [D: $i] :
( ( C @ D )
& ( B
@ ^ [E: $i] :
( ( E != D )
& ( C @ E ) ) ) ) )
| ~ ( cP @ A ) ),
inference(cnf,[status(esa)],[3]) ).
thf(11,plain,
! [B: ( $i > $o ) > $o,A: ( $i > $o ) > $o] :
( ( sk1 @ A )
| ~ ( sk3 @ A @ B )
| ( sk3 @ A
@ ^ [C: $i > $o] :
? [D: $i] :
( ( C @ D )
& ( B
@ ^ [E: $i] :
( ( E != D )
& ( C @ E ) ) ) ) )
| ~ ( cP @ A ) ),
inference(simp,[status(thm)],[4]) ).
thf(157,plain,
! [C: ( $i > $o ) > $o,B: ( $i > $o ) > $o,A: ( $i > $o ) > $o] :
( ( sk1 @ A )
| ~ ( cP @ A )
| ( sk1 @ B )
| ( sk3 @ B
@ ^ [D: $i > $o] :
? [E: $i] :
( ( D @ E )
& ( C
@ ^ [F: $i] :
( ( F != E )
& ( D @ F ) ) ) ) )
| ~ ( cP @ B )
| ( ( sk3 @ A @ A )
!= ( sk3 @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[5,11]) ).
thf(158,plain,
! [A: ( $i > $o ) > $o] :
( ( sk1 @ A )
| ~ ( cP @ A )
| ( sk1 @ A )
| ( sk3 @ A
@ ^ [B: $i > $o] :
? [C: $i] :
( ( B @ C )
& ( A
@ ^ [D: $i] :
( ( D != C )
& ( B @ D ) ) ) ) )
| ~ ( cP @ A ) ),
inference(pattern_uni,[status(thm)],[157:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(199,plain,
! [A: ( $i > $o ) > $o] :
( ( sk1 @ A )
| ~ ( cP @ A )
| ( sk3 @ A
@ ^ [B: $i > $o] :
? [C: $i] :
( ( B @ C )
& ( A
@ ^ [D: $i] :
( ( D != C )
& ( B @ D ) ) ) ) ) ),
inference(simp,[status(thm)],[158]) ).
thf(9,plain,
( cP
@ ^ [A: $i > $o] :
? [B: $i] :
( ( A @ B )
& ~ ? [C: $i] :
( ( C != B )
& ( A @ C ) ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(7,plain,
! [A: ( $i > $o ) > $o] :
( ( sk1 @ A )
| ~ ( sk3 @ A
@ ^ [B: $i > $o] :
? [C: $i] :
( ( B @ C )
& ? [D: $i] :
( ( D != C )
& ( B @ D )
& ~ ? [E: $i] :
( ( E != D )
& ( E != C )
& ( B @ E ) ) ) ) )
| ~ ( cP @ A ) ),
inference(cnf,[status(esa)],[3]) ).
thf(65,plain,
! [A: ( $i > $o ) > $o] :
( ( sk1 @ A )
| ~ ( sk3 @ A
@ ^ [B: $i > $o] :
? [C: $i] :
( ( B @ C )
& ? [D: $i] :
( ( D != C )
& ( B @ D )
& ~ ? [E: $i] :
( ( E != D )
& ( E != C )
& ( B @ E ) ) ) ) )
| ( ( cP
@ ^ [B: $i > $o] :
? [C: $i] :
( ( B @ C )
& ~ ? [D: $i] :
( ( D != C )
& ( B @ D ) ) ) )
!= ( cP @ A ) ) ),
inference(paramod_ordered,[status(thm)],[9,7]) ).
thf(66,plain,
( ( sk1
@ ^ [A: $i > $o] :
? [B: $i] :
( ( A @ B )
& ~ ? [C: $i] :
( ( C != B )
& ( A @ C ) ) ) )
| ~ ( sk3
@ ^ [A: $i > $o] :
? [B: $i] :
( ( A @ B )
& ~ ? [C: $i] :
( ( C != B )
& ( A @ C ) ) )
@ ^ [A: $i > $o] :
? [B: $i] :
( ( A @ B )
& ? [C: $i] :
( ( C != B )
& ( A @ C )
& ~ ? [D: $i] :
( ( D != C )
& ( D != B )
& ( A @ D ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[65:[bind(A,$thf( ^ [B: $i > $o] : ? [C: $i] : ( ( B @ C ) & ~ ( ? [D: $i] : ( ( D != C ) & ( B @ D ) ) ) ) ))]]) ).
thf(8,plain,
! [A: ( $i > $o ) > $o] :
( ( sk2 @ A
@ ^ [B: $i > $o] :
~ ? [C: $i] : ( B @ C ) )
| ~ ( sk1 @ A ) ),
inference(cnf,[status(esa)],[3]) ).
thf(6,plain,
! [B: ( $i > $o ) > $o,A: ( $i > $o ) > $o] :
( ~ ( sk2 @ A @ B )
| ( sk2 @ A
@ ^ [C: $i > $o] :
? [D: $i] :
( ( C @ D )
& ( B
@ ^ [E: $i] :
( ( E != D )
& ( C @ E ) ) ) ) )
| ~ ( sk1 @ A ) ),
inference(cnf,[status(esa)],[3]) ).
thf(10,plain,
! [A: ( $i > $o ) > $o] :
( ~ ( sk2 @ A @ A )
| ~ ( sk1 @ A ) ),
inference(cnf,[status(esa)],[3]) ).
thf(15,plain,
! [C: ( $i > $o ) > $o,B: ( $i > $o ) > $o,A: ( $i > $o ) > $o] :
( ~ ( sk2 @ A @ B )
| ~ ( sk1 @ A )
| ~ ( sk1 @ C )
| ( ( sk2 @ A
@ ^ [D: $i > $o] :
? [E: $i] :
( ( D @ E )
& ( B
@ ^ [F: $i] :
( ( F != E )
& ( D @ F ) ) ) ) )
!= ( sk2 @ C @ C ) ) ),
inference(paramod_ordered,[status(thm)],[6,10]) ).
thf(19,plain,
! [A: ( $i > $o ) > $o] :
( ~ ( sk2
@ ^ [B: $i > $o] :
? [C: $i] :
( ( B @ C )
& ( A
@ ^ [D: $i] :
( ( D != C )
& ( B @ D ) ) ) )
@ A )
| ~ ( sk1
@ ^ [B: $i > $o] :
? [C: $i] :
( ( B @ C )
& ( A
@ ^ [D: $i] :
( ( D != C )
& ( B @ D ) ) ) ) )
| ~ ( sk1
@ ^ [B: $i > $o] :
? [C: $i] :
( ( B @ C )
& ( A
@ ^ [D: $i] :
( ( D != C )
& ( B @ D ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[15:[bind(A,$thf( ^ [D: $i > $o] : ? [E: $i] : ( ( D @ E ) & ( B @ ^ [F: $i] : ( ( F != E ) & ( D @ F ) ) ) ) )),bind(B,$thf( B )),bind(C,$thf( ^ [D: $i > $o] : ? [E: $i] : ( ( D @ E ) & ( B @ ^ [F: $i] : ( ( F != E ) & ( D @ F ) ) ) ) ))]]) ).
thf(22,plain,
! [A: ( $i > $o ) > $o] :
( ~ ( sk2
@ ^ [B: $i > $o] :
? [C: $i] :
( ( B @ C )
& ( A
@ ^ [D: $i] :
( ( D != C )
& ( B @ D ) ) ) )
@ A )
| ~ ( sk1
@ ^ [B: $i > $o] :
? [C: $i] :
( ( B @ C )
& ( A
@ ^ [D: $i] :
( ( D != C )
& ( B @ D ) ) ) ) ) ),
inference(simp,[status(thm)],[19]) ).
thf(25,plain,
! [B: ( $i > $o ) > $o,A: ( $i > $o ) > $o] :
( ~ ( sk1 @ A )
| ~ ( sk1
@ ^ [C: $i > $o] :
? [D: $i] :
( ( C @ D )
& ( B
@ ^ [E: $i] :
( ( E != D )
& ( C @ E ) ) ) ) )
| ( ( sk2 @ A
@ ^ [C: $i > $o] :
~ ? [D: $i] : ( C @ D ) )
!= ( sk2
@ ^ [C: $i > $o] :
? [D: $i] :
( ( C @ D )
& ( B
@ ^ [E: $i] :
( ( E != D )
& ( C @ E ) ) ) )
@ B ) ) ),
inference(paramod_ordered,[status(thm)],[8,22]) ).
thf(27,plain,
( ~ ( sk1
@ ^ [A: $i > $o] :
? [B: $i] :
( ( A @ B )
& ~ ? [C: $i] :
( ( C != B )
& ( A @ C ) ) ) )
| ~ ( sk1
@ ^ [A: $i > $o] :
? [B: $i] :
( ( A @ B )
& ~ ? [C: $i] :
( ( C != B )
& ( A @ C ) ) ) ) ),
inference(pre_uni,[status(thm)],[25:[bind(A,$thf( ^ [C: $i > $o] : ? [D: $i] : ( ( C @ D ) & ~ ( ? [E: $i] : ( ( E != D ) & ( C @ E ) ) ) ) )),bind(B,$thf( ^ [C: $i > $o] : ~ ( ? [D: $i] : ( C @ D ) ) ))]]) ).
thf(29,plain,
~ ( sk1
@ ^ [A: $i > $o] :
? [B: $i] :
( ( A @ B )
& ~ ? [C: $i] :
( ( C != B )
& ( A @ C ) ) ) ),
inference(simp,[status(thm)],[27]) ).
thf(206,plain,
( $false
| ~ ( sk3
@ ^ [A: $i > $o] :
? [B: $i] :
( ( A @ B )
& ~ ? [C: $i] :
( ( C != B )
& ( A @ C ) ) )
@ ^ [A: $i > $o] :
? [B: $i] :
( ( A @ B )
& ? [C: $i] :
( ( C != B )
& ( A @ C )
& ~ ? [D: $i] :
( ( D != C )
& ( D != B )
& ( A @ D ) ) ) ) ) ),
inference(rewrite,[status(thm)],[66,29]) ).
thf(207,plain,
~ ( sk3
@ ^ [A: $i > $o] :
? [B: $i] :
( ( A @ B )
& ~ ? [C: $i] :
( ( C != B )
& ( A @ C ) ) )
@ ^ [A: $i > $o] :
? [B: $i] :
( ( A @ B )
& ? [C: $i] :
( ( C != B )
& ( A @ C )
& ~ ? [D: $i] :
( ( D != C )
& ( D != B )
& ( A @ D ) ) ) ) ),
inference(simp,[status(thm)],[206]) ).
thf(246,plain,
! [A: ( $i > $o ) > $o] :
( ( sk1 @ A )
| ~ ( cP @ A )
| ( ( sk3 @ A
@ ^ [B: $i > $o] :
? [C: $i] :
( ( B @ C )
& ( A
@ ^ [D: $i] :
( ( D != C )
& ( B @ D ) ) ) ) )
!= ( sk3
@ ^ [B: $i > $o] :
? [C: $i] :
( ( B @ C )
& ~ ? [D: $i] :
( ( D != C )
& ( B @ D ) ) )
@ ^ [B: $i > $o] :
? [C: $i] :
( ( B @ C )
& ? [D: $i] :
( ( D != C )
& ( B @ D )
& ~ ? [E: $i] :
( ( E != D )
& ( E != C )
& ( B @ E ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[199,207]) ).
thf(250,plain,
( ( sk1
@ ^ [A: $i > $o] :
? [B: $i] :
( ( A @ B )
& ~ ? [C: $i] :
( ( C != B )
& ( A @ C ) ) ) )
| ~ ( cP
@ ^ [A: $i > $o] :
? [B: $i] :
( ( A @ B )
& ~ ? [C: $i] :
( ( C != B )
& ( A @ C ) ) ) ) ),
inference(pre_uni,[status(thm)],[246:[bind(A,$thf( ^ [B: $i > $o] : ? [C: $i] : ( ( B @ C ) & ~ ( ? [D: $i] : ( ( D != C ) & ( B @ D ) ) ) ) ))]]) ).
thf(254,plain,
( $false
| ~ $true ),
inference(rewrite,[status(thm)],[250,9,29]) ).
thf(255,plain,
$false,
inference(simp,[status(thm)],[254]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.09 % Problem : SEV292^5 : TPTP v8.2.0. Bugfixed v6.2.0.
% 0.04/0.11 % Command : run_Leo-III %s %d
% 0.11/0.31 % Computer : n002.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Sun May 19 18:45:54 EDT 2024
% 0.11/0.31 % CPUTime :
% 0.92/0.92 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.31/1.09 % [INFO] Parsing done (160ms).
% 1.31/1.10 % [INFO] Running in sequential loop mode.
% 1.70/1.44 % [INFO] eprover registered as external prover.
% 1.85/1.45 % [INFO] cvc4 registered as external prover.
% 1.85/1.45 % [INFO] Scanning for conjecture ...
% 2.08/1.56 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.08/1.59 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.08/1.59 % [INFO] Problem is higher-order (TPTP THF).
% 2.08/1.60 % [INFO] Type checking passed.
% 2.08/1.60 % [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 ...
% 58.93/15.60 % [INFO] Killing All external provers ...
% 58.93/15.60 % Time passed: 15141ms (effective reasoning time: 14497ms)
% 58.93/15.60 % 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)>
% 58.93/15.60 % Axioms used in derivation (0):
% 58.93/15.60 % No. of inferences in proof: 28
% 58.93/15.60 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 15141 ms resp. 14497 ms w/o parsing
% 58.93/15.66 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 58.93/15.66 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------