TSTP Solution File: SEV087^5 by Leo-III-SAT---1.7.15
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.15
% Problem : SEV087^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d SAT
% Computer : n028.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 15:59:30 EDT 2024
% Result : Theorem 11.28s 2.98s
% Output : Refutation 11.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 1
% Syntax : Number of formulae : 34 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 377 ( 186 equ; 112 cnn)
% Maximal formula atoms : 8 ( 11 avg)
% Number of connectives : 476 ( 49 ~; 62 |; 15 &; 344 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 166 ( 166 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 69 ( 42 ^ 24 !; 3 ?; 69 :)
% 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(sk5_type,type,
sk5: ( ( $i > $o ) > ( $i > $o ) > $o ) > $i > $o ).
thf(sk6_type,type,
sk6: ( ( $i > $o ) > ( $i > $o ) > $o ) > $i > $o ).
thf(1,conjecture,
? [A: ( $i > $o ) > ( $i > $o ) > $o] :
( ~ ( A
@ ^ [B: $i] : $true
@ ^ [B: $i] : $false )
& ! [B: $i > $o] : ( A @ B @ B )
& ! [B: $i > $o,C: $i > $o,D: $i > $o] :
( ( ( A @ B @ C )
& ( A @ C @ D ) )
=> ( A @ B @ D ) )
& ! [B: $i > $o,C: $i > $o] :
( ( ( A @ B @ C )
& ( A @ C @ B ) )
=> ( B = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM120H_pme) ).
thf(2,negated_conjecture,
~ ? [A: ( $i > $o ) > ( $i > $o ) > $o] :
( ~ ( A
@ ^ [B: $i] : $true
@ ^ [B: $i] : $false )
& ! [B: $i > $o] : ( A @ B @ B )
& ! [B: $i > $o,C: $i > $o,D: $i > $o] :
( ( ( A @ B @ C )
& ( A @ C @ D ) )
=> ( A @ B @ D ) )
& ! [B: $i > $o,C: $i > $o] :
( ( ( A @ B @ C )
& ( A @ C @ B ) )
=> ( B = C ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ? [A: ( $i > $o ) > ( $i > $o ) > $o] :
( ~ ( A
@ ^ [B: $i] : $true
@ ^ [B: $i] : $false )
& ! [B: $i > $o] : ( A @ B @ B )
& ! [B: $i > $o,C: $i > $o,D: $i > $o] :
( ( ( A @ B @ C )
& ( A @ C @ D ) )
=> ( A @ B @ D ) )
& ! [B: $i > $o,C: $i > $o] :
( ( ( A @ B @ C )
& ( A @ C @ B ) )
=> ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(7,plain,
! [A: ( $i > $o ) > ( $i > $o ) > $o] :
( ( A
@ ^ [B: $i] : $true
@ ^ [B: $i] : $false )
| ~ ( A @ ( sk1 @ A ) @ ( sk1 @ A ) )
| ( A @ ( sk2 @ A ) @ ( sk3 @ A ) )
| ( A @ ( sk6 @ A ) @ ( sk5 @ A ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(18,plain,
( ( ( ^ [A: $i] : $true )
= ( ^ [A: $i] : $false ) )
| ( ( sk1 @ ( (=) @ ( $i > $o ) ) )
!= ( sk1 @ ( (=) @ ( $i > $o ) ) ) )
| ( ( sk2 @ ( (=) @ ( $i > $o ) ) )
= ( sk3 @ ( (=) @ ( $i > $o ) ) ) )
| ( ( sk6 @ ( (=) @ ( $i > $o ) ) )
= ( sk5 @ ( (=) @ ( $i > $o ) ) ) ) ),
inference(replace_andrewseq,[status(thm)],[7:[bind(A,$thf( (=) @ ( $i > $o ) ))]]) ).
thf(34,plain,
( ( ( ^ [A: $i] : $false )
= ( ^ [A: $i] : $true ) )
| ( ( sk1 @ ( (=) @ ( $i > $o ) ) )
!= ( sk1 @ ( (=) @ ( $i > $o ) ) ) )
| ( ( sk3 @ ( (=) @ ( $i > $o ) ) )
= ( sk2 @ ( (=) @ ( $i > $o ) ) ) )
| ( ( sk6 @ ( (=) @ ( $i > $o ) ) )
= ( sk5 @ ( (=) @ ( $i > $o ) ) ) ) ),
inference(lifteq,[status(thm)],[18]) ).
thf(35,plain,
( ( ( sk3 @ ( (=) @ ( $i > $o ) ) )
= ( sk2 @ ( (=) @ ( $i > $o ) ) ) )
| ( ( sk6 @ ( (=) @ ( $i > $o ) ) )
= ( sk5 @ ( (=) @ ( $i > $o ) ) ) ) ),
inference(simp,[status(thm)],[34]) ).
thf(10,plain,
! [A: ( $i > $o ) > ( $i > $o ) > $o] :
( ( A
@ ^ [B: $i] : $true
@ ^ [B: $i] : $false )
| ~ ( A @ ( sk1 @ A ) @ ( sk1 @ A ) )
| ~ ( A @ ( sk2 @ A ) @ ( sk4 @ A ) )
| ( A @ ( sk6 @ A ) @ ( sk5 @ A ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(14,plain,
( ( ( ^ [A: $i] : $true )
= ( ^ [A: $i] : $false ) )
| ( ( sk1 @ ( (=) @ ( $i > $o ) ) )
!= ( sk1 @ ( (=) @ ( $i > $o ) ) ) )
| ( ( sk2 @ ( (=) @ ( $i > $o ) ) )
!= ( sk4 @ ( (=) @ ( $i > $o ) ) ) )
| ( ( sk6 @ ( (=) @ ( $i > $o ) ) )
= ( sk5 @ ( (=) @ ( $i > $o ) ) ) ) ),
inference(replace_andrewseq,[status(thm)],[10:[bind(A,$thf( (=) @ ( $i > $o ) ))]]) ).
thf(23,plain,
( ( ( ^ [A: $i] : $false )
= ( ^ [A: $i] : $true ) )
| ( ( sk1 @ ( (=) @ ( $i > $o ) ) )
!= ( sk1 @ ( (=) @ ( $i > $o ) ) ) )
| ( ( sk4 @ ( (=) @ ( $i > $o ) ) )
!= ( sk2 @ ( (=) @ ( $i > $o ) ) ) )
| ( ( sk6 @ ( (=) @ ( $i > $o ) ) )
= ( sk5 @ ( (=) @ ( $i > $o ) ) ) ) ),
inference(lifteq,[status(thm)],[14]) ).
thf(24,plain,
( ( ( sk4 @ ( (=) @ ( $i > $o ) ) )
!= ( sk2 @ ( (=) @ ( $i > $o ) ) ) )
| ( ( sk6 @ ( (=) @ ( $i > $o ) ) )
= ( sk5 @ ( (=) @ ( $i > $o ) ) ) ) ),
inference(simp,[status(thm)],[23]) ).
thf(6,plain,
! [A: ( $i > $o ) > ( $i > $o ) > $o] :
( ( A
@ ^ [B: $i] : $true
@ ^ [B: $i] : $false )
| ~ ( A @ ( sk1 @ A ) @ ( sk1 @ A ) )
| ~ ( A @ ( sk2 @ A ) @ ( sk4 @ A ) )
| ( ( sk5 @ A )
!= ( sk6 @ A ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(15,plain,
( ( ( ^ [A: $i] : $true )
= ( ^ [A: $i] : $false ) )
| ( ( sk1 @ ( (=) @ ( $i > $o ) ) )
!= ( sk1 @ ( (=) @ ( $i > $o ) ) ) )
| ( ( sk2 @ ( (=) @ ( $i > $o ) ) )
!= ( sk4 @ ( (=) @ ( $i > $o ) ) ) )
| ( ( sk5 @ ( (=) @ ( $i > $o ) ) )
!= ( sk6 @ ( (=) @ ( $i > $o ) ) ) ) ),
inference(replace_andrewseq,[status(thm)],[6:[bind(A,$thf( (=) @ ( $i > $o ) ))]]) ).
thf(41,plain,
( ( ( ^ [A: $i] : $false )
= ( ^ [A: $i] : $true ) )
| ( ( sk1 @ ( (=) @ ( $i > $o ) ) )
!= ( sk1 @ ( (=) @ ( $i > $o ) ) ) )
| ( ( sk4 @ ( (=) @ ( $i > $o ) ) )
!= ( sk2 @ ( (=) @ ( $i > $o ) ) ) )
| ( ( sk6 @ ( (=) @ ( $i > $o ) ) )
!= ( sk5 @ ( (=) @ ( $i > $o ) ) ) ) ),
inference(lifteq,[status(thm)],[15]) ).
thf(42,plain,
( ( ( sk4 @ ( (=) @ ( $i > $o ) ) )
!= ( sk2 @ ( (=) @ ( $i > $o ) ) ) )
| ( ( sk6 @ ( (=) @ ( $i > $o ) ) )
!= ( sk5 @ ( (=) @ ( $i > $o ) ) ) ) ),
inference(simp,[status(thm)],[41]) ).
thf(62,plain,
( ( ( sk4 @ ( (=) @ ( $i > $o ) ) )
!= ( sk2 @ ( (=) @ ( $i > $o ) ) ) )
| ( ( sk6 @ ( (=) @ ( $i > $o ) ) )
!= ( sk6 @ ( (=) @ ( $i > $o ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[24,42]) ).
thf(63,plain,
( ( sk4 @ ( (=) @ ( $i > $o ) ) )
!= ( sk2 @ ( (=) @ ( $i > $o ) ) ) ),
inference(pattern_uni,[status(thm)],[62:[]]) ).
thf(8,plain,
! [A: ( $i > $o ) > ( $i > $o ) > $o] :
( ( A
@ ^ [B: $i] : $true
@ ^ [B: $i] : $false )
| ~ ( A @ ( sk1 @ A ) @ ( sk1 @ A ) )
| ( A @ ( sk3 @ A ) @ ( sk4 @ A ) )
| ( A @ ( sk6 @ A ) @ ( sk5 @ A ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(20,plain,
( ( ( ^ [A: $i] : $true )
= ( ^ [A: $i] : $false ) )
| ( ( sk1 @ ( (=) @ ( $i > $o ) ) )
!= ( sk1 @ ( (=) @ ( $i > $o ) ) ) )
| ( ( sk3 @ ( (=) @ ( $i > $o ) ) )
= ( sk4 @ ( (=) @ ( $i > $o ) ) ) )
| ( ( sk6 @ ( (=) @ ( $i > $o ) ) )
= ( sk5 @ ( (=) @ ( $i > $o ) ) ) ) ),
inference(replace_andrewseq,[status(thm)],[8:[bind(A,$thf( (=) @ ( $i > $o ) ))]]) ).
thf(25,plain,
( ( ( ^ [A: $i] : $false )
= ( ^ [A: $i] : $true ) )
| ( ( sk1 @ ( (=) @ ( $i > $o ) ) )
!= ( sk1 @ ( (=) @ ( $i > $o ) ) ) )
| ( ( sk4 @ ( (=) @ ( $i > $o ) ) )
= ( sk3 @ ( (=) @ ( $i > $o ) ) ) )
| ( ( sk6 @ ( (=) @ ( $i > $o ) ) )
= ( sk5 @ ( (=) @ ( $i > $o ) ) ) ) ),
inference(lifteq,[status(thm)],[20]) ).
thf(26,plain,
( ( ( sk4 @ ( (=) @ ( $i > $o ) ) )
= ( sk3 @ ( (=) @ ( $i > $o ) ) ) )
| ( ( sk6 @ ( (=) @ ( $i > $o ) ) )
= ( sk5 @ ( (=) @ ( $i > $o ) ) ) ) ),
inference(simp,[status(thm)],[25]) ).
thf(5,plain,
! [A: ( $i > $o ) > ( $i > $o ) > $o] :
( ( A
@ ^ [B: $i] : $true
@ ^ [B: $i] : $false )
| ~ ( A @ ( sk1 @ A ) @ ( sk1 @ A ) )
| ( A @ ( sk3 @ A ) @ ( sk4 @ A ) )
| ( ( sk5 @ A )
!= ( sk6 @ A ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(13,plain,
( ( ( ^ [A: $i] : $true )
= ( ^ [A: $i] : $false ) )
| ( ( sk1 @ ( (=) @ ( $i > $o ) ) )
!= ( sk1 @ ( (=) @ ( $i > $o ) ) ) )
| ( ( sk3 @ ( (=) @ ( $i > $o ) ) )
= ( sk4 @ ( (=) @ ( $i > $o ) ) ) )
| ( ( sk5 @ ( (=) @ ( $i > $o ) ) )
!= ( sk6 @ ( (=) @ ( $i > $o ) ) ) ) ),
inference(replace_andrewseq,[status(thm)],[5:[bind(A,$thf( (=) @ ( $i > $o ) ))]]) ).
thf(30,plain,
( ( ( ^ [A: $i] : $false )
= ( ^ [A: $i] : $true ) )
| ( ( sk1 @ ( (=) @ ( $i > $o ) ) )
!= ( sk1 @ ( (=) @ ( $i > $o ) ) ) )
| ( ( sk4 @ ( (=) @ ( $i > $o ) ) )
= ( sk3 @ ( (=) @ ( $i > $o ) ) ) )
| ( ( sk6 @ ( (=) @ ( $i > $o ) ) )
!= ( sk5 @ ( (=) @ ( $i > $o ) ) ) ) ),
inference(lifteq,[status(thm)],[13]) ).
thf(31,plain,
( ( ( sk4 @ ( (=) @ ( $i > $o ) ) )
= ( sk3 @ ( (=) @ ( $i > $o ) ) ) )
| ( ( sk6 @ ( (=) @ ( $i > $o ) ) )
!= ( sk5 @ ( (=) @ ( $i > $o ) ) ) ) ),
inference(simp,[status(thm)],[30]) ).
thf(57,plain,
( ( ( sk4 @ ( (=) @ ( $i > $o ) ) )
= ( sk3 @ ( (=) @ ( $i > $o ) ) ) )
| ( ( sk6 @ ( (=) @ ( $i > $o ) ) )
!= ( sk6 @ ( (=) @ ( $i > $o ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[26,31]) ).
thf(58,plain,
( ( sk4 @ ( (=) @ ( $i > $o ) ) )
= ( sk3 @ ( (=) @ ( $i > $o ) ) ) ),
inference(pattern_uni,[status(thm)],[57:[]]) ).
thf(65,plain,
( ( sk3 @ ( (=) @ ( $i > $o ) ) )
!= ( sk2 @ ( (=) @ ( $i > $o ) ) ) ),
inference(rewrite,[status(thm)],[63,58]) ).
thf(4,plain,
! [A: ( $i > $o ) > ( $i > $o ) > $o] :
( ( A
@ ^ [B: $i] : $true
@ ^ [B: $i] : $false )
| ~ ( A @ ( sk1 @ A ) @ ( sk1 @ A ) )
| ( A @ ( sk2 @ A ) @ ( sk3 @ A ) )
| ( ( sk5 @ A )
!= ( sk6 @ A ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(21,plain,
( ( ( ^ [A: $i] : $true )
= ( ^ [A: $i] : $false ) )
| ( ( sk1 @ ( (=) @ ( $i > $o ) ) )
!= ( sk1 @ ( (=) @ ( $i > $o ) ) ) )
| ( ( sk2 @ ( (=) @ ( $i > $o ) ) )
= ( sk3 @ ( (=) @ ( $i > $o ) ) ) )
| ( ( sk5 @ ( (=) @ ( $i > $o ) ) )
!= ( sk6 @ ( (=) @ ( $i > $o ) ) ) ) ),
inference(replace_andrewseq,[status(thm)],[4:[bind(A,$thf( (=) @ ( $i > $o ) ))]]) ).
thf(28,plain,
( ( ( ^ [A: $i] : $false )
= ( ^ [A: $i] : $true ) )
| ( ( sk1 @ ( (=) @ ( $i > $o ) ) )
!= ( sk1 @ ( (=) @ ( $i > $o ) ) ) )
| ( ( sk3 @ ( (=) @ ( $i > $o ) ) )
= ( sk2 @ ( (=) @ ( $i > $o ) ) ) )
| ( ( sk6 @ ( (=) @ ( $i > $o ) ) )
!= ( sk5 @ ( (=) @ ( $i > $o ) ) ) ) ),
inference(lifteq,[status(thm)],[21]) ).
thf(29,plain,
( ( ( sk3 @ ( (=) @ ( $i > $o ) ) )
= ( sk2 @ ( (=) @ ( $i > $o ) ) ) )
| ( ( sk6 @ ( (=) @ ( $i > $o ) ) )
!= ( sk5 @ ( (=) @ ( $i > $o ) ) ) ) ),
inference(simp,[status(thm)],[28]) ).
thf(67,plain,
( ( sk6 @ ( (=) @ ( $i > $o ) ) )
!= ( sk5 @ ( (=) @ ( $i > $o ) ) ) ),
inference(simplifyReflect,[status(thm)],[29,65]) ).
thf(387,plain,
$false,
inference(simplifyReflect,[status(thm)],[35,65,67]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEV087^5 : TPTP v8.2.0. Released v4.0.0.
% 0.07/0.12 % Command : run_Leo-III %s %d SAT
% 0.12/0.33 % Computer : n028.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 21 19:17:40 EDT 2024
% 0.12/0.33 % CPUTime :
% 1.04/0.91 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.30/1.03 % [INFO] Parsing done (116ms).
% 1.30/1.03 % [INFO] Running in sequential loop mode.
% 1.72/1.23 % [INFO] nitpick registered as external prover.
% 1.72/1.23 % [INFO] Scanning for conjecture ...
% 1.72/1.28 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.95/1.30 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.95/1.30 % [INFO] Problem is higher-order (TPTP THF).
% 1.95/1.31 % [INFO] Type checking passed.
% 1.95/1.31 % [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 ...
% 11.28/2.98 % [INFO] Killing All external provers ...
% 11.28/2.98 % Time passed: 2456ms (effective reasoning time: 1941ms)
% 11.28/2.98 % 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)>
% 11.28/2.98 % Axioms used in derivation (0):
% 11.28/2.98 % No. of inferences in proof: 34
% 11.28/2.98 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2456 ms resp. 1941 ms w/o parsing
% 11.28/3.06 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 11.28/3.06 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------