TSTP Solution File: SWW400-1 by Leo-III-SAT---1.7.15
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.15
% Problem : SWW400-1 : TPTP v8.2.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d SAT
% 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 : Mon Jun 24 18:25:04 EDT 2024
% Result : Unsatisfiable 75.08s 12.90s
% Output : Refutation 75.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 7
% Syntax : Number of formulae : 48 ( 28 unt; 0 typ; 0 def)
% Number of atoms : 79 ( 40 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 497 ( 33 ~; 27 |; 0 &; 437 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 102 ( 0 ^ 102 !; 0 ?; 102 :)
% Comments :
%------------------------------------------------------------------------------
thf(heap_type,type,
heap: $i > $o ).
thf(sep_type,type,
sep: $i > $i > $i ).
thf(lseg_type,type,
lseg: $i > $i > $i ).
thf(x1_type,type,
x1: $i ).
thf(nil_type,type,
nil: $i ).
thf(emp_type,type,
emp: $i ).
thf(next_type,type,
next: $i > $i > $i ).
thf(x2_type,type,
x2: $i ).
thf(2,axiom,
! [C: $i,B: $i,A: $i] :
( ( sep @ A @ ( sep @ B @ C ) )
= ( sep @ B @ ( sep @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associative_commutative) ).
thf(18,plain,
! [C: $i,B: $i,A: $i] :
( ( sep @ A @ ( sep @ B @ C ) )
= ( sep @ B @ ( sep @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(19,plain,
! [C: $i,B: $i,A: $i] :
( ( sep @ A @ ( sep @ B @ C ) )
= ( sep @ B @ ( sep @ A @ C ) ) ),
inference(lifteq,[status(thm)],[18]) ).
thf(3,axiom,
! [B: $i,A: $i] :
( ( sep @ ( lseg @ A @ A ) @ B )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',normalization) ).
thf(20,plain,
! [B: $i,A: $i] :
( ( sep @ ( lseg @ A @ A ) @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(21,plain,
! [B: $i,A: $i] :
( ( sep @ ( lseg @ A @ A ) @ B )
= B ),
inference(lifteq,[status(thm)],[20]) ).
thf(87,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( sep @ B @ ( sep @ A @ C ) )
= E )
| ( ( sep @ A @ ( sep @ B @ C ) )
!= ( sep @ ( lseg @ D @ D ) @ E ) ) ),
inference(paramod_ordered,[status(thm)],[19,21]) ).
thf(88,plain,
! [C: $i,B: $i,A: $i] :
( ( sep @ B @ ( sep @ ( lseg @ A @ A ) @ C ) )
= ( sep @ B @ C ) ),
inference(pattern_uni,[status(thm)],[87:[bind(A,$thf( lseg @ G @ G )),bind(B,$thf( H )),bind(C,$thf( I )),bind(D,$thf( G )),bind(E,$thf( sep @ H @ I ))]]) ).
thf(141,plain,
! [C: $i,B: $i,A: $i] :
( ( sep @ B @ ( sep @ ( lseg @ A @ A ) @ C ) )
= ( sep @ B @ C ) ),
inference(simp,[status(thm)],[88]) ).
thf(218,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( sep @ B @ C )
= E )
| ( ( sep @ B @ ( sep @ ( lseg @ A @ A ) @ C ) )
!= ( sep @ ( lseg @ D @ D ) @ E ) ) ),
inference(paramod_ordered,[status(thm)],[141,21]) ).
thf(219,plain,
! [C: $i,B: $i,A: $i] :
( ( sep @ ( lseg @ A @ A ) @ B )
= ( sep @ ( lseg @ C @ C ) @ B ) ),
inference(pattern_uni,[status(thm)],[218:[bind(A,$thf( K )),bind(B,$thf( lseg @ G @ G )),bind(C,$thf( I )),bind(D,$thf( G )),bind(E,$thf( sep @ ( lseg @ K @ K ) @ I ))]]) ).
thf(280,plain,
! [C: $i,B: $i,A: $i] :
( ( sep @ ( lseg @ A @ A ) @ B )
= ( sep @ ( lseg @ C @ C ) @ B ) ),
inference(simp,[status(thm)],[219]) ).
thf(8665,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( sep @ ( lseg @ C @ C ) @ B )
= E )
| ( ( sep @ ( lseg @ A @ A ) @ B )
!= ( sep @ ( lseg @ D @ D ) @ E ) ) ),
inference(paramod_ordered,[status(thm)],[280,21]) ).
thf(8666,plain,
! [B: $i,A: $i] :
( ( sep @ ( lseg @ B @ B ) @ A )
= A ),
inference(pattern_uni,[status(thm)],[8665:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( A )),bind(E,$thf( B ))]]) ).
thf(9175,plain,
! [B: $i,A: $i] :
( ( sep @ ( lseg @ B @ B ) @ A )
= A ),
inference(simp,[status(thm)],[8666]) ).
thf(15,axiom,
heap @ ( sep @ ( next @ x2 @ nil ) @ ( sep @ ( lseg @ x1 @ x2 ) @ emp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',premise_3) ).
thf(51,plain,
heap @ ( sep @ ( next @ x2 @ nil ) @ ( sep @ ( lseg @ x1 @ x2 ) @ emp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(114,plain,
! [C: $i,B: $i,A: $i] :
( ( heap @ ( sep @ ( next @ x2 @ nil ) @ ( sep @ A @ ( sep @ B @ C ) ) ) )
| ( ( sep @ B @ ( sep @ A @ C ) )
!= ( sep @ ( lseg @ x1 @ x2 ) @ emp ) ) ),
inference(paramod_ordered,[status(thm)],[19,51]) ).
thf(130,plain,
! [C: $i,B: $i,A: $i] :
( ( heap @ ( sep @ ( next @ x2 @ nil ) @ ( sep @ A @ ( sep @ B @ C ) ) ) )
| ( B
!= ( lseg @ x1 @ x2 ) )
| ( ( sep @ A @ C )
!= emp ) ),
inference(simp,[status(thm)],[114]) ).
thf(137,plain,
! [B: $i,A: $i] :
( ( heap @ ( sep @ ( next @ x2 @ nil ) @ ( sep @ A @ ( sep @ ( lseg @ x1 @ x2 ) @ B ) ) ) )
| ( ( sep @ A @ B )
!= emp ) ),
inference(simp,[status(thm)],[130]) ).
thf(29258,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( heap @ ( sep @ ( next @ x2 @ nil ) @ ( sep @ C @ ( sep @ ( lseg @ x1 @ x2 ) @ D ) ) ) )
| ( A != emp )
| ( ( sep @ ( lseg @ B @ B ) @ A )
!= ( sep @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[9175,137]) ).
thf(29259,plain,
! [B: $i,A: $i] :
( ( heap @ ( sep @ ( next @ x2 @ nil ) @ ( sep @ ( lseg @ B @ B ) @ ( sep @ ( lseg @ x1 @ x2 ) @ A ) ) ) )
| ( A != emp ) ),
inference(pattern_uni,[status(thm)],[29258:[bind(A,$thf( A )),bind(B,$thf( F )),bind(C,$thf( lseg @ F @ F )),bind(D,$thf( A ))]]) ).
thf(29597,plain,
! [A: $i] : ( heap @ ( sep @ ( next @ x2 @ nil ) @ ( sep @ ( lseg @ A @ A ) @ ( sep @ ( lseg @ x1 @ x2 ) @ emp ) ) ) ),
inference(simp,[status(thm)],[29259]) ).
thf(9,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( heap @ ( sep @ ( next @ A @ B ) @ ( sep @ ( lseg @ B @ C ) @ D ) ) )
| ( A = B )
| ( heap @ ( sep @ ( lseg @ A @ C ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unfolding_2) ).
thf(35,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( heap @ ( sep @ ( next @ A @ B ) @ ( sep @ ( lseg @ B @ C ) @ D ) ) )
| ( A = B )
| ( heap @ ( sep @ ( lseg @ A @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(36,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( heap @ ( sep @ ( next @ A @ B ) @ ( sep @ ( lseg @ B @ C ) @ D ) ) )
| ( A = B )
| ( heap @ ( sep @ ( lseg @ A @ C ) @ D ) ) ),
inference(cnf,[status(esa)],[35]) ).
thf(37,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( heap @ ( sep @ ( next @ A @ B ) @ ( sep @ ( lseg @ B @ C ) @ D ) ) )
| ( heap @ ( sep @ ( lseg @ A @ C ) @ D ) ) ),
inference(lifteq,[status(thm)],[36]) ).
thf(30425,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = C )
| ( heap @ ( sep @ ( lseg @ B @ D ) @ E ) )
| ( ( heap @ ( sep @ ( next @ x2 @ nil ) @ ( sep @ ( lseg @ A @ A ) @ ( sep @ ( lseg @ x1 @ x2 ) @ emp ) ) ) )
!= ( heap @ ( sep @ ( next @ B @ C ) @ ( sep @ ( lseg @ C @ D ) @ E ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[29597,37]) ).
thf(30426,plain,
( ( x2 = nil )
| ( heap @ ( sep @ ( lseg @ x2 @ nil ) @ ( sep @ ( lseg @ x1 @ x2 ) @ emp ) ) ) ),
inference(pattern_uni,[status(thm)],[30425:[bind(A,$thf( nil )),bind(B,$thf( x2 )),bind(C,$thf( nil )),bind(D,$thf( nil )),bind(E,$thf( sep @ ( lseg @ x1 @ x2 ) @ emp ))]]) ).
thf(10,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( heap @ ( sep @ ( lseg @ A @ B ) @ ( sep @ ( lseg @ B @ nil ) @ C ) ) )
| ( heap @ ( sep @ ( lseg @ A @ nil ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unfolding_3) ).
thf(38,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( heap @ ( sep @ ( lseg @ A @ B ) @ ( sep @ ( lseg @ B @ nil ) @ C ) ) )
| ( heap @ ( sep @ ( lseg @ A @ nil ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(39,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( heap @ ( sep @ ( lseg @ A @ B ) @ ( sep @ ( lseg @ B @ nil ) @ C ) ) )
| ( heap @ ( sep @ ( lseg @ A @ nil ) @ C ) ) ),
inference(cnf,[status(esa)],[38]) ).
thf(1,negated_conjecture,
~ ( heap @ ( sep @ ( lseg @ x1 @ nil ) @ emp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conclusion_1) ).
thf(16,plain,
~ ( heap @ ( sep @ ( lseg @ x1 @ nil ) @ emp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(17,plain,
~ ( heap @ ( sep @ ( lseg @ x1 @ nil ) @ emp ) ),
inference(polarity_switch,[status(thm)],[16]) ).
thf(7506,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( heap @ ( sep @ ( lseg @ A @ B ) @ ( sep @ ( lseg @ B @ nil ) @ C ) ) )
| ( ( heap @ ( sep @ ( lseg @ A @ nil ) @ C ) )
!= ( heap @ ( sep @ ( lseg @ x1 @ nil ) @ emp ) ) ) ),
inference(paramod_ordered,[status(thm)],[39,17]) ).
thf(7507,plain,
! [A: $i] :
~ ( heap @ ( sep @ ( lseg @ x1 @ A ) @ ( sep @ ( lseg @ A @ nil ) @ emp ) ) ),
inference(pattern_uni,[status(thm)],[7506:[bind(A,$thf( x1 )),bind(B,$thf( B )),bind(C,$thf( emp ))]]) ).
thf(7640,plain,
! [A: $i] :
~ ( heap @ ( sep @ ( lseg @ x1 @ A ) @ ( sep @ ( lseg @ A @ nil ) @ emp ) ) ),
inference(simp,[status(thm)],[7507]) ).
thf(7841,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( heap @ ( sep @ B @ ( sep @ A @ C ) ) )
| ( ( sep @ A @ ( sep @ B @ C ) )
!= ( sep @ ( lseg @ x1 @ D ) @ ( sep @ ( lseg @ D @ nil ) @ emp ) ) ) ),
inference(paramod_ordered,[status(thm)],[19,7640]) ).
thf(7842,plain,
! [A: $i] :
~ ( heap @ ( sep @ ( lseg @ A @ nil ) @ ( sep @ ( lseg @ x1 @ A ) @ emp ) ) ),
inference(pattern_uni,[status(thm)],[7841:[bind(A,$thf( lseg @ x1 @ G )),bind(B,$thf( lseg @ G @ nil )),bind(C,$thf( emp )),bind(D,$thf( G ))]]) ).
thf(7875,plain,
! [A: $i] :
~ ( heap @ ( sep @ ( lseg @ A @ nil ) @ ( sep @ ( lseg @ x1 @ A ) @ emp ) ) ),
inference(simp,[status(thm)],[7842]) ).
thf(32324,plain,
( ( x2 = nil )
| $false ),
inference(rewrite,[status(thm)],[30426,7875]) ).
thf(32325,plain,
x2 = nil,
inference(simp,[status(thm)],[32324]) ).
thf(14,axiom,
nil != x2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',premise_2) ).
thf(48,plain,
nil != x2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(49,plain,
nil != x2,
inference(polarity_switch,[status(thm)],[48]) ).
thf(50,plain,
x2 != nil,
inference(lifteq,[status(thm)],[49]) ).
thf(32326,plain,
$false,
inference(simplifyReflect,[status(thm)],[32325,50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWW400-1 : TPTP v8.2.0. Released v5.2.0.
% 0.00/0.12 % Command : run_Leo-III %s %d SAT
% 0.12/0.33 % Computer : n002.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 : Wed Jun 19 07:03:40 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.82/0.85 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.20/0.97 % [INFO] Parsing done (112ms).
% 1.20/0.98 % [INFO] Running in sequential loop mode.
% 1.71/1.18 % [INFO] nitpick registered as external prover.
% 1.71/1.19 % [INFO] Scanning for conjecture ...
% 1.88/1.24 % [INFO] Found a conjecture (or negated_conjecture) and 14 axioms. Running axiom selection ...
% 1.88/1.26 % [INFO] Axiom selection finished. Selected 14 axioms (removed 0 axioms).
% 1.88/1.28 % [INFO] Problem is propositional (TPTP CNF).
% 1.88/1.29 % [INFO] Type checking passed.
% 1.88/1.29 % [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 ...
% 75.08/12.89 % [INFO] Killing All external provers ...
% 75.08/12.90 % Time passed: 12372ms (effective reasoning time: 11914ms)
% 75.08/12.90 % Axioms used in derivation (6): premise_2, associative_commutative, normalization, unfolding_3, premise_3, unfolding_2
% 75.08/12.90 % No. of inferences in proof: 48
% 75.08/12.90 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 12372 ms resp. 11914 ms w/o parsing
% 75.08/12.93 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 75.08/12.93 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------