TSTP Solution File: SWW412-1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SWW412-1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n012.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 : Fri May 19 12:23:51 EDT 2023
% Result : Unsatisfiable 3.02s 1.64s
% Output : Refutation 3.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 30
% Syntax : Number of formulae : 51 ( 27 unt; 10 typ; 0 def)
% Number of atoms : 61 ( 30 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 348 ( 34 ~; 20 |; 0 &; 294 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 76 ( 0 ^; 76 !; 0 ?; 76 :)
% 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(x2_type,type,
x2: $i ).
thf(nil_type,type,
nil: $i ).
thf(x1_type,type,
x1: $i ).
thf(emp_type,type,
emp: $i ).
thf(x3_type,type,
x3: $i ).
thf(next_type,type,
next: $i > $i > $i ).
thf(x4_type,type,
x4: $i ).
thf(20,axiom,
! [B: $i,A: $i] :
( ~ ( heap @ ( sep @ ( lseg @ nil @ A ) @ B ) )
| ( A = nil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wellformedness_2) ).
thf(69,plain,
! [B: $i,A: $i] :
( ~ ( heap @ ( sep @ ( lseg @ nil @ A ) @ B ) )
| ( A = nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(15,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( heap @ ( sep @ ( next @ A @ B ) @ ( sep @ ( next @ A @ C ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wellformedness_3) ).
thf(56,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( heap @ ( sep @ ( next @ A @ B ) @ ( sep @ ( next @ A @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(7,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( heap @ ( sep @ ( lseg @ A @ B ) @ ( sep @ ( lseg @ A @ C ) @ D ) ) )
| ( A = B )
| ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wellformedness_5) ).
thf(37,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( heap @ ( sep @ ( lseg @ A @ B ) @ ( sep @ ( lseg @ A @ C ) @ D ) ) )
| ( A = B )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(17,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/sandbox2/benchmark/theBenchmark.p',unfolding_2) ).
thf(61,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)],[17]) ).
thf(1,negated_conjecture,
~ ( heap @ ( sep @ ( lseg @ x2 @ nil ) @ ( sep @ ( lseg @ x1 @ nil ) @ emp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conclusion_1) ).
thf(21,plain,
~ ( heap @ ( sep @ ( lseg @ x2 @ nil ) @ ( sep @ ( lseg @ x1 @ nil ) @ emp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ( sep @ ( lseg @ A @ A ) @ B )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',normalization) ).
thf(41,plain,
! [B: $i,A: $i] :
( ( sep @ ( lseg @ A @ A ) @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(14,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( heap @ ( sep @ ( lseg @ A @ B ) @ ( sep @ ( lseg @ B @ C ) @ ( sep @ ( next @ C @ D ) @ E ) ) ) )
| ( heap @ ( sep @ ( lseg @ A @ C ) @ ( sep @ ( next @ C @ D ) @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unfolding_4) ).
thf(54,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( heap @ ( sep @ ( lseg @ A @ B ) @ ( sep @ ( lseg @ B @ C ) @ ( sep @ ( next @ C @ D ) @ E ) ) ) )
| ( heap @ ( sep @ ( lseg @ A @ C ) @ ( sep @ ( next @ C @ D ) @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(19,axiom,
nil != x1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',premise_1) ).
thf(66,plain,
nil != x1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(12,axiom,
x3 != x2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',premise_4) ).
thf(48,plain,
x3 != x2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(5,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( heap @ ( sep @ ( lseg @ A @ B ) @ ( sep @ ( lseg @ B @ C ) @ ( sep @ ( lseg @ C @ D ) @ E ) ) ) )
| ( C = D )
| ( heap @ ( sep @ ( lseg @ A @ C ) @ ( sep @ ( lseg @ C @ D ) @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unfolding_5) ).
thf(31,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( heap @ ( sep @ ( lseg @ A @ B ) @ ( sep @ ( lseg @ B @ C ) @ ( sep @ ( lseg @ C @ D ) @ E ) ) ) )
| ( C = D )
| ( heap @ ( sep @ ( lseg @ A @ C ) @ ( sep @ ( lseg @ C @ D ) @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(10,axiom,
x1 != x2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',premise_5) ).
thf(43,plain,
x1 != x2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(16,axiom,
nil != x2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',premise_2) ).
thf(58,plain,
nil != x2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(13,axiom,
x2 != x4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',premise_7) ).
thf(51,plain,
x2 != x4,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(11,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/sandbox2/benchmark/theBenchmark.p',unfolding_3) ).
thf(46,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)],[11]) ).
thf(4,axiom,
! [C: $i,B: $i,A: $i] :
( ( sep @ A @ ( sep @ B @ C ) )
= ( sep @ B @ ( sep @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associative_commutative) ).
thf(29,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)],[4]) ).
thf(6,axiom,
x1 != x4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',premise_6) ).
thf(34,plain,
x1 != x4,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(18,axiom,
! [B: $i,A: $i] :
~ ( heap @ ( sep @ ( next @ nil @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wellformedness_1) ).
thf(64,plain,
! [B: $i,A: $i] :
~ ( heap @ ( sep @ ( next @ nil @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(8,axiom,
heap @ ( sep @ ( lseg @ x3 @ nil ) @ ( sep @ ( lseg @ x4 @ nil ) @ ( sep @ ( next @ x1 @ x4 ) @ ( sep @ ( next @ x2 @ x3 ) @ emp ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',premise_8) ).
thf(40,plain,
heap @ ( sep @ ( lseg @ x3 @ nil ) @ ( sep @ ( lseg @ x4 @ nil ) @ ( sep @ ( next @ x1 @ x4 ) @ ( sep @ ( next @ x2 @ x3 ) @ emp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(3,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( heap @ ( sep @ ( next @ A @ B ) @ ( sep @ ( lseg @ A @ C ) @ D ) ) )
| ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wellformedness_4) ).
thf(26,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( heap @ ( sep @ ( next @ A @ B ) @ ( sep @ ( lseg @ A @ C ) @ D ) ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(2,axiom,
x3 != x1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',premise_3) ).
thf(23,plain,
x3 != x1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(74,plain,
$false,
inference(cvc4,[status(thm)],[69,56,37,61,21,41,54,66,48,31,43,58,51,46,29,34,64,40,26,23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWW412-1 : TPTP v8.1.2. Released v5.2.0.
% 0.07/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n012.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu May 18 22:01:33 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.83/0.84 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.19/0.96 % [INFO] Parsing done (116ms).
% 1.19/0.97 % [INFO] Running in sequential loop mode.
% 1.56/1.15 % [INFO] eprover registered as external prover.
% 1.56/1.15 % [INFO] cvc4 registered as external prover.
% 1.56/1.16 % [INFO] Scanning for conjecture ...
% 1.73/1.21 % [INFO] Found a conjecture and 19 axioms. Running axiom selection ...
% 1.73/1.25 % [INFO] Axiom selection finished. Selected 19 axioms (removed 0 axioms).
% 1.73/1.27 % [INFO] Problem is propositional (TPTP CNF).
% 1.73/1.27 % [INFO] Type checking passed.
% 1.73/1.28 % [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 ...
% 3.02/1.64 % External prover 'cvc4' found a proof!
% 3.02/1.64 % [INFO] Killing All external provers ...
% 3.02/1.64 % Time passed: 1115ms (effective reasoning time: 666ms)
% 3.02/1.64 % 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)>
% 3.02/1.64 % Axioms used in derivation (19): premise_5, premise_2, wellformedness_2, premise_6, wellformedness_3, wellformedness_4, unfolding_2, premise_1, premise_4, wellformedness_1, premise_7, wellformedness_5, associative_commutative, unfolding_5, normalization, unfolding_3, unfolding_4, premise_8, premise_3
% 3.02/1.64 % No. of inferences in proof: 41
% 3.02/1.64 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1115 ms resp. 666 ms w/o parsing
% 3.22/1.72 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.22/1.72 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------