TSTP Solution File: SWW423-1 by Leo-III---1.7.15
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.15
% Problem : SWW423-1 : TPTP v8.2.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% 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 18:22:32 EDT 2024
% Result : Unsatisfiable 3.56s 2.21s
% Output : Refutation 3.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 16
% Syntax : Number of formulae : 33 ( 19 unt; 0 typ; 0 def)
% Number of atoms : 53 ( 22 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 332 ( 26 ~; 20 |; 0 &; 286 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 9 usr; 6 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(x1_type,type,
x1: $i ).
thf(nil_type,type,
nil: $i ).
thf(x3_type,type,
x3: $i ).
thf(emp_type,type,
emp: $i ).
thf(x2_type,type,
x2: $i ).
thf(next_type,type,
next: $i > $i > $i ).
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/sandbox/benchmark/theBenchmark.p',unfolding_5) ).
thf(24,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,
! [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/sandbox/benchmark/theBenchmark.p',unfolding_4) ).
thf(38,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)],[10]) ).
thf(16,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(54,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)],[16]) ).
thf(9,axiom,
x2 != x1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',premise_2) ).
thf(35,plain,
x2 != x1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(14,axiom,
nil != x1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',premise_1) ).
thf(48,plain,
nil != x1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(12,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/sandbox/benchmark/theBenchmark.p',wellformedness_5) ).
thf(43,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)],[12]) ).
thf(11,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(40,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)],[11]) ).
thf(3,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( heap @ ( sep @ ( next @ A @ B ) @ ( sep @ ( next @ A @ C ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wellformedness_3) ).
thf(20,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)],[3]) ).
thf(13,axiom,
! [B: $i,A: $i] :
( ( sep @ ( lseg @ A @ A ) @ B )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',normalization) ).
thf(46,plain,
! [B: $i,A: $i] :
( ( sep @ ( lseg @ A @ A ) @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(8,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( heap @ ( sep @ ( next @ A @ B ) @ ( sep @ ( lseg @ A @ C ) @ D ) ) )
| ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wellformedness_4) ).
thf(32,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)],[8]) ).
thf(1,negated_conjecture,
~ ( heap @ ( sep @ ( lseg @ x1 @ nil ) @ ( sep @ ( lseg @ x3 @ nil ) @ emp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conclusion_1) ).
thf(17,plain,
~ ( heap @ ( sep @ ( lseg @ x1 @ nil ) @ ( sep @ ( lseg @ x3 @ nil ) @ emp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(4,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(22,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 != x3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',premise_3) ).
thf(27,plain,
x1 != x3,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(7,axiom,
! [B: $i,A: $i] :
~ ( heap @ ( sep @ ( next @ nil @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wellformedness_1) ).
thf(30,plain,
! [B: $i,A: $i] :
~ ( heap @ ( sep @ ( next @ nil @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(15,axiom,
! [B: $i,A: $i] :
( ~ ( heap @ ( sep @ ( lseg @ nil @ A ) @ B ) )
| ( A = nil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wellformedness_2) ).
thf(51,plain,
! [B: $i,A: $i] :
( ~ ( heap @ ( sep @ ( lseg @ nil @ A ) @ B ) )
| ( A = nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(2,axiom,
heap @ ( sep @ ( lseg @ x2 @ nil ) @ ( sep @ ( lseg @ x3 @ nil ) @ ( sep @ ( next @ x1 @ x2 ) @ emp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',premise_4) ).
thf(19,plain,
heap @ ( sep @ ( lseg @ x2 @ nil ) @ ( sep @ ( lseg @ x3 @ nil ) @ ( sep @ ( next @ x1 @ x2 ) @ emp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(56,plain,
$false,
inference(e,[status(thm)],[24,38,54,35,48,43,40,20,46,32,17,22,27,30,51,19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SWW423-1 : TPTP v8.2.0. Released v5.2.0.
% 0.00/0.09 % Command : run_Leo-III %s %d THM
% 0.08/0.29 % Computer : n026.cluster.edu
% 0.08/0.29 % Model : x86_64 x86_64
% 0.08/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.29 % Memory : 8042.1875MB
% 0.08/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.29 % CPULimit : 300
% 0.08/0.29 % WCLimit : 300
% 0.08/0.29 % DateTime : Wed Jun 19 08:20:40 EDT 2024
% 0.08/0.29 % CPUTime :
% 0.93/0.91 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.17/1.07 % [INFO] Parsing done (164ms).
% 1.33/1.09 % [INFO] Running in sequential loop mode.
% 1.81/1.45 % [INFO] eprover registered as external prover.
% 1.81/1.46 % [INFO] Scanning for conjecture ...
% 1.96/1.55 % [INFO] Found a conjecture (or negated_conjecture) and 15 axioms. Running axiom selection ...
% 2.24/1.60 % [INFO] Axiom selection finished. Selected 15 axioms (removed 0 axioms).
% 2.33/1.64 % [INFO] Problem is propositional (TPTP CNF).
% 2.33/1.64 % [INFO] Type checking passed.
% 2.33/1.65 % [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 ...
% 3.56/2.21 % External prover 'e' found a proof!
% 3.56/2.21 % [INFO] Killing All external provers ...
% 3.56/2.21 % Time passed: 1758ms (effective reasoning time: 1112ms)
% 3.56/2.21 % Axioms used in derivation (15): premise_2, wellformedness_2, wellformedness_3, wellformedness_4, premise_3, unfolding_2, premise_1, premise_4, wellformedness_1, wellformedness_5, associative_commutative, unfolding_5, normalization, unfolding_3, unfolding_4
% 3.56/2.21 % No. of inferences in proof: 33
% 3.56/2.21 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 1758 ms resp. 1112 ms w/o parsing
% 3.79/2.27 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.79/2.27 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------