TSTP Solution File: SWW443-1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SWW443-1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% 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 : Fri May 19 12:23:54 EDT 2023
% Result : Unsatisfiable 74.37s 24.24s
% Output : Refutation 74.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 60
% Syntax : Number of formulae : 96 ( 56 unt; 25 typ; 0 def)
% Number of atoms : 92 ( 61 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 433 ( 63 ~; 21 |; 0 &; 349 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 28 ( 25 usr; 23 con; 0-2 aty)
% Number of variables : 76 ( 0 ^; 76 !; 0 ?; 76 :)
% Comments :
%------------------------------------------------------------------------------
thf(x1_type,type,
x1: $i ).
thf(heap_type,type,
heap: $i > $o ).
thf(emp_type,type,
emp: $i ).
thf(x4_type,type,
x4: $i ).
thf(x19_type,type,
x19: $i ).
thf(sep_type,type,
sep: $i > $i > $i ).
thf(x2_type,type,
x2: $i ).
thf(x8_type,type,
x8: $i ).
thf(x11_type,type,
x11: $i ).
thf(x15_type,type,
x15: $i ).
thf(x14_type,type,
x14: $i ).
thf(x16_type,type,
x16: $i ).
thf(x13_type,type,
x13: $i ).
thf(x5_type,type,
x5: $i ).
thf(x6_type,type,
x6: $i ).
thf(x17_type,type,
x17: $i ).
thf(x18_type,type,
x18: $i ).
thf(x3_type,type,
x3: $i ).
thf(lseg_type,type,
lseg: $i > $i > $i ).
thf(x9_type,type,
x9: $i ).
thf(next_type,type,
next: $i > $i > $i ).
thf(nil_type,type,
nil: $i ).
thf(x10_type,type,
x10: $i ).
thf(x12_type,type,
x12: $i ).
thf(x7_type,type,
x7: $i ).
thf(13,axiom,
x17 != x18,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',premise_7) ).
thf(69,plain,
x17 != x18,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(32,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(120,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)],[32]) ).
thf(21,axiom,
x8 != x9,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',premise_13) ).
thf(92,plain,
x8 != x9,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(35,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(129,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)],[35]) ).
thf(26,axiom,
x1 != x15,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',premise_18) ).
thf(105,plain,
x1 != x15,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(5,axiom,
x11 != x15,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',premise_4) ).
thf(45,plain,
x11 != x15,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(33,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(123,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)],[33]) ).
thf(14,axiom,
x3 != x5,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',premise_6) ).
thf(72,plain,
x3 != x5,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(15,axiom,
x11 != x16,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',premise_2) ).
thf(75,plain,
x11 != x16,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(34,axiom,
x1 != x6,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',premise_16) ).
thf(126,plain,
x1 != x6,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(4,axiom,
x2 != x8,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',premise_8) ).
thf(42,plain,
x2 != x8,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(2,axiom,
x4 != x19,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',premise_15) ).
thf(37,plain,
x4 != x19,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(9,axiom,
x5 != x15,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',premise_22) ).
thf(57,plain,
x5 != x15,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(16,axiom,
x13 != x19,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',premise_20) ).
thf(78,plain,
x13 != x19,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(20,axiom,
x14 != x18,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',premise_11) ).
thf(89,plain,
x14 != x18,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(30,axiom,
heap @ ( sep @ ( lseg @ x10 @ x1 ) @ ( sep @ ( lseg @ x18 @ x15 ) @ ( sep @ ( lseg @ x1 @ x14 ) @ ( sep @ ( lseg @ x1 @ x3 ) @ ( sep @ ( lseg @ x12 @ x13 ) @ ( sep @ ( lseg @ x2 @ x5 ) @ ( sep @ ( lseg @ x2 @ x12 ) @ ( sep @ ( lseg @ x2 @ x18 ) @ ( sep @ ( lseg @ x2 @ x8 ) @ ( sep @ ( lseg @ x9 @ x5 ) @ ( sep @ ( lseg @ x7 @ x5 ) @ ( sep @ ( lseg @ x11 @ x9 ) @ ( sep @ ( lseg @ x11 @ x7 ) @ emp ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',premise_23) ).
thf(116,plain,
heap @ ( sep @ ( lseg @ x10 @ x1 ) @ ( sep @ ( lseg @ x18 @ x15 ) @ ( sep @ ( lseg @ x1 @ x14 ) @ ( sep @ ( lseg @ x1 @ x3 ) @ ( sep @ ( lseg @ x12 @ x13 ) @ ( sep @ ( lseg @ x2 @ x5 ) @ ( sep @ ( lseg @ x2 @ x12 ) @ ( sep @ ( lseg @ x2 @ x18 ) @ ( sep @ ( lseg @ x2 @ x8 ) @ ( sep @ ( lseg @ x9 @ x5 ) @ ( sep @ ( lseg @ x7 @ x5 ) @ ( sep @ ( lseg @ x11 @ x9 ) @ ( sep @ ( lseg @ x11 @ x7 ) @ emp ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(10,axiom,
x2 != x13,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',premise_9) ).
thf(60,plain,
x2 != x13,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(31,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(117,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)],[31]) ).
thf(8,axiom,
x11 != x13,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',premise_3) ).
thf(54,plain,
x11 != x13,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(19,axiom,
x4 != x18,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',premise_14) ).
thf(86,plain,
x4 != x18,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(17,axiom,
! [B: $i,A: $i] :
( ( sep @ ( lseg @ A @ A ) @ B )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',normalization) ).
thf(81,plain,
! [B: $i,A: $i] :
( ( sep @ ( lseg @ A @ A ) @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(23,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(98,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)],[23]) ).
thf(25,axiom,
! [B: $i,A: $i] :
~ ( heap @ ( sep @ ( next @ nil @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wellformedness_1) ).
thf(103,plain,
! [B: $i,A: $i] :
~ ( heap @ ( sep @ ( next @ nil @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(12,axiom,
x6 != x13,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',premise_1) ).
thf(66,plain,
x6 != x13,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(27,axiom,
! [B: $i,A: $i] :
( ~ ( heap @ ( sep @ ( lseg @ nil @ A ) @ B ) )
| ( A = nil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wellformedness_2) ).
thf(108,plain,
! [B: $i,A: $i] :
( ~ ( heap @ ( sep @ ( lseg @ nil @ A ) @ B ) )
| ( A = nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(6,axiom,
x2 != x14,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',premise_10) ).
thf(48,plain,
x2 != x14,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(11,axiom,
x5 != x16,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',premise_21) ).
thf(63,plain,
x5 != x16,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(22,axiom,
x1 != x14,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',premise_19) ).
thf(95,plain,
x1 != x14,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(3,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(40,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)],[3]) ).
thf(29,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(114,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)],[29]) ).
thf(1,negated_conjecture,
( ( x1 = x1 )
| ~ ( heap @ emp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conclusion_1) ).
thf(36,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(7,axiom,
x14 != x16,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',premise_12) ).
thf(51,plain,
x14 != x16,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(28,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(111,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)],[28]) ).
thf(18,axiom,
x3 != x4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',premise_5) ).
thf(83,plain,
x3 != x4,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(24,axiom,
x1 != x13,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',premise_17) ).
thf(100,plain,
x1 != x13,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(17453,plain,
$false,
inference(cvc4,[status(thm)],[69,120,92,129,105,45,123,72,75,126,42,37,57,78,89,116,60,117,54,86,81,98,103,66,108,48,63,95,40,114,36,51,111,83,100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWW443-1 : TPTP v8.1.2. Released v5.2.0.
% 0.07/0.16 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n028.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Thu May 18 22:44:04 EDT 2023
% 0.16/0.37 % CPUTime :
% 1.05/0.91 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.43/1.10 % [INFO] Parsing done (187ms).
% 1.43/1.12 % [INFO] Running in sequential loop mode.
% 1.87/1.34 % [INFO] eprover registered as external prover.
% 1.87/1.35 % [INFO] cvc4 registered as external prover.
% 1.87/1.35 % [INFO] Scanning for conjecture ...
% 2.00/1.42 % [INFO] Found a conjecture and 34 axioms. Running axiom selection ...
% 2.24/1.47 % [INFO] Axiom selection finished. Selected 34 axioms (removed 0 axioms).
% 2.32/1.50 % [INFO] Problem is propositional (TPTP CNF).
% 2.32/1.51 % [INFO] Type checking passed.
% 2.32/1.51 % [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 ...
% 74.37/24.24 % External prover 'cvc4' found a proof!
% 74.37/24.24 % [INFO] Killing All external provers ...
% 74.37/24.24 % Time passed: 23721ms (effective reasoning time: 23112ms)
% 74.37/24.24 % 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)>
% 74.37/24.24 % Axioms used in derivation (34): premise_20, wellformedness_2, premise_6, premise_23, premise_15, wellformedness_3, premise_12, premise_16, premise_11, premise_18, premise_1, premise_4, wellformedness_1, premise_7, premise_5, premise_19, premise_14, premise_2, wellformedness_5, premise_13, associative_commutative, unfolding_5, normalization, premise_9, unfolding_3, unfolding_4, premise_22, wellformedness_4, premise_8, premise_3, unfolding_2, premise_17, premise_21, premise_10
% 74.37/24.24 % No. of inferences in proof: 71
% 74.37/24.24 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 23721 ms resp. 23112 ms w/o parsing
% 74.79/24.29 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 74.79/24.29 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------