TSTP Solution File: QUA002^1 by Leo-III---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : QUA002^1 : TPTP v8.2.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n008.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 : Tue May 21 02:30:25 EDT 2024
% Result : Theorem 14.54s 4.44s
% Output : Refutation 14.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 25 ( 11 unt; 5 typ; 1 def)
% Number of atoms : 60 ( 56 equ; 0 cnn)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 64 ( 18 ~; 27 |; 0 &; 19 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 16 ( 10 ^ 6 !; 0 ?; 16 :)
% Comments :
%------------------------------------------------------------------------------
thf(sup_type,type,
sup: ( $i > $o ) > $i ).
thf(addition_type,type,
addition: $i > $i > $i ).
thf(addition_def,definition,
( addition
= ( ^ [A: $i,B: $i] : ( sup @ ( union @ ( singleton @ A ) @ ( singleton @ B ) ) ) ) ) ).
thf(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: $i ).
thf(sk3_type,type,
sk3: $i ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ( addition @ A @ B )
= ( addition @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',addition_comm) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( addition @ A @ B )
= ( addition @ B @ A ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(10,plain,
~ ! [A: $i,B: $i] :
( ( sup
@ ^ [C: $i] :
( ( C = A )
| ( C = B ) ) )
= ( sup
@ ^ [C: $i] :
( ( C = B )
| ( C = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(11,plain,
( ( sup
@ ^ [A: $i] :
( ( A = sk1 )
| ( A = sk2 ) ) )
!= ( sup
@ ^ [A: $i] :
( ( A = sk2 )
| ( A = sk1 ) ) ) ),
inference(cnf,[status(esa)],[10]) ).
thf(12,plain,
( ( sup
@ ^ [A: $i] :
( ( A = sk1 )
| ( A = sk2 ) ) )
!= ( sup
@ ^ [A: $i] :
( ( A = sk2 )
| ( A = sk1 ) ) ) ),
inference(lifteq,[status(thm)],[11]) ).
thf(50,plain,
( ( ^ [A: $i] :
( ( A = sk1 )
| ( A = sk2 ) ) )
!= ( ^ [A: $i] :
( ( A = sk2 )
| ( A = sk1 ) ) ) ),
inference(simp,[status(thm)],[12]) ).
thf(68,plain,
( ( ( sk3 = sk1 )
| ( sk3 = sk2 ) )
!= ( ( sk3 = sk2 )
| ( sk3 = sk1 ) ) ),
inference(func_ext,[status(esa)],[50]) ).
thf(302,plain,
( ( sk3 = sk1 )
| ( sk3 = sk2 )
| ( sk3 = sk2 )
| ( sk3 = sk1 ) ),
inference(bool_ext,[status(thm)],[68]) ).
thf(341,plain,
( ( sk3 = sk2 )
| ( sk3 = sk1 )
| ( sk3 = sk1 )
| ( sk3 = sk2 ) ),
inference(cnf,[status(esa)],[302]) ).
thf(342,plain,
( ( sk3 = sk2 )
| ( sk3 = sk1 )
| ( sk3 = sk1 )
| ( sk3 = sk2 ) ),
inference(lifteq,[status(thm)],[341]) ).
thf(343,plain,
( ( sk3 = sk2 )
| ( sk3 = sk1 ) ),
inference(simp,[status(thm)],[342]) ).
thf(301,plain,
( ~ ( ( sk3 = sk1 )
| ( sk3 = sk2 ) )
| ~ ( ( sk3 = sk2 )
| ( sk3 = sk1 ) ) ),
inference(bool_ext,[status(thm)],[68]) ).
thf(333,plain,
( ( sk3 != sk1 )
| ( sk3 != sk1 ) ),
inference(cnf,[status(esa)],[301]) ).
thf(336,plain,
( ( sk3 != sk1 )
| ( sk3 != sk1 ) ),
inference(lifteq,[status(thm)],[333]) ).
thf(337,plain,
sk3 != sk1,
inference(simp,[status(thm)],[336]) ).
thf(335,plain,
( ( sk3 != sk2 )
| ( sk3 != sk2 ) ),
inference(cnf,[status(esa)],[301]) ).
thf(339,plain,
( ( sk3 != sk2 )
| ( sk3 != sk2 ) ),
inference(lifteq,[status(thm)],[335]) ).
thf(340,plain,
sk3 != sk2,
inference(simp,[status(thm)],[339]) ).
thf(349,plain,
$false,
inference(simplifyReflect,[status(thm)],[343,337,340]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : QUA002^1 : TPTP v8.2.0. Released v4.1.0.
% 0.07/0.14 % Command : run_Leo-III %s %d
% 0.14/0.35 % Computer : n008.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon May 20 13:37:09 EDT 2024
% 0.14/0.35 % CPUTime :
% 1.14/1.07 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.63/1.27 % [INFO] Parsing done (193ms).
% 1.63/1.29 % [INFO] Running in sequential loop mode.
% 2.26/1.67 % [INFO] eprover registered as external prover.
% 2.26/1.67 % [INFO] cvc4 registered as external prover.
% 2.26/1.68 % [INFO] Scanning for conjecture ...
% 2.48/1.81 % [INFO] Found a conjecture (or negated_conjecture) and 7 axioms. Running axiom selection ...
% 2.59/1.85 % [INFO] Axiom selection finished. Selected 7 axioms (removed 0 axioms).
% 2.71/1.86 % [INFO] Problem is higher-order (TPTP THF).
% 2.71/1.86 % [INFO] Type checking passed.
% 2.71/1.87 % [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 ...
% 14.54/4.43 % [INFO] Killing All external provers ...
% 14.54/4.44 % Time passed: 3917ms (effective reasoning time: 3143ms)
% 14.54/4.44 % 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)>
% 14.54/4.44 % Axioms used in derivation (0):
% 14.54/4.44 % No. of inferences in proof: 19
% 14.54/4.44 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 3917 ms resp. 3143 ms w/o parsing
% 14.57/4.47 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 14.57/4.47 % [INFO] Killing All external provers ...
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