TSTP Solution File: ITP019+2 by Leo-III-SAT---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.10
% Problem : ITP019+2 : TPTP v8.1.2. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n020.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 7 10:35:57 EDT 2024
% Result : Theorem 123.14s 23.39s
% Output : Refutation 123.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of formulae : 25 ( 7 unt; 8 typ; 0 def)
% Number of atoms : 37 ( 25 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 150 ( 18 ~; 8 |; 1 &; 112 @)
% ( 1 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 7 con; 0-2 aty)
% Number of variables : 8 ( 0 ^ 8 !; 0 ?; 8 :)
% Comments :
%------------------------------------------------------------------------------
thf(mem_type,type,
mem: $i > $i > $o ).
thf(ty_2Epair_2Eprod_type,type,
ty_2Epair_2Eprod: $i > $i > $i ).
thf(ty_2Erealax_2Ereal_type,type,
ty_2Erealax_2Ereal: $i ).
thf(ap_type,type,
ap: $i > $i > $i ).
thf(c_2Ecomplex_2Ecomplex__of__num_type,type,
c_2Ecomplex_2Ecomplex__of__num: $i ).
thf(c_2Enum_2E0_type,type,
c_2Enum_2E0: $i ).
thf(c_2Ecomplex_2Ecomplex__inv_type,type,
c_2Ecomplex_2Ecomplex__inv: $i ).
thf(sk1_type,type,
sk1: $i ).
thf(1,conjecture,
! [A: $i] :
( ( mem @ A @ ( ty_2Epair_2Eprod @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) )
=> ( ( A
!= ( ap @ c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 ) )
=> ( ( ap @ c_2Ecomplex_2Ecomplex__inv @ A )
!= ( ap @ c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2Ecomplex_2ECOMPLEX__INV__NZ) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( mem @ A @ ( ty_2Epair_2Eprod @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) )
=> ( ( A
!= ( ap @ c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 ) )
=> ( ( ap @ c_2Ecomplex_2Ecomplex__inv @ A )
!= ( ap @ c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(35,plain,
~ ! [A: $i] :
( ( mem @ A @ ( ty_2Epair_2Eprod @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) )
=> ( ( A
!= ( ap @ c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 ) )
=> ( ( ap @ c_2Ecomplex_2Ecomplex__inv @ A )
!= ( ap @ c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(36,plain,
( ( ap @ c_2Ecomplex_2Ecomplex__inv @ sk1 )
= ( ap @ c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 ) ),
inference(cnf,[status(esa)],[35]) ).
thf(39,plain,
( ( ap @ c_2Ecomplex_2Ecomplex__inv @ sk1 )
= ( ap @ c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 ) ),
inference(lifteq,[status(thm)],[36]) ).
thf(34,axiom,
! [A: $i] :
( ( mem @ A @ ( ty_2Epair_2Eprod @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) )
=> ( ( ( ap @ c_2Ecomplex_2Ecomplex__inv @ A )
= ( ap @ c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 ) )
<=> ( A
= ( ap @ c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2Ecomplex_2ECOMPLEX__INV__EQ__0) ).
thf(114,plain,
! [A: $i] :
( ( mem @ A @ ( ty_2Epair_2Eprod @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) )
=> ( ( ( ( ap @ c_2Ecomplex_2Ecomplex__inv @ A )
= ( ap @ c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 ) )
=> ( A
= ( ap @ c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 ) ) )
& ( ( A
= ( ap @ c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 ) )
=> ( ( ap @ c_2Ecomplex_2Ecomplex__inv @ A )
= ( ap @ c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(115,plain,
! [A: $i] :
( ~ ( mem @ A @ ( ty_2Epair_2Eprod @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) )
| ( ( ap @ c_2Ecomplex_2Ecomplex__inv @ A )
!= ( ap @ c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 ) )
| ( A
= ( ap @ c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 ) ) ),
inference(cnf,[status(esa)],[114]) ).
thf(117,plain,
! [A: $i] :
( ( ( ap @ c_2Ecomplex_2Ecomplex__inv @ A )
!= ( ap @ c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 ) )
| ( A
= ( ap @ c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 ) )
| ~ ( mem @ A @ ( ty_2Epair_2Eprod @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) ) ),
inference(lifteq,[status(thm)],[115]) ).
thf(34438,plain,
! [A: $i] :
( ( A
= ( ap @ c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 ) )
| ~ ( mem @ A @ ( ty_2Epair_2Eprod @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) )
| ( ( ap @ c_2Ecomplex_2Ecomplex__inv @ sk1 )
!= ( ap @ c_2Ecomplex_2Ecomplex__inv @ A ) ) ),
inference(paramod_ordered,[status(thm)],[39,117]) ).
thf(34439,plain,
( ( ( ap @ c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 )
= sk1 )
| ~ ( mem @ sk1 @ ( ty_2Epair_2Eprod @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) ) ),
inference(pattern_uni,[status(thm)],[34438:[bind(A,$thf( sk1 ))]]) ).
thf(38,plain,
mem @ sk1 @ ( ty_2Epair_2Eprod @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ),
inference(cnf,[status(esa)],[35]) ).
thf(48528,plain,
( ( ( ap @ c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 )
= sk1 )
| ~ $true ),
inference(rewrite,[status(thm)],[34439,38]) ).
thf(48529,plain,
( ( ap @ c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 )
= sk1 ),
inference(simp,[status(thm)],[48528]) ).
thf(37,plain,
( sk1
!= ( ap @ c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 ) ),
inference(cnf,[status(esa)],[35]) ).
thf(40,plain,
( ( ap @ c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 )
!= sk1 ),
inference(lifteq,[status(thm)],[37]) ).
thf(48530,plain,
$false,
inference(simplifyReflect,[status(thm)],[48529,40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ITP019+2 : TPTP v8.1.2. Bugfixed v7.5.0.
% 0.07/0.15 % Command : run_Leo-III %s %d
% 0.15/0.37 % Computer : n020.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Mon May 6 22:16:09 EDT 2024
% 0.15/0.37 % CPUTime :
% 0.92/0.85 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.19/0.98 % [INFO] Parsing done (130ms).
% 1.34/0.99 % [INFO] Running in sequential loop mode.
% 1.74/1.19 % [INFO] nitpick registered as external prover.
% 1.74/1.20 % [INFO] Scanning for conjecture ...
% 1.96/1.26 % [INFO] Found a conjecture and 32 axioms. Running axiom selection ...
% 1.96/1.31 % [INFO] Axiom selection finished. Selected 32 axioms (removed 0 axioms).
% 2.16/1.35 % [INFO] Problem is first-order (TPTP FOF).
% 2.16/1.36 % [INFO] Type checking passed.
% 2.33/1.36 % [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 ...
% 123.14/23.38 % [INFO] Killing All external provers ...
% 123.14/23.39 % Time passed: 22860ms (effective reasoning time: 22394ms)
% 123.14/23.39 % 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)>
% 123.14/23.39 % Axioms used in derivation (1): conj_thm_2Ecomplex_2ECOMPLEX__INV__EQ__0
% 123.14/23.39 % No. of inferences in proof: 17
% 123.14/23.39 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 22860 ms resp. 22394 ms w/o parsing
% 123.14/23.42 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 123.14/23.42 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------