TSTP Solution File: ITP209_4 by Leo-III---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : ITP209_4 : TPTP v8.1.2. Released v8.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n009.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 07:48:53 EDT 2024
% Result : Theorem 3.89s 1.87s
% Output : Refutation 3.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 22
% Syntax : Number of formulae : 37 ( 16 unt; 9 typ; 0 def)
% Number of atoms : 137 ( 27 equ; 0 cnn)
% Maximal formula atoms : 6 ( 4 avg)
% Number of connectives : 1025 ( 2 ~; 0 |; 4 &;1004 @)
% ( 1 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 9 usr; 6 con; 0-4 aty)
% Number of variables : 110 ( 0 ^ 103 !; 0 ?; 110 :)
% ( 7 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(a_type,type,
a: $tType ).
thf(syntax_ac_operator_type,type,
syntax_ac_operator:
!>[TA: $tType] : ( ( fun @ TA @ ( fun @ TA @ TA ) ) > $o ) ).
thf(syntax7388354845996824322omatch_type,type,
syntax7388354845996824322omatch:
!>[TA: $tType,TB: $tType] : ( TB > TA > $o ) ).
thf(syntax2379306206330768139omatch_type,type,
syntax2379306206330768139omatch:
!>[TA: $tType,TB: $tType] : ( TB > TA > $o ) ).
thf(aa_type,type,
aa:
!>[TA: $tType,TB: $tType] : ( ( fun @ TB @ TA ) > TB > TA ) ).
thf(a2_type,type,
a2: a ).
thf(b_type,type,
b: a ).
thf(c_type,type,
c: a ).
thf(f_type,type,
f: fun @ a @ ( fun @ a @ a ) ).
thf(5,axiom,
! [A: a,B: a,C: a] :
( ( aa @ a @ a @ ( aa @ a @ ( fun @ a @ a ) @ f @ A ) @ ( aa @ a @ a @ ( aa @ a @ ( fun @ a @ a ) @ f @ B ) @ C ) )
= ( aa @ a @ a @ ( aa @ a @ ( fun @ a @ a ) @ f @ B ) @ ( aa @ a @ a @ ( aa @ a @ ( fun @ a @ a ) @ f @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_left__commute) ).
thf(21,plain,
! [A: a,B: a,C: a] :
( ( aa @ a @ a @ ( aa @ a @ ( fun @ a @ a ) @ f @ A ) @ ( aa @ a @ a @ ( aa @ a @ ( fun @ a @ a ) @ f @ B ) @ C ) )
= ( aa @ a @ a @ ( aa @ a @ ( fun @ a @ a ) @ f @ B ) @ ( aa @ a @ a @ ( aa @ a @ ( fun @ a @ a ) @ f @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(7,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA] : ( syntax2379306206330768139omatch @ TB @ TA @ A @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_syntax__nomatch__def) ).
thf(27,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA] : ( syntax2379306206330768139omatch @ TB @ TA @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(4,axiom,
! [A: a,B: a] :
( ( aa @ a @ a @ ( aa @ a @ ( fun @ a @ a ) @ f @ A ) @ B )
= ( aa @ a @ a @ ( aa @ a @ ( fun @ a @ a ) @ f @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_commute) ).
thf(18,plain,
! [A: a,B: a] :
( ( aa @ a @ a @ ( aa @ a @ ( fun @ a @ a ) @ f @ A ) @ B )
= ( aa @ a @ a @ ( aa @ a @ ( fun @ a @ a ) @ f @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(9,axiom,
! [TA: $tType,A: fun @ TA @ ( fun @ TA @ TA )] :
( ! [B: TA,C: TA,D: TA] :
( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ A @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ A @ B ) @ C ) ) @ D )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ A @ B ) @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ A @ C ) @ D ) ) )
=> ( ! [B: TA,C: TA] :
( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ A @ B ) @ C )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ A @ C ) @ B ) )
=> ( syntax_ac_operator @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_ac__operator_Ointro) ).
thf(31,plain,
! [TA: $tType,A: fun @ TA @ ( fun @ TA @ TA )] :
( ! [B: TA,C: TA,D: TA] :
( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ A @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ A @ B ) @ C ) ) @ D )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ A @ B ) @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ A @ C ) @ D ) ) )
=> ( ! [B: TA,C: TA] :
( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ A @ B ) @ C )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ A @ C ) @ B ) )
=> ( syntax_ac_operator @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(13,axiom,
! [TA: $tType,A: fun @ TA @ ( fun @ TA @ TA ),B: TA,C: TA,D: TA] :
( ( syntax_ac_operator @ TA @ A )
=> ( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ A @ B ) @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ A @ C ) @ D ) )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ A @ C ) @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ A @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_ac__operator_Oleft__commute) ).
thf(43,plain,
! [TA: $tType,A: fun @ TA @ ( fun @ TA @ TA ),B: TA,C: TA,D: TA] :
( ( syntax_ac_operator @ TA @ A )
=> ( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ A @ B ) @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ A @ C ) @ D ) )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ A @ C ) @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ A @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(12,axiom,
! [TA: $tType,A: fun @ TA @ ( fun @ TA @ TA ),B: TA,C: TA,D: TA] :
( ( syntax_ac_operator @ TA @ A )
=> ( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ A @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ A @ B ) @ C ) ) @ D )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ A @ B ) @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ A @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_ac__operator_Oright__assoc) ).
thf(40,plain,
! [TA: $tType,A: fun @ TA @ ( fun @ TA @ TA ),B: TA,C: TA,D: TA] :
( ( syntax_ac_operator @ TA @ A )
=> ( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ A @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ A @ B ) @ C ) ) @ D )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ A @ B ) @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ A @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(1,conjecture,
( ( aa @ a @ a @ ( aa @ a @ ( fun @ a @ a ) @ f @ ( aa @ a @ a @ ( aa @ a @ ( fun @ a @ a ) @ f @ a2 ) @ b ) ) @ c )
= ( aa @ a @ a @ ( aa @ a @ ( fun @ a @ a ) @ f @ ( aa @ a @ a @ ( aa @ a @ ( fun @ a @ a ) @ f @ a2 ) @ c ) ) @ b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
( ( aa @ a @ a @ ( aa @ a @ ( fun @ a @ a ) @ f @ ( aa @ a @ a @ ( aa @ a @ ( fun @ a @ a ) @ f @ a2 ) @ b ) ) @ c )
!= ( aa @ a @ a @ ( aa @ a @ ( fun @ a @ a ) @ f @ ( aa @ a @ a @ ( aa @ a @ ( fun @ a @ a ) @ f @ a2 ) @ c ) ) @ b ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(15,plain,
( ( aa @ a @ a @ ( aa @ a @ ( fun @ a @ a ) @ f @ ( aa @ a @ a @ ( aa @ a @ ( fun @ a @ a ) @ f @ a2 ) @ b ) ) @ c )
!= ( aa @ a @ a @ ( aa @ a @ ( fun @ a @ a ) @ f @ ( aa @ a @ a @ ( aa @ a @ ( fun @ a @ a ) @ f @ a2 ) @ c ) ) @ b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,axiom,
! [A: a,B: a,C: a] :
( ( aa @ a @ a @ ( aa @ a @ ( fun @ a @ a ) @ f @ ( aa @ a @ a @ ( aa @ a @ ( fun @ a @ a ) @ f @ A ) @ B ) ) @ C )
= ( aa @ a @ a @ ( aa @ a @ ( fun @ a @ a ) @ f @ A ) @ ( aa @ a @ a @ ( aa @ a @ ( fun @ a @ a ) @ f @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_right__assoc) ).
thf(24,plain,
! [A: a,B: a,C: a] :
( ( aa @ a @ a @ ( aa @ a @ ( fun @ a @ a ) @ f @ ( aa @ a @ a @ ( aa @ a @ ( fun @ a @ a ) @ f @ A ) @ B ) ) @ C )
= ( aa @ a @ a @ ( aa @ a @ ( fun @ a @ a ) @ f @ A ) @ ( aa @ a @ a @ ( aa @ a @ ( fun @ a @ a ) @ f @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(11,axiom,
! [TA: $tType,A: fun @ TA @ ( fun @ TA @ TA ),B: TA,C: TA,D: TA] :
( ( syntax_ac_operator @ TA @ A )
=> ( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ A @ B ) @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ A @ C ) @ D ) )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ A @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ A @ B ) @ C ) ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_ac__operator_Oleft__assoc) ).
thf(37,plain,
! [TA: $tType,A: fun @ TA @ ( fun @ TA @ TA ),B: TA,C: TA,D: TA] :
( ( syntax_ac_operator @ TA @ A )
=> ( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ A @ B ) @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ A @ C ) @ D ) )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ A @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ A @ B ) @ C ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(14,axiom,
! [TA: $tType,A: fun @ TA @ ( fun @ TA @ TA )] :
( ( syntax_ac_operator @ TA @ A )
<=> ( ! [B: TA,C: TA,D: TA] :
( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ A @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ A @ B ) @ C ) ) @ D )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ A @ B ) @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ A @ C ) @ D ) ) )
& ! [B: TA,C: TA] :
( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ A @ B ) @ C )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ A @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_ac__operator__def) ).
thf(46,plain,
! [TA: $tType,A: fun @ TA @ ( fun @ TA @ TA )] :
( ( ( syntax_ac_operator @ TA @ A )
=> ( ! [B: TA,C: TA,D: TA] :
( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ A @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ A @ B ) @ C ) ) @ D )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ A @ B ) @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ A @ C ) @ D ) ) )
& ! [B: TA,C: TA] :
( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ A @ B ) @ C )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ A @ C ) @ B ) ) ) )
& ( ( ! [B: TA,C: TA,D: TA] :
( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ A @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ A @ B ) @ C ) ) @ D )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ A @ B ) @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ A @ C ) @ D ) ) )
& ! [B: TA,C: TA] :
( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ A @ B ) @ C )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ A @ C ) @ B ) ) )
=> ( syntax_ac_operator @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(8,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA] : ( syntax7388354845996824322omatch @ TB @ TA @ A @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_syntax__fo__nomatch__def) ).
thf(29,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA] : ( syntax7388354845996824322omatch @ TB @ TA @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(10,axiom,
! [TA: $tType,A: fun @ TA @ ( fun @ TA @ TA ),B: TA,C: TA] :
( ( syntax_ac_operator @ TA @ A )
=> ( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ A @ B ) @ C )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_ac__operator_Ocommute) ).
thf(34,plain,
! [TA: $tType,A: fun @ TA @ ( fun @ TA @ TA ),B: TA,C: TA] :
( ( syntax_ac_operator @ TA @ A )
=> ( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ A @ B ) @ C )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(3,axiom,
syntax_ac_operator @ a @ f,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_ac__operator__axioms) ).
thf(17,plain,
syntax_ac_operator @ a @ f,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(54,plain,
$false,
inference(e,[status(thm)],[21,27,18,31,43,40,15,24,37,46,29,34,17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : ITP209_4 : TPTP v8.1.2. Released v8.0.0.
% 0.11/0.15 % Command : run_Leo-III %s %d
% 0.15/0.35 % Computer : n009.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % 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 : Mon May 6 14:35:38 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.85/0.85 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.19/0.99 % [INFO] Parsing done (136ms).
% 1.19/1.00 % [INFO] Running in sequential loop mode.
% 1.86/1.21 % [INFO] eprover registered as external prover.
% 1.86/1.21 % [INFO] cvc4 registered as external prover.
% 1.86/1.22 % [INFO] Scanning for conjecture ...
% 1.95/1.29 % [INFO] Found a conjecture and 12 axioms. Running axiom selection ...
% 1.95/1.32 % [INFO] Axiom selection finished. Selected 12 axioms (removed 0 axioms).
% 2.26/1.37 % [INFO] Problem is typed first-order (TPTP TFF).
% 2.26/1.38 % [INFO] Type checking passed.
% 2.26/1.38 % [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 ...
% 3.89/1.86 % External prover 'e' found a proof!
% 3.89/1.86 % [INFO] Killing All external provers ...
% 3.89/1.87 % Time passed: 1345ms (effective reasoning time: 863ms)
% 3.89/1.87 % 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)>
% 3.89/1.87 % Axioms used in derivation (12): fact_9_ac__operator_Oright__assoc, fact_2_left__commute, fact_10_ac__operator_Oleft__commute, fact_0_ac__operator__axioms, fact_3_right__assoc, fact_4_syntax__nomatch__def, fact_6_ac__operator_Ointro, fact_8_ac__operator_Oleft__assoc, fact_5_syntax__fo__nomatch__def, fact_7_ac__operator_Ocommute, fact_1_commute, fact_11_ac__operator__def
% 3.89/1.87 % No. of inferences in proof: 28
% 3.89/1.87 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1345 ms resp. 863 ms w/o parsing
% 3.89/1.91 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.89/1.91 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------