%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP209_2 : TPTP v9.3.1. Released v8.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:36:44 AM UTC 2026
% Result : Theorem 5.02s 2.72s
% Output : Refutation 5.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 15
% Syntax : Number of formulae : 32 ( 20 unt; 0 typ; 0 def)
% Number of atoms : 141 ( 27 equ; 0 cnn)
% Maximal formula atoms : 6 ( 4 avg)
% Number of connectives : 1021 ( 4 ~; 0 |; 4 &; 998 @)
% ( 1 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 6 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 12 usr; 8 con; 0-4 aty)
% Number of variables : 103 ( 0 ^; 103 !; 0 ?; 103 :)
% Comments :
%------------------------------------------------------------------------------
thf(bool_type,type,
bool: $tType ).
thf(a_type,type,
a: $tType ).
thf(syntax_ac_operator_decl,type,
syntax_ac_operator:
!>[TA: $tType] : ( ( TA @ ( TA @ fun ) @ ( TA @ fun ) ) > $o ) ).
thf(syntax7388354845996824322omatch_decl,type,
syntax7388354845996824322omatch:
!>[TA: $tType,TB: $tType] : ( TB > TA > $o ) ).
thf(syntax2379306206330768139omatch_decl,type,
syntax2379306206330768139omatch:
!>[TA: $tType,TB: $tType] : ( TB > TA > $o ) ).
thf(aa_decl,type,
aa:
!>[TA: $tType,TB: $tType] : ( ( TA @ ( TB @ fun ) ) > TB > TA ) ).
thf(fFalse_decl,type,
fFalse: bool ).
thf(fTrue_decl,type,
fTrue: bool ).
thf(pp_decl,type,
pp: bool > $o ).
thf(a2_decl,type,
a2: a ).
thf(b_decl,type,
b: a ).
thf(c_decl,type,
c: a ).
thf(f_decl,type,
f: a @ ( a @ fun ) @ ( a @ fun ) ).
thf(12,axiom,
! [TA: $tType,A: TA @ ( TA @ fun ) @ ( TA @ fun ),B: TA,C: TA,D: TA] :
( ( A @ ( TA @ syntax_ac_operator ) )
=> ( ( D @ ( C @ ( B @ ( A @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( A @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( D @ ( C @ ( A @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( B @ ( A @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_ac__operator_Oright__assoc) ).
thf(42,plain,
! [TA: $tType,A: TA @ ( TA @ fun ) @ ( TA @ fun ),B: TA,C: TA,D: TA] :
( ( A @ ( TA @ syntax_ac_operator ) )
=> ( ( D @ ( C @ ( B @ ( A @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( A @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( D @ ( C @ ( A @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( B @ ( A @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(9,axiom,
! [TA: $tType,A: TA @ ( TA @ fun ) @ ( TA @ fun )] :
( ! [B: TA,C: TA,D: TA] :
( ( D @ ( C @ ( B @ ( A @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( A @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( D @ ( C @ ( A @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( B @ ( A @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) )
=> ( ! [B: TA,C: TA] :
( ( C @ ( B @ ( A @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( B @ ( C @ ( A @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) )
=> ( A @ ( TA @ syntax_ac_operator ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_ac__operator_Ointro) ).
thf(33,plain,
! [TA: $tType,A: TA @ ( TA @ fun ) @ ( TA @ fun )] :
( ! [B: TA,C: TA,D: TA] :
( ( D @ ( C @ ( B @ ( A @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( A @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( D @ ( C @ ( A @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( B @ ( A @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) )
=> ( ! [B: TA,C: TA] :
( ( C @ ( B @ ( A @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( B @ ( C @ ( A @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) )
=> ( A @ ( TA @ syntax_ac_operator ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(11,axiom,
! [TA: $tType,A: TA @ ( TA @ fun ) @ ( TA @ fun ),B: TA,C: TA,D: TA] :
( ( A @ ( TA @ syntax_ac_operator ) )
=> ( ( D @ ( C @ ( A @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( B @ ( A @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( D @ ( C @ ( B @ ( A @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( A @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_ac__operator_Oleft__assoc) ).
thf(39,plain,
! [TA: $tType,A: TA @ ( TA @ fun ) @ ( TA @ fun ),B: TA,C: TA,D: TA] :
( ( A @ ( TA @ syntax_ac_operator ) )
=> ( ( D @ ( C @ ( A @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( B @ ( A @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( D @ ( C @ ( B @ ( A @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( A @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(14,axiom,
! [TA: $tType,A: TA @ ( TA @ fun ) @ ( TA @ fun )] :
( ( A @ ( TA @ syntax_ac_operator ) )
<=> ( ! [B: TA,C: TA] :
( ( C @ ( B @ ( A @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( B @ ( C @ ( A @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) )
& ! [B: TA,C: TA,D: TA] :
( ( D @ ( C @ ( B @ ( A @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( A @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( D @ ( C @ ( A @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( B @ ( A @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_ac__operator__def) ).
thf(48,plain,
! [TA: $tType,A: TA @ ( TA @ fun ) @ ( TA @ fun )] :
( ( ( ! [B: TA,C: TA] :
( ( C @ ( B @ ( A @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( B @ ( C @ ( A @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) )
& ! [B: TA,C: TA,D: TA] :
( ( D @ ( C @ ( B @ ( A @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( A @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( D @ ( C @ ( A @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( B @ ( A @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) )
=> ( A @ ( TA @ syntax_ac_operator ) ) )
& ( ( A @ ( TA @ syntax_ac_operator ) )
=> ( ! [B: TA,C: TA] :
( ( C @ ( B @ ( A @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( B @ ( C @ ( A @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) )
& ! [B: TA,C: TA,D: TA] :
( ( D @ ( C @ ( B @ ( A @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( A @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( D @ ( C @ ( A @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( B @ ( A @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(8,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA] : ( B @ ( A @ ( TA @ ( TB @ syntax7388354845996824322omatch ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_syntax__fo__nomatch__def) ).
thf(31,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA] : ( B @ ( A @ ( TA @ ( TB @ syntax7388354845996824322omatch ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(16,axiom,
~ ( fFalse @ pp ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_1_1_U) ).
thf(58,plain,
~ ( fFalse @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(4,axiom,
! [A: a,B: a] :
( ( B @ ( A @ ( f @ ( a @ ( a @ fun ) @ ( a @ aa ) ) ) @ ( a @ ( a @ aa ) ) ) )
= ( A @ ( B @ ( f @ ( a @ ( a @ fun ) @ ( a @ aa ) ) ) @ ( a @ ( a @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_commute) ).
thf(20,plain,
! [A: a,B: a] :
( ( B @ ( A @ ( f @ ( a @ ( a @ fun ) @ ( a @ aa ) ) ) @ ( a @ ( a @ aa ) ) ) )
= ( A @ ( B @ ( f @ ( a @ ( a @ fun ) @ ( a @ aa ) ) ) @ ( a @ ( a @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(15,axiom,
fTrue @ pp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_2_1_U) ).
thf(57,plain,
fTrue @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(7,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA] : ( B @ ( A @ ( TA @ ( TB @ syntax2379306206330768139omatch ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_syntax__nomatch__def) ).
thf(29,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA] : ( B @ ( A @ ( TA @ ( TB @ syntax2379306206330768139omatch ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(13,axiom,
! [TA: $tType,A: TA @ ( TA @ fun ) @ ( TA @ fun ),B: TA,C: TA,D: TA] :
( ( A @ ( TA @ syntax_ac_operator ) )
=> ( ( D @ ( C @ ( A @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( B @ ( A @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( D @ ( B @ ( A @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( C @ ( A @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_ac__operator_Oleft__commute) ).
thf(45,plain,
! [TA: $tType,A: TA @ ( TA @ fun ) @ ( TA @ fun ),B: TA,C: TA,D: TA] :
( ( A @ ( TA @ syntax_ac_operator ) )
=> ( ( D @ ( C @ ( A @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( B @ ( A @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( D @ ( B @ ( A @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( C @ ( A @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(1,conjecture,
( ( c @ ( b @ ( a2 @ ( f @ ( a @ ( a @ fun ) @ ( a @ aa ) ) ) @ ( a @ ( a @ aa ) ) ) @ ( f @ ( a @ ( a @ fun ) @ ( a @ aa ) ) ) @ ( a @ ( a @ aa ) ) ) )
= ( b @ ( c @ ( a2 @ ( f @ ( a @ ( a @ fun ) @ ( a @ aa ) ) ) @ ( a @ ( a @ aa ) ) ) @ ( f @ ( a @ ( a @ fun ) @ ( a @ aa ) ) ) @ ( a @ ( a @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
( ( c @ ( b @ ( a2 @ ( f @ ( a @ ( a @ fun ) @ ( a @ aa ) ) ) @ ( a @ ( a @ aa ) ) ) @ ( f @ ( a @ ( a @ fun ) @ ( a @ aa ) ) ) @ ( a @ ( a @ aa ) ) ) )
!= ( b @ ( c @ ( a2 @ ( f @ ( a @ ( a @ fun ) @ ( a @ aa ) ) ) @ ( a @ ( a @ aa ) ) ) @ ( f @ ( a @ ( a @ fun ) @ ( a @ aa ) ) ) @ ( a @ ( a @ aa ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(17,plain,
( ( c @ ( b @ ( a2 @ ( f @ ( a @ ( a @ fun ) @ ( a @ aa ) ) ) @ ( a @ ( a @ aa ) ) ) @ ( f @ ( a @ ( a @ fun ) @ ( a @ aa ) ) ) @ ( a @ ( a @ aa ) ) ) )
!= ( b @ ( c @ ( a2 @ ( f @ ( a @ ( a @ fun ) @ ( a @ aa ) ) ) @ ( a @ ( a @ aa ) ) ) @ ( f @ ( a @ ( a @ fun ) @ ( a @ aa ) ) ) @ ( a @ ( a @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,axiom,
! [A: a,B: a,C: a] :
( ( C @ ( B @ ( A @ ( f @ ( a @ ( a @ fun ) @ ( a @ aa ) ) ) @ ( a @ ( a @ aa ) ) ) @ ( f @ ( a @ ( a @ fun ) @ ( a @ aa ) ) ) @ ( a @ ( a @ aa ) ) ) )
= ( C @ ( B @ ( f @ ( a @ ( a @ fun ) @ ( a @ aa ) ) ) @ ( a @ ( a @ aa ) ) ) @ ( A @ ( f @ ( a @ ( a @ fun ) @ ( a @ aa ) ) ) @ ( a @ ( a @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_right__assoc) ).
thf(26,plain,
! [A: a,B: a,C: a] :
( ( C @ ( B @ ( A @ ( f @ ( a @ ( a @ fun ) @ ( a @ aa ) ) ) @ ( a @ ( a @ aa ) ) ) @ ( f @ ( a @ ( a @ fun ) @ ( a @ aa ) ) ) @ ( a @ ( a @ aa ) ) ) )
= ( C @ ( B @ ( f @ ( a @ ( a @ fun ) @ ( a @ aa ) ) ) @ ( a @ ( a @ aa ) ) ) @ ( A @ ( f @ ( a @ ( a @ fun ) @ ( a @ aa ) ) ) @ ( a @ ( a @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(5,axiom,
! [A: a,B: a,C: a] :
( ( C @ ( B @ ( f @ ( a @ ( a @ fun ) @ ( a @ aa ) ) ) @ ( a @ ( a @ aa ) ) ) @ ( A @ ( f @ ( a @ ( a @ fun ) @ ( a @ aa ) ) ) @ ( a @ ( a @ aa ) ) ) )
= ( C @ ( A @ ( f @ ( a @ ( a @ fun ) @ ( a @ aa ) ) ) @ ( a @ ( a @ aa ) ) ) @ ( B @ ( f @ ( a @ ( a @ fun ) @ ( a @ aa ) ) ) @ ( a @ ( a @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_left__commute) ).
thf(23,plain,
! [A: a,B: a,C: a] :
( ( C @ ( B @ ( f @ ( a @ ( a @ fun ) @ ( a @ aa ) ) ) @ ( a @ ( a @ aa ) ) ) @ ( A @ ( f @ ( a @ ( a @ fun ) @ ( a @ aa ) ) ) @ ( a @ ( a @ aa ) ) ) )
= ( C @ ( A @ ( f @ ( a @ ( a @ fun ) @ ( a @ aa ) ) ) @ ( a @ ( a @ aa ) ) ) @ ( B @ ( f @ ( a @ ( a @ fun ) @ ( a @ aa ) ) ) @ ( a @ ( a @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(10,axiom,
! [TA: $tType,A: TA @ ( TA @ fun ) @ ( TA @ fun ),B: TA,C: TA] :
( ( A @ ( TA @ syntax_ac_operator ) )
=> ( ( C @ ( B @ ( A @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( B @ ( C @ ( A @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_ac__operator_Ocommute) ).
thf(36,plain,
! [TA: $tType,A: TA @ ( TA @ fun ) @ ( TA @ fun ),B: TA,C: TA] :
( ( A @ ( TA @ syntax_ac_operator ) )
=> ( ( C @ ( B @ ( A @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( B @ ( C @ ( A @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(3,axiom,
f @ ( a @ syntax_ac_operator ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_ac__operator__axioms) ).
thf(19,plain,
f @ ( a @ syntax_ac_operator ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(60,plain,
$false,
inference(e,[status(thm)],[42,33,39,48,31,58,20,57,29,45,17,26,23,36,19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP209_2 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.12/0.39 % Computer : n017.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Fri Sep 25 18:03:32 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.85/0.96 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.22/1.19 % [INFO] Parsing done (219ms).
% 1.44/1.20 % [INFO] Running in sequential loop mode.
% 2.10/1.60 % [INFO] eprover registered as external prover.
% 2.10/1.61 % [INFO] Scanning for conjecture ...
% 2.28/1.74 % [INFO] Found a conjecture (or negated_conjecture) and 14 axioms. Running axiom selection ...
% 2.28/1.78 % [INFO] Axiom selection finished. Selected 14 axioms (removed 0 axioms).
% 2.50/1.87 % [INFO] Problem is typed first-order (TPTP TFF).
% 2.50/1.88 % [INFO] Type checking passed.
% 2.50/1.89 % [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 ...
% 5.02/2.71 % External prover 'e' found a proof!
% 5.02/2.72 % [INFO] Killing All external provers ...
% 5.02/2.72 % Time passed: 2192ms (effective reasoning time: 1509ms)
% 5.02/2.72 % 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)>
% 5.02/2.72 % Axioms used in derivation (14): 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, help_pp_1_1_U, 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, help_pp_2_1_U
% 5.02/2.72 % No. of inferences in proof: 32
% 5.02/2.72 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2192 ms resp. 1509 ms w/o parsing
% 5.36/2.80 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.36/2.80 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------