%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP209_3 : 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 : n014.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 4.08s 7.50s
% Output : Refutation 4.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 11
% Syntax : Number of formulae : 24 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 43 ( 27 equ; 0 cnn)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 396 ( 2 ~; 0 |; 4 &; 375 @)
% ( 1 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 75 ( 0 ^; 75 !; 0 ?; 75 :)
% Comments :
%------------------------------------------------------------------------------
thf(fun_a_fun_a_a_type,type,
fun_a_fun_a_a: $tType ).
thf(fun_a_a_type,type,
fun_a_a: $tType ).
thf(a_type,type,
a: $tType ).
thf(syntax_ac_operator_a_decl,type,
syntax_ac_operator_a: fun_a_fun_a_a > $o ).
thf(aa_a_fun_a_a_decl,type,
aa_a_fun_a_a: fun_a_fun_a_a > a > fun_a_a ).
thf(aa_a_a_decl,type,
aa_a_a: fun_a_a > a > a ).
thf(a2_decl,type,
a2: a ).
thf(b_decl,type,
b: a ).
thf(c_decl,type,
c: a ).
thf(f_decl,type,
f: fun_a_fun_a_a ).
thf(7,axiom,
! [A: fun_a_fun_a_a] :
( ! [B: a,C: a,D: a] :
( ( D @ ( C @ ( B @ ( A @ aa_a_fun_a_a ) @ aa_a_a ) @ ( A @ aa_a_fun_a_a ) @ aa_a_a ) )
= ( D @ ( C @ ( A @ aa_a_fun_a_a ) @ aa_a_a ) @ ( B @ ( A @ aa_a_fun_a_a ) @ aa_a_a ) ) )
=> ( ! [B: a,C: a] :
( ( C @ ( B @ ( A @ aa_a_fun_a_a ) @ aa_a_a ) )
= ( B @ ( C @ ( A @ aa_a_fun_a_a ) @ aa_a_a ) ) )
=> ( A @ syntax_ac_operator_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_ac__operator_Ointro) ).
thf(25,plain,
! [A: fun_a_fun_a_a] :
( ! [B: a,C: a,D: a] :
( ( D @ ( C @ ( B @ ( A @ aa_a_fun_a_a ) @ aa_a_a ) @ ( A @ aa_a_fun_a_a ) @ aa_a_a ) )
= ( D @ ( C @ ( A @ aa_a_fun_a_a ) @ aa_a_a ) @ ( B @ ( A @ aa_a_fun_a_a ) @ aa_a_a ) ) )
=> ( ! [B: a,C: a] :
( ( C @ ( B @ ( A @ aa_a_fun_a_a ) @ aa_a_a ) )
= ( B @ ( C @ ( A @ aa_a_fun_a_a ) @ aa_a_a ) ) )
=> ( A @ syntax_ac_operator_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(8,axiom,
! [A: fun_a_fun_a_a,B: a,C: a] :
( ( A @ syntax_ac_operator_a )
=> ( ( C @ ( B @ ( A @ aa_a_fun_a_a ) @ aa_a_a ) )
= ( B @ ( C @ ( A @ aa_a_fun_a_a ) @ aa_a_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_ac__operator_Ocommute) ).
thf(28,plain,
! [A: fun_a_fun_a_a,B: a,C: a] :
( ( A @ syntax_ac_operator_a )
=> ( ( C @ ( B @ ( A @ aa_a_fun_a_a ) @ aa_a_a ) )
= ( B @ ( C @ ( A @ aa_a_fun_a_a ) @ aa_a_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(1,conjecture,
( ( c @ ( b @ ( a2 @ ( f @ aa_a_fun_a_a ) @ aa_a_a ) @ ( f @ aa_a_fun_a_a ) @ aa_a_a ) )
= ( b @ ( c @ ( a2 @ ( f @ aa_a_fun_a_a ) @ aa_a_a ) @ ( f @ aa_a_fun_a_a ) @ aa_a_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
( ( c @ ( b @ ( a2 @ ( f @ aa_a_fun_a_a ) @ aa_a_a ) @ ( f @ aa_a_fun_a_a ) @ aa_a_a ) )
!= ( b @ ( c @ ( a2 @ ( f @ aa_a_fun_a_a ) @ aa_a_a ) @ ( f @ aa_a_fun_a_a ) @ aa_a_a ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(13,plain,
( ( c @ ( b @ ( a2 @ ( f @ aa_a_fun_a_a ) @ aa_a_a ) @ ( f @ aa_a_fun_a_a ) @ aa_a_a ) )
!= ( b @ ( c @ ( a2 @ ( f @ aa_a_fun_a_a ) @ aa_a_a ) @ ( f @ aa_a_fun_a_a ) @ aa_a_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(9,axiom,
! [A: fun_a_fun_a_a,B: a,C: a,D: a] :
( ( A @ syntax_ac_operator_a )
=> ( ( D @ ( C @ ( A @ aa_a_fun_a_a ) @ aa_a_a ) @ ( B @ ( A @ aa_a_fun_a_a ) @ aa_a_a ) )
= ( D @ ( C @ ( B @ ( A @ aa_a_fun_a_a ) @ aa_a_a ) @ ( A @ aa_a_fun_a_a ) @ aa_a_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_ac__operator_Oleft__assoc) ).
thf(32,plain,
! [A: fun_a_fun_a_a,B: a,C: a,D: a] :
( ( A @ syntax_ac_operator_a )
=> ( ( D @ ( C @ ( A @ aa_a_fun_a_a ) @ aa_a_a ) @ ( B @ ( A @ aa_a_fun_a_a ) @ aa_a_a ) )
= ( D @ ( C @ ( B @ ( A @ aa_a_fun_a_a ) @ aa_a_a ) @ ( A @ aa_a_fun_a_a ) @ aa_a_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(4,axiom,
! [A: a,B: a] :
( ( B @ ( A @ ( f @ aa_a_fun_a_a ) @ aa_a_a ) )
= ( A @ ( B @ ( f @ aa_a_fun_a_a ) @ aa_a_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_commute) ).
thf(16,plain,
! [A: a,B: a] :
( ( B @ ( A @ ( f @ aa_a_fun_a_a ) @ aa_a_a ) )
= ( A @ ( B @ ( f @ aa_a_fun_a_a ) @ aa_a_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(11,axiom,
! [A: fun_a_fun_a_a,B: a,C: a,D: a] :
( ( A @ syntax_ac_operator_a )
=> ( ( D @ ( C @ ( A @ aa_a_fun_a_a ) @ aa_a_a ) @ ( B @ ( A @ aa_a_fun_a_a ) @ aa_a_a ) )
= ( D @ ( B @ ( A @ aa_a_fun_a_a ) @ aa_a_a ) @ ( C @ ( A @ aa_a_fun_a_a ) @ aa_a_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_ac__operator_Oleft__commute) ).
thf(40,plain,
! [A: fun_a_fun_a_a,B: a,C: a,D: a] :
( ( A @ syntax_ac_operator_a )
=> ( ( D @ ( C @ ( A @ aa_a_fun_a_a ) @ aa_a_a ) @ ( B @ ( A @ aa_a_fun_a_a ) @ aa_a_a ) )
= ( D @ ( B @ ( A @ aa_a_fun_a_a ) @ aa_a_a ) @ ( C @ ( A @ aa_a_fun_a_a ) @ aa_a_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(3,axiom,
f @ syntax_ac_operator_a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_ac__operator__axioms) ).
thf(15,plain,
f @ syntax_ac_operator_a,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(6,axiom,
! [A: a,B: a,C: a] :
( ( C @ ( B @ ( A @ ( f @ aa_a_fun_a_a ) @ aa_a_a ) @ ( f @ aa_a_fun_a_a ) @ aa_a_a ) )
= ( C @ ( B @ ( f @ aa_a_fun_a_a ) @ aa_a_a ) @ ( A @ ( f @ aa_a_fun_a_a ) @ aa_a_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_right__assoc) ).
thf(22,plain,
! [A: a,B: a,C: a] :
( ( C @ ( B @ ( A @ ( f @ aa_a_fun_a_a ) @ aa_a_a ) @ ( f @ aa_a_fun_a_a ) @ aa_a_a ) )
= ( C @ ( B @ ( f @ aa_a_fun_a_a ) @ aa_a_a ) @ ( A @ ( f @ aa_a_fun_a_a ) @ aa_a_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(12,axiom,
! [A: fun_a_fun_a_a] :
( ( A @ syntax_ac_operator_a )
<=> ( ! [B: a,C: a] :
( ( C @ ( B @ ( A @ aa_a_fun_a_a ) @ aa_a_a ) )
= ( B @ ( C @ ( A @ aa_a_fun_a_a ) @ aa_a_a ) ) )
& ! [B: a,C: a,D: a] :
( ( D @ ( C @ ( B @ ( A @ aa_a_fun_a_a ) @ aa_a_a ) @ ( A @ aa_a_fun_a_a ) @ aa_a_a ) )
= ( D @ ( C @ ( A @ aa_a_fun_a_a ) @ aa_a_a ) @ ( B @ ( A @ aa_a_fun_a_a ) @ aa_a_a ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_ac__operator__def) ).
thf(44,plain,
! [A: fun_a_fun_a_a] :
( ( ( ! [B: a,C: a] :
( ( C @ ( B @ ( A @ aa_a_fun_a_a ) @ aa_a_a ) )
= ( B @ ( C @ ( A @ aa_a_fun_a_a ) @ aa_a_a ) ) )
& ! [B: a,C: a,D: a] :
( ( D @ ( C @ ( B @ ( A @ aa_a_fun_a_a ) @ aa_a_a ) @ ( A @ aa_a_fun_a_a ) @ aa_a_a ) )
= ( D @ ( C @ ( A @ aa_a_fun_a_a ) @ aa_a_a ) @ ( B @ ( A @ aa_a_fun_a_a ) @ aa_a_a ) ) ) )
=> ( A @ syntax_ac_operator_a ) )
& ( ( A @ syntax_ac_operator_a )
=> ( ! [B: a,C: a] :
( ( C @ ( B @ ( A @ aa_a_fun_a_a ) @ aa_a_a ) )
= ( B @ ( C @ ( A @ aa_a_fun_a_a ) @ aa_a_a ) ) )
& ! [B: a,C: a,D: a] :
( ( D @ ( C @ ( B @ ( A @ aa_a_fun_a_a ) @ aa_a_a ) @ ( A @ aa_a_fun_a_a ) @ aa_a_a ) )
= ( D @ ( C @ ( A @ aa_a_fun_a_a ) @ aa_a_a ) @ ( B @ ( A @ aa_a_fun_a_a ) @ aa_a_a ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(10,axiom,
! [A: fun_a_fun_a_a,B: a,C: a,D: a] :
( ( A @ syntax_ac_operator_a )
=> ( ( D @ ( C @ ( B @ ( A @ aa_a_fun_a_a ) @ aa_a_a ) @ ( A @ aa_a_fun_a_a ) @ aa_a_a ) )
= ( D @ ( C @ ( A @ aa_a_fun_a_a ) @ aa_a_a ) @ ( B @ ( A @ aa_a_fun_a_a ) @ aa_a_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_ac__operator_Oright__assoc) ).
thf(36,plain,
! [A: fun_a_fun_a_a,B: a,C: a,D: a] :
( ( A @ syntax_ac_operator_a )
=> ( ( D @ ( C @ ( B @ ( A @ aa_a_fun_a_a ) @ aa_a_a ) @ ( A @ aa_a_fun_a_a ) @ aa_a_a ) )
= ( D @ ( C @ ( A @ aa_a_fun_a_a ) @ aa_a_a ) @ ( B @ ( A @ aa_a_fun_a_a ) @ aa_a_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(5,axiom,
! [A: a,B: a,C: a] :
( ( C @ ( B @ ( f @ aa_a_fun_a_a ) @ aa_a_a ) @ ( A @ ( f @ aa_a_fun_a_a ) @ aa_a_a ) )
= ( C @ ( A @ ( f @ aa_a_fun_a_a ) @ aa_a_a ) @ ( B @ ( f @ aa_a_fun_a_a ) @ aa_a_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_left__commute) ).
thf(19,plain,
! [A: a,B: a,C: a] :
( ( C @ ( B @ ( f @ aa_a_fun_a_a ) @ aa_a_a ) @ ( A @ ( f @ aa_a_fun_a_a ) @ aa_a_a ) )
= ( C @ ( A @ ( f @ aa_a_fun_a_a ) @ aa_a_a ) @ ( B @ ( f @ aa_a_fun_a_a ) @ aa_a_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(56,plain,
$false,
inference(e,[status(thm)],[25,28,13,32,16,40,15,22,44,36,19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP209_3 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.08 % 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
% 0.13/5.41 % Computer : n014.cluster.edu
% 0.13/5.41 % Model : x86_64 x86_64
% 0.13/5.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/5.41 % Memory : 8046.5625MB
% 0.13/5.41 % OS : Linux 6.8.0-71-generic
% 0.13/5.41 % CPULimit : 300
% 0.13/5.41 % WCLimit : 300
% 0.13/5.41 % DateTime : Fri Sep 25 18:07:52 UTC 2026
% 0.13/5.41 % CPUTime :
% 0.13/5.41 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
% 0.18/6.00 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.16/6.18 % [INFO] Parsing done (183ms).
% 1.34/6.20 % [INFO] Running in sequential loop mode.
% 1.86/6.58 % [INFO] eprover registered as external prover.
% 1.86/6.59 % [INFO] Scanning for conjecture ...
% 2.06/6.69 % [INFO] Found a conjecture (or negated_conjecture) and 10 axioms. Running axiom selection ...
% 2.21/6.73 % [INFO] Axiom selection finished. Selected 10 axioms (removed 0 axioms).
% 2.21/6.79 % [INFO] Problem is typed first-order (TPTP TFF).
% 2.21/6.79 % [INFO] Type checking passed.
% 2.41/6.80 % [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 ...
% 3.78/7.49 % External prover 'e' found a proof!
% 3.78/7.50 % [INFO] Killing All external provers ...
% 3.78/7.50 % Time passed: 1939ms (effective reasoning time: 1292ms)
% 3.78/7.50 % 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)>
% 4.08/7.50 % Axioms used in derivation (10): fact_5_ac__operator_Ocommute, fact_7_ac__operator_Oright__assoc, fact_8_ac__operator_Oleft__commute, fact_4_ac__operator_Ointro, fact_0_ac__operator__axioms, fact_1_commute, fact_9_ac__operator__def, fact_2_left__commute, fact_3_right__assoc, fact_6_ac__operator_Oleft__assoc
% 4.08/7.50 % No. of inferences in proof: 24
% 4.08/7.50 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1939 ms resp. 1292 ms w/o parsing
% 4.08/7.57 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.08/7.57 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------