%------------------------------------------------------------------------------
% 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 : n001.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 : Wed Sep 30 08:07:11 AM UTC 2026
% Result : Theorem 7.87s 3.06s
% Output : Refutation 7.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 13
% Syntax : Number of formulae : 28 ( 18 unt; 0 typ; 0 def)
% Number of atoms : 54 ( 31 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 218 ( 2 ~; 0 |; 2 &; 202 @)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 24 ( 24 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 5 con; 0-4 aty)
% Number of variables : 98 ( 10 ^; 88 !; 0 ?; 98 :)
% Comments :
%------------------------------------------------------------------------------
thf(a_type,type,
a: $tType ).
thf(syntax_ac_operator_decl,type,
syntax_ac_operator:
!>[TA: $tType] : ( ( TA > TA > TA ) > $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(a2_decl,type,
a2: a ).
thf(b_decl,type,
b: a ).
thf(c_decl,type,
c: a ).
thf(f_decl,type,
f: a > a > a ).
thf(7,axiom,
! [TA: $tType,TB: $tType] :
( ( syntax2379306206330768139omatch @ TA @ TB )
= ( ^ [A: TA,B: TB] : $true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_syntax__nomatch__def) ).
thf(27,plain,
! [TA: $tType,TB: $tType] :
( ( syntax2379306206330768139omatch @ TA @ TB )
= ( ^ [A: TA,B: TB] : $true ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(11,axiom,
! [TA: $tType,A: TA > TA > TA,B: TA,C: TA,D: TA] :
( ( syntax_ac_operator @ TA @ A )
=> ( ( A @ B @ ( A @ C @ D ) )
= ( A @ ( A @ B @ C ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_ac__operator_Oleft__assoc) ).
thf(39,plain,
! [TA: $tType,A: TA > TA > TA,B: TA,C: TA,D: TA] :
( ( syntax_ac_operator @ TA @ A )
=> ( ( A @ B @ ( A @ C @ D ) )
= ( A @ ( A @ B @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(1,conjecture,
( ( f @ ( f @ a2 @ b ) @ c )
= ( f @ ( f @ a2 @ c ) @ b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
( ( f @ ( f @ a2 @ b ) @ c )
!= ( f @ ( f @ a2 @ c ) @ b ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(15,plain,
( ( f @ ( f @ a2 @ b ) @ c )
!= ( f @ ( f @ a2 @ c ) @ b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(12,axiom,
! [TA: $tType,A: TA > TA > TA,B: TA,C: TA,D: TA] :
( ( syntax_ac_operator @ TA @ A )
=> ( ( A @ ( A @ B @ C ) @ D )
= ( A @ B @ ( A @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_ac__operator_Oright__assoc) ).
thf(42,plain,
! [TA: $tType,A: TA > TA > TA,B: TA,C: TA,D: TA] :
( ( syntax_ac_operator @ TA @ A )
=> ( ( A @ ( A @ B @ C ) @ D )
= ( A @ B @ ( A @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(6,axiom,
! [A: a,B: a,C: a] :
( ( f @ ( f @ A @ B ) @ C )
= ( f @ A @ ( f @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_right__assoc) ).
thf(24,plain,
! [A: a,B: a,C: a] :
( ( f @ ( f @ A @ B ) @ C )
= ( f @ A @ ( f @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(5,axiom,
! [A: a,B: a,C: a] :
( ( f @ A @ ( f @ B @ C ) )
= ( f @ B @ ( f @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_left__commute) ).
thf(21,plain,
! [A: a,B: a,C: a] :
( ( f @ A @ ( f @ B @ C ) )
= ( f @ B @ ( f @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(9,axiom,
! [TA: $tType,A: TA > TA > TA] :
( ! [B: TA,C: TA,D: TA] :
( ( A @ ( A @ B @ C ) @ D )
= ( A @ B @ ( A @ C @ D ) ) )
=> ( ! [B: TA,C: TA] :
( ( A @ B @ C )
= ( A @ C @ B ) )
=> ( syntax_ac_operator @ TA @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_ac__operator_Ointro) ).
thf(33,plain,
! [TA: $tType,A: TA > TA > TA] :
( ! [B: TA,C: TA,D: TA] :
( ( A @ ( A @ B @ C ) @ D )
= ( A @ B @ ( A @ C @ D ) ) )
=> ( ! [B: TA,C: TA] :
( ( A @ B @ C )
= ( A @ C @ B ) )
=> ( syntax_ac_operator @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(13,axiom,
! [TA: $tType,A: TA > TA > TA,B: TA,C: TA,D: TA] :
( ( syntax_ac_operator @ TA @ A )
=> ( ( A @ B @ ( A @ C @ D ) )
= ( A @ C @ ( A @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_ac__operator_Oleft__commute) ).
thf(45,plain,
! [TA: $tType,A: TA > TA > TA,B: TA,C: TA,D: TA] :
( ( syntax_ac_operator @ TA @ A )
=> ( ( A @ B @ ( A @ C @ D ) )
= ( A @ C @ ( A @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(3,axiom,
syntax_ac_operator @ a @ f,
file('/export/starexec/sandbox2/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(14,axiom,
! [TA: $tType] :
( ( syntax_ac_operator @ TA )
= ( ^ [A: TA > TA > TA] :
( ! [B: TA,C: TA,D: TA] :
( ( A @ ( A @ B @ C ) @ D )
= ( A @ B @ ( A @ C @ D ) ) )
& ! [B: TA,C: TA] :
( ( A @ B @ C )
= ( A @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_ac__operator__def) ).
thf(48,plain,
! [TA: $tType] :
( ( syntax_ac_operator @ TA )
= ( ^ [A: TA > TA > TA] :
( ! [B: TA,C: TA,D: TA] :
( ( A @ ( A @ B @ C ) @ D )
= ( A @ B @ ( A @ C @ D ) ) )
& ! [B: TA,C: TA] :
( ( A @ B @ C )
= ( A @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(4,axiom,
! [A: a,B: a] :
( ( f @ A @ B )
= ( f @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_commute) ).
thf(18,plain,
! [A: a,B: a] :
( ( f @ A @ B )
= ( f @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(10,axiom,
! [TA: $tType,A: TA > TA > TA,B: TA,C: TA] :
( ( syntax_ac_operator @ TA @ A )
=> ( ( A @ B @ C )
= ( A @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_ac__operator_Ocommute) ).
thf(36,plain,
! [TA: $tType,A: TA > TA > TA,B: TA,C: TA] :
( ( syntax_ac_operator @ TA @ A )
=> ( ( A @ B @ C )
= ( A @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(8,axiom,
! [TA: $tType,TB: $tType] :
( ( syntax7388354845996824322omatch @ TA @ TB )
= ( ^ [A: TA,B: TB] : $true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_syntax__fo__nomatch__def) ).
thf(30,plain,
! [TA: $tType,TB: $tType] :
( ( syntax7388354845996824322omatch @ TA @ TB )
= ( ^ [A: TA,B: TB] : $true ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(51,plain,
$false,
inference(e,[status(thm)],[27,39,15,42,24,21,33,45,17,48,18,36,30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP209^2 : 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
% 0.13/0.24 % Computer : n001.cluster.edu
% 0.13/0.24 % Model : x86_64 x86_64
% 0.13/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.24 % Memory : 8046.5625MB
% 0.13/0.24 % OS : Linux 6.8.0-71-generic
% 0.13/0.24 % CPULimit : 300
% 0.13/0.24 % WCLimit : 300
% 0.13/0.24 % DateTime : Tue Sep 29 20:19:45 UTC 2026
% 0.13/0.24 % CPUTime :
% 0.13/0.24 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
% 1.05/0.82 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.55/1.04 % [INFO] Parsing done (216ms).
% 1.55/1.05 % [INFO] Running in sequential loop mode.
% 2.22/1.45 % [INFO] eprover registered as external prover.
% 2.22/1.46 % [INFO] Scanning for conjecture ...
% 2.44/1.55 % [INFO] Found a conjecture (or negated_conjecture) and 12 axioms. Running axiom selection ...
% 2.44/1.59 % [INFO] Axiom selection finished. Selected 12 axioms (removed 0 axioms).
% 2.62/1.64 % [INFO] Problem is higher-order (TPTP THF).
% 2.62/1.65 % [INFO] Type checking passed.
% 2.62/1.65 % [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 ...
% 7.87/3.06 % External prover 'e' found a proof!
% 7.87/3.06 % [INFO] Killing All external provers ...
% 7.87/3.06 % Time passed: 2673ms (effective reasoning time: 1997ms)
% 7.87/3.06 % 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)>
% 7.87/3.06 % 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
% 7.87/3.06 % No. of inferences in proof: 28
% 7.87/3.06 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2673 ms resp. 1997 ms w/o parsing
% 7.87/3.11 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 7.87/3.11 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------