%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYP118^1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n011.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 08:50:41 AM UTC 2026
% Result : Theorem 11.04s 4.15s
% Output : Refutation 11.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 21 ( 17 unt; 0 typ; 3 def)
% Number of atoms : 28 ( 27 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 345 ( 19 ~; 4 |; 0 &; 322 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 4 ( 4 usr)
% Number of type conns : 31 ( 31 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 4 usr; 1 con; 0-6 aty)
% Number of variables : 77 ( 18 ^; 56 !; 0 ?; 77 :)
% ( 0 !>; 0 ?*; 0 @-; 3 @+)
% Comments :
%------------------------------------------------------------------------------
thf(skt1_type,type,
skt1: $tType ).
thf(skt2_type,type,
skt2: $tType ).
thf(skt3_type,type,
skt3: $tType ).
thf(skt4_type,type,
skt4: $tType ).
thf(o_decl,type,
o:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TC > TA ) > ( TB > TC ) > TB > TA ) ).
thf(sk1_decl,type,
sk1: skt2 > skt1 ).
thf(sk2_decl,type,
sk2: skt4 > skt2 ).
thf(sk3_decl,type,
sk3: skt3 > skt4 ).
thf(sk1_def,definition,
( sk1
= ( @+[A: skt2 > skt1] :
~ ! [B: skt4 > skt2,C: skt3 > skt4] :
( ( o @ skt2 @ skt3 @ skt1 @ A @ ( o @ skt4 @ skt3 @ skt2 @ B @ C ) )
= ( o @ skt4 @ skt3 @ skt1 @ ( o @ skt2 @ skt4 @ skt1 @ A @ B ) @ C ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: skt4 > skt2] :
~ ! [B: skt3 > skt4] :
( ( o @ skt2 @ skt3 @ skt1 @ sk1 @ ( o @ skt4 @ skt3 @ skt2 @ A @ B ) )
= ( o @ skt4 @ skt3 @ skt1 @ ( o @ skt2 @ skt4 @ skt1 @ sk1 @ A ) @ B ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: skt3 > skt4] :
( ( o @ skt2 @ skt3 @ skt1 @ sk1 @ ( o @ skt4 @ skt3 @ skt2 @ sk2 @ A ) )
!= ( o @ skt4 @ skt3 @ skt1 @ ( o @ skt2 @ skt4 @ skt1 @ sk1 @ sk2 ) @ A ) ) ) ) ).
thf(3,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC,B: TA > TB] :
( ( o @ TB @ TA @ TC @ A @ B )
= ( ^ [C: TA] : ( A @ ( B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','trivia/o_DEF_') ).
thf(7,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC,B: TA > TB] :
( ( o @ TB @ TA @ TC @ A @ B )
= ( ^ [C: TA] : ( A @ ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(8,plain,
! [TA: $tType,TB: $tType,TC: $tType,B: TC > TB,A: TB > TA] :
( ( o @ TB @ TC @ TA @ A @ B )
= ( ^ [C: TC] : ( A @ ( B @ C ) ) ) ),
inference(cnf,[status(esa)],[7]) ).
thf(9,plain,
! [TA: $tType,TB: $tType,TC: $tType,B: TC > TB,A: TB > TA] :
( ( o @ TB @ TC @ TA @ A @ B )
= ( ^ [C: TC] : ( A @ ( B @ C ) ) ) ),
inference(lifteq,[status(thm)],[8]) ).
thf(1,conjecture,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TC > TD,B: TA > TC,C: TB > TA] :
( ( o @ TC @ TB @ TD @ A @ ( o @ TA @ TB @ TC @ B @ C ) )
= ( o @ TA @ TB @ TD @ ( o @ TC @ TA @ TD @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','trivia/o_ASSOC_') ).
thf(2,negated_conjecture,
~ ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TC > TD,B: TA > TC,C: TB > TA] :
( ( o @ TC @ TB @ TD @ A @ ( o @ TA @ TB @ TC @ B @ C ) )
= ( o @ TA @ TB @ TD @ ( o @ TC @ TA @ TD @ A @ B ) @ C ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(4,plain,
~ ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TC > TD,B: TA > TC,C: TB > TA] :
( ( o @ TC @ TB @ TD @ A @ ( o @ TA @ TB @ TC @ B @ C ) )
= ( o @ TA @ TB @ TD @ ( o @ TC @ TA @ TD @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(5,plain,
( ( o @ skt2 @ skt3 @ skt1 @ sk1 @ ( o @ skt4 @ skt3 @ skt2 @ sk2 @ sk3 ) )
!= ( o @ skt4 @ skt3 @ skt1 @ ( o @ skt2 @ skt4 @ skt1 @ sk1 @ sk2 ) @ sk3 ) ),
inference(cnf,[status(esa)],[4]) ).
thf(6,plain,
( ( o @ skt2 @ skt3 @ skt1 @ sk1 @ ( o @ skt4 @ skt3 @ skt2 @ sk2 @ sk3 ) )
!= ( o @ skt4 @ skt3 @ skt1 @ ( o @ skt2 @ skt4 @ skt1 @ sk1 @ sk2 ) @ sk3 ) ),
inference(lifteq,[status(thm)],[5]) ).
thf(12,plain,
! [TB: $tType,B: skt3 > TB,A: TB > skt2] :
( ( ( o @ skt2 @ skt3 @ skt1 @ sk1
@ ^ [C: skt3] : ( A @ ( B @ C ) ) )
!= ( o @ skt4 @ skt3 @ skt1 @ ( o @ skt2 @ skt4 @ skt1 @ sk1 @ sk2 ) @ sk3 ) )
| ( ( o @ TB @ skt3 @ skt2 @ A @ B )
!= ( o @ skt4 @ skt3 @ skt2 @ sk2 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[9,6]) ).
thf(13,plain,
( ( o @ skt2 @ skt3 @ skt1 @ sk1
@ ^ [A: skt3] : ( sk2 @ ( sk3 @ A ) ) )
!= ( o @ skt4 @ skt3 @ skt1 @ ( o @ skt2 @ skt4 @ skt1 @ sk1 @ sk2 ) @ sk3 ) ),
inference(pattern_uni,[status(thm)],[12:[bind(A,$thf( sk2 )),bind(B,$thf( sk3 )),bind_type(TA,$thf( TA )),bind_type(TB,$thf( skt4 ))]]) ).
thf(43,plain,
! [TB: $tType,B: skt3 > TB,A: TB > skt1] :
( ( ( ^ [C: skt3] : ( A @ ( B @ C ) ) )
!= ( o @ skt4 @ skt3 @ skt1 @ ( o @ skt2 @ skt4 @ skt1 @ sk1 @ sk2 ) @ sk3 ) )
| ( ( o @ TB @ skt3 @ skt1 @ A @ B )
!= ( o @ skt2 @ skt3 @ skt1 @ sk1
@ ^ [C: skt3] : ( sk2 @ ( sk3 @ C ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[9,13]) ).
thf(44,plain,
( ( ^ [A: skt3] : ( sk1 @ ( sk2 @ ( sk3 @ A ) ) ) )
!= ( o @ skt4 @ skt3 @ skt1 @ ( o @ skt2 @ skt4 @ skt1 @ sk1 @ sk2 ) @ sk3 ) ),
inference(pattern_uni,[status(thm)],[43:[bind(A,$thf( sk1 )),bind(B,$thf( ^ [C: skt3] : ( sk2 @ ( sk3 @ C ) ) )),bind_type(TA,$thf( TA )),bind_type(TB,$thf( skt2 ))]]) ).
thf(60,plain,
! [TB: $tType,B: skt4 > TB,A: TB > skt1] :
( ( ( o @ skt4 @ skt3 @ skt1
@ ^ [C: skt4] : ( A @ ( B @ C ) )
@ sk3 )
!= ( ^ [C: skt3] : ( sk1 @ ( sk2 @ ( sk3 @ C ) ) ) ) )
| ( ( o @ TB @ skt4 @ skt1 @ A @ B )
!= ( o @ skt2 @ skt4 @ skt1 @ sk1 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[9,44]) ).
thf(61,plain,
( ( o @ skt4 @ skt3 @ skt1
@ ^ [A: skt4] : ( sk1 @ ( sk2 @ A ) )
@ sk3 )
!= ( ^ [A: skt3] : ( sk1 @ ( sk2 @ ( sk3 @ A ) ) ) ) ),
inference(pattern_uni,[status(thm)],[60:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 )),bind_type(TA,$thf( TA )),bind_type(TB,$thf( skt2 ))]]) ).
thf(232,plain,
! [TB: $tType,B: skt3 > TB,A: TB > skt1] :
( ( ( ^ [C: skt3] : ( A @ ( B @ C ) ) )
!= ( ^ [C: skt3] : ( sk1 @ ( sk2 @ ( sk3 @ C ) ) ) ) )
| ( ( o @ TB @ skt3 @ skt1 @ A @ B )
!= ( o @ skt4 @ skt3 @ skt1
@ ^ [C: skt4] : ( sk1 @ ( sk2 @ C ) )
@ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[9,61]) ).
thf(233,plain,
( ( ^ [A: skt3] : ( sk1 @ ( sk2 @ ( sk3 @ A ) ) ) )
!= ( ^ [A: skt3] : ( sk1 @ ( sk2 @ ( sk3 @ A ) ) ) ) ),
inference(pattern_uni,[status(thm)],[232:[bind(A,$thf( ^ [C: skt4] : ( sk1 @ ( sk2 @ C ) ) )),bind(B,$thf( sk3 )),bind_type(TA,$thf( TA )),bind_type(TB,$thf( skt4 ))]]) ).
thf(251,plain,
$false,
inference(simp,[status(thm)],[233]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYP118^1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.09/0.19 % Computer : n011.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 17:29:16 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.89/0.77 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.21/0.95 % [INFO] Parsing done (175ms).
% 1.21/0.96 % [INFO] Running in sequential loop mode.
% 1.76/1.36 % [INFO] eprover registered as external prover.
% 1.76/1.37 % [INFO] Scanning for conjecture ...
% 1.97/1.47 % [INFO] Found a conjecture (or negated_conjecture) and 1 axioms. Running axiom selection ...
% 2.14/1.50 % [INFO] Axiom selection finished. Selected 1 axioms (removed 0 axioms).
% 2.14/1.51 % [INFO] Problem is higher-order (TPTP THF).
% 2.14/1.52 % [INFO] Type checking passed.
% 2.14/1.52 % [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 ...
% 11.04/4.14 % [INFO] Killing All external provers ...
% 11.04/4.14 % Time passed: 3802ms (effective reasoning time: 3172ms)
% 11.04/4.15 % 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)>
% 11.04/4.15 % Axioms used in derivation (1): trivia/o_DEF_
% 11.04/4.15 % No. of inferences in proof: 18
% 11.04/4.15 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 3802 ms resp. 3172 ms w/o parsing
% 11.37/4.21 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 11.37/4.21 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------