%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU940^5 : TPTP v9.3.1. Released v4.0.0.
% 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 : n007.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 08:29:37 AM UTC 2026
% Result : Theorem 11.81s 3.83s
% Output : Refutation 10.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 5
% Syntax : Number of formulae : 37 ( 16 unt; 0 typ; 4 def)
% Number of atoms : 94 ( 69 equ; 34 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 385 ( 58 ~; 34 |; 19 &; 261 @)
% ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 79 ( 79 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 138 ( 101 ^; 29 !; 4 ?; 138 :)
% ( 0 !>; 0 ?*; 0 @-; 4 @+)
% Comments :
%------------------------------------------------------------------------------
thf(sk1_decl,type,
sk1: $i > $o ).
thf(sk2_decl,type,
sk2: ( ( $i > $i ) > $o ) > $i > $i ).
thf(sk3_decl,type,
sk3: ( ( $i > $i ) > $o ) > $i > $i ).
thf(sk4_decl,type,
sk4: ( ( $i > $i ) > $o ) > $i ).
thf(sk6_decl,type,
sk6: $i ).
thf(sk9_decl,type,
sk9: $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i > $o] :
~ ? [B: ( $i > $i ) > $o] :
( ( B
@ ^ [C: $i] : C )
& ! [C: $i > $i,D: $i > $i] :
( ( ( B @ C )
& ( B @ D ) )
=> ( ( B
@ ^ [E: $i] : ( C @ ( D @ E ) ) )
& ! [E: $i] :
( ( A @ E )
=> ( A @ ( C @ E ) ) ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( ^ [A: ( $i > $i ) > $o] :
@+[B: $i > $i] :
~ ! [C: $i > $i] :
( ( ( A @ B )
& ( A @ C ) )
=> ( ( A
@ ^ [D: $i] : ( B @ ( C @ D ) ) )
& ! [D: $i] :
( ( sk1 @ D )
=> ( sk1 @ ( B @ D ) ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( ^ [A: ( $i > $i ) > $o] :
@+[B: $i > $i] :
~ ( ( ( A @ ( sk2 @ A ) )
& ( A @ B ) )
=> ( ( A
@ ^ [C: $i] : ( sk2 @ A @ ( B @ C ) ) )
& ! [C: $i] :
( ( sk1 @ C )
=> ( sk1 @ ( sk2 @ A @ C ) ) ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( ^ [A: ( $i > $i ) > $o] :
@+[B: $i] :
~ ( ( sk1 @ B )
=> ( sk1 @ ( sk2 @ A @ B ) ) ) ) ) ).
thf(1,conjecture,
! [A: $i > $o] :
? [B: ( $i > $i ) > $o] :
( ( B
@ ^ [C: $i] : C )
& ! [C: $i > $i,D: $i > $i] :
( ( ( B @ C )
& ( B @ D ) )
=> ( ( B
@ ^ [E: $i] : ( C @ ( D @ E ) ) )
& ! [E: $i] :
( ( A @ E )
=> ( A @ ( C @ E ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM112A_pme) ).
thf(2,negated_conjecture,
~ ! [A: $i > $o] :
? [B: ( $i > $i ) > $o] :
( ( B
@ ^ [C: $i] : C )
& ! [C: $i > $i,D: $i > $i] :
( ( ( B @ C )
& ( B @ D ) )
=> ( ( B
@ ^ [E: $i] : ( C @ ( D @ E ) ) )
& ! [E: $i] :
( ( A @ E )
=> ( A @ ( C @ E ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: $i > $o] :
? [B: ( $i > $i ) > $o] :
( ( B
@ ^ [C: $i] : C )
& ! [C: $i > $i,D: $i > $i] :
( ( ( B @ C )
& ( B @ D ) )
=> ( ( B
@ ^ [E: $i] : ( C @ ( D @ E ) ) )
& ! [E: $i] :
( ( A @ E )
=> ( A @ ( C @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
! [A: ( $i > $i ) > $o] :
( ( ~ ( A
@ ^ [B: $i] : B )
| ( A @ ( sk2 @ A ) ) )
& ( ~ ( A
@ ^ [B: $i] : B )
| ( A @ ( sk3 @ A ) ) )
& ( ~ ( A
@ ^ [B: $i] : B )
| ~ ( A
@ ^ [B: $i] : ( sk2 @ A @ ( sk3 @ A @ B ) ) )
| ( sk1 @ ( sk4 @ A ) ) )
& ( ~ ( A
@ ^ [B: $i] : B )
| ~ ( A
@ ^ [B: $i] : ( sk2 @ A @ ( sk3 @ A @ B ) ) )
| ~ ( sk1 @ ( sk2 @ A @ ( sk4 @ A ) ) ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(7,plain,
! [A: ( $i > $i ) > $o] :
( ~ ( A
@ ^ [B: $i] : B )
| ~ ( A
@ ^ [B: $i] : ( sk2 @ A @ ( sk3 @ A @ B ) ) )
| ( sk1 @ ( sk4 @ A ) ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(5,plain,
! [A: ( $i > $i ) > $o] :
( ~ ( A
@ ^ [B: $i] : B )
| ( A @ ( sk2 @ A ) ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(9,plain,
( ( ( ^ [A: $i] : A )
!= ( ^ [A: $i] : A ) )
| ( ( ^ [A: $i] : A )
= ( sk2
@ ( (=) @ ( $i > $i )
@ ^ [A: $i] : A ) ) ) ),
inference(replace_leibeq,[status(thm)],[5:[bind(A,$thf( (=) @ ( $i > $i ) @ ^ [B: $i] : B ))]]) ).
thf(13,plain,
( ( ( ^ [A: $i] : A )
!= ( ^ [A: $i] : A ) )
| ( ( sk2
@ ( (=) @ ( $i > $i )
@ ^ [A: $i] : A ) )
= ( ^ [A: $i] : A ) ) ),
inference(lifteq,[status(thm)],[9]) ).
thf(14,plain,
( ( sk2
@ ( (=) @ ( $i > $i )
@ ^ [A: $i] : A ) )
= ( ^ [A: $i] : A ) ),
inference(simp,[status(thm)],[13]) ).
thf(16,plain,
! [A: $i] :
( ( sk2
@ ( (=) @ ( $i > $i )
@ ^ [B: $i] : B )
@ A )
= A ),
inference(func_ext,[status(esa)],[14]) ).
thf(8,plain,
! [A: ( $i > $i ) > $o] :
( ~ ( A
@ ^ [B: $i] : B )
| ~ ( A
@ ^ [B: $i] : ( sk2 @ A @ ( sk3 @ A @ B ) ) )
| ~ ( sk1 @ ( sk2 @ A @ ( sk4 @ A ) ) ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(21,plain,
! [B: ( $i > $i ) > $o,A: $i] :
( ~ ( B
@ ^ [C: $i] : C )
| ~ ( B
@ ^ [C: $i] : ( sk2 @ B @ ( sk3 @ B @ C ) ) )
| ~ ( sk1 @ A )
| ( ( sk2
@ ( (=) @ ( $i > $i )
@ ^ [C: $i] : C )
@ A )
!= ( sk2 @ B @ ( sk4 @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[16,8]) ).
thf(22,plain,
( ( ( ^ [A: $i] : A )
!= ( ^ [A: $i] : A ) )
| ( ( ^ [A: $i] : A )
!= ( ^ [A: $i] :
( sk2
@ ( (=) @ ( $i > $i )
@ ^ [B: $i] : B )
@ ( sk3
@ ( (=) @ ( $i > $i )
@ ^ [B: $i] : B )
@ A ) ) ) )
| ~ ( sk1
@ ( sk4
@ ( (=) @ ( $i > $i )
@ ^ [A: $i] : A ) ) ) ),
inference(pattern_uni,[status(thm)],[21:[bind(A,$thf( sk4 @ ( (=) @ ( $i > $i ) @ ^ [C: $i] : C ) )),bind(B,$thf( (=) @ ( $i > $i ) @ ^ [C: $i] : C ))]]) ).
thf(31,plain,
( ( ( ^ [A: $i] : A )
!= ( ^ [A: $i] : A ) )
| ( ( ^ [A: $i] :
( sk2
@ ( (=) @ ( $i > $i )
@ ^ [B: $i] : B )
@ ( sk3
@ ( (=) @ ( $i > $i )
@ ^ [B: $i] : B )
@ A ) ) )
!= ( ^ [A: $i] : A ) )
| ~ ( sk1
@ ( sk4
@ ( (=) @ ( $i > $i )
@ ^ [A: $i] : A ) ) ) ),
inference(lifteq,[status(thm)],[22]) ).
thf(50,plain,
( ( ( ^ [A: $i] :
( sk2
@ ( (=) @ ( $i > $i )
@ ^ [B: $i] : B )
@ ( sk3
@ ( (=) @ ( $i > $i )
@ ^ [B: $i] : B )
@ A ) ) )
!= ( ^ [A: $i] : A ) )
| ~ ( sk1
@ ( sk4
@ ( (=) @ ( $i > $i )
@ ^ [A: $i] : A ) ) ) ),
inference(simp,[status(thm)],[31]) ).
thf(182,plain,
( ( ( sk3
@ ( (=) @ ( $i > $i )
@ ^ [A: $i] : A ) )
!= ( ^ [A: $i] : A ) )
| ~ ( sk1
@ ( sk4
@ ( (=) @ ( $i > $i )
@ ^ [A: $i] : A ) ) ) ),
inference(rewrite,[status(thm)],[50,16]) ).
thf(183,plain,
( ( ( sk3
@ ( (=) @ ( $i > $i )
@ ^ [A: $i] : A )
@ sk6 )
!= sk6 )
| ~ ( sk1
@ ( sk4
@ ( (=) @ ( $i > $i )
@ ^ [A: $i] : A ) ) ) ),
inference(func_ext,[status(esa)],[182]) ).
thf(6,plain,
! [A: ( $i > $i ) > $o] :
( ~ ( A
@ ^ [B: $i] : B )
| ( A @ ( sk3 @ A ) ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(10,plain,
( ( ( ^ [A: $i] : A )
!= ( ^ [A: $i] : A ) )
| ( ( ^ [A: $i] : A )
= ( sk3
@ ( (=) @ ( $i > $i )
@ ^ [A: $i] : A ) ) ) ),
inference(replace_leibeq,[status(thm)],[6:[bind(A,$thf( (=) @ ( $i > $i ) @ ^ [B: $i] : B ))]]) ).
thf(11,plain,
( ( ( ^ [A: $i] : A )
!= ( ^ [A: $i] : A ) )
| ( ( sk3
@ ( (=) @ ( $i > $i )
@ ^ [A: $i] : A ) )
= ( ^ [A: $i] : A ) ) ),
inference(lifteq,[status(thm)],[10]) ).
thf(12,plain,
( ( sk3
@ ( (=) @ ( $i > $i )
@ ^ [A: $i] : A ) )
= ( ^ [A: $i] : A ) ),
inference(simp,[status(thm)],[11]) ).
thf(15,plain,
! [A: $i] :
( ( sk3
@ ( (=) @ ( $i > $i )
@ ^ [B: $i] : B )
@ A )
= A ),
inference(func_ext,[status(esa)],[12]) ).
thf(190,plain,
( ( sk6 != sk6 )
| ~ ( sk1
@ ( sk4
@ ( (=) @ ( $i > $i )
@ ^ [A: $i] : A ) ) ) ),
inference(rewrite,[status(thm)],[183,15]) ).
thf(191,plain,
~ ( sk1
@ ( sk4
@ ( (=) @ ( $i > $i )
@ ^ [A: $i] : A ) ) ),
inference(simp,[status(thm)],[190]) ).
thf(412,plain,
! [A: ( $i > $i ) > $o] :
( ~ ( A
@ ^ [B: $i] : B )
| ~ ( A
@ ^ [B: $i] : ( sk2 @ A @ ( sk3 @ A @ B ) ) )
| ~ $true
| ( ( sk1 @ ( sk4 @ A ) )
!= ( sk1
@ ( sk4
@ ( (=) @ ( $i > $i )
@ ^ [B: $i] : B ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[7,191]) ).
thf(413,plain,
! [A: ( $i > $i ) > $o] :
( ~ ( A
@ ^ [B: $i] : B )
| ~ ( A
@ ^ [B: $i] : ( sk2 @ A @ ( sk3 @ A @ B ) ) )
| ( ( sk1 @ ( sk4 @ A ) )
!= ( sk1
@ ( sk4
@ ( (=) @ ( $i > $i )
@ ^ [B: $i] : B ) ) ) ) ),
inference(simp,[status(thm)],[412]) ).
thf(414,plain,
( ( ( ^ [A: $i] : A )
!= ( ^ [A: $i] : A ) )
| ( ( ^ [A: $i] : A )
!= ( ^ [A: $i] :
( sk2
@ ( (=) @ ( $i > $i )
@ ^ [B: $i] : B )
@ ( sk3
@ ( (=) @ ( $i > $i )
@ ^ [B: $i] : B )
@ A ) ) ) ) ),
inference(pattern_uni,[status(thm)],[413:[bind(A,$thf( (=) @ ( $i > $i ) @ ^ [B: $i] : B ))]]) ).
thf(443,plain,
( ( ( ^ [A: $i] : A )
!= ( ^ [A: $i] : A ) )
| ( ( ^ [A: $i] :
( sk2
@ ( (=) @ ( $i > $i )
@ ^ [B: $i] : B )
@ ( sk3
@ ( (=) @ ( $i > $i )
@ ^ [B: $i] : B )
@ A ) ) )
!= ( ^ [A: $i] : A ) ) ),
inference(lifteq,[status(thm)],[414]) ).
thf(532,plain,
( ( ^ [A: $i] :
( sk2
@ ( (=) @ ( $i > $i )
@ ^ [B: $i] : B )
@ ( sk3
@ ( (=) @ ( $i > $i )
@ ^ [B: $i] : B )
@ A ) ) )
!= ( ^ [A: $i] : A ) ),
inference(simp,[status(thm)],[443]) ).
thf(613,plain,
( ( sk3
@ ( (=) @ ( $i > $i )
@ ^ [A: $i] : A ) )
!= ( ^ [A: $i] : A ) ),
inference(rewrite,[status(thm)],[532,16]) ).
thf(614,plain,
( ( sk3
@ ( (=) @ ( $i > $i )
@ ^ [A: $i] : A )
@ sk9 )
!= sk9 ),
inference(func_ext,[status(esa)],[613]) ).
thf(617,plain,
sk9 != sk9,
inference(rewrite,[status(thm)],[614,15]) ).
thf(618,plain,
$false,
inference(simp,[status(thm)],[617]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU940^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % 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
% 0.11/0.22 % Computer : n007.cluster.edu
% 0.11/0.22 % Model : x86_64 x86_64
% 0.11/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.22 % Memory : 8046.5625MB
% 0.11/0.22 % OS : Linux 6.8.0-71-generic
% 0.11/0.22 % CPULimit : 300
% 0.11/0.22 % WCLimit : 300
% 0.11/0.22 % DateTime : Tue Sep 29 14:47:57 UTC 2026
% 0.11/0.22 % CPUTime :
% 0.11/0.22 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
% 1.05/0.80 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.24/0.98 % [INFO] Parsing done (175ms).
% 1.24/0.99 % [INFO] Running in sequential loop mode.
% 1.86/1.39 % [INFO] eprover registered as external prover.
% 2.06/1.40 % [INFO] Scanning for conjecture ...
% 2.06/1.48 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.23/1.52 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.23/1.52 % [INFO] Problem is higher-order (TPTP THF).
% 2.23/1.52 % [INFO] Type checking passed.
% 2.23/1.53 % [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 ...
% 11.81/3.83 % [INFO] Killing All external provers ...
% 11.81/3.83 % Time passed: 3461ms (effective reasoning time: 2830ms)
% 11.81/3.83 % 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)>
% 11.81/3.83 % Axioms used in derivation (0):
% 11.81/3.83 % No. of inferences in proof: 33
% 11.81/3.83 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 3461 ms resp. 2830 ms w/o parsing
% 10.68/3.91 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 10.68/3.91 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------