%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEV242^5 : TPTP v9.3.1. Released v4.0.0.
% 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 : n008.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 08:37:03 AM UTC 2026
% Result : Theorem 27.19s 7.25s
% Output : Refutation 21.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 6
% Syntax : Number of formulae : 38 ( 17 unt; 0 typ; 5 def)
% Number of atoms : 185 ( 75 equ; 0 cnn)
% Maximal formula atoms : 8 ( 4 avg)
% Number of connectives : 254 ( 45 ~; 58 |; 23 &; 116 @)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 51 ( 51 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 80 ( 24 ^; 35 !; 16 ?; 80 :)
% ( 0 !>; 0 ?*; 0 @-; 5 @+)
% Comments :
%------------------------------------------------------------------------------
thf(sk1_decl,type,
sk1: ( $i > $o ) > ( $i > $o ) > $i ).
thf(sk2_decl,type,
sk2: ( $i > $o ) > $o ).
thf(sk3_decl,type,
sk3: $i > $o ).
thf(sk4_decl,type,
sk4: $i > $o ).
thf(sk5_decl,type,
sk5: $i ).
thf(sk7_decl,type,
sk7: $i > $o ).
thf(sk1_def,definition,
( sk1
= ( ^ [A: $i > $o,B: $i > $o] :
@+[C: $i] :
( ( B @ C )
!= ( A @ C ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: ( $i > $o ) > $o] :
~ ! [B: $i > $o,C: $i > $o] :
( ( A
@ ^ [D: $i] :
? [E: $i > $o] :
( ( ( E = B )
| ( E = C ) )
& ( E @ D ) ) )
=> ( A
@ ^ [D: $i] :
( ( B @ D )
| ( C @ D ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i > $o] :
~ ! [B: $i > $o] :
( ( sk2
@ ^ [C: $i] :
? [D: $i > $o] :
( ( ( D = A )
| ( D = B ) )
& ( D @ C ) ) )
=> ( sk2
@ ^ [C: $i] :
( ( A @ C )
| ( B @ C ) ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: $i > $o] :
~ ( ( sk2
@ ^ [B: $i] :
? [C: $i > $o] :
( ( ( C = sk3 )
| ( C = A ) )
& ( C @ B ) ) )
=> ( sk2
@ ^ [B: $i] :
( ( sk3 @ B )
| ( A @ B ) ) ) ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( @+[A: $i > $o] :
( ( ( A = sk3 )
| ( A = sk4 ) )
& ( A @ sk5 ) ) ) ) ).
thf(1,conjecture,
( ! [A: $i > $o,B: $i > $o] :
( ! [C: $i] :
( ( A @ C )
= ( B @ C ) )
=> ( A = B ) )
=> ! [A: ( $i > $o ) > $o,B: $i > $o,C: $i > $o] :
( ( A
@ ^ [D: $i] :
? [E: $i > $o] :
( ( ( E = B )
| ( E = C ) )
& ( E @ D ) ) )
=> ( A
@ ^ [D: $i] :
( ( B @ D )
| ( C @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM4A_pme) ).
thf(2,negated_conjecture,
~ ( ! [A: $i > $o,B: $i > $o] :
( ! [C: $i] :
( ( A @ C )
= ( B @ C ) )
=> ( A = B ) )
=> ! [A: ( $i > $o ) > $o,B: $i > $o,C: $i > $o] :
( ( A
@ ^ [D: $i] :
? [E: $i > $o] :
( ( ( E = B )
| ( E = C ) )
& ( E @ D ) ) )
=> ( A
@ ^ [D: $i] :
( ( B @ D )
| ( C @ D ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: $i > $o,B: $i > $o] :
( ! [C: $i] :
( ( A @ C )
= ( B @ C ) )
=> ( A = B ) )
=> ! [A: ( $i > $o ) > $o,B: $i > $o,C: $i > $o] :
( ( A
@ ^ [D: $i] :
? [E: $i > $o] :
( ( ( E = B )
| ( E = C ) )
& ( E @ D ) ) )
=> ( A
@ ^ [D: $i] :
( ( B @ D )
| ( C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
! [B: $i > $o,A: $i > $o] :
( ( ( ( A @ ( sk1 @ B @ A ) )
!= ( B @ ( sk1 @ B @ A ) ) )
| ( A = B ) )
& ( sk2
@ ^ [C: $i] :
? [D: $i > $o] :
( ( ( D = sk3 )
| ( D = sk4 ) )
& ( D @ C ) ) )
& ~ ( sk2
@ ^ [C: $i] :
( ( sk3 @ C )
| ( sk4 @ C ) ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(6,plain,
( sk2
@ ^ [A: $i] :
? [B: $i > $o] :
( ( ( B = sk3 )
| ( B = sk4 ) )
& ( B @ A ) ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(7,plain,
~ ( sk2
@ ^ [A: $i] :
( ( sk3 @ A )
| ( sk4 @ A ) ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(9,plain,
( ~ $true
| ( ( sk2
@ ^ [A: $i] :
? [B: $i > $o] :
( ( ( B = sk3 )
| ( B = sk4 ) )
& ( B @ A ) ) )
!= ( sk2
@ ^ [A: $i] :
( ( sk3 @ A )
| ( sk4 @ A ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[6,7]) ).
thf(10,plain,
( ( sk2
@ ^ [A: $i] :
? [B: $i > $o] :
( ( ( B = sk3 )
| ( B = sk4 ) )
& ( B @ A ) ) )
!= ( sk2
@ ^ [A: $i] :
( ( sk3 @ A )
| ( sk4 @ A ) ) ) ),
inference(simp,[status(thm)],[9]) ).
thf(11,plain,
( ( ^ [A: $i] :
? [B: $i > $o] :
( ( ( B = sk3 )
| ( B = sk4 ) )
& ( B @ A ) ) )
!= ( ^ [A: $i] :
( ( sk3 @ A )
| ( sk4 @ A ) ) ) ),
inference(simp,[status(thm)],[10]) ).
thf(12,plain,
( ( ? [A: $i > $o] :
( ( ( A = sk3 )
| ( A = sk4 ) )
& ( A @ sk5 ) ) )
!= ( ( sk3 @ sk5 )
| ( sk4 @ sk5 ) ) ),
inference(func_ext,[status(esa)],[11]) ).
thf(13,plain,
( ~ ? [A: $i > $o] :
( ( ( A = sk3 )
| ( A = sk4 ) )
& ( A @ sk5 ) )
| ~ ( ( sk3 @ sk5 )
| ( sk4 @ sk5 ) ) ),
inference(bool_ext,[status(thm)],[12]) ).
thf(15,plain,
! [A: $i > $o] :
( ( ( A != sk3 )
| ~ ( A @ sk5 )
| ~ ( sk3 @ sk5 ) )
& ( ( A != sk3 )
| ~ ( A @ sk5 )
| ~ ( sk4 @ sk5 ) )
& ( ( A != sk4 )
| ~ ( A @ sk5 )
| ~ ( sk3 @ sk5 ) )
& ( ( A != sk4 )
| ~ ( A @ sk5 )
| ~ ( sk4 @ sk5 ) ) ),
inference(cnf,[status(esa)],[13]) ).
thf(16,plain,
! [A: $i > $o] :
( ( A != sk3 )
| ~ ( A @ sk5 )
| ~ ( sk3 @ sk5 ) ),
inference(cnfConj,[status(thm)],[15]) ).
thf(20,plain,
! [A: $i > $o] :
( ( A != sk3 )
| ~ ( A @ sk5 )
| ~ ( sk3 @ sk5 ) ),
inference(lifteq,[status(thm)],[16]) ).
thf(21,plain,
~ ( sk3 @ sk5 ),
inference(simp,[status(thm)],[20]) ).
thf(32,plain,
( ( ? [A: $i > $o] :
( ( ( A = sk3 )
| ( A = sk4 ) )
& ( A @ sk5 ) ) )
!= ( $false
| ( sk4 @ sk5 ) ) ),
inference(rewrite,[status(thm)],[12,21]) ).
thf(33,plain,
( ( ? [A: $i > $o] :
( ( ( A = sk3 )
| ( A = sk4 ) )
& ( A @ sk5 ) ) )
!= ( sk4 @ sk5 ) ),
inference(simp,[status(thm)],[32]) ).
thf(19,plain,
! [A: $i > $o] :
( ( A != sk4 )
| ~ ( A @ sk5 )
| ~ ( sk4 @ sk5 ) ),
inference(cnfConj,[status(thm)],[15]) ).
thf(26,plain,
! [A: $i > $o] :
( ( A != sk4 )
| ~ ( A @ sk5 )
| ~ ( sk4 @ sk5 ) ),
inference(lifteq,[status(thm)],[19]) ).
thf(27,plain,
~ ( sk4 @ sk5 ),
inference(simp,[status(thm)],[26]) ).
thf(86,plain,
? [A: $i > $o] :
( ( ( A = sk3 )
| ( A = sk4 ) )
& ( A @ sk5 ) ),
inference(rewrite,[status(thm)],[33,27]) ).
thf(87,plain,
( ( ( sk7 = sk3 )
| ( sk7 = sk4 ) )
& ( sk7 @ sk5 ) ),
inference(cnf,[status(esa)],[86]) ).
thf(89,plain,
sk7 @ sk5,
inference(cnfConj,[status(thm)],[87]) ).
thf(88,plain,
( ( sk7 = sk3 )
| ( sk7 = sk4 ) ),
inference(cnfConj,[status(thm)],[87]) ).
thf(223,plain,
( ( sk7 = sk3 )
| ( sk7 = sk4 ) ),
inference(lifteq,[status(thm)],[88]) ).
thf(224,plain,
! [B: $i,A: $i] :
( ( ( sk7 @ A )
= ( sk3 @ A ) )
| ( ( sk7 @ B )
= ( sk4 @ B ) ) ),
inference(func_ext,[status(esa)],[223]) ).
thf(244,plain,
! [B: $i,A: $i] :
( ( ( sk7 @ A )
= ( sk3 @ A ) )
| ( sk4 @ B )
| ( ( sk7 @ B )
!= ( sk7 @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[224,89]) ).
thf(245,plain,
! [A: $i] :
( ( ( sk7 @ A )
= ( sk3 @ A ) )
| ( sk4 @ sk5 ) ),
inference(pattern_uni,[status(thm)],[244:[bind(A,$thf( A )),bind(B,$thf( sk5 ))]]) ).
thf(537,plain,
! [A: $i] :
( ( ( sk7 @ A )
= ( sk3 @ A ) )
| $false ),
inference(rewrite,[status(thm)],[245,27]) ).
thf(538,plain,
! [A: $i] :
( ( sk7 @ A )
= ( sk3 @ A ) ),
inference(simp,[status(thm)],[537]) ).
thf(539,plain,
sk3 @ sk5,
inference(rewrite,[status(thm)],[89,538]) ).
thf(1024,plain,
$false,
inference(rewrite,[status(thm)],[539,21]) ).
thf(1025,plain,
$false,
inference(simp,[status(thm)],[1024]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV242^5 : TPTP v9.3.1. Released v4.0.0.
% 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
% 0.12/0.23 % Computer : n008.cluster.edu
% 0.12/0.23 % Model : x86_64 x86_64
% 0.12/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.23 % Memory : 8046.5625MB
% 0.12/0.23 % OS : Linux 6.8.0-71-generic
% 0.12/0.24 % CPULimit : 300
% 0.12/0.24 % WCLimit : 300
% 0.12/0.24 % DateTime : Tue Sep 29 15:27:39 UTC 2026
% 0.12/0.24 % CPUTime :
% 0.12/0.24 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
% 1.09/0.80 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.35/0.91 % [INFO] Parsing done (103ms).
% 1.35/0.92 % [INFO] Running in sequential loop mode.
% 1.62/1.13 % [INFO] eprover registered as external prover.
% 1.62/1.13 % [INFO] Scanning for conjecture ...
% 1.84/1.18 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.00/1.20 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.00/1.20 % [INFO] Problem is higher-order (TPTP THF).
% 2.00/1.20 % [INFO] Type checking passed.
% 2.00/1.21 % [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 ...
% 27.19/7.24 % [INFO] Killing All external provers ...
% 27.19/7.25 % Time passed: 6810ms (effective reasoning time: 6319ms)
% 27.19/7.25 % 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)>
% 27.19/7.25 % Axioms used in derivation (0):
% 27.19/7.25 % No. of inferences in proof: 33
% 27.19/7.25 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 6810 ms resp. 6319 ms w/o parsing
% 21.96/7.31 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 21.96/7.31 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------