%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU906^5 : 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 : n015.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 08:29:34 AM UTC 2026
% Result : Theorem 12.88s 4.53s
% Output : Refutation 12.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 3
% Syntax : Number of formulae : 27 ( 13 unt; 0 typ; 2 def)
% Number of atoms : 70 ( 29 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 174 ( 20 ~; 13 |; 1 &; 134 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 17 ( 17 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 51 ( 14 ^; 31 !; 4 ?; 51 :)
% ( 0 !>; 0 ?*; 0 @-; 2 @+)
% Comments :
%------------------------------------------------------------------------------
thf(f_decl,type,
f: $i > $i ).
thf(cS_decl,type,
cS: $i > $o ).
thf(sk1_decl,type,
sk1: ( $i > $o ) > $i ).
thf(sk2_decl,type,
sk2: $i > $i ).
thf(sk1_def,definition,
( sk1
= ( ^ [A: $i > $o] :
@+[B: $i] :
( ( cS @ B )
!= ( A @ ( f @ B ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i > $i] :
! [B: $i] :
( ( A @ ( f @ B ) )
= B ) ) ) ).
thf(1,conjecture,
( ! [A: $i,B: $i] :
( ( ( f @ A )
= ( f @ B ) )
=> ( A = B ) )
=> ? [A: $i > $o] :
! [B: $i] :
( ( cS @ B )
= ( A @ ( f @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cSV5_pme) ).
thf(2,negated_conjecture,
~ ( ! [A: $i,B: $i] :
( ( ( f @ A )
= ( f @ B ) )
=> ( A = B ) )
=> ? [A: $i > $o] :
! [B: $i] :
( ( cS @ B )
= ( A @ ( f @ B ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: $i,B: $i] :
( ( ( f @ A )
= ( f @ B ) )
=> ( A = B ) )
=> ? [A: $i > $o] :
! [B: $i] :
( ( cS @ B )
= ( A @ ( f @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
! [C: $i > $o,B: $i,A: $i] :
( ( ( ( f @ A )
!= ( f @ B ) )
| ( A = B ) )
& ( ( cS @ ( sk1 @ C ) )
!= ( C @ ( f @ ( sk1 @ C ) ) ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(5,plain,
! [B: $i,A: $i] :
( ( ( f @ A )
!= ( f @ B ) )
| ( A = B ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(7,plain,
! [B: $i,A: $i] :
( ( ( f @ A )
!= ( f @ B ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[5]) ).
thf(8,plain,
? [A: $i > $i] :
! [B: $i] :
( ( A @ ( f @ B ) )
= B ),
inference(detectInverse,[status(thm)],[7]) ).
thf(9,plain,
! [A: $i] :
( ( sk2 @ ( f @ A ) )
= A ),
inference(cnf,[status(esa)],[8]) ).
thf(12,plain,
! [A: $i] :
( ( sk2 @ ( f @ A ) )
= A ),
inference(lifteq,[status(thm)],[9]) ).
thf(6,plain,
! [A: $i > $o] :
( ( cS @ ( sk1 @ A ) )
!= ( A @ ( f @ ( sk1 @ A ) ) ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(10,plain,
! [A: $i > $o] :
( ( cS @ ( sk1 @ A ) )
!= ( A @ ( f @ ( sk1 @ A ) ) ) ),
inference(lifteq,[status(thm)],[6]) ).
thf(11,plain,
! [A: $i > $o] :
( ( cS @ ( sk1 @ A ) )
!= ( A @ ( f @ ( sk1 @ A ) ) ) ),
inference(simp,[status(thm)],[10]) ).
thf(14,plain,
! [A: $i > $o] :
( ( cS @ ( sk1 @ A ) )
| ( A @ ( f @ ( sk1 @ A ) ) ) ),
inference(bool_ext,[status(thm)],[11]) ).
thf(72,plain,
! [A: $i > $i] :
( ( cS
@ ( sk1
@ ^ [B: $i] : ( cS @ ( A @ B ) ) ) )
| ( cS
@ ( A
@ ( f
@ ( sk1
@ ^ [B: $i] : ( cS @ ( A @ B ) ) ) ) ) ) ),
inference(prim_subst,[status(thm)],[14:[bind(A,$thf( ^ [C: $i] : ( cS @ ( B @ C ) ) ))]]) ).
thf(98,plain,
! [A: $i > $i] :
( ( cS
@ ( sk1
@ ^ [B: $i] : ( cS @ ( A @ B ) ) ) )
| ( cS
@ ( A
@ ( f
@ ( sk1
@ ^ [B: $i] : ( cS @ ( A @ B ) ) ) ) ) ) ),
inference(simp,[status(thm)],[72]) ).
thf(367,plain,
! [B: $i > $i,A: $i] :
( ( cS
@ ( sk1
@ ^ [C: $i] : ( cS @ ( B @ C ) ) ) )
| ( cS @ A )
| ( ( sk2 @ ( f @ A ) )
!= ( B
@ ( f
@ ( sk1
@ ^ [C: $i] : ( cS @ ( B @ C ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[12,98]) ).
thf(389,plain,
( ( cS
@ ( sk1
@ ^ [A: $i] : ( cS @ ( sk2 @ A ) ) ) )
| ( cS
@ ( sk1
@ ^ [A: $i] : ( cS @ ( sk2 @ A ) ) ) ) ),
inference(pre_uni,[status(thm)],[367:[bind(A,$thf( sk1 @ ^ [C: $i] : ( cS @ ( sk2 @ C ) ) )),bind(B,$thf( sk2 ))]]) ).
thf(396,plain,
( cS
@ ( sk1
@ ^ [A: $i] : ( cS @ ( sk2 @ A ) ) ) ),
inference(simp,[status(thm)],[389]) ).
thf(13,plain,
! [A: $i > $o] :
( ~ ( cS @ ( sk1 @ A ) )
| ~ ( A @ ( f @ ( sk1 @ A ) ) ) ),
inference(bool_ext,[status(thm)],[11]) ).
thf(427,plain,
! [A: $i > $o] :
( ~ $true
| ~ ( A @ ( f @ ( sk1 @ A ) ) )
| ( ( cS
@ ( sk1
@ ^ [B: $i] : ( cS @ ( sk2 @ B ) ) ) )
!= ( cS @ ( sk1 @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[396,13]) ).
thf(428,plain,
! [A: $i > $o] :
( ~ ( A @ ( f @ ( sk1 @ A ) ) )
| ( ( cS
@ ( sk1
@ ^ [B: $i] : ( cS @ ( sk2 @ B ) ) ) )
!= ( cS @ ( sk1 @ A ) ) ) ),
inference(simp,[status(thm)],[427]) ).
thf(429,plain,
~ ( cS
@ ( sk2
@ ( f
@ ( sk1
@ ^ [A: $i] : ( cS @ ( sk2 @ A ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[428:[bind(A,$thf( ^ [B: $i] : ( cS @ ( sk2 @ B ) ) ))]]) ).
thf(656,plain,
~ ( cS
@ ( sk1
@ ^ [A: $i] : ( cS @ ( sk2 @ A ) ) ) ),
inference(rewrite,[status(thm)],[429,12]) ).
thf(657,plain,
$false,
inference(rewrite,[status(thm)],[396,656]) ).
thf(658,plain,
$false,
inference(simp,[status(thm)],[657]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU906^5 : 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
% 0.11/0.21 % Computer : n015.cluster.edu
% 0.11/0.21 % Model : x86_64 x86_64
% 0.11/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.21 % Memory : 8046.5625MB
% 0.11/0.21 % OS : Linux 6.8.0-71-generic
% 0.11/0.21 % CPULimit : 300
% 0.11/0.21 % WCLimit : 300
% 0.11/0.21 % DateTime : Tue Sep 29 14:48:17 UTC 2026
% 0.11/0.21 % CPUTime :
% 0.11/0.21 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
% 0.85/0.78 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.17/0.96 % [INFO] Parsing done (179ms).
% 1.17/0.97 % [INFO] Running in sequential loop mode.
% 1.92/1.42 % [INFO] eprover registered as external prover.
% 1.92/1.43 % [INFO] Scanning for conjecture ...
% 2.08/1.53 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.08/1.56 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.08/1.56 % [INFO] Problem is higher-order (TPTP THF).
% 2.08/1.57 % [INFO] Type checking passed.
% 2.08/1.57 % [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 ...
% 12.88/4.51 % [INFO] Killing All external provers ...
% 12.88/4.52 % Time passed: 4167ms (effective reasoning time: 3539ms)
% 12.88/4.52 % 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)>
% 12.88/4.52 % Axioms used in derivation (0):
% 12.88/4.52 % No. of inferences in proof: 25
% 12.88/4.53 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 4167 ms resp. 3539 ms w/o parsing
% 12.88/4.59 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 12.88/4.59 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------