%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO506_8 : TPTP v9.3.1. Released v8.0.0.
% 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 : n005.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 : Sun Sep 27 09:44:50 AM UTC 2026
% Result : Theorem 3.20s 2.37s
% Output : Refutation 3.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 22 ( 12 unt; 0 typ; 2 def)
% Number of atoms : 67 ( 51 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 121 ( 28 ~; 16 |; 2 &; 75 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 3 usr; 4 con; 0-3 aty)
% Number of variables : 43 ( 0 ^; 41 !; 0 ?; 43 :)
% ( 0 !>; 0 ?*; 0 @-; 2 @+)
% Comments :
%------------------------------------------------------------------------------
thf(c_decl,type,
c: $o > $i > $i > $i ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ! [B: $i] :
( ( B @ ( A @ ( ( A = B ) @ c ) ) )
= B ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
( ( A @ ( sk1 @ ( ( sk1 = A ) @ c ) ) )
!= A ) ) ) ).
thf(1,conjecture,
( ~ ! [A: $i,B: $i] :
( ( B @ ( A @ ( $false @ c ) ) )
= B )
| ~ ! [A: $i,B: $i] :
( ( B @ ( A @ ( $true @ c ) ) )
= A )
| ! [A: $i,B: $i] :
( ( B @ ( A @ ( ( A = B ) @ c ) ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',claim) ).
thf(2,negated_conjecture,
~ ( ~ ! [A: $i,B: $i] :
( ( B @ ( A @ ( $false @ c ) ) )
= B )
| ~ ! [A: $i,B: $i] :
( ( B @ ( A @ ( $true @ c ) ) )
= A )
| ! [A: $i,B: $i] :
( ( B @ ( A @ ( ( A = B ) @ c ) ) )
= B ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ~ ! [A: $i,B: $i] :
( ( B @ ( A @ ( $false @ c ) ) )
= B )
| ~ ! [A: $i,B: $i] :
( ( B @ ( A @ ( $true @ c ) ) )
= A )
| ! [A: $i,B: $i] :
( ( B @ ( A @ ( ( A = B ) @ c ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( $false @ c ) ) )
= D )
& ( ( B @ ( A @ ( $true @ c ) ) )
= A )
& ( ( sk2 @ ( sk1 @ ( ( sk1 = sk2 ) @ c ) ) )
!= sk2 ) ),
inference(cnf,[status(esa)],[3]) ).
thf(7,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( $false @ c ) ) )
= B ),
inference(cnfConj,[status(thm)],[4]) ).
thf(10,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( $false @ c ) ) )
= B ),
inference(lifteq,[status(thm)],[7]) ).
thf(11,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( $false @ c ) ) )
= B ),
inference(simp,[status(thm)],[10]) ).
thf(5,plain,
( ( sk2 @ ( sk1 @ ( ( sk1 = sk2 ) @ c ) ) )
!= sk2 ),
inference(cnfConj,[status(thm)],[4]) ).
thf(8,plain,
( ( sk2 @ ( sk1 @ ( ( sk1 = sk2 ) @ c ) ) )
!= sk2 ),
inference(lifteq,[status(thm)],[5]) ).
thf(18,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( $false @ c ) ) )
!= ( sk2 @ ( sk1 @ ( ( sk1 = sk2 ) @ c ) ) ) )
| ( B != sk2 ) ),
inference(paramod_ordered,[status(thm)],[11,8]) ).
thf(22,plain,
! [A: $i] :
( ( sk2 != sk2 )
| ( A != sk1 )
| ( sk1 = sk2 ) ),
inference(simp,[status(thm)],[18]) ).
thf(25,plain,
! [A: $i] :
( ( sk2 != sk2 )
| ( A != sk1 )
| ( sk2 = sk1 ) ),
inference(lifteq,[status(thm)],[22]) ).
thf(26,plain,
sk2 = sk1,
inference(simp,[status(thm)],[25]) ).
thf(6,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( $true @ c ) ) )
= A ),
inference(cnfConj,[status(thm)],[4]) ).
thf(9,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( $true @ c ) ) )
= A ),
inference(lifteq,[status(thm)],[6]) ).
thf(12,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( $true @ c ) ) )
!= ( sk2 @ ( sk1 @ ( ( sk1 = sk2 ) @ c ) ) ) )
| ( A != sk2 ) ),
inference(paramod_ordered,[status(thm)],[9,8]) ).
thf(14,plain,
! [A: $i] :
( ( A != sk2 )
| ( sk2 != sk1 )
| ( sk1 != sk2 ) ),
inference(simp,[status(thm)],[12]) ).
thf(16,plain,
! [A: $i] :
( ( A != sk2 )
| ( sk2 != sk1 )
| ( sk2 != sk1 ) ),
inference(lifteq,[status(thm)],[14]) ).
thf(17,plain,
sk2 != sk1,
inference(simp,[status(thm)],[16]) ).
thf(31,plain,
$false,
inference(simplifyReflect,[status(thm)],[26,17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO506_8 : TPTP v9.3.1. Released v8.0.0.
% 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
% 0.14/0.41 % Computer : n005.cluster.edu
% 0.14/0.41 % Model : x86_64 x86_64
% 0.14/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.41 % Memory : 8046.5625MB
% 0.14/0.41 % OS : Linux 6.8.0-71-generic
% 0.14/0.41 % CPULimit : 300
% 0.14/0.41 % WCLimit : 300
% 0.14/0.41 % DateTime : Sat Sep 26 19:25:18 UTC 2026
% 0.14/0.41 % CPUTime :
% 0.14/0.41 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
% 0.82/1.00 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.19/1.17 % [INFO] Parsing done (164ms).
% 1.19/1.18 % [INFO] Running in sequential loop mode.
% 1.69/1.58 % [INFO] eprover registered as external prover.
% 1.69/1.58 % [INFO] Scanning for conjecture ...
% 1.88/1.69 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.02/1.72 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.02/1.72 % [INFO] Problem is typed first-order (TPTP TFF).
% 2.02/1.73 % [INFO] Type checking passed.
% 2.02/1.73 % [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 ...
% 3.20/2.36 % [INFO] Killing All external provers ...
% 3.20/2.37 % Time passed: 1810ms (effective reasoning time: 1180ms)
% 3.20/2.37 % 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)>
% 3.20/2.37 % Axioms used in derivation (0):
% 3.20/2.37 % No. of inferences in proof: 20
% 3.20/2.37 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1810 ms resp. 1180 ms w/o parsing
% 3.50/2.42 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.50/2.42 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------