%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO499^1 : 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 : n013.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 08:46:01 AM UTC 2026
% Result : Theorem 4.46s 2.44s
% Output : Refutation 4.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 1
% Syntax : Number of formulae : 31 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 164 ( 51 equ; 0 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 156 ( 41 ~; 26 |; 5 &; 84 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 0 ( 0 ^; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
thf(a_decl,type,
a: $o ).
thf(b_decl,type,
b: $o ).
thf(c_decl,type,
c: $o ).
thf(f_decl,type,
f: $o > $i ).
thf(f1_decl,type,
f1: $o > $i ).
thf(f2_decl,type,
f2: $o > $i ).
thf(g_decl,type,
g: $o > $i ).
thf(g1_decl,type,
g1: $o > $i ).
thf(g2_decl,type,
g2: $o > $i ).
thf(1,conjecture,
( ( ( f @ a )
= ( g @ b ) )
| ( ( f @ b )
!= ( g @ a ) )
| ( ( f1 @ a )
= ( g1 @ c ) )
| ( ( f1 @ c )
!= ( g1 @ a ) )
| ( ( f2 @ b )
= ( g2 @ c ) )
| ( ( f2 @ c )
!= ( g2 @ b ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
thf(2,negated_conjecture,
~ ( ( ( f @ a )
= ( g @ b ) )
| ( ( f @ b )
!= ( g @ a ) )
| ( ( f1 @ a )
= ( g1 @ c ) )
| ( ( f1 @ c )
!= ( g1 @ a ) )
| ( ( f2 @ b )
= ( g2 @ c ) )
| ( ( f2 @ c )
!= ( g2 @ b ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ( ( f @ a )
= ( g @ b ) )
| ( ( f @ b )
!= ( g @ a ) )
| ( ( f1 @ a )
= ( g1 @ c ) )
| ( ( f1 @ c )
!= ( g1 @ a ) )
| ( ( f2 @ b )
= ( g2 @ c ) )
| ( ( f2 @ c )
!= ( g2 @ b ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
( ( ( f @ a )
!= ( g @ b ) )
& ( ( f @ b )
= ( g @ a ) )
& ( ( f1 @ a )
!= ( g1 @ c ) )
& ( ( f1 @ c )
= ( g1 @ a ) )
& ( ( f2 @ b )
!= ( g2 @ c ) )
& ( ( f2 @ c )
= ( g2 @ b ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(9,plain,
( ( f @ b )
= ( g @ a ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(14,plain,
( ( g @ a )
= ( f @ b ) ),
inference(lifteq,[status(thm)],[9]) ).
thf(8,plain,
( ( f @ a )
!= ( g @ b ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(16,plain,
( ( g @ b )
!= ( f @ a ) ),
inference(lifteq,[status(thm)],[8]) ).
thf(33,plain,
( ( ( f @ b )
!= ( f @ a ) )
| ( ( g @ b )
!= ( g @ a ) ) ),
inference(paramod_ordered,[status(thm)],[14,16]) ).
thf(36,plain,
( ( b != a )
| ( b != a ) ),
inference(simp,[status(thm)],[33]) ).
thf(37,plain,
b != a,
inference(simp,[status(thm)],[36]) ).
thf(6,plain,
( ( f1 @ a )
!= ( g1 @ c ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(13,plain,
( ( g1 @ c )
!= ( f1 @ a ) ),
inference(lifteq,[status(thm)],[6]) ).
thf(7,plain,
( ( f1 @ c )
= ( g1 @ a ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(15,plain,
( ( g1 @ a )
= ( f1 @ c ) ),
inference(lifteq,[status(thm)],[7]) ).
thf(40,plain,
( ( ( f1 @ c )
!= ( f1 @ a ) )
| ( ( g1 @ c )
!= ( g1 @ a ) ) ),
inference(paramod_ordered,[status(thm)],[15,13]) ).
thf(43,plain,
( ( c != a )
| ( c != a ) ),
inference(simp,[status(thm)],[40]) ).
thf(44,plain,
c != a,
inference(simp,[status(thm)],[43]) ).
thf(45,plain,
( ~ c
| ~ a ),
inference(bool_ext,[status(thm)],[44]) ).
thf(10,plain,
( ( f2 @ b )
!= ( g2 @ c ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(12,plain,
( ( g2 @ c )
!= ( f2 @ b ) ),
inference(lifteq,[status(thm)],[10]) ).
thf(39,plain,
( b
| a ),
inference(bool_ext,[status(thm)],[37]) ).
thf(5,plain,
( ( f2 @ c )
= ( g2 @ b ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(11,plain,
( ( g2 @ b )
= ( f2 @ c ) ),
inference(lifteq,[status(thm)],[5]) ).
thf(17,plain,
( ( ( f2 @ c )
!= ( f2 @ b ) )
| ( ( g2 @ c )
!= ( g2 @ b ) ) ),
inference(paramod_ordered,[status(thm)],[11,12]) ).
thf(20,plain,
( ( c != b )
| ( c != b ) ),
inference(simp,[status(thm)],[17]) ).
thf(21,plain,
c != b,
inference(simp,[status(thm)],[20]) ).
thf(23,plain,
( c
| b ),
inference(bool_ext,[status(thm)],[21]) ).
thf(38,plain,
( ~ b
| ~ a ),
inference(bool_ext,[status(thm)],[37]) ).
thf(22,plain,
( ~ c
| ~ b ),
inference(bool_ext,[status(thm)],[21]) ).
thf(103,plain,
$false,
inference(e,[status(thm)],[37,14,13,45,12,39,3,16,11,23,15,38,21,22,44]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO499^1 : 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
% 0.09/0.20 % Computer : n013.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 17:10:06 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 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
% 0.89/0.78 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.23/0.97 % [INFO] Parsing done (189ms).
% 1.23/0.99 % [INFO] Running in sequential loop mode.
% 2.03/1.40 % [INFO] eprover registered as external prover.
% 2.03/1.41 % [INFO] Scanning for conjecture ...
% 2.21/1.50 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.21/1.53 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.21/1.53 % [INFO] Problem is higher-order (TPTP THF).
% 2.21/1.54 % [INFO] Type checking passed.
% 2.21/1.55 % [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 ...
% 4.46/2.44 % External prover 'e' found a proof!
% 4.46/2.44 % [INFO] Killing All external provers ...
% 4.46/2.44 % Time passed: 2088ms (effective reasoning time: 1443ms)
% 4.46/2.44 % 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)>
% 4.46/2.44 % Axioms used in derivation (0):
% 4.46/2.44 % No. of inferences in proof: 31
% 4.46/2.44 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2088 ms resp. 1443 ms w/o parsing
% 4.46/2.48 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.46/2.48 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------