%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO629-1 : TPTP v9.3.1. Released v7.1.0.
% 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 09:45:03 AM UTC 2026
% Result : Unsatisfiable 2.64s 1.51s
% Output : Refutation 2.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 12
% Syntax : Number of formulae : 25 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 41 ( 0 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 182 ( 20 ~; 16 |; 0 &; 146 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 26 ( 0 ^; 26 !; 0 ?; 26 :)
% Comments :
%------------------------------------------------------------------------------
thf('E_decl',type,
'E': $i > $i > $o ).
thf(f_decl,type,
f: $i > $i ).
thf(g_decl,type,
g: $i > $i ).
thf(iLEQ_decl,type,
iLEQ: $i > $i > $o ).
thf('0_decl',type,
'0': $i ).
thf(s_decl,type,
s: $i > $i ).
thf('LE_decl',type,
'LE': $i > $i > $o ).
thf(7,axiom,
! [A: $i] :
( ( A @ g @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ g @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1_07) ).
thf(24,plain,
! [A: $i] :
( ( A @ g @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ g @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(9,axiom,
! [A: $i] : ( A @ g @ ( A @ iLEQ ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_3_09) ).
thf(28,plain,
! [A: $i] : ( A @ g @ ( A @ iLEQ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(1,axiom,
! [A: $i] :
~ ( A @ g @ f @ ( A @ f @ 'E' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_8_01) ).
thf(13,plain,
! [A: $i] :
~ ( A @ g @ f @ ( A @ f @ 'E' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(12,axiom,
! [A: $i] : ( A @ ( A @ iLEQ ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_9_12) ).
thf(32,plain,
! [A: $i] : ( A @ ( A @ iLEQ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(6,axiom,
! [B: $i,A: $i] :
( ( '0' @ ( B @ f @ 'LE' ) )
| ( B @ f @ ( '0' @ 'E' ) )
| ~ ( B @ ( A @ iLEQ ) )
| ~ ( '0' @ s @ ( A @ f @ 'LE' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_10_06) ).
thf(22,plain,
! [B: $i,A: $i] :
( ( '0' @ ( B @ f @ 'LE' ) )
| ( B @ f @ ( '0' @ 'E' ) )
| ~ ( B @ ( A @ iLEQ ) )
| ~ ( '0' @ s @ ( A @ f @ 'LE' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(4,axiom,
! [A: $i] :
( ( '0' @ s @ ( A @ f @ 'LE' ) )
| ( A @ f @ ( '0' @ s @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_6_04) ).
thf(18,plain,
! [A: $i] :
( ( '0' @ s @ ( A @ f @ 'LE' ) )
| ( A @ f @ ( '0' @ s @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(3,axiom,
! [A: $i] :
( ( A @ g @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ g @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_11_03) ).
thf(16,plain,
! [A: $i] :
( ( A @ g @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ g @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(8,axiom,
! [A: $i] :
~ ( '0' @ ( A @ g @ f @ 'LE' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_2_08) ).
thf(26,plain,
! [A: $i] :
~ ( '0' @ ( A @ g @ f @ 'LE' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(11,axiom,
! [A: $i] :
~ ( A @ g @ f @ ( A @ f @ 'E' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_4_11) ).
thf(30,plain,
! [A: $i] :
~ ( A @ g @ f @ ( A @ f @ 'E' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(2,axiom,
! [A: $i] : ( A @ ( A @ iLEQ ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_0_02) ).
thf(15,plain,
! [A: $i] : ( A @ ( A @ iLEQ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(5,axiom,
! [A: $i] :
~ ( '0' @ ( A @ f @ 'LE' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_7_05) ).
thf(20,plain,
! [A: $i] :
~ ( '0' @ ( A @ f @ 'LE' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(10,axiom,
! [A: $i] : ( A @ g @ ( A @ iLEQ ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_5_10) ).
thf(29,plain,
! [A: $i] : ( A @ g @ ( A @ iLEQ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(33,plain,
$false,
inference(e,[status(thm)],[24,28,13,32,22,18,16,26,30,15,20,29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO629-1 : TPTP v9.3.1. Released v7.1.0.
% 0.00/0.07 % 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
% 0.13/0.40 % Computer : n005.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Sat Sep 26 19:40:19 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 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
% 0.69/0.71 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.92/0.81 % [INFO] Parsing done (94ms).
% 0.92/0.82 % [INFO] Running in sequential loop mode.
% 1.09/1.01 % [INFO] eprover registered as external prover.
% 1.09/1.01 % [INFO] Scanning for conjecture ...
% 1.39/1.04 % [INFO] 12 axioms and no conjecture found.
% 1.39/1.07 % [INFO] Problem is propositional (TPTP CNF).
% 1.39/1.07 % [INFO] Type checking passed.
% 1.39/1.07 % [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 ...
% 2.64/1.51 % External prover 'e' found a proof!
% 2.64/1.51 % [INFO] Killing All external provers ...
% 2.64/1.51 % Time passed: 1005ms (effective reasoning time: 687ms)
% 2.64/1.51 % Axioms used in derivation (12): clause_2_08, clause_9_12, clause_3_09, clause_5_10, clause_6_04, clause_11_03, clause_4_11, clause_10_06, clause_7_05, clause_0_02, clause_1_07, clause_8_01
% 2.64/1.51 % No. of inferences in proof: 25
% 2.64/1.51 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 1005 ms resp. 687 ms w/o parsing
% 2.64/1.56 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.64/1.56 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------