%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO633-1 : TPTP v9.3.1. Released v7.1.0.
% 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 : n016.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 09:45:04 AM UTC 2026
% Result : Unsatisfiable 5.96s 3.46s
% Output : Refutation 6.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 13
% Syntax : Number of formulae : 27 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 93 ( 0 equ; 0 cnn)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 808 ( 68 ~; 66 |; 0 &; 674 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 15 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 94 ( 0 ^; 94 !; 0 ?; 94 :)
% Comments :
%------------------------------------------------------------------------------
thf('E_decl',type,
'E': $i > $i > $o ).
thf(f_decl,type,
f: $i > $i ).
thf(s_decl,type,
s: $i > $i ).
thf('0_decl',type,
'0': $i ).
thf('LEQ_decl',type,
'LEQ': $i > $i > $o ).
thf('AP_decl',type,
'AP': $i > $i > $i ).
thf(8,axiom,
! [B: $i,A: $i] : ( B @ ( A @ ( '0' @ s @ s @ s @ s @ s @ 'AP' ) @ 'LEQ' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_7_08) ).
thf(25,plain,
! [B: $i,A: $i] : ( B @ ( A @ ( '0' @ s @ s @ s @ s @ s @ 'AP' ) @ 'LEQ' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(1,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( '0' @ s @ s @ s @ s @ s @ s @ 'AP' ) @ ( D @ ( '0' @ s @ s @ 'AP' ) @ 'LEQ' ) )
| ~ ( '0' @ s @ s @ s @ ( C @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ ( B @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ ( A @ f @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_3_01) ).
thf(14,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( '0' @ s @ s @ s @ s @ s @ s @ 'AP' ) @ ( D @ ( '0' @ s @ s @ 'AP' ) @ 'LEQ' ) )
| ~ ( '0' @ s @ s @ s @ ( C @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ ( B @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ ( A @ f @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(4,axiom,
! [A: $i] : ( '0' @ s @ s @ s @ s @ ( A @ f @ 'E' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_6_04) ).
thf(20,plain,
! [A: $i] : ( '0' @ s @ s @ s @ s @ ( A @ f @ 'E' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(6,axiom,
! [B: $i,A: $i] : ( B @ ( A @ ( '0' @ s @ s @ s @ s @ 'AP' ) @ 'LEQ' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_11_06) ).
thf(22,plain,
! [B: $i,A: $i] : ( B @ ( A @ ( '0' @ s @ s @ s @ s @ 'AP' ) @ 'LEQ' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(3,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( '0' @ s @ s @ s @ s @ s @ ( F @ f @ 'E' ) )
| ~ ( '0' @ ( E @ f @ 'E' ) )
| ~ ( '0' @ s @ ( D @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ ( C @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ ( B @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ ( A @ f @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_5_03) ).
thf(18,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( '0' @ s @ s @ s @ s @ s @ ( F @ f @ 'E' ) )
| ~ ( '0' @ ( E @ f @ 'E' ) )
| ~ ( '0' @ s @ ( D @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ ( C @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ ( B @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ ( A @ f @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(2,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( '0' @ s @ s @ s @ s @ s @ s @ 'AP' ) @ ( E @ ( '0' @ s @ 'AP' ) @ 'LEQ' ) )
| ~ ( '0' @ s @ s @ ( D @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ ( C @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ ( B @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ ( A @ f @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_0_02) ).
thf(16,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( '0' @ s @ s @ s @ s @ s @ s @ 'AP' ) @ ( E @ ( '0' @ s @ 'AP' ) @ 'LEQ' ) )
| ~ ( '0' @ s @ s @ ( D @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ ( C @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ ( B @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ ( A @ f @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(11,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( '0' @ s @ s @ s @ 'AP' ) @ 'LEQ' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ ( B @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ ( A @ f @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_9_11) ).
thf(30,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( '0' @ s @ s @ s @ 'AP' ) @ 'LEQ' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ ( B @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ ( A @ f @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(10,axiom,
! [B: $i,A: $i] :
( ( '0' @ s @ s @ s @ ( B @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ ( B @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ ( A @ f @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1_10) ).
thf(28,plain,
! [B: $i,A: $i] :
( ( '0' @ s @ s @ s @ ( B @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ ( B @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ ( A @ f @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(5,axiom,
! [A: $i] : ( '0' @ s @ s @ s @ s @ s @ ( A @ f @ 'E' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_8_05) ).
thf(21,plain,
! [A: $i] : ( '0' @ s @ s @ s @ s @ s @ ( A @ f @ 'E' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(12,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( '0' @ s @ s @ ( D @ ( '0' @ s @ s @ s @ s @ s @ s @ 'AP' ) @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ ( C @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ ( B @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ ( A @ f @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_4_12) ).
thf(32,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( '0' @ s @ s @ ( D @ ( '0' @ s @ s @ s @ s @ s @ s @ 'AP' ) @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ ( C @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ ( B @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ ( A @ f @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(13,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( '0' @ s @ s @ s @ s @ s @ s @ 'AP' ) @ ( F @ ( '0' @ 'AP' ) @ 'LEQ' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ ( E @ f @ 'E' ) )
| ~ ( '0' @ s @ ( D @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ ( C @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ ( B @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ ( A @ f @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_10_13) ).
thf(34,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( '0' @ s @ s @ s @ s @ s @ s @ 'AP' ) @ ( F @ ( '0' @ 'AP' ) @ 'LEQ' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ ( E @ f @ 'E' ) )
| ~ ( '0' @ s @ ( D @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ ( C @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ ( B @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ ( A @ f @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(9,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( '0' @ s @ ( E @ ( '0' @ s @ s @ s @ s @ s @ s @ 'AP' ) @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ ( D @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ ( C @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ ( B @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ ( A @ f @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_12_09) ).
thf(26,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( '0' @ s @ ( E @ ( '0' @ s @ s @ s @ s @ s @ s @ 'AP' ) @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ ( D @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ ( C @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ ( B @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ ( A @ f @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(7,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( '0' @ ( F @ ( '0' @ s @ s @ s @ s @ s @ s @ 'AP' ) @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ ( E @ f @ 'E' ) )
| ~ ( '0' @ s @ ( D @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ ( C @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ ( B @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ ( A @ f @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_2_07) ).
thf(23,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( '0' @ ( F @ ( '0' @ s @ s @ s @ s @ s @ s @ 'AP' ) @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ ( E @ f @ 'E' ) )
| ~ ( '0' @ s @ ( D @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ ( C @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ ( B @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ ( A @ f @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(36,plain,
$false,
inference(e,[status(thm)],[25,14,20,22,18,16,30,28,21,32,34,26,23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SYO633-1 : TPTP v9.3.1. Released v7.1.0.
% 0.00/0.11 % 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
% 0.20/0.46 % Computer : n016.cluster.edu
% 0.20/0.46 % Model : x86_64 x86_64
% 0.20/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.46 % Memory : 8046.5625MB
% 0.20/0.46 % OS : Linux 6.8.0-71-generic
% 0.20/0.46 % CPULimit : 300
% 0.20/0.46 % WCLimit : 300
% 0.20/0.46 % DateTime : Sat Sep 26 19:45:30 UTC 2026
% 0.20/0.46 % CPUTime :
% 0.20/0.46 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
% 1.29/1.28 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.82/1.58 % [INFO] Parsing done (288ms).
% 1.82/1.60 % [INFO] Running in sequential loop mode.
% 3.06/2.20 % [INFO] eprover registered as external prover.
% 3.06/2.21 % [INFO] Scanning for conjecture ...
% 3.26/2.30 % [INFO] 13 axioms and no conjecture found.
% 3.46/2.44 % [INFO] Problem is propositional (TPTP CNF).
% 3.46/2.44 % [INFO] Type checking passed.
% 3.46/2.45 % [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 ...
% 5.96/3.46 % External prover 'e' found a proof!
% 5.96/3.46 % [INFO] Killing All external provers ...
% 5.96/3.46 % Time passed: 2793ms (effective reasoning time: 1852ms)
% 5.96/3.46 % Axioms used in derivation (13): clause_12_09, clause_0_02, clause_4_12, clause_5_03, clause_2_07, clause_3_01, clause_6_04, clause_1_10, clause_10_13, clause_9_11, clause_7_08, clause_11_06, clause_8_05
% 5.96/3.46 % No. of inferences in proof: 27
% 5.96/3.46 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2793 ms resp. 1852 ms w/o parsing
% 6.21/3.56 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.21/3.56 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------