TSTP Solution File: SYO633-1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SYO633-1 : TPTP v8.1.2. Released v7.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 12:36:44 EDT 2023
% Result : Unsatisfiable 3.03s 1.76s
% Output : Refutation 3.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 19
% Syntax : Number of formulae : 33 ( 9 unt; 6 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 : 8 ( 8 >; 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\'_type',type,
'\'E\'': $i > $i > $o ).
thf(f_type,type,
f: $i > $i ).
thf(s_type,type,
s: $i > $i ).
thf('\'0\'_type',type,
'\'0\'': $i ).
thf('\'LEQ\'_type',type,
'\'LEQ\'': $i > $i > $o ).
thf('\'AP\'_type',type,
'\'AP\'': $i > $i > $i ).
thf(8,axiom,
! [B: $i,A: $i] : ( '\'LEQ\'' @ ( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ A ) @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_7_08) ).
thf(25,plain,
! [B: $i,A: $i] : ( '\'LEQ\'' @ ( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ A ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(1,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ( '\'LEQ\'' @ ( '\'AP\'' @ ( s @ ( s @ '\'0\'' ) ) @ D ) @ ( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_3_01) ).
thf(14,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ( '\'LEQ\'' @ ( '\'AP\'' @ ( s @ ( s @ '\'0\'' ) ) @ D ) @ ( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(4,axiom,
! [A: $i] : ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_6_04) ).
thf(20,plain,
! [A: $i] : ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(6,axiom,
! [B: $i,A: $i] : ( '\'LEQ\'' @ ( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ A ) @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_11_06) ).
thf(22,plain,
! [B: $i,A: $i] : ( '\'LEQ\'' @ ( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ A ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(3,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( f @ E ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( f @ F ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ),
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] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( f @ E ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( f @ F ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(2,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( s @ ( s @ '\'0\'' ) ) )
| ( '\'LEQ\'' @ ( '\'AP\'' @ ( s @ '\'0\'' ) @ E ) @ ( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) @ 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\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( s @ ( s @ '\'0\'' ) ) )
| ( '\'LEQ\'' @ ( '\'AP\'' @ ( s @ '\'0\'' ) @ E ) @ ( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(11,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
| ( '\'LEQ\'' @ ( '\'AP\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_9_11) ).
thf(30,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
| ( '\'LEQ\'' @ ( '\'AP\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(10,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1_10) ).
thf(28,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(5,axiom,
! [A: $i] : ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_8_05) ).
thf(21,plain,
! [A: $i] : ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(12,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ( '\'E\'' @ ( f @ ( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) @ D ) ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_4_12) ).
thf(32,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ( '\'E\'' @ ( f @ ( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) @ D ) ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(13,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( f @ E ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
| ( '\'LEQ\'' @ ( '\'AP\'' @ '\'0\'' @ F ) @ ( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) @ F ) ) ),
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] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( f @ E ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
| ( '\'LEQ\'' @ ( '\'AP\'' @ '\'0\'' @ F ) @ ( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(9,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( s @ ( s @ '\'0\'' ) ) )
| ( '\'E\'' @ ( f @ ( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) @ E ) ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_12_09) ).
thf(26,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( s @ ( s @ '\'0\'' ) ) )
| ( '\'E\'' @ ( f @ ( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) @ E ) ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(7,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( f @ E ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
| ( '\'E\'' @ ( f @ ( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) @ F ) ) @ '\'0\'' ) ),
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] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( f @ E ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
| ( '\'E\'' @ ( f @ ( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) @ F ) ) @ '\'0\'' ) ),
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
% 0.03/0.11 % Problem : SYO633-1 : TPTP v8.1.2. Released v7.1.0.
% 0.14/0.14 % Command : run_Leo-III %s %d
% 0.14/0.35 % Computer : n006.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu May 18 18:04:37 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.97/0.87 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.13/1.02 % [INFO] Parsing done (141ms).
% 1.35/1.03 % [INFO] Running in sequential loop mode.
% 1.74/1.23 % [INFO] eprover registered as external prover.
% 1.74/1.23 % [INFO] cvc4 registered as external prover.
% 1.74/1.23 % [INFO] Scanning for conjecture ...
% 1.78/1.27 % [INFO] 13 axioms and no conjecture found.
% 1.99/1.32 % [INFO] Problem is propositional (TPTP CNF).
% 1.99/1.33 % [INFO] Type checking passed.
% 1.99/1.33 % [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 ...
% 3.03/1.75 % External prover 'e' found a proof!
% 3.03/1.76 % [INFO] Killing All external provers ...
% 3.03/1.76 % Time passed: 1246ms (effective reasoning time: 726ms)
% 3.03/1.76 % 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
% 3.03/1.76 % No. of inferences in proof: 27
% 3.03/1.76 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1246 ms resp. 726 ms w/o parsing
% 3.61/1.81 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.61/1.81 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------