TSTP Solution File: NUN066+1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : NUN066+1 : TPTP v8.1.2. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n010.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 11:46:13 EDT 2023
% Result : Theorem 59.47s 10.07s
% Output : Refutation 59.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 24
% Syntax : Number of formulae : 45 ( 3 unt; 5 typ; 0 def)
% Number of atoms : 169 ( 0 equ; 0 cnn)
% Maximal formula atoms : 7 ( 4 avg)
% Number of connectives : 563 ( 88 ~; 64 |; 65 &; 346 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 5 usr; 1 con; 0-3 aty)
% Number of variables : 149 ( 0 ^; 106 !; 43 ?; 149 :)
% Comments :
%------------------------------------------------------------------------------
thf(r1_type,type,
r1: $i > $o ).
thf(r2_type,type,
r2: $i > $i > $o ).
thf(id_type,type,
id: $i > $i > $o ).
thf(r4_type,type,
r4: $i > $i > $i > $o ).
thf(r3_type,type,
r3: $i > $i > $i > $o ).
thf(10,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( id @ A @ D )
| ~ ( id @ B @ E )
| ~ ( id @ C @ F )
| ( ~ ( r3 @ A @ B @ C )
& ~ ( r3 @ D @ E @ F ) )
| ( ( r3 @ A @ B @ C )
& ( r3 @ D @ E @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_10) ).
thf(56,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( id @ A @ D )
| ~ ( id @ B @ E )
| ~ ( id @ C @ F )
| ( ~ ( r3 @ A @ B @ C )
& ~ ( r3 @ D @ E @ F ) )
| ( ( r3 @ A @ B @ C )
& ( r3 @ D @ E @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ! [D: $i] :
( ~ ( id @ D @ C )
| ~ ( r2 @ A @ D ) )
| ~ ( r2 @ B @ C ) )
| ( id @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_3a) ).
thf(52,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ! [D: $i] :
( ~ ( id @ D @ C )
| ~ ( r2 @ A @ D ) )
| ~ ( r2 @ B @ C ) )
| ( id @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ~ ( id @ A @ B )
| ( id @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_6) ).
thf(85,plain,
! [A: $i,B: $i] :
( ~ ( id @ A @ B )
| ( id @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(14,axiom,
! [A: $i,B: $i] :
? [C: $i] :
( ? [D: $i] :
( ( id @ D @ C )
& ? [E: $i] :
( ( r2 @ B @ E )
& ( r3 @ A @ E @ D ) ) )
& ? [D: $i] :
( ( r2 @ D @ C )
& ( r3 @ A @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1a) ).
thf(77,plain,
! [A: $i,B: $i] :
? [C: $i] :
( ? [D: $i] :
( ( id @ D @ C )
& ? [E: $i] :
( ( r2 @ B @ E )
& ( r3 @ A @ E @ D ) ) )
& ? [D: $i] :
( ( r2 @ D @ C )
& ( r3 @ A @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(4,axiom,
! [A: $i,B: $i] :
? [C: $i] :
( ? [D: $i] :
( ( id @ D @ C )
& ? [E: $i] :
( ( r2 @ B @ E )
& ( r4 @ A @ E @ D ) ) )
& ? [D: $i] :
( ( r3 @ D @ A @ C )
& ( r4 @ A @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2a) ).
thf(34,plain,
! [A: $i,B: $i] :
? [C: $i] :
( ? [D: $i] :
( ( id @ D @ C )
& ? [E: $i] :
( ( r2 @ B @ E )
& ( r4 @ A @ E @ D ) ) )
& ? [D: $i] :
( ( r3 @ D @ A @ C )
& ( r4 @ A @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ~ ( id @ C @ B )
| ~ ( r1 @ C ) )
| ~ ( r2 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_7a) ).
thf(54,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ~ ( id @ C @ B )
| ~ ( r1 @ C ) )
| ~ ( r2 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(20,axiom,
! [A: $i,B: $i] :
( ~ ( id @ A @ B )
| ( ~ ( r1 @ A )
& ~ ( r1 @ B ) )
| ( ( r1 @ A )
& ( r1 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_8) ).
thf(103,plain,
! [A: $i,B: $i] :
( ~ ( id @ A @ B )
| ( ~ ( r1 @ A )
& ~ ( r1 @ B ) )
| ( ( r1 @ A )
& ( r1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(7,axiom,
! [A: $i] :
? [B: $i] :
( ( id @ B @ A )
& ? [C: $i] :
( ( r1 @ C )
& ( r3 @ A @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4a) ).
thf(48,plain,
! [A: $i] :
? [B: $i] :
( ( id @ B @ A )
& ? [C: $i] :
( ( r1 @ C )
& ( r3 @ A @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(12,axiom,
! [A: $i] :
( ? [B: $i] :
( ( id @ A @ B )
& ( r1 @ B ) )
| ? [B: $i,C: $i] :
( ( id @ A @ C )
& ( r2 @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_6a) ).
thf(67,plain,
! [A: $i] :
( ? [B: $i] :
( ( id @ A @ B )
& ( r1 @ B ) )
| ? [B: $i,C: $i] :
( ( id @ A @ C )
& ( r2 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(17,axiom,
! [A: $i,B: $i] :
? [C: $i] :
! [D: $i] :
( ( ( id @ D @ C )
& ( r4 @ A @ B @ D ) )
| ( ~ ( r4 @ A @ B @ D )
& ~ ( id @ D @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4) ).
thf(87,plain,
! [A: $i,B: $i] :
? [C: $i] :
! [D: $i] :
( ( ( id @ D @ C )
& ( r4 @ A @ B @ D ) )
| ( ~ ( r4 @ A @ B @ D )
& ~ ( id @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( id @ A @ B )
| ( id @ A @ C )
| ~ ( id @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_7) ).
thf(40,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( id @ A @ B )
| ( id @ A @ C )
| ~ ( id @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(11,axiom,
! [A: $i] :
? [B: $i] :
! [C: $i] :
( ( ( id @ C @ B )
& ( r2 @ A @ C ) )
| ( ~ ( r2 @ A @ C )
& ~ ( id @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2) ).
thf(62,plain,
! [A: $i] :
? [B: $i] :
! [C: $i] :
( ( ( id @ C @ B )
& ( r2 @ A @ C ) )
| ( ~ ( r2 @ A @ C )
& ~ ( id @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(15,axiom,
! [A: $i] : ( id @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_5) ).
thf(83,plain,
! [A: $i] : ( id @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(3,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( id @ A @ D )
| ~ ( id @ B @ E )
| ~ ( id @ C @ F )
| ( ~ ( r4 @ A @ B @ C )
& ~ ( r4 @ D @ E @ F ) )
| ( ( r4 @ A @ B @ C )
& ( r4 @ D @ E @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_11) ).
thf(28,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( id @ A @ D )
| ~ ( id @ B @ E )
| ~ ( id @ C @ F )
| ( ~ ( r4 @ A @ B @ C )
& ~ ( r4 @ D @ E @ F ) )
| ( ( r4 @ A @ B @ C )
& ( r4 @ D @ E @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(1,conjecture,
? [A: $i] :
( ! [B: $i] :
( ! [C: $i] :
( ! [D: $i] :
( ~ ( r1 @ D )
| ~ ( r2 @ D @ C ) )
| ~ ( r2 @ C @ B ) )
| ~ ( id @ A @ B ) )
& ! [B: $i] :
( ~ ( id @ A @ B )
| ~ ( r1 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonzerononetwoexistid) ).
thf(2,negated_conjecture,
~ ? [A: $i] :
( ! [B: $i] :
( ! [C: $i] :
( ! [D: $i] :
( ~ ( r1 @ D )
| ~ ( r2 @ D @ C ) )
| ~ ( r2 @ C @ B ) )
| ~ ( id @ A @ B ) )
& ! [B: $i] :
( ~ ( id @ A @ B )
| ~ ( r1 @ B ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(21,plain,
~ ? [A: $i] :
( ! [B: $i] :
( ! [C: $i] :
( ! [D: $i] :
( ~ ( r1 @ D )
| ~ ( r2 @ D @ C ) )
| ~ ( r2 @ C @ B ) )
| ~ ( id @ A @ B ) )
& ! [B: $i] :
( ~ ( id @ A @ B )
| ~ ( r1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(18,axiom,
! [A: $i,B: $i] :
? [C: $i] :
! [D: $i] :
( ( ( id @ D @ C )
& ( r3 @ A @ B @ D ) )
| ( ~ ( r3 @ A @ B @ D )
& ~ ( id @ D @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_3) ).
thf(92,plain,
! [A: $i,B: $i] :
? [C: $i] :
! [D: $i] :
( ( ( id @ D @ C )
& ( r3 @ A @ B @ D ) )
| ( ~ ( r3 @ A @ B @ D )
& ~ ( id @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(19,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( id @ A @ C )
| ~ ( id @ B @ D )
| ( ~ ( r2 @ A @ B )
& ~ ( r2 @ C @ D ) )
| ( ( r2 @ A @ B )
& ( r2 @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_9) ).
thf(97,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( id @ A @ C )
| ~ ( id @ B @ D )
| ( ~ ( r2 @ A @ B )
& ~ ( r2 @ C @ D ) )
| ( ( r2 @ A @ B )
& ( r2 @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(13,axiom,
! [A: $i] :
? [B: $i] :
( ? [C: $i] :
( ( r1 @ C )
& ( r4 @ A @ C @ B ) )
& ? [C: $i] :
( ( id @ B @ C )
& ( r1 @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_5a) ).
thf(72,plain,
! [A: $i] :
? [B: $i] :
( ? [C: $i] :
( ( r1 @ C )
& ( r4 @ A @ C @ B ) )
& ? [C: $i] :
( ( id @ B @ C )
& ( r1 @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(6,axiom,
? [A: $i] :
! [B: $i] :
( ( ( id @ B @ A )
& ( r1 @ B ) )
| ( ~ ( r1 @ B )
& ~ ( id @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1) ).
thf(43,plain,
? [A: $i] :
! [B: $i] :
( ( ( id @ B @ A )
& ( r1 @ B ) )
| ( ~ ( r1 @ B )
& ~ ( id @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(18805,plain,
$false,
inference(e,[status(thm)],[56,52,85,77,34,54,103,48,67,87,40,62,83,28,21,92,97,72,43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : NUN066+1 : TPTP v8.1.2. Released v7.3.0.
% 0.03/0.15 % Command : run_Leo-III %s %d
% 0.14/0.35 % Computer : n010.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 21:02:13 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.98/0.88 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.20/1.02 % [INFO] Parsing done (139ms).
% 1.20/1.03 % [INFO] Running in sequential loop mode.
% 1.82/1.23 % [INFO] eprover registered as external prover.
% 1.82/1.23 % [INFO] cvc4 registered as external prover.
% 1.82/1.23 % [INFO] Scanning for conjecture ...
% 1.90/1.29 % [INFO] Found a conjecture and 18 axioms. Running axiom selection ...
% 2.11/1.33 % [INFO] Axiom selection finished. Selected 18 axioms (removed 0 axioms).
% 2.11/1.37 % [INFO] Problem is first-order (TPTP FOF).
% 2.11/1.37 % [INFO] Type checking passed.
% 2.33/1.37 % [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 ...
% 59.47/10.07 % External prover 'e' found a proof!
% 59.47/10.07 % [INFO] Killing All external provers ...
% 59.47/10.07 % Time passed: 9558ms (effective reasoning time: 9034ms)
% 59.47/10.07 % 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)>
% 59.47/10.07 % Axioms used in derivation (18): axiom_7, axiom_10, axiom_1a, axiom_4a, axiom_2, axiom_6, axiom_3, axiom_7a, axiom_8, axiom_6a, axiom_5, axiom_3a, axiom_11, axiom_9, axiom_4, axiom_1, axiom_2a, axiom_5a
% 59.47/10.07 % No. of inferences in proof: 40
% 59.47/10.07 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 9558 ms resp. 9034 ms w/o parsing
% 59.47/10.10 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 59.47/10.10 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------