TSTP Solution File: NUN066+2 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : NUN066+2 : TPTP v8.1.2. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n009.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 3.41s 1.89s
% Output : Refutation 3.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 16
% Syntax : Number of formulae : 30 ( 1 unt; 4 typ; 0 def)
% Number of atoms : 107 ( 40 equ; 0 cnn)
% Maximal formula atoms : 6 ( 4 avg)
% Number of connectives : 263 ( 48 ~; 32 |; 49 &; 134 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 4 usr; 1 con; 0-3 aty)
% Number of variables : 101 ( 0 ^; 58 !; 43 ?; 101 :)
% Comments :
%------------------------------------------------------------------------------
thf(r1_type,type,
r1: $i > $o ).
thf(r2_type,type,
r2: $i > $i > $o ).
thf(r3_type,type,
r3: $i > $i > $i > $o ).
thf(r4_type,type,
r4: $i > $i > $i > $o ).
thf(1,conjecture,
? [A: $i] :
( ! [B: $i] :
( ! [C: $i] :
( ! [D: $i] :
( ~ ( r1 @ D )
| ~ ( r2 @ D @ C ) )
| ~ ( r2 @ C @ B ) )
| ( A != B ) )
& ! [B: $i] :
( ~ ( r1 @ B )
| ( A != B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonzerononetwoexist) ).
thf(2,negated_conjecture,
~ ? [A: $i] :
( ! [B: $i] :
( ! [C: $i] :
( ! [D: $i] :
( ~ ( r1 @ D )
| ~ ( r2 @ D @ C ) )
| ~ ( r2 @ C @ B ) )
| ( A != B ) )
& ! [B: $i] :
( ~ ( r1 @ B )
| ( A != B ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(14,plain,
~ ? [A: $i] :
( ! [B: $i] :
( ! [C: $i] :
( ! [D: $i] :
( ~ ( r1 @ D )
| ~ ( r2 @ D @ C ) )
| ~ ( r2 @ C @ B ) )
| ( A != B ) )
& ! [B: $i] :
( ~ ( r1 @ B )
| ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(12,axiom,
! [A: $i] :
( ? [B: $i] :
( ( r1 @ B )
& ( A = B ) )
| ? [B: $i,C: $i] :
( ( r2 @ B @ C )
& ( A = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_6a) ).
thf(92,plain,
! [A: $i] :
( ? [B: $i] :
( ( r1 @ B )
& ( A = B ) )
| ? [B: $i,C: $i] :
( ( r2 @ B @ C )
& ( A = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(6,axiom,
! [A: $i,B: $i] :
? [C: $i] :
! [D: $i] :
( ( ~ ( r4 @ A @ B @ D )
& ( D != C ) )
| ( ( r4 @ A @ B @ D )
& ( D = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4) ).
thf(53,plain,
! [A: $i,B: $i] :
? [C: $i] :
! [D: $i] :
( ( ~ ( r4 @ A @ B @ D )
& ( D != C ) )
| ( ( r4 @ A @ B @ D )
& ( D = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ! [D: $i] :
( ~ ( r2 @ A @ D )
| ( D != C ) )
| ~ ( r2 @ B @ C ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_3a) ).
thf(77,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ! [D: $i] :
( ~ ( r2 @ A @ D )
| ( D != C ) )
| ~ ( r2 @ B @ C ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(11,axiom,
! [A: $i] :
? [B: $i] :
( ? [C: $i] :
( ( r1 @ C )
& ( r4 @ A @ C @ B ) )
& ? [C: $i] :
( ( r1 @ C )
& ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_5a) ).
thf(86,plain,
! [A: $i] :
? [B: $i] :
( ? [C: $i] :
( ( r1 @ C )
& ( r4 @ A @ C @ B ) )
& ? [C: $i] :
( ( r1 @ C )
& ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(10,axiom,
! [A: $i] :
? [B: $i] :
( ? [C: $i] :
( ( r1 @ C )
& ( r3 @ A @ C @ B ) )
& ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4a) ).
thf(81,plain,
! [A: $i] :
? [B: $i] :
( ? [C: $i] :
( ( r1 @ C )
& ( r3 @ A @ C @ B ) )
& ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(7,axiom,
! [A: $i,B: $i] :
? [C: $i] :
( ? [D: $i] :
( ? [E: $i] :
( ( r2 @ B @ E )
& ( r3 @ A @ E @ D ) )
& ( D = C ) )
& ? [D: $i] :
( ( r2 @ D @ C )
& ( r3 @ A @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1a) ).
thf(63,plain,
! [A: $i,B: $i] :
? [C: $i] :
( ? [D: $i] :
( ? [E: $i] :
( ( r2 @ B @ E )
& ( r3 @ A @ E @ D ) )
& ( D = C ) )
& ? [D: $i] :
( ( r2 @ D @ C )
& ( r3 @ A @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(5,axiom,
! [A: $i,B: $i] :
? [C: $i] :
! [D: $i] :
( ( ~ ( r3 @ A @ B @ D )
& ( D != C ) )
| ( ( r3 @ A @ B @ D )
& ( D = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_3) ).
thf(43,plain,
! [A: $i,B: $i] :
? [C: $i] :
! [D: $i] :
( ( ~ ( r3 @ A @ B @ D )
& ( D != C ) )
| ( ( r3 @ A @ B @ D )
& ( D = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(3,axiom,
? [A: $i] :
! [B: $i] :
( ( ~ ( r1 @ B )
& ( B != A ) )
| ( ( r1 @ B )
& ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1) ).
thf(23,plain,
? [A: $i] :
! [B: $i] :
( ( ~ ( r1 @ B )
& ( B != A ) )
| ( ( r1 @ B )
& ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ~ ( r1 @ C )
| ( C != B ) )
| ~ ( r2 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_7a) ).
thf(100,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ~ ( r1 @ C )
| ( C != B ) )
| ~ ( r2 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(8,axiom,
! [A: $i,B: $i] :
? [C: $i] :
( ? [D: $i] :
( ? [E: $i] :
( ( r2 @ B @ E )
& ( r4 @ A @ E @ D ) )
& ( D = C ) )
& ? [D: $i] :
( ( r3 @ D @ A @ C )
& ( r4 @ A @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2a) ).
thf(70,plain,
! [A: $i,B: $i] :
? [C: $i] :
( ? [D: $i] :
( ? [E: $i] :
( ( r2 @ B @ E )
& ( r4 @ A @ E @ D ) )
& ( D = C ) )
& ? [D: $i] :
( ( r3 @ D @ A @ C )
& ( r4 @ A @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(4,axiom,
! [A: $i] :
? [B: $i] :
! [C: $i] :
( ( ~ ( r2 @ A @ C )
& ( C != B ) )
| ( ( r2 @ A @ C )
& ( C = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2) ).
thf(33,plain,
! [A: $i] :
? [B: $i] :
! [C: $i] :
( ( ~ ( r2 @ A @ C )
& ( C != B ) )
| ( ( r2 @ A @ C )
& ( C = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(104,plain,
$false,
inference(e,[status(thm)],[14,92,53,77,86,81,63,43,23,100,70,33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14 % Problem : NUN066+2 : TPTP v8.1.2. Released v7.3.0.
% 0.14/0.17 % Command : run_Leo-III %s %d
% 0.18/0.38 % Computer : n009.cluster.edu
% 0.18/0.38 % Model : x86_64 x86_64
% 0.18/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.38 % Memory : 8042.1875MB
% 0.18/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.38 % CPULimit : 300
% 0.18/0.38 % WCLimit : 300
% 0.18/0.39 % DateTime : Thu May 18 21:11:48 EDT 2023
% 0.18/0.39 % CPUTime :
% 0.98/0.89 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.43/1.03 % [INFO] Parsing done (136ms).
% 1.43/1.04 % [INFO] Running in sequential loop mode.
% 1.83/1.26 % [INFO] eprover registered as external prover.
% 1.83/1.26 % [INFO] cvc4 registered as external prover.
% 1.88/1.27 % [INFO] Scanning for conjecture ...
% 2.01/1.32 % [INFO] Found a conjecture and 11 axioms. Running axiom selection ...
% 2.10/1.35 % [INFO] Axiom selection finished. Selected 11 axioms (removed 0 axioms).
% 2.10/1.38 % [INFO] Problem is first-order (TPTP FOF).
% 2.10/1.39 % [INFO] Type checking passed.
% 2.10/1.39 % [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 ...
% 3.41/1.89 % External prover 'e' found a proof!
% 3.41/1.89 % [INFO] Killing All external provers ...
% 3.41/1.89 % Time passed: 1344ms (effective reasoning time: 846ms)
% 3.41/1.89 % 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)>
% 3.41/1.89 % Axioms used in derivation (11): axiom_1a, axiom_4a, axiom_2, axiom_3, axiom_7a, axiom_6a, axiom_3a, axiom_4, axiom_1, axiom_2a, axiom_5a
% 3.41/1.89 % No. of inferences in proof: 26
% 3.41/1.89 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1344 ms resp. 846 ms w/o parsing
% 3.83/1.98 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.83/1.98 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------