TSTP Solution File: TOP051-1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : TOP051-1 : TPTP v8.1.2. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n022.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 12:39:01 EDT 2023
% Result : Unsatisfiable 2.68s 1.63s
% Output : Refutation 2.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 27
% Syntax : Number of formulae : 42 ( 29 unt; 13 typ; 0 def)
% Number of atoms : 29 ( 28 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 114 ( 2 ~; 0 |; 0 &; 112 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 13 usr; 12 con; 0-10 aty)
% Number of variables : 12 ( 0 ^; 12 !; 0 ?; 12 :)
% Comments :
%------------------------------------------------------------------------------
thf(tuple_type,type,
tuple: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i ).
thf(a1_type,type,
a1: $i ).
thf(a6_type,type,
a6: $i ).
thf(a5_type,type,
a5: $i ).
thf(a2_type,type,
a2: $i ).
thf(a7_type,type,
a7: $i ).
thf(a3_type,type,
a3: $i ).
thf(a4_type,type,
a4: $i ).
thf(a9_type,type,
a9: $i ).
thf(a10_type,type,
a10: $i ).
thf(a8_type,type,
a8: $i ).
thf(a11_type,type,
a11: $i ).
thf(product_type,type,
product: $i > $i > $i ).
thf(3,axiom,
! [B: $i,A: $i] :
( ( product @ ( product @ A @ B ) @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutory_quandle_01) ).
thf(20,plain,
! [B: $i,A: $i] :
( ( product @ ( product @ A @ B ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(4,axiom,
! [C: $i,B: $i,A: $i] :
( ( product @ ( product @ A @ B ) @ C )
= ( product @ ( product @ A @ C ) @ ( product @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutory_quandle_02) ).
thf(22,plain,
! [C: $i,B: $i,A: $i] :
( ( product @ ( product @ A @ B ) @ C )
= ( product @ ( product @ A @ C ) @ ( product @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(2,axiom,
! [A: $i] :
( ( product @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutory_quandle) ).
thf(18,plain,
! [A: $i] :
( ( product @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(1,negated_conjecture,
( ( tuple @ a1 @ a6 @ a5 @ a2 @ a7 @ a3 @ a4 @ a9 @ a10 @ a8 )
!= ( tuple @ a2 @ a7 @ a6 @ a3 @ a8 @ a4 @ a5 @ a10 @ a11 @ a9 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal) ).
thf(15,plain,
( ( tuple @ a1 @ a6 @ a5 @ a2 @ a7 @ a3 @ a4 @ a9 @ a10 @ a8 )
!= ( tuple @ a2 @ a7 @ a6 @ a3 @ a8 @ a4 @ a5 @ a10 @ a11 @ a9 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(14,axiom,
( ( product @ a10 @ a5 )
= a11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_11) ).
thf(42,plain,
( ( product @ a10 @ a5 )
= a11 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(5,axiom,
( ( product @ a1 @ a6 )
= a2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot) ).
thf(24,plain,
( ( product @ a1 @ a6 )
= a2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(7,axiom,
( ( product @ a3 @ a1 )
= a4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_04) ).
thf(28,plain,
( ( product @ a3 @ a1 )
= a4 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(12,axiom,
( ( product @ a8 @ a6 )
= a9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_09) ).
thf(38,plain,
( ( product @ a8 @ a6 )
= a9 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(9,axiom,
( ( product @ a5 @ a9 )
= a6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_06) ).
thf(32,plain,
( ( product @ a5 @ a9 )
= a6 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(10,axiom,
( ( product @ a6 @ a2 )
= a7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_07) ).
thf(34,plain,
( ( product @ a6 @ a2 )
= a7 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(13,axiom,
( ( product @ a9 @ a4 )
= a10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_10) ).
thf(40,plain,
( ( product @ a9 @ a4 )
= a10 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(6,axiom,
( ( product @ a2 @ a7 )
= a3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_03) ).
thf(26,plain,
( ( product @ a2 @ a7 )
= a3 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(11,axiom,
( ( product @ a7 @ a3 )
= a8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_08) ).
thf(36,plain,
( ( product @ a7 @ a3 )
= a8 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(8,axiom,
( ( product @ a4 @ a10 )
= a5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knot_05) ).
thf(30,plain,
( ( product @ a4 @ a10 )
= a5 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(56,plain,
$false,
inference(e,[status(thm)],[20,22,18,15,42,24,28,38,32,34,40,26,36,30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : TOP051-1 : TPTP v8.1.2. Released v8.1.0.
% 0.07/0.16 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n022.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Thu May 18 20:09:48 EDT 2023
% 0.16/0.37 % CPUTime :
% 0.96/0.87 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.13/0.98 % [INFO] Parsing done (117ms).
% 1.13/0.99 % [INFO] Running in sequential loop mode.
% 1.61/1.19 % [INFO] eprover registered as external prover.
% 1.61/1.19 % [INFO] cvc4 registered as external prover.
% 1.61/1.20 % [INFO] Scanning for conjecture ...
% 1.82/1.25 % [INFO] Found a conjecture and 13 axioms. Running axiom selection ...
% 1.82/1.27 % [INFO] Axiom selection finished. Selected 13 axioms (removed 0 axioms).
% 1.94/1.28 % [INFO] Problem is propositional (TPTP CNF).
% 1.94/1.29 % [INFO] Type checking passed.
% 1.94/1.29 % [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 ...
% 2.68/1.62 % External prover 'e' found a proof!
% 2.68/1.62 % [INFO] Killing All external provers ...
% 2.68/1.62 % Time passed: 1089ms (effective reasoning time: 628ms)
% 2.68/1.62 % 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)>
% 2.68/1.62 % Axioms used in derivation (13): knot_07, knot_10, involutory_quandle, knot_03, knot_05, knot_08, involutory_quandle_02, involutory_quandle_01, knot_04, knot_11, knot_06, knot, knot_09
% 2.68/1.62 % No. of inferences in proof: 29
% 2.68/1.63 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1089 ms resp. 628 ms w/o parsing
% 2.68/1.65 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.68/1.65 % [INFO] Killing All external provers ...
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