TSTP Solution File: TOP053-1 by Leo-III---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : TOP053-1 : TPTP v8.1.2. Released v8.1.0.
% 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 : Tue May 7 08:36:35 EDT 2024
% Result : Unsatisfiable 2.82s 1.88s
% Output : Refutation 3.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 36
% Syntax : Number of formulae : 56 ( 39 unt; 17 typ; 0 def)
% Number of atoms : 39 ( 38 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 150 ( 2 ~; 0 |; 0 &; 148 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 16 ( 16 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 17 usr; 16 con; 0-14 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 > $i > $i > $i > $i ).
thf(a1_type,type,
a1: $i ).
thf(a2_type,type,
a2: $i ).
thf(a3_type,type,
a3: $i ).
thf(a4_type,type,
a4: $i ).
thf(a5_type,type,
a5: $i ).
thf(a6_type,type,
a6: $i ).
thf(a7_type,type,
a7: $i ).
thf(a8_type,type,
a8: $i ).
thf(a9_type,type,
a9: $i ).
thf(a10_type,type,
a10: $i ).
thf(a11_type,type,
a11: $i ).
thf(a12_type,type,
a12: $i ).
thf(a13_type,type,
a13: $i ).
thf(a14_type,type,
a14: $i ).
thf(a15_type,type,
a15: $i ).
thf(product_type,type,
product: $i > $i > $i ).
thf(7,axiom,
( ( product @ a5 @ a6 )
= a7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_04) ).
thf(33,plain,
( ( product @ a5 @ a6 )
= a7 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(17,axiom,
( ( product @ a8 @ a2 )
= a9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_06) ).
thf(53,plain,
( ( product @ a8 @ a2 )
= a9 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(11,axiom,
( ( product @ a9 @ a1 )
= a10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_07) ).
thf(41,plain,
( ( product @ a9 @ a1 )
= a10 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(13,axiom,
( ( product @ a13 @ a8 )
= a6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_10) ).
thf(45,plain,
( ( product @ a13 @ a8 )
= a6 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( product @ ( product @ A @ B ) @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutory_quandle_01) ).
thf(27,plain,
! [B: $i,A: $i] :
( ( product @ ( product @ A @ B ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(15,axiom,
( ( product @ a2 @ a12 )
= a14 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_12) ).
thf(49,plain,
( ( product @ a2 @ a12 )
= a14 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(10,axiom,
( ( product @ a7 @ a3 )
= a8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_05) ).
thf(39,plain,
( ( product @ a7 @ a3 )
= a8 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(8,axiom,
( ( product @ a15 @ a8 )
= a4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_14) ).
thf(35,plain,
( ( product @ a15 @ a8 )
= a4 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(6,axiom,
( ( product @ a10 @ a11 )
= a12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_08) ).
thf(31,plain,
( ( product @ a10 @ a11 )
= a12 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(12,axiom,
( ( product @ a3 @ a4 )
= a5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_03) ).
thf(43,plain,
( ( product @ a3 @ a4 )
= a5 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(16,axiom,
( ( product @ a6 @ a7 )
= a2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_11) ).
thf(51,plain,
( ( product @ a6 @ a7 )
= a2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(14,axiom,
( ( product @ a14 @ a3 )
= a15 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_13) ).
thf(47,plain,
( ( product @ a14 @ a3 )
= a15 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(9,axiom,
( ( product @ a4 @ a7 )
= a11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_15) ).
thf(37,plain,
( ( product @ a4 @ a7 )
= a11 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(3,axiom,
! [C: $i,B: $i,A: $i] :
( ( product @ ( product @ A @ B ) @ C )
= ( product @ ( product @ A @ C ) @ ( product @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutory_quandle_02) ).
thf(25,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)],[3]) ).
thf(1,negated_conjecture,
( ( tuple @ a1 @ a2 @ a3 @ a4 @ a5 @ a6 @ a7 @ a8 @ a9 @ a10 @ a11 @ a12 @ a13 @ a14 )
!= ( tuple @ a2 @ a3 @ a4 @ a5 @ a6 @ a7 @ a8 @ a9 @ a10 @ a11 @ a12 @ a13 @ a14 @ a15 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal) ).
thf(20,plain,
( ( tuple @ a1 @ a2 @ a3 @ a4 @ a5 @ a6 @ a7 @ a8 @ a9 @ a10 @ a11 @ a12 @ a13 @ a14 )
!= ( tuple @ a2 @ a3 @ a4 @ a5 @ a6 @ a7 @ a8 @ a9 @ a10 @ a11 @ a12 @ a13 @ a14 @ a15 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(19,axiom,
( ( product @ a11 @ a10 )
= a1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_16) ).
thf(57,plain,
( ( product @ a11 @ a10 )
= a1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(5,axiom,
( ( product @ a12 @ a3 )
= a13 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_09) ).
thf(29,plain,
( ( product @ a12 @ a3 )
= a13 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(18,axiom,
( ( product @ a1 @ a2 )
= a3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot) ).
thf(55,plain,
( ( product @ a1 @ a2 )
= a3 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(2,axiom,
! [A: $i] :
( ( product @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutory_quandle) ).
thf(23,plain,
! [A: $i] :
( ( product @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(63,plain,
$false,
inference(e,[status(thm)],[33,53,41,45,27,49,39,35,31,43,51,47,37,25,20,57,29,55,23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : TOP053-1 : TPTP v8.1.2. Released v8.1.0.
% 0.17/0.18 % Command : run_Leo-III %s %d
% 0.18/0.39 % Computer : n009.cluster.edu
% 0.18/0.39 % Model : x86_64 x86_64
% 0.18/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.39 % Memory : 8042.1875MB
% 0.18/0.39 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.40 % CPULimit : 300
% 0.18/0.40 % WCLimit : 300
% 0.18/0.40 % DateTime : Mon May 6 13:49:09 EDT 2024
% 0.18/0.40 % CPUTime :
% 1.00/0.96 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.29/1.10 % [INFO] Parsing done (133ms).
% 1.29/1.10 % [INFO] Running in sequential loop mode.
% 1.65/1.35 % [INFO] eprover registered as external prover.
% 1.65/1.35 % [INFO] cvc4 registered as external prover.
% 1.65/1.36 % [INFO] Scanning for conjecture ...
% 1.78/1.42 % [INFO] Found a conjecture and 18 axioms. Running axiom selection ...
% 2.00/1.46 % [INFO] Axiom selection finished. Selected 18 axioms (removed 0 axioms).
% 2.00/1.47 % [INFO] Problem is propositional (TPTP CNF).
% 2.00/1.48 % [INFO] Type checking passed.
% 2.00/1.48 % [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 ...
% 2.82/1.87 % External prover 'e' found a proof!
% 2.82/1.87 % [INFO] Killing All external provers ...
% 2.82/1.87 % Time passed: 1321ms (effective reasoning time: 765ms)
% 2.82/1.87 % 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)>
% 2.82/1.88 % Axioms used in derivation (18): knot_07, involutory_quandle, knot_03, knot_12, knot_13, knot_08, involutory_quandle_02, involutory_quandle_01, knot_04, knot_15, knot_10, knot_14, knot_11, knot_06, knot_05, knot_16, knot, knot_09
% 2.82/1.88 % No. of inferences in proof: 39
% 2.82/1.88 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1321 ms resp. 765 ms w/o parsing
% 3.17/1.95 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.17/1.95 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------