TSTP Solution File: TOP050-1 by Leo-III---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : TOP050-1 : 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 08:36:34 EDT 2024
% Result : Unsatisfiable 3.27s 1.88s
% Output : Refutation 3.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 69
% Syntax : Number of formulae : 105 ( 71 unt; 34 typ; 0 def)
% Number of atoms : 71 ( 70 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 282 ( 2 ~; 0 |; 0 &; 280 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 33 ( 33 >; 0 *; 0 +; 0 <<)
% Number of symbols : 36 ( 34 usr; 33 con; 0-31 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 > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i ).
thf(a1_type,type,
a1: $i ).
thf(a30_type,type,
a30: $i ).
thf(a31_type,type,
a31: $i ).
thf(a2_type,type,
a2: $i ).
thf(a24_type,type,
a24: $i ).
thf(a25_type,type,
a25: $i ).
thf(a3_type,type,
a3: $i ).
thf(a28_type,type,
a28: $i ).
thf(a29_type,type,
a29: $i ).
thf(a4_type,type,
a4: $i ).
thf(a10_type,type,
a10: $i ).
thf(a11_type,type,
a11: $i ).
thf(a5_type,type,
a5: $i ).
thf(a14_type,type,
a14: $i ).
thf(a15_type,type,
a15: $i ).
thf(a6_type,type,
a6: $i ).
thf(a7_type,type,
a7: $i ).
thf(a18_type,type,
a18: $i ).
thf(a19_type,type,
a19: $i ).
thf(a8_type,type,
a8: $i ).
thf(a9_type,type,
a9: $i ).
thf(a16_type,type,
a16: $i ).
thf(a17_type,type,
a17: $i ).
thf(a12_type,type,
a12: $i ).
thf(a13_type,type,
a13: $i ).
thf(a20_type,type,
a20: $i ).
thf(a21_type,type,
a21: $i ).
thf(a22_type,type,
a22: $i ).
thf(a23_type,type,
a23: $i ).
thf(a26_type,type,
a26: $i ).
thf(a27_type,type,
a27: $i ).
thf(a32_type,type,
a32: $i ).
thf(product_type,type,
product: $i > $i > $i ).
thf(25,axiom,
( ( product @ a24 @ a3 )
= a25 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_24) ).
thf(85,plain,
( ( product @ a24 @ a3 )
= a25 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(9,axiom,
( ( product @ a21 @ a25 )
= a22 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_21) ).
thf(53,plain,
( ( product @ a21 @ a25 )
= a22 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(21,axiom,
( ( product @ a4 @ a11 )
= a5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_05) ).
thf(77,plain,
( ( product @ a4 @ a11 )
= a5 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
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(41,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(5,axiom,
( ( product @ a10 @ a7 )
= a11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_10) ).
thf(45,plain,
( ( product @ a10 @ a7 )
= a11 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(12,axiom,
( ( product @ a32 @ a21 )
= a1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_32) ).
thf(59,plain,
( ( product @ a32 @ a21 )
= a1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(16,axiom,
( ( product @ a12 @ a19 )
= a13 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_12) ).
thf(67,plain,
( ( product @ a12 @ a19 )
= a13 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( product @ ( product @ A @ B ) @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutory_quandle_01) ).
thf(43,plain,
! [B: $i,A: $i] :
( ( product @ ( product @ A @ B ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(10,axiom,
( ( product @ a27 @ a21 )
= a28 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_27) ).
thf(55,plain,
( ( product @ a27 @ a21 )
= a28 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(20,axiom,
( ( product @ a29 @ a1 )
= a30 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_29) ).
thf(75,plain,
( ( product @ a29 @ a1 )
= a30 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(22,axiom,
( ( product @ a8 @ a5 )
= a9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_08) ).
thf(79,plain,
( ( product @ a8 @ a5 )
= a9 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(6,axiom,
( ( product @ a23 @ a21 )
= a24 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_23) ).
thf(47,plain,
( ( product @ a23 @ a21 )
= a24 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(24,axiom,
( ( product @ a5 @ a15 )
= a6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_06) ).
thf(83,plain,
( ( product @ a5 @ a15 )
= a6 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(17,axiom,
( ( product @ a31 @ a3 )
= a32 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_31) ).
thf(69,plain,
( ( product @ a31 @ a3 )
= a32 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(33,axiom,
( ( product @ a18 @ a15 )
= a19 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_18) ).
thf(101,plain,
( ( product @ a18 @ a15 )
= a19 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(29,axiom,
( ( product @ a13 @ a7 )
= a14 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_13) ).
thf(93,plain,
( ( product @ a13 @ a7 )
= a14 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(11,axiom,
( ( product @ a22 @ a31 )
= a23 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_22) ).
thf(57,plain,
( ( product @ a22 @ a31 )
= a23 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(13,axiom,
( ( product @ a19 @ a11 )
= a20 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_19) ).
thf(61,plain,
( ( product @ a19 @ a11 )
= a20 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(27,axiom,
( ( product @ a20 @ a29 )
= a21 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_20) ).
thf(89,plain,
( ( product @ a20 @ a29 )
= a21 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(15,axiom,
( ( product @ a15 @ a5 )
= a16 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_15) ).
thf(65,plain,
( ( product @ a15 @ a5 )
= a16 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(31,axiom,
( ( product @ a17 @ a9 )
= a18 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_17) ).
thf(97,plain,
( ( product @ a17 @ a9 )
= a18 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(19,axiom,
( ( product @ a26 @ a1 )
= a27 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_26) ).
thf(73,plain,
( ( product @ a26 @ a1 )
= a27 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(35,axiom,
( ( product @ a9 @ a17 )
= a10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_09) ).
thf(105,plain,
( ( product @ a9 @ a17 )
= a10 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(18,axiom,
( ( product @ a3 @ a29 )
= a4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_04) ).
thf(71,plain,
( ( product @ a3 @ a29 )
= a4 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(7,axiom,
( ( product @ a16 @ a19 )
= a17 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_16) ).
thf(49,plain,
( ( product @ a16 @ a19 )
= a17 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(23,axiom,
( ( product @ a11 @ a5 )
= a12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_11) ).
thf(81,plain,
( ( product @ a11 @ a5 )
= a12 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(2,axiom,
! [A: $i] :
( ( product @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutory_quandle) ).
thf(39,plain,
! [A: $i] :
( ( product @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(34,axiom,
( ( product @ a25 @ a23 )
= a26 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_25) ).
thf(103,plain,
( ( product @ a25 @ a23 )
= a26 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(28,axiom,
( ( product @ a30 @ a23 )
= a31 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_30) ).
thf(91,plain,
( ( product @ a30 @ a23 )
= a31 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(14,axiom,
( ( product @ a1 @ a31 )
= a2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot) ).
thf(63,plain,
( ( product @ a1 @ a31 )
= a2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(30,axiom,
( ( product @ a2 @ a25 )
= a3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_03) ).
thf(95,plain,
( ( product @ a2 @ a25 )
= a3 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(32,axiom,
( ( product @ a28 @ a3 )
= a29 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_28) ).
thf(99,plain,
( ( product @ a28 @ a3 )
= a29 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(26,axiom,
( ( product @ a7 @ a19 )
= a8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_07) ).
thf(87,plain,
( ( product @ a7 @ a19 )
= a8 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(1,negated_conjecture,
( ( tuple @ a1 @ a30 @ a31 @ a2 @ a24 @ a25 @ a3 @ a28 @ a29 @ a4 @ a10 @ a11 @ a5 @ a14 @ a15 @ a6 @ a7 @ a18 @ a19 @ a8 @ a9 @ a16 @ a17 @ a12 @ a13 @ a20 @ a21 @ a22 @ a23 @ a26 @ a27 )
!= ( tuple @ a2 @ a31 @ a32 @ a3 @ a25 @ a26 @ a4 @ a29 @ a30 @ a5 @ a11 @ a12 @ a6 @ a15 @ a16 @ a7 @ a8 @ a19 @ a20 @ a9 @ a10 @ a17 @ a18 @ a13 @ a14 @ a21 @ a22 @ a23 @ a24 @ a27 @ a28 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal) ).
thf(36,plain,
( ( tuple @ a1 @ a30 @ a31 @ a2 @ a24 @ a25 @ a3 @ a28 @ a29 @ a4 @ a10 @ a11 @ a5 @ a14 @ a15 @ a6 @ a7 @ a18 @ a19 @ a8 @ a9 @ a16 @ a17 @ a12 @ a13 @ a20 @ a21 @ a22 @ a23 @ a26 @ a27 )
!= ( tuple @ a2 @ a31 @ a32 @ a3 @ a25 @ a26 @ a4 @ a29 @ a30 @ a5 @ a11 @ a12 @ a6 @ a15 @ a16 @ a7 @ a8 @ a19 @ a20 @ a9 @ a10 @ a17 @ a18 @ a13 @ a14 @ a21 @ a22 @ a23 @ a24 @ a27 @ a28 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(8,axiom,
( ( product @ a14 @ a17 )
= a15 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_14) ).
thf(51,plain,
( ( product @ a14 @ a17 )
= a15 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(119,plain,
$false,
inference(e,[status(thm)],[85,53,77,41,45,59,67,43,55,75,79,47,83,69,101,93,57,61,89,65,97,73,105,71,49,81,39,103,91,63,95,99,87,36,51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : TOP050-1 : TPTP v8.1.2. Released v8.1.0.
% 0.15/0.17 % Command : run_Leo-III %s %d
% 0.17/0.38 % Computer : n009.cluster.edu
% 0.17/0.38 % Model : x86_64 x86_64
% 0.17/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.38 % Memory : 8042.1875MB
% 0.17/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.38 % CPULimit : 300
% 0.17/0.38 % WCLimit : 300
% 0.17/0.38 % DateTime : Mon May 6 13:46:39 EDT 2024
% 0.17/0.39 % CPUTime :
% 0.95/0.89 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.18/1.01 % [INFO] Parsing done (126ms).
% 1.18/1.02 % [INFO] Running in sequential loop mode.
% 1.59/1.24 % [INFO] eprover registered as external prover.
% 1.74/1.24 % [INFO] cvc4 registered as external prover.
% 1.74/1.25 % [INFO] Scanning for conjecture ...
% 1.92/1.31 % [INFO] Found a conjecture and 34 axioms. Running axiom selection ...
% 2.05/1.36 % [INFO] Axiom selection finished. Selected 34 axioms (removed 0 axioms).
% 2.05/1.38 % [INFO] Problem is propositional (TPTP CNF).
% 2.05/1.38 % [INFO] Type checking passed.
% 2.05/1.39 % [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 ...
% 3.27/1.88 % External prover 'e' found a proof!
% 3.27/1.88 % [INFO] Killing All external provers ...
% 3.27/1.88 % Time passed: 1332ms (effective reasoning time: 852ms)
% 3.27/1.88 % 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)>
% 3.27/1.88 % Axioms used in derivation (34): knot_19, knot_21, knot_29, knot_03, knot_12, knot_27, knot_23, knot_31, involutory_quandle_02, involutory_quandle_01, knot_04, knot_26, knot_18, knot_32, knot_07, knot_15, knot_10, knot_11, knot_06, knot_17, knot_14, knot_22, involutory_quandle, knot_25, knot_28, knot_30, knot_05, knot_16, knot, knot_09, knot_24, knot_13, knot_20, knot_08
% 3.27/1.88 % No. of inferences in proof: 71
% 3.27/1.88 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1332 ms resp. 852 ms w/o parsing
% 3.64/1.93 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.64/1.93 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------