TSTP Solution File: GRP129-1.003 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : GRP129-1.003 : TPTP v8.1.2. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n019.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 11:13:16 EDT 2023
% Result : Unsatisfiable 2.65s 1.57s
% Output : Refutation 2.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 20
% Syntax : Number of formulae : 35 ( 19 unt; 6 typ; 0 def)
% Number of atoms : 53 ( 0 equ; 0 cnn)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 174 ( 32 ~; 24 |; 0 &; 118 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 6 usr; 4 con; 0-3 aty)
% Number of variables : 36 ( 0 ^; 36 !; 0 ?; 36 :)
% Comments :
%------------------------------------------------------------------------------
thf(product_type,type,
product: $i > $i > $i > $o ).
thf(group_element_type,type,
group_element: $i > $o ).
thf(e_1_type,type,
e_1: $i ).
thf(e_2_type,type,
e_2: $i ).
thf(e_3_type,type,
e_3: $i ).
thf(equalish_type,type,
equalish: $i > $i > $o ).
thf(7,axiom,
~ ( equalish @ e_2 @ e_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_is_not_e_1) ).
thf(24,plain,
~ ( equalish @ e_2 @ e_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(5,axiom,
~ ( equalish @ e_1 @ e_2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_2) ).
thf(20,plain,
~ ( equalish @ e_1 @ e_2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(6,axiom,
~ ( equalish @ e_1 @ e_3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_3) ).
thf(22,plain,
~ ( equalish @ e_1 @ e_3 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(3,axiom,
group_element @ e_2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_2) ).
thf(18,plain,
group_element @ e_2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(8,axiom,
~ ( equalish @ e_2 @ e_3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_is_not_e_3) ).
thf(26,plain,
~ ( equalish @ e_2 @ e_3 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(1,negated_conjecture,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( product @ A @ B @ C )
| ~ ( product @ B @ C @ D )
| ( product @ C @ A @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qg3) ).
thf(15,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( product @ A @ B @ C )
| ~ ( product @ B @ C @ D )
| ( product @ C @ A @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(9,axiom,
~ ( equalish @ e_3 @ e_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_is_not_e_1) ).
thf(28,plain,
~ ( equalish @ e_3 @ e_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(14,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( product @ A @ B @ C )
| ~ ( product @ D @ B @ C )
| ( equalish @ A @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_left_cancellation) ).
thf(38,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( product @ A @ B @ C )
| ~ ( product @ D @ B @ C )
| ( equalish @ A @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(2,axiom,
group_element @ e_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_1) ).
thf(17,plain,
group_element @ e_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(11,axiom,
! [B: $i,A: $i] :
( ~ ( group_element @ A )
| ~ ( group_element @ B )
| ( product @ A @ B @ e_1 )
| ( product @ A @ B @ e_2 )
| ( product @ A @ B @ e_3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_total_function1) ).
thf(32,plain,
! [B: $i,A: $i] :
( ~ ( group_element @ A )
| ~ ( group_element @ B )
| ( product @ A @ B @ e_1 )
| ( product @ A @ B @ e_2 )
| ( product @ A @ B @ e_3 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(12,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( product @ A @ B @ C )
| ~ ( product @ A @ B @ D )
| ( equalish @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_total_function2) ).
thf(34,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( product @ A @ B @ C )
| ~ ( product @ A @ B @ D )
| ( equalish @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(13,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( product @ A @ B @ C )
| ~ ( product @ A @ D @ C )
| ( equalish @ B @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_right_cancellation) ).
thf(36,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( product @ A @ B @ C )
| ~ ( product @ A @ D @ C )
| ( equalish @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(10,axiom,
~ ( equalish @ e_3 @ e_2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_is_not_e_2) ).
thf(30,plain,
~ ( equalish @ e_3 @ e_2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(4,axiom,
group_element @ e_3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_3) ).
thf(19,plain,
group_element @ e_3,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(40,plain,
$false,
inference(cvc4,[status(thm)],[24,20,22,18,26,15,28,38,17,32,34,36,30,19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP129-1.003 : TPTP v8.1.2. Released v1.2.0.
% 0.06/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n019.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Fri May 19 02:05:28 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.84/0.83 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.22/0.95 % [INFO] Parsing done (114ms).
% 1.22/0.96 % [INFO] Running in sequential loop mode.
% 1.49/1.15 % [INFO] eprover registered as external prover.
% 1.49/1.15 % [INFO] cvc4 registered as external prover.
% 1.49/1.16 % [INFO] Scanning for conjecture ...
% 1.72/1.21 % [INFO] Found a conjecture and 13 axioms. Running axiom selection ...
% 1.81/1.23 % [INFO] Axiom selection finished. Selected 13 axioms (removed 0 axioms).
% 1.92/1.25 % [INFO] Problem is propositional (TPTP CNF).
% 1.92/1.25 % [INFO] Type checking passed.
% 1.92/1.25 % [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 ...
% 2.65/1.56 % External prover 'cvc4' found a proof!
% 2.65/1.56 % [INFO] Killing All external provers ...
% 2.65/1.57 % Time passed: 1051ms (effective reasoning time: 607ms)
% 2.65/1.57 % 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)>
% 2.65/1.57 % Axioms used in derivation (13): e_3_is_not_e_2, element_2, product_right_cancellation, product_total_function2, product_total_function1, e_1_is_not_e_2, e_2_is_not_e_1, element_1, e_1_is_not_e_3, e_3_is_not_e_1, product_left_cancellation, e_2_is_not_e_3, element_3
% 2.65/1.57 % No. of inferences in proof: 29
% 2.65/1.57 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1051 ms resp. 607 ms w/o parsing
% 2.65/1.60 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.65/1.60 % [INFO] Killing All external provers ...
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