TSTP Solution File: GRP129-4.004 by Leo-III---1.7.7
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : GRP129-4.004 : TPTP v8.1.2. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n010.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 3.90s 2.04s
% Output : Refutation 3.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 32
% Syntax : Number of formulae : 58 ( 33 unt; 7 typ; 0 def)
% Number of atoms : 105 ( 0 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 356 ( 60 ~; 54 |; 0 &; 242 @)
% ( 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 : 8 ( 7 usr; 5 con; 0-3 aty)
% Number of variables : 60 ( 0 ^; 60 !; 0 ?; 60 :)
% 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(equalish_type,type,
equalish: $i > $i > $o ).
thf(e_3_type,type,
e_3: $i ).
thf(e_4_type,type,
e_4: $i ).
thf(e_2_type,type,
e_2: $i ).
thf(18,axiom,
~ ( equalish @ e_3 @ e_2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_is_not_e_2) ).
thf(57,plain,
~ ( equalish @ e_3 @ e_2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(20,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(60,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)],[20]) ).
thf(16,axiom,
~ ( equalish @ e_4 @ e_2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_4_is_not_e_2) ).
thf(53,plain,
~ ( equalish @ e_4 @ e_2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(10,axiom,
~ ( equalish @ e_4 @ e_3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_4_is_not_e_3) ).
thf(41,plain,
~ ( equalish @ e_4 @ e_3 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(14,axiom,
~ ( equalish @ e_4 @ e_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_4_is_not_e_1) ).
thf(49,plain,
~ ( equalish @ e_4 @ e_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(9,axiom,
~ ( equalish @ e_1 @ e_2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_2) ).
thf(39,plain,
~ ( equalish @ e_1 @ e_2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(23,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(66,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)],[23]) ).
thf(6,axiom,
group_element @ e_4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_4) ).
thf(35,plain,
group_element @ e_4,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(11,axiom,
~ ( equalish @ e_1 @ e_3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_3) ).
thf(43,plain,
~ ( equalish @ e_1 @ e_3 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(25,axiom,
! [B: $i,A: $i] :
( ~ ( group_element @ A )
| ~ ( group_element @ B )
| ( product @ A @ e_1 @ B )
| ( product @ A @ e_2 @ B )
| ( product @ A @ e_3 @ B )
| ( product @ A @ e_4 @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',column_surjectivity) ).
thf(70,plain,
! [B: $i,A: $i] :
( ~ ( group_element @ A )
| ~ ( group_element @ B )
| ( product @ A @ e_1 @ B )
| ( product @ A @ e_2 @ B )
| ( product @ A @ e_3 @ B )
| ( product @ A @ e_4 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(5,axiom,
~ ( equalish @ e_3 @ e_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_is_not_e_1) ).
thf(33,plain,
~ ( equalish @ e_3 @ e_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(3,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(28,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)],[3]) ).
thf(8,axiom,
group_element @ e_3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_3) ).
thf(38,plain,
group_element @ e_3,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(4,axiom,
group_element @ e_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_1) ).
thf(32,plain,
group_element @ e_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(12,axiom,
~ ( equalish @ e_3 @ e_4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_is_not_e_4) ).
thf(45,plain,
~ ( equalish @ e_3 @ e_4 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(22,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(64,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)],[22]) ).
thf(19,axiom,
group_element @ e_2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_2) ).
thf(59,plain,
group_element @ e_2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(2,negated_conjecture,
! [D: $i,C: $i,B: $i,A: $i] :
( ( product @ A @ B @ C )
| ~ ( product @ B @ D @ C )
| ~ ( product @ D @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qg3_2) ).
thf(27,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( product @ A @ B @ C )
| ~ ( product @ B @ D @ C )
| ~ ( product @ D @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(1,negated_conjecture,
! [D: $i,C: $i,B: $i,A: $i] :
( ( product @ A @ B @ C )
| ~ ( product @ C @ A @ D )
| ~ ( product @ B @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qg3_1) ).
thf(26,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( product @ A @ B @ C )
| ~ ( product @ C @ A @ D )
| ~ ( product @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(17,axiom,
~ ( equalish @ e_2 @ e_3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_is_not_e_3) ).
thf(55,plain,
~ ( equalish @ e_2 @ e_3 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(7,axiom,
~ ( equalish @ e_1 @ e_4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_4) ).
thf(36,plain,
~ ( equalish @ e_1 @ e_4 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(15,axiom,
~ ( equalish @ e_2 @ e_4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_is_not_e_4) ).
thf(51,plain,
~ ( equalish @ e_2 @ e_4 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(13,axiom,
~ ( equalish @ e_2 @ e_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_is_not_e_1) ).
thf(47,plain,
~ ( equalish @ e_2 @ e_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(24,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 )
| ( product @ A @ B @ e_4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_total_function1) ).
thf(68,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 )
| ( product @ A @ B @ e_4 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(21,axiom,
! [B: $i,A: $i] :
( ~ ( group_element @ A )
| ~ ( group_element @ B )
| ( product @ e_1 @ A @ B )
| ( product @ e_2 @ A @ B )
| ( product @ e_3 @ A @ B )
| ( product @ e_4 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',row_surjectivity) ).
thf(62,plain,
! [B: $i,A: $i] :
( ~ ( group_element @ A )
| ~ ( group_element @ B )
| ( product @ e_1 @ A @ B )
| ( product @ e_2 @ A @ B )
| ( product @ e_3 @ A @ B )
| ( product @ e_4 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(104,plain,
$false,
inference(e,[status(thm)],[57,60,53,41,49,39,66,35,43,70,33,28,38,32,45,64,59,27,26,55,36,51,47,68,62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP129-4.004 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.12/0.15 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n010.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 : Fri May 19 01:28:58 EDT 2023
% 0.16/0.37 % CPUTime :
% 1.07/0.93 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.30/1.07 % [INFO] Parsing done (139ms).
% 1.30/1.08 % [INFO] Running in sequential loop mode.
% 1.73/1.29 % [INFO] eprover registered as external prover.
% 1.73/1.29 % [INFO] cvc4 registered as external prover.
% 1.73/1.29 % [INFO] Scanning for conjecture ...
% 1.94/1.35 % [INFO] Found a conjecture and 22 axioms. Running axiom selection ...
% 2.09/1.40 % [INFO] Axiom selection finished. Selected 22 axioms (removed 0 axioms).
% 2.09/1.42 % [INFO] Problem is propositional (TPTP CNF).
% 2.09/1.42 % [INFO] Type checking passed.
% 2.09/1.43 % [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 ...
% 3.90/2.03 % External prover 'e' found a proof!
% 3.90/2.03 % [INFO] Killing All external provers ...
% 3.90/2.03 % Time passed: 1505ms (effective reasoning time: 951ms)
% 3.90/2.03 % 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)>
% 3.90/2.04 % Axioms used in derivation (22): e_3_is_not_e_2, element_4, element_2, product_right_cancellation, column_surjectivity, product_total_function1, e_1_is_not_e_2, e_2_is_not_e_1, e_1_is_not_e_3, e_1_is_not_e_4, e_3_is_not_e_1, product_left_cancellation, row_surjectivity, e_2_is_not_e_3, element_3, e_4_is_not_e_2, product_total_function2, e_3_is_not_e_4, element_1, e_4_is_not_e_3, e_2_is_not_e_4, e_4_is_not_e_1
% 3.90/2.04 % No. of inferences in proof: 51
% 3.90/2.04 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1505 ms resp. 951 ms w/o parsing
% 3.90/2.07 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.90/2.07 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------