TSTP Solution File: GRP124-7.004 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : GRP124-7.004 : TPTP v8.1.2. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n006.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 11:13:13 EDT 2023
% Result : Unsatisfiable 3.14s 1.74s
% Output : Refutation 3.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 48
% Syntax : Number of formulae : 86 ( 55 unt; 11 typ; 0 def)
% Number of atoms : 127 ( 0 equ; 0 cnn)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 406 ( 66 ~; 52 |; 0 &; 288 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 16 ( 16 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 11 usr; 5 con; 0-3 aty)
% Number of variables : 74 ( 0 ^; 74 !; 0 ?; 74 :)
% Comments :
%------------------------------------------------------------------------------
thf(product1_type,type,
product1: $i > $i > $i > $o ).
thf(product2_type,type,
product2: $i > $i > $i > $o ).
thf(next_type,type,
next: $i > $i > $o ).
thf(e_3_type,type,
e_3: $i ).
thf(e_4_type,type,
e_4: $i ).
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(greater_type,type,
greater: $i > $i > $o ).
thf(e_2_type,type,
e_2: $i ).
thf(product_type,type,
product: $i > $i > $i > $o ).
thf(13,axiom,
~ ( equalish @ e_2 @ e_4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_is_not_e_4) ).
thf(56,plain,
~ ( equalish @ e_2 @ e_4 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(4,axiom,
~ ( equalish @ e_3 @ e_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_is_not_e_1) ).
thf(42,plain,
~ ( equalish @ e_3 @ e_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(31,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( product1 @ A @ B @ C )
| ~ ( product1 @ D @ B @ C )
| ( equalish @ A @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product1_left_cancellation) ).
thf(84,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( product1 @ A @ B @ C )
| ~ ( product1 @ D @ B @ C )
| ( equalish @ A @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(17,axiom,
greater @ e_4 @ e_3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_4_greater_e_3) ).
thf(61,plain,
greater @ e_4 @ e_3,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(16,axiom,
group_element @ e_2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_2) ).
thf(60,plain,
group_element @ e_2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(1,negated_conjecture,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( product1 @ A @ B @ C )
| ~ ( product1 @ C @ A @ D )
| ( product2 @ D @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qg2a) ).
thf(38,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( product1 @ A @ B @ C )
| ~ ( product1 @ C @ A @ D )
| ( product2 @ D @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(35,axiom,
! [B: $i,A: $i] :
( ~ ( group_element @ A )
| ~ ( group_element @ B )
| ( product2 @ A @ B @ e_1 )
| ( product2 @ A @ B @ e_2 )
| ( product2 @ A @ B @ e_3 )
| ( product2 @ A @ B @ e_4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product2_total_function1) ).
thf(92,plain,
! [B: $i,A: $i] :
( ~ ( group_element @ A )
| ~ ( group_element @ B )
| ( product2 @ A @ B @ e_1 )
| ( product2 @ A @ B @ e_2 )
| ( product2 @ A @ B @ e_3 )
| ( product2 @ A @ B @ e_4 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(11,axiom,
~ ( equalish @ e_4 @ e_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_4_is_not_e_1) ).
thf(53,plain,
~ ( equalish @ e_4 @ e_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(3,axiom,
group_element @ e_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_1) ).
thf(41,plain,
group_element @ e_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(25,axiom,
~ ( equalish @ e_4 @ e_2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_4_is_not_e_2) ).
thf(73,plain,
~ ( equalish @ e_4 @ e_2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(21,axiom,
~ ( equalish @ e_1 @ e_3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_3) ).
thf(66,plain,
~ ( equalish @ e_1 @ e_3 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(29,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( product1 @ A @ B @ C )
| ~ ( product1 @ A @ B @ D )
| ( equalish @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product1_total_function2) ).
thf(80,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( product1 @ A @ B @ C )
| ~ ( product1 @ A @ B @ D )
| ( equalish @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(9,axiom,
group_element @ e_3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_3) ).
thf(50,plain,
group_element @ e_3,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(10,axiom,
~ ( equalish @ e_1 @ e_2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_2) ).
thf(51,plain,
~ ( equalish @ e_1 @ e_2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(34,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( product1 @ A @ B @ C )
| ~ ( product1 @ A @ D @ C )
| ( equalish @ B @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product1_right_cancellation) ).
thf(90,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( product1 @ A @ B @ C )
| ~ ( product1 @ A @ D @ C )
| ( equalish @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(23,axiom,
~ ( equalish @ e_3 @ e_4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_is_not_e_4) ).
thf(69,plain,
~ ( equalish @ e_3 @ e_4 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(33,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( product2 @ A @ B @ C )
| ~ ( product2 @ D @ B @ C )
| ( equalish @ A @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product2_left_cancellation) ).
thf(88,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( product2 @ A @ B @ C )
| ~ ( product2 @ D @ B @ C )
| ( equalish @ A @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(27,axiom,
~ ( equalish @ e_3 @ e_2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_is_not_e_2) ).
thf(77,plain,
~ ( equalish @ e_3 @ e_2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(37,axiom,
! [A: $i] : ( product2 @ A @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product2_idempotence) ).
thf(96,plain,
! [A: $i] : ( product2 @ A @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(6,axiom,
~ ( equalish @ e_1 @ e_4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_4) ).
thf(45,plain,
~ ( equalish @ e_1 @ e_4 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(20,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( product @ A @ e_1 @ B )
| ~ ( next @ A @ C )
| ~ ( greater @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',no_redundancy) ).
thf(64,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( product @ A @ e_1 @ B )
| ~ ( next @ A @ C )
| ~ ( greater @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(5,axiom,
group_element @ e_4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_4) ).
thf(44,plain,
group_element @ e_4,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(15,axiom,
next @ e_1 @ e_2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_then_e_2) ).
thf(59,plain,
next @ e_1 @ e_2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(24,axiom,
~ ( equalish @ e_2 @ e_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_is_not_e_1) ).
thf(71,plain,
~ ( equalish @ e_2 @ e_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(32,axiom,
! [B: $i,A: $i] :
( ~ ( group_element @ A )
| ~ ( group_element @ B )
| ( product1 @ A @ B @ e_1 )
| ( product1 @ A @ B @ e_2 )
| ( product1 @ A @ B @ e_3 )
| ( product1 @ A @ B @ e_4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product1_total_function1) ).
thf(86,plain,
! [B: $i,A: $i] :
( ~ ( group_element @ A )
| ~ ( group_element @ B )
| ( product1 @ A @ B @ e_1 )
| ( product1 @ A @ B @ e_2 )
| ( product1 @ A @ B @ e_3 )
| ( product1 @ A @ B @ e_4 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(8,axiom,
~ ( equalish @ e_4 @ e_3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_4_is_not_e_3) ).
thf(48,plain,
~ ( equalish @ e_4 @ e_3 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(19,axiom,
greater @ e_2 @ e_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_greater_e_1) ).
thf(63,plain,
greater @ e_2 @ e_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(2,axiom,
next @ e_3 @ e_4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_then_e_4) ).
thf(40,plain,
next @ e_3 @ e_4,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(12,axiom,
greater @ e_4 @ e_2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_4_greater_e_2) ).
thf(55,plain,
greater @ e_4 @ e_2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(26,axiom,
~ ( equalish @ e_2 @ e_3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_is_not_e_3) ).
thf(75,plain,
~ ( equalish @ e_2 @ e_3 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(14,axiom,
greater @ e_3 @ e_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_greater_e_1) ).
thf(58,plain,
greater @ e_3 @ e_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(30,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( product2 @ A @ B @ C )
| ~ ( product2 @ A @ B @ D )
| ( equalish @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product2_total_function2) ).
thf(82,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( product2 @ A @ B @ C )
| ~ ( product2 @ A @ B @ D )
| ( equalish @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(28,axiom,
! [A: $i] : ( product1 @ A @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product1_idempotence) ).
thf(79,plain,
! [A: $i] : ( product1 @ A @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(36,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( product2 @ A @ B @ C )
| ~ ( product2 @ A @ D @ C )
| ( equalish @ B @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product2_right_cancellation) ).
thf(94,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( product2 @ A @ B @ C )
| ~ ( product2 @ A @ D @ C )
| ( equalish @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(7,axiom,
greater @ e_4 @ e_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_4_greater_e_1) ).
thf(47,plain,
greater @ e_4 @ e_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(22,axiom,
greater @ e_3 @ e_2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_greater_e_2) ).
thf(68,plain,
greater @ e_3 @ e_2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(18,axiom,
next @ e_2 @ e_3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_then_e_3) ).
thf(62,plain,
next @ e_2 @ e_3,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(97,plain,
$false,
inference(e,[status(thm)],[56,42,84,61,60,38,92,53,41,73,66,80,50,51,90,69,88,77,96,45,64,44,59,71,86,48,63,40,55,75,58,82,79,94,47,68,62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP124-7.004 : TPTP v8.1.2. Released v1.2.0.
% 0.03/0.15 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n006.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 01:51:07 EDT 2023
% 0.16/0.37 % CPUTime :
% 0.97/0.86 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.30/0.99 % [INFO] Parsing done (130ms).
% 1.30/1.00 % [INFO] Running in sequential loop mode.
% 1.70/1.19 % [INFO] eprover registered as external prover.
% 1.70/1.20 % [INFO] cvc4 registered as external prover.
% 1.70/1.20 % [INFO] Scanning for conjecture ...
% 1.86/1.26 % [INFO] Found a conjecture and 36 axioms. Running axiom selection ...
% 1.92/1.30 % [INFO] Axiom selection finished. Selected 36 axioms (removed 0 axioms).
% 2.15/1.32 % [INFO] Problem is propositional (TPTP CNF).
% 2.15/1.33 % [INFO] Type checking passed.
% 2.15/1.33 % [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 ...
% 3.14/1.74 % External prover 'e' found a proof!
% 3.14/1.74 % [INFO] Killing All external provers ...
% 3.14/1.74 % Time passed: 1208ms (effective reasoning time: 738ms)
% 3.14/1.74 % 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)>
% 3.14/1.74 % Axioms used in derivation (36): e_3_is_not_e_2, element_4, product1_left_cancellation, e_2_then_e_3, element_2, e_4_greater_e_1, e_3_greater_e_2, e_4_is_not_e_2, e_1_is_not_e_2, product2_idempotence, e_1_is_not_e_3, e_1_is_not_e_4, e_3_is_not_e_1, e_1_then_e_2, e_2_is_not_e_3, element_3, e_4_greater_e_2, product2_total_function1, product1_idempotence, product2_left_cancellation, e_3_then_e_4, product1_total_function1, e_2_greater_e_1, e_2_is_not_e_1, product2_right_cancellation, e_3_is_not_e_4, product1_right_cancellation, element_1, e_4_is_not_e_3, no_redundancy, product1_total_function2, e_3_greater_e_1, e_4_greater_e_3, product2_total_function2, e_2_is_not_e_4, e_4_is_not_e_1
% 3.14/1.74 % No. of inferences in proof: 75
% 3.14/1.74 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1208 ms resp. 738 ms w/o parsing
% 3.40/1.79 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.40/1.79 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------