TSTP Solution File: GRP123-3.003 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : GRP123-3.003 : TPTP v8.1.2. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n013.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 11:13:12 EDT 2023
% Result : Unsatisfiable 3.02s 1.75s
% Output : Refutation 3.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 42
% Syntax : Number of formulae : 75 ( 41 unt; 10 typ; 0 def)
% Number of atoms : 143 ( 0 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 476 ( 86 ~; 78 |; 0 &; 312 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 10 usr; 5 con; 0-3 aty)
% Number of variables : 94 ( 0 ^; 94 !; 0 ?; 94 :)
% Comments :
%------------------------------------------------------------------------------
thf(product_type,type,
product: $i > $i > $i > $o ).
thf(equalish_type,type,
equalish: $i > $i > $o ).
thf(group_element_type,type,
group_element: $i > $o ).
thf(e_1_type,type,
e_1: $i ).
thf(cycle_type,type,
cycle: $i > $i > $o ).
thf(e_0_type,type,
e_0: $i ).
thf(next_type,type,
next: $i > $i > $o ).
thf(greater_type,type,
greater: $i > $i > $o ).
thf(e_2_type,type,
e_2: $i ).
thf(e_3_type,type,
e_3: $i ).
thf(26,axiom,
~ ( equalish @ e_1 @ e_3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_3) ).
thf(69,plain,
~ ( equalish @ e_1 @ e_3 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(19,axiom,
~ ( equalish @ e_3 @ e_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_is_not_e_1) ).
thf(56,plain,
~ ( equalish @ e_3 @ e_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(17,axiom,
! [A: $i] :
( ~ ( group_element @ A )
| ( cycle @ A @ e_0 )
| ( cycle @ A @ e_1 )
| ( cycle @ A @ e_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cycle2) ).
thf(52,plain,
! [A: $i] :
( ~ ( group_element @ A )
| ( cycle @ A @ e_0 )
| ( cycle @ A @ e_1 )
| ( cycle @ A @ e_2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(11,axiom,
greater @ e_3 @ e_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_greater_e_2) ).
thf(46,plain,
greater @ e_3 @ e_2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(21,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( cycle @ A @ B )
| ~ ( cycle @ C @ D )
| ~ ( next @ A @ C )
| ~ ( greater @ B @ e_0 )
| ~ ( next @ D @ E )
| ( equalish @ B @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cycle4) ).
thf(60,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( cycle @ A @ B )
| ~ ( cycle @ C @ D )
| ~ ( next @ A @ C )
| ~ ( greater @ B @ e_0 )
| ~ ( next @ D @ E )
| ( equalish @ B @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(24,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( cycle @ A @ B )
| ~ ( product @ A @ e_1 @ C )
| ~ ( greater @ B @ e_0 )
| ~ ( next @ A @ D )
| ( equalish @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cycle7) ).
thf(65,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( cycle @ A @ B )
| ~ ( product @ A @ e_1 @ C )
| ~ ( greater @ B @ e_0 )
| ~ ( next @ A @ D )
| ( equalish @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(30,axiom,
! [B: $i,A: $i] :
( ~ ( cycle @ A @ e_0 )
| ~ ( product @ A @ e_1 @ B )
| ~ ( greater @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cycle6) ).
thf(77,plain,
! [B: $i,A: $i] :
( ~ ( cycle @ A @ e_0 )
| ~ ( product @ A @ e_1 @ B )
| ~ ( greater @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(6,axiom,
next @ e_1 @ e_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_then_e_2) ).
thf(41,plain,
next @ e_1 @ e_2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(28,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( product @ A @ B @ C )
| ~ ( product @ A @ D @ C )
| ( equalish @ B @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_right_cancellation) ).
thf(73,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)],[28]) ).
thf(9,axiom,
greater @ e_2 @ e_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_greater_e_1) ).
thf(44,plain,
greater @ e_2 @ e_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(32,axiom,
~ ( equalish @ e_3 @ e_2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_is_not_e_2) ).
thf(81,plain,
~ ( equalish @ e_3 @ e_2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(8,axiom,
next @ e_2 @ e_3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_then_e_3) ).
thf(43,plain,
next @ e_2 @ e_3,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(5,axiom,
next @ e_0 @ e_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_0_then_e_1) ).
thf(40,plain,
next @ e_0 @ e_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(16,axiom,
greater @ e_3 @ e_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_greater_e_1) ).
thf(51,plain,
greater @ e_3 @ e_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(31,axiom,
~ ( equalish @ e_2 @ e_3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_is_not_e_3) ).
thf(79,plain,
~ ( equalish @ e_2 @ e_3 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(7,axiom,
group_element @ e_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_2) ).
thf(42,plain,
group_element @ e_2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(3,axiom,
group_element @ e_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_1) ).
thf(37,plain,
group_element @ e_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(4,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( cycle @ A @ B )
| ~ ( cycle @ C @ e_0 )
| ~ ( cycle @ D @ E )
| ~ ( next @ C @ D )
| ~ ( greater @ C @ A )
| ~ ( greater @ B @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cycle5) ).
thf(38,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( cycle @ A @ B )
| ~ ( cycle @ C @ e_0 )
| ~ ( cycle @ D @ E )
| ~ ( next @ C @ D )
| ~ ( greater @ C @ A )
| ~ ( greater @ B @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(1,negated_conjecture,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( product @ A @ B @ C )
| ~ ( product @ D @ E @ C )
| ~ ( product @ F @ B @ A )
| ~ ( product @ F @ E @ D )
| ( equalish @ A @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg1_1) ).
thf(33,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( product @ A @ B @ C )
| ~ ( product @ D @ E @ C )
| ~ ( product @ F @ B @ A )
| ~ ( product @ F @ E @ D )
| ( equalish @ A @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(2,negated_conjecture,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( product @ A @ B @ C )
| ~ ( product @ D @ E @ C )
| ~ ( product @ F @ B @ A )
| ~ ( product @ F @ E @ D )
| ( equalish @ B @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg1_2) ).
thf(34,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( product @ A @ B @ C )
| ~ ( product @ D @ E @ C )
| ~ ( product @ F @ B @ A )
| ~ ( product @ F @ E @ D )
| ( equalish @ B @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(10,axiom,
group_element @ e_3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_3) ).
thf(45,plain,
group_element @ e_3,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(27,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( product @ A @ B @ C )
| ~ ( product @ A @ B @ D )
| ( equalish @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_total_function2) ).
thf(71,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)],[27]) ).
thf(18,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/sandbox/benchmark/theBenchmark.p',product_total_function1) ).
thf(54,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)],[18]) ).
thf(14,axiom,
greater @ e_3 @ e_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_greater_e_0) ).
thf(49,plain,
greater @ e_3 @ e_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(13,axiom,
greater @ e_2 @ e_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_greater_e_0) ).
thf(48,plain,
greater @ e_2 @ e_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(23,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( cycle @ A @ B )
| ~ ( cycle @ A @ C )
| ( equalish @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cycle1) ).
thf(63,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( cycle @ A @ B )
| ~ ( cycle @ A @ C )
| ( equalish @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(15,axiom,
cycle @ e_3 @ e_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cycle3) ).
thf(50,plain,
cycle @ e_3 @ e_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(25,axiom,
~ ( equalish @ e_1 @ e_2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_2) ).
thf(67,plain,
~ ( equalish @ e_1 @ e_2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(29,axiom,
~ ( equalish @ e_2 @ e_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_is_not_e_1) ).
thf(75,plain,
~ ( equalish @ e_2 @ e_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
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/sandbox/benchmark/theBenchmark.p',product_left_cancellation) ).
thf(58,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(12,axiom,
greater @ e_1 @ e_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_greater_e_0) ).
thf(47,plain,
greater @ e_1 @ e_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(22,axiom,
! [A: $i] : ( product @ A @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_idempotence) ).
thf(62,plain,
! [A: $i] : ( product @ A @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(83,plain,
$false,
inference(e,[status(thm)],[69,56,52,46,60,65,77,41,73,44,81,43,40,51,79,42,37,38,33,34,45,71,54,49,48,63,50,67,75,58,47,62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : GRP123-3.003 : TPTP v8.1.2. Released v1.2.0.
% 0.13/0.15 % Command : run_Leo-III %s %d
% 0.16/0.36 % Computer : n013.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Fri May 19 01:42:36 EDT 2023
% 0.16/0.36 % CPUTime :
% 0.96/0.89 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.35/1.03 % [INFO] Parsing done (138ms).
% 1.35/1.04 % [INFO] Running in sequential loop mode.
% 1.71/1.24 % [INFO] eprover registered as external prover.
% 1.71/1.24 % [INFO] cvc4 registered as external prover.
% 1.76/1.24 % [INFO] Scanning for conjecture ...
% 1.76/1.30 % [INFO] Found a conjecture and 30 axioms. Running axiom selection ...
% 1.95/1.35 % [INFO] Axiom selection finished. Selected 30 axioms (removed 0 axioms).
% 2.17/1.37 % [INFO] Problem is propositional (TPTP CNF).
% 2.17/1.37 % [INFO] Type checking passed.
% 2.17/1.38 % [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 ...
% 3.02/1.74 % External prover 'e' found a proof!
% 3.02/1.74 % [INFO] Killing All external provers ...
% 3.02/1.74 % Time passed: 1228ms (effective reasoning time: 698ms)
% 3.02/1.74 % 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)>
% 3.02/1.75 % Axioms used in derivation (30): e_3_is_not_e_2, cycle2, cycle7, product_right_cancellation, e_3_greater_e_2, e_1_is_not_e_2, element_1, e_3_greater_e_1, cycle4, e_1_is_not_e_3, e_2_greater_e_0, e_3_greater_e_0, e_3_is_not_e_1, e_1_then_e_2, e_2_is_not_e_3, e_0_then_e_1, element_3, cycle6, e_2_then_e_3, element_2, cycle1, product_total_function2, product_idempotence, product_total_function1, cycle5, e_2_greater_e_1, e_2_is_not_e_1, e_1_greater_e_0, product_left_cancellation, cycle3
% 3.02/1.75 % No. of inferences in proof: 65
% 3.02/1.75 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1228 ms resp. 698 ms w/o parsing
% 3.37/1.78 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.37/1.78 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------