%------------------------------------------------------------------------------
% File : CSE---1.7
% Problem : GRP034-3 : TPTP v8.2.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n027.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 : Mon Jun 24 06:38:34 EDT 2024
% Result : Unsatisfiable 0.49s 0.61s
% Output : CNFRefutation 0.49s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10 % Problem : GRP034-3 : TPTP v8.2.0. Released v1.0.0.
% 0.05/0.10 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.09/0.30 % Computer : n027.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Thu Jun 20 10:59:24 EDT 2024
% 0.09/0.30 % CPUTime :
% 0.46/0.56 start to proof:theBenchmark
% 0.49/0.61 %-------------------------------------------
% 0.49/0.61 % File :CSE---1.7
% 0.49/0.61 % Problem :theBenchmark
% 0.49/0.61 % Transform :cnf
% 0.49/0.61 % Format :tptp:raw
% 0.49/0.61 % Command :java -jar mcs_scs.jar %d %s
% 0.49/0.61
% 0.49/0.61 % Result :Theorem 0.010000s
% 0.49/0.61 % Output :CNFRefutation 0.010000s
% 0.49/0.61 %-------------------------------------------
% 0.49/0.61 %--------------------------------------------------------------------------
% 0.49/0.61 % File : GRP034-3 : TPTP v8.2.0. Released v1.0.0.
% 0.49/0.61 % Domain : Group Theory (Subgroups)
% 0.49/0.61 % Problem : In subgroups, inverse is closed
% 0.49/0.61 % Version : [Wos65] axioms.
% 0.49/0.61 % English :
% 0.49/0.61
% 0.49/0.61 % Refs : [Wos65] Wos (1965), Unpublished Note
% 0.49/0.61 % : [MOW76] McCharen et al. (1976), Problems and Experiments for a
% 0.49/0.61 % : [WM76] Wilson & Minker (1976), Resolution, Refinements, and S
% 0.49/0.61 % Source : [SPRFN]
% 0.49/0.61 % Names : Problem 14 [Wos65]
% 0.49/0.61 % : wos14 [WM76]
% 0.49/0.61 % : wos_nie [SPRFN]
% 0.49/0.61
% 0.49/0.61 % Status : Unsatisfiable
% 0.49/0.61 % Rating : 0.00 v5.3.0, 0.08 v5.2.0, 0.00 v2.0.0
% 0.49/0.61 % Syntax : Number of clauses : 11 ( 7 unt; 0 nHn; 6 RR)
% 0.49/0.61 % Number of literals : 22 ( 1 equ; 12 neg)
% 0.49/0.61 % Maximal clause size : 4 ( 2 avg)
% 0.49/0.61 % Maximal term depth : 2 ( 1 avg)
% 0.49/0.61 % Number of predicates : 3 ( 2 usr; 0 prp; 1-3 aty)
% 0.49/0.61 % Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% 0.49/0.61 % Number of variables : 25 ( 0 sgn)
% 0.49/0.61 % SPC : CNF_UNS_RFO_SEQ_HRN
% 0.49/0.61
% 0.49/0.61 % Comments : Proves one of the [MOW76] axioms.
% 0.49/0.61 %--------------------------------------------------------------------------
% 0.49/0.61 %----Include group theory axioms
% 0.49/0.61 include('Axioms/GRP003-0.ax').
% 0.49/0.61 %----Include sub-group theory axioms
% 0.49/0.61 include('Axioms/GRP003-2.ax').
% 0.49/0.61 %--------------------------------------------------------------------------
% 0.49/0.61 cnf(a_is_in_subgroup,hypothesis,
% 0.49/0.61 subgroup_member(a) ).
% 0.49/0.61
% 0.49/0.61 cnf(prove_a_inverse_is_in_subgroup,negated_conjecture,
% 0.49/0.61 ~ subgroup_member(inverse(a)) ).
% 0.49/0.61
% 0.49/0.61 %--------------------------------------------------------------------------
% 0.49/0.61 %-------------------------------------------
% 0.49/0.61 % Proof found
% 0.49/0.61 % SZS status Theorem for theBenchmark
% 0.49/0.61 % SZS output start Proof
% 0.49/0.62 %ClaNum:21(EqnAxiom:10)
% 0.49/0.62 %VarNum:50(SingletonVarNum:25)
% 0.49/0.62 %MaxLitNum:4
% 0.49/0.62 %MaxfuncDepth:1
% 0.49/0.62 %SharedTerms:5
% 0.49/0.62 %goalClause: 17
% 0.49/0.62 %singleGoalClaCount:1
% 0.49/0.62 [11]P1(a1)
% 0.49/0.62 [17]~P1(f3(a1))
% 0.49/0.62 [12]P2(x121,a2,x121)
% 0.49/0.62 [13]P2(a2,x131,x131)
% 0.49/0.62 [14]P2(x141,f3(x141),a2)
% 0.49/0.62 [15]P2(f3(x151),x151,a2)
% 0.49/0.62 [16]P2(x161,x162,f4(x161,x162))
% 0.49/0.62 [19]~P2(x193,x194,x191)+E(x191,x192)+~P2(x193,x194,x192)
% 0.49/0.62 [18]P1(x181)+~P1(x182)+~P1(x183)+~P2(x183,f3(x182),x181)
% 0.49/0.62 [20]~P2(x206,x204,x201)+P2(x201,x202,x203)+~P2(x204,x202,x205)+~P2(x206,x205,x203)
% 0.49/0.62 [21]~P2(x211,x216,x214)+P2(x211,x212,x213)+~P2(x214,x215,x213)+~P2(x216,x215,x212)
% 0.49/0.62 %EqnAxiom
% 0.49/0.62 [1]E(x11,x11)
% 0.49/0.62 [2]E(x22,x21)+~E(x21,x22)
% 0.49/0.62 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.49/0.62 [4]~E(x41,x42)+E(f3(x41),f3(x42))
% 0.49/0.62 [5]~E(x51,x52)+E(f4(x51,x53),f4(x52,x53))
% 0.49/0.62 [6]~E(x61,x62)+E(f4(x63,x61),f4(x63,x62))
% 0.49/0.62 [7]~P1(x71)+P1(x72)+~E(x71,x72)
% 0.49/0.62 [8]P2(x82,x83,x84)+~E(x81,x82)+~P2(x81,x83,x84)
% 0.49/0.62 [9]P2(x93,x92,x94)+~E(x91,x92)+~P2(x93,x91,x94)
% 0.49/0.62 [10]P2(x103,x104,x102)+~E(x101,x102)+~P2(x103,x104,x101)
% 0.49/0.62
% 0.49/0.62 %-------------------------------------------
% 0.49/0.62 cnf(22,plain,
% 0.49/0.62 (E(x221,f4(a2,x221))),
% 0.49/0.62 inference(scs_inference,[],[13,16,19])).
% 0.49/0.62 cnf(23,plain,
% 0.49/0.62 (P2(x231,x232,f4(x231,x232))),
% 0.49/0.62 inference(rename_variables,[],[16])).
% 0.49/0.62 cnf(26,plain,
% 0.49/0.62 (P2(a2,x261,x261)),
% 0.49/0.62 inference(rename_variables,[],[13])).
% 0.49/0.62 cnf(27,plain,
% 0.49/0.62 (P2(a2,f4(a2,a2),a2)),
% 0.49/0.62 inference(scs_inference,[],[13,26,16,19,8,9])).
% 0.49/0.62 cnf(28,plain,
% 0.49/0.62 (P2(a2,x281,x281)),
% 0.49/0.62 inference(rename_variables,[],[13])).
% 0.49/0.62 cnf(29,plain,
% 0.49/0.62 (P2(x291,f3(x291),f4(a2,a2))),
% 0.49/0.62 inference(scs_inference,[],[13,26,16,14,19,8,9,10])).
% 0.49/0.62 cnf(30,plain,
% 0.49/0.62 (~P1(a2)),
% 0.49/0.62 inference(scs_inference,[],[17,11,13,26,28,16,14,19,8,9,10,18])).
% 0.49/0.62 cnf(31,plain,
% 0.49/0.62 (P2(a2,x311,x311)),
% 0.49/0.62 inference(rename_variables,[],[13])).
% 0.49/0.62 cnf(33,plain,
% 0.49/0.62 (P2(f4(f3(x331),a2),x331,a2)),
% 0.49/0.62 inference(scs_inference,[],[17,11,13,26,28,31,16,23,14,15,19,8,9,10,18,20])).
% 0.49/0.63 cnf(44,plain,
% 0.49/0.63 (E(f4(a2,x441),x441)),
% 0.49/0.63 inference(scs_inference,[],[22,2])).
% 0.49/0.63 cnf(46,plain,
% 0.49/0.63 (E(x461,f4(a2,x461))),
% 0.49/0.63 inference(rename_variables,[],[22])).
% 0.49/0.63 cnf(47,plain,
% 0.49/0.63 (E(f4(f3(x471),x471),a2)),
% 0.49/0.63 inference(scs_inference,[],[11,16,15,22,2,7,19])).
% 0.49/0.63 cnf(49,plain,
% 0.49/0.63 (P2(x491,x492,f4(x491,x492))),
% 0.49/0.63 inference(rename_variables,[],[16])).
% 0.49/0.63 cnf(52,plain,
% 0.49/0.63 (P2(x521,x522,f4(x521,x522))),
% 0.49/0.63 inference(rename_variables,[],[16])).
% 0.49/0.63 cnf(54,plain,
% 0.49/0.63 (P2(f4(f3(x541),a2),x541,a2)),
% 0.49/0.63 inference(rename_variables,[],[33])).
% 0.49/0.63 cnf(57,plain,
% 0.49/0.63 (P1(f4(a1,f3(a1)))),
% 0.49/0.63 inference(scs_inference,[],[11,33,54,16,49,52,15,22,46,2,7,19,8,9,10,18])).
% 0.49/0.63 cnf(58,plain,
% 0.49/0.63 (P2(x581,x582,f4(x581,x582))),
% 0.49/0.63 inference(rename_variables,[],[16])).
% 0.49/0.63 cnf(65,plain,
% 0.49/0.63 (P2(a2,f3(f4(a2,a2)),a2)),
% 0.49/0.63 inference(scs_inference,[],[11,33,54,16,49,52,58,15,29,22,46,27,2,7,19,8,9,10,18,21,20])).
% 0.49/0.63 cnf(72,plain,
% 0.49/0.63 (E(f4(a2,x721),x721)),
% 0.49/0.63 inference(rename_variables,[],[44])).
% 0.49/0.63 cnf(74,plain,
% 0.49/0.63 (P2(a2,x741,x741)),
% 0.49/0.63 inference(rename_variables,[],[13])).
% 0.49/0.63 cnf(78,plain,
% 0.49/0.63 (E(x781,f4(a2,x781))),
% 0.49/0.63 inference(rename_variables,[],[22])).
% 0.49/0.63 cnf(83,plain,
% 0.49/0.63 ($false),
% 0.49/0.63 inference(scs_inference,[],[57,30,65,13,74,16,14,44,72,47,22,78,2,3,19,7,8,9,10,18]),
% 0.49/0.63 ['proof']).
% 0.49/0.63 % SZS output end Proof
% 0.49/0.63 % Total time :0.010000s
%------------------------------------------------------------------------------