%------------------------------------------------------------------------------
% File : CSE---1.7
% Problem : GRP038-3 : 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 : n029.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 06:38:35 EDT 2024
% Result : Unsatisfiable 0.54s 0.61s
% Output : CNFRefutation 0.54s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP038-3 : TPTP v8.2.0. Released v1.0.0.
% 0.11/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.12/0.33 % Computer : n029.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 20 12:07:24 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.19/0.57 start to proof:theBenchmark
% 0.54/0.61 %-------------------------------------------
% 0.54/0.61 % File :CSE---1.7
% 0.54/0.61 % Problem :theBenchmark
% 0.54/0.61 % Transform :cnf
% 0.54/0.61 % Format :tptp:raw
% 0.54/0.61 % Command :java -jar mcs_scs.jar %d %s
% 0.54/0.61
% 0.54/0.61 % Result :Theorem 0.000000s
% 0.54/0.61 % Output :CNFRefutation 0.000000s
% 0.54/0.61 %-------------------------------------------
% 0.54/0.61 %--------------------------------------------------------------------------
% 0.54/0.61 % File : GRP038-3 : TPTP v8.2.0. Released v1.0.0.
% 0.54/0.61 % Domain : Group Theory (Subgroups)
% 0.54/0.61 % Problem : In subgroups, if a and b are members, then a.b^-1 is a member
% 0.54/0.61 % Version : [Wos65] axioms : Augmented.
% 0.54/0.61 % English :
% 0.54/0.61
% 0.54/0.61 % Refs : [Wos65] Wos (1965), Unpublished Note
% 0.54/0.61 % : [WM76] Wilson & Minker (1976), Resolution, Refinements, and S
% 0.54/0.61 % Source : [SPRFN]
% 0.54/0.61 % Names : Problem 18 [Wos65]
% 0.54/0.61 % : wos18 [WM76]
% 0.54/0.61
% 0.54/0.61 % Status : Unsatisfiable
% 0.54/0.61 % Rating : 0.00 v6.0.0, 0.11 v5.5.0, 0.06 v5.4.0, 0.07 v5.3.0, 0.17 v5.2.0, 0.12 v5.1.0, 0.00 v2.0.0
% 0.54/0.61 % Syntax : Number of clauses : 15 ( 10 unt; 0 nHn; 10 RR)
% 0.54/0.61 % Number of literals : 27 ( 1 equ; 13 neg)
% 0.54/0.61 % Maximal clause size : 4 ( 1 avg)
% 0.54/0.61 % Maximal term depth : 2 ( 1 avg)
% 0.54/0.61 % Number of predicates : 3 ( 2 usr; 0 prp; 1-3 aty)
% 0.54/0.61 % Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% 0.54/0.61 % Number of variables : 26 ( 0 sgn)
% 0.54/0.61 % SPC : CNF_UNS_RFO_SEQ_HRN
% 0.54/0.61
% 0.54/0.61 % Comments : This is trivial - its an axiom.
% 0.54/0.61 % : Two extra lemmas are supplied.
% 0.54/0.61 %--------------------------------------------------------------------------
% 0.54/0.61 %----Include group theory axioms
% 0.54/0.61 include('Axioms/GRP003-0.ax').
% 0.54/0.61 %----Include sub-group theory axioms
% 0.54/0.61 include('Axioms/GRP003-2.ax').
% 0.54/0.61 %--------------------------------------------------------------------------
% 0.54/0.61 %----The next two clauses are dependent lemmas
% 0.54/0.61 cnf(closure_of_inverse,axiom,
% 0.54/0.61 ( ~ subgroup_member(A)
% 0.54/0.61 | subgroup_member(inverse(A)) ) ).
% 0.54/0.61
% 0.54/0.61 cnf(identity_is_in_subgroup,axiom,
% 0.54/0.61 subgroup_member(identity) ).
% 0.54/0.61
% 0.54/0.61 cnf(a_is_in_subgroup,hypothesis,
% 0.54/0.61 subgroup_member(a) ).
% 0.54/0.61
% 0.54/0.61 cnf(b_is_in_subgroup,hypothesis,
% 0.54/0.61 subgroup_member(b) ).
% 0.54/0.61
% 0.54/0.61 cnf(a_times_inverse_b_is_c,hypothesis,
% 0.54/0.61 product(a,inverse(b),c) ).
% 0.54/0.61
% 0.54/0.61 cnf(prove_c_is_in_subgroup,negated_conjecture,
% 0.54/0.61 ~ subgroup_member(c) ).
% 0.54/0.61
% 0.54/0.61 %--------------------------------------------------------------------------
% 0.54/0.61 %-------------------------------------------
% 0.54/0.61 % Proof found
% 0.54/0.61 % SZS status Theorem for theBenchmark
% 0.54/0.61 % SZS output start Proof
% 0.54/0.61 %ClaNum:25(EqnAxiom:10)
% 0.54/0.61 %VarNum:52(SingletonVarNum:26)
% 0.54/0.61 %MaxLitNum:4
% 0.54/0.61 %MaxfuncDepth:1
% 0.54/0.61 %SharedTerms:10
% 0.54/0.61 %goalClause: 20
% 0.54/0.61 %singleGoalClaCount:1
% 0.54/0.61 [11]P1(a1)
% 0.54/0.61 [12]P1(a2)
% 0.54/0.61 [13]P1(a3)
% 0.54/0.61 [20]~P1(a4)
% 0.54/0.61 [16]P2(a2,f5(a3),a4)
% 0.54/0.61 [14]P2(x141,a1,x141)
% 0.54/0.61 [15]P2(a1,x151,x151)
% 0.54/0.61 [17]P2(x171,f5(x171),a1)
% 0.54/0.61 [18]P2(f5(x181),x181,a1)
% 0.54/0.61 [19]P2(x191,x192,f6(x191,x192))
% 0.54/0.61 [21]~P1(x211)+P1(f5(x211))
% 0.54/0.61 [23]~P2(x233,x234,x231)+E(x231,x232)+~P2(x233,x234,x232)
% 0.54/0.61 [22]P1(x221)+~P1(x222)+~P1(x223)+~P2(x223,f5(x222),x221)
% 0.54/0.61 [24]~P2(x246,x244,x241)+P2(x241,x242,x243)+~P2(x244,x242,x245)+~P2(x246,x245,x243)
% 0.54/0.61 [25]~P2(x251,x256,x254)+P2(x251,x252,x253)+~P2(x254,x255,x253)+~P2(x256,x255,x252)
% 0.54/0.61 %EqnAxiom
% 0.54/0.61 [1]E(x11,x11)
% 0.54/0.61 [2]E(x22,x21)+~E(x21,x22)
% 0.54/0.61 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.54/0.61 [4]~E(x41,x42)+E(f5(x41),f5(x42))
% 0.54/0.61 [5]~E(x51,x52)+E(f6(x51,x53),f6(x52,x53))
% 0.54/0.61 [6]~E(x61,x62)+E(f6(x63,x61),f6(x63,x62))
% 0.54/0.61 [7]~P1(x71)+P1(x72)+~E(x71,x72)
% 0.54/0.61 [8]P2(x82,x83,x84)+~E(x81,x82)+~P2(x81,x83,x84)
% 0.54/0.61 [9]P2(x93,x92,x94)+~E(x91,x92)+~P2(x93,x91,x94)
% 0.54/0.61 [10]P2(x103,x104,x102)+~E(x101,x102)+~P2(x103,x104,x101)
% 0.54/0.61
% 0.54/0.61 %-------------------------------------------
% 0.54/0.62 cnf(26,plain,
% 0.54/0.62 (E(x261,f6(a1,x261))),
% 0.54/0.62 inference(scs_inference,[],[15,19,23])).
% 0.54/0.62 cnf(27,plain,
% 0.54/0.62 (P2(x271,x272,f6(x271,x272))),
% 0.54/0.62 inference(rename_variables,[],[19])).
% 0.54/0.62 cnf(30,plain,
% 0.54/0.62 (P2(a1,x301,x301)),
% 0.54/0.62 inference(rename_variables,[],[15])).
% 0.54/0.62 cnf(32,plain,
% 0.54/0.62 (P2(a1,x321,x321)),
% 0.54/0.62 inference(rename_variables,[],[15])).
% 0.54/0.62 cnf(34,plain,
% 0.54/0.62 (P1(f5(a1))),
% 0.54/0.62 inference(scs_inference,[],[15,30,32,19,17,11,23,8,9,10,22])).
% 0.54/0.62 cnf(35,plain,
% 0.54/0.62 (P2(a1,x351,x351)),
% 0.54/0.62 inference(rename_variables,[],[15])).
% 0.54/0.62 cnf(37,plain,
% 0.54/0.62 (P2(f6(f5(x371),a1),x371,a1)),
% 0.54/0.62 inference(scs_inference,[],[15,30,32,35,19,27,17,18,11,23,8,9,10,22,24])).
% 0.54/0.62 cnf(50,plain,
% 0.54/0.62 (E(x501,f6(a1,x501))),
% 0.54/0.62 inference(rename_variables,[],[26])).
% 0.54/0.62 cnf(52,plain,
% 0.54/0.62 (E(x521,f6(a1,x521))),
% 0.54/0.62 inference(rename_variables,[],[26])).
% 0.54/0.62 cnf(55,plain,
% 0.54/0.62 (P2(x551,x552,f6(x551,x552))),
% 0.54/0.62 inference(rename_variables,[],[19])).
% 0.54/0.62 cnf(58,plain,
% 0.54/0.62 (E(x581,f6(a1,x581))),
% 0.54/0.62 inference(rename_variables,[],[26])).
% 0.54/0.62 cnf(60,plain,
% 0.54/0.62 (P2(f6(f5(x601),a1),x601,a1)),
% 0.54/0.62 inference(rename_variables,[],[37])).
% 0.54/0.62 cnf(66,plain,
% 0.54/0.62 ($false),
% 0.54/0.62 inference(scs_inference,[],[20,34,37,60,12,13,16,19,55,18,26,50,52,58,2,7,8,23,10,9,25,22]),
% 0.54/0.62 ['proof']).
% 0.54/0.62 % SZS output end Proof
% 0.54/0.62 % Total time :0.000000s
%------------------------------------------------------------------------------