%------------------------------------------------------------------------------
% File : CSE---1.7
% Problem : GRP036-3 : 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 : n021.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 4.81s 4.85s
% Output : CNFRefutation 4.81s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : GRP036-3 : TPTP v8.2.0. Released v1.0.0.
% 0.10/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.33 % Computer : n021.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Thu Jun 20 09:28:54 EDT 2024
% 0.13/0.33 % CPUTime :
% 0.20/0.57 start to proof:theBenchmark
% 4.75/4.84 %-------------------------------------------
% 4.75/4.84 % File :CSE---1.7
% 4.75/4.84 % Problem :theBenchmark
% 4.75/4.84 % Transform :cnf
% 4.75/4.84 % Format :tptp:raw
% 4.75/4.84 % Command :java -jar mcs_scs.jar %d %s
% 4.75/4.84
% 4.75/4.84 % Result :Theorem 4.240000s
% 4.75/4.84 % Output :CNFRefutation 4.240000s
% 4.75/4.84 %-------------------------------------------
% 4.75/4.84 %--------------------------------------------------------------------------
% 4.75/4.85 % File : GRP036-3 : TPTP v8.2.0. Released v1.0.0.
% 4.75/4.85 % Domain : Group Theory (Subgroups)
% 4.75/4.85 % Problem : In subgroups, the identity element is unique
% 4.75/4.85 % Version : [Wos65] axioms.
% 4.75/4.85 % English :
% 4.75/4.85
% 4.75/4.85 % Refs : [Wos65] Wos (1965), Unpublished Note
% 4.75/4.85 % : [WM76] Wilson & Minker (1976), Resolution, Refinements, and S
% 4.75/4.85 % Source : [SPRFN]
% 4.75/4.85 % Names : Problem 16 [Wos65]
% 4.75/4.85 % : wos16 [WM76]
% 4.75/4.85
% 4.75/4.85 % Status : Unsatisfiable
% 4.75/4.85 % Rating : 0.00 v5.5.0, 0.06 v5.4.0, 0.00 v5.3.0, 0.08 v5.2.0, 0.00 v2.0.0
% 4.75/4.85 % Syntax : Number of clauses : 16 ( 7 unt; 0 nHn; 11 RR)
% 4.75/4.85 % Number of literals : 32 ( 2 equ; 17 neg)
% 4.75/4.85 % Maximal clause size : 4 ( 2 avg)
% 4.75/4.85 % Maximal term depth : 2 ( 1 avg)
% 4.75/4.85 % Number of predicates : 3 ( 2 usr; 0 prp; 1-3 aty)
% 4.75/4.85 % Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% 4.81/4.85 % Number of variables : 30 ( 0 sgn)
% 4.81/4.85 % SPC : CNF_UNS_RFO_SEQ_HRN
% 4.81/4.85
% 4.81/4.85 % Comments :
% 4.81/4.85 %--------------------------------------------------------------------------
% 4.81/4.85 %----Include group theory axioms
% 4.81/4.85 include('Axioms/GRP003-0.ax').
% 4.81/4.85 %----Include sub-group theory axioms
% 4.81/4.85 include('Axioms/GRP003-2.ax').
% 4.81/4.85 %--------------------------------------------------------------------------
% 4.81/4.85 cnf(another_left_identity,hypothesis,
% 4.81/4.85 ( ~ subgroup_member(A)
% 4.81/4.85 | product(another_identity,A,A) ) ).
% 4.81/4.85
% 4.81/4.85 cnf(another_right_identity,hypothesis,
% 4.81/4.85 ( ~ subgroup_member(A)
% 4.81/4.85 | product(A,another_identity,A) ) ).
% 4.81/4.85
% 4.81/4.85 cnf(another_right_inverse,hypothesis,
% 4.81/4.85 ( ~ subgroup_member(A)
% 4.81/4.85 | product(A,another_inverse(A),another_identity) ) ).
% 4.81/4.85
% 4.81/4.85 cnf(another_left_inverse,hypothesis,
% 4.81/4.85 ( ~ subgroup_member(A)
% 4.81/4.85 | product(another_inverse(A),A,another_identity) ) ).
% 4.81/4.85
% 4.81/4.85 cnf(another_inverse_in_subgroup,hypothesis,
% 4.81/4.85 ( ~ subgroup_member(A)
% 4.81/4.85 | subgroup_member(another_inverse(A)) ) ).
% 4.81/4.85
% 4.81/4.85 cnf(another_identity_in_subgroup,hypothesis,
% 4.81/4.85 subgroup_member(another_identity) ).
% 4.81/4.85
% 4.81/4.85 cnf(prove_identity_equals_another_identity,negated_conjecture,
% 4.81/4.85 identity != another_identity ).
% 4.81/4.85
% 4.81/4.85 %--------------------------------------------------------------------------
% 4.81/4.85 %-------------------------------------------
% 4.81/4.85 % Proof found
% 4.81/4.85 % SZS status Theorem for theBenchmark
% 4.81/4.85 % SZS output start Proof
% 4.81/4.85 %ClaNum:27(EqnAxiom:11)
% 4.81/4.85 %VarNum:64(SingletonVarNum:30)
% 4.81/4.85 %MaxLitNum:4
% 4.81/4.85 %MaxfuncDepth:1
% 4.81/4.85 %SharedTerms:4
% 4.81/4.85 %goalClause: 18
% 4.81/4.85 %singleGoalClaCount:1
% 4.81/4.85 [12]P1(a1)
% 4.81/4.85 [18]~E(a1,a2)
% 4.81/4.85 [13]P2(x131,a2,x131)
% 4.81/4.85 [14]P2(a2,x141,x141)
% 4.81/4.85 [15]P2(x151,f4(x151),a2)
% 4.81/4.85 [16]P2(f4(x161),x161,a2)
% 4.81/4.85 [17]P2(x171,x172,f5(x171,x172))
% 4.81/4.85 [20]~P1(x201)+P2(x201,a1,x201)
% 4.81/4.85 [21]~P1(x211)+P2(a1,x211,x211)
% 4.81/4.85 [19]~P1(x191)+P1(f3(x191))
% 4.81/4.85 [22]~P1(x221)+P2(x221,f3(x221),a1)
% 4.81/4.85 [23]~P1(x231)+P2(f3(x231),x231,a1)
% 4.81/4.85 [25]~P2(x253,x254,x251)+E(x251,x252)+~P2(x253,x254,x252)
% 4.81/4.85 [24]P1(x241)+~P1(x242)+~P1(x243)+~P2(x243,f4(x242),x241)
% 4.81/4.85 [26]~P2(x266,x264,x261)+P2(x261,x262,x263)+~P2(x264,x262,x265)+~P2(x266,x265,x263)
% 4.81/4.85 [27]~P2(x271,x276,x274)+P2(x271,x272,x273)+~P2(x274,x275,x273)+~P2(x276,x275,x272)
% 4.81/4.85 %EqnAxiom
% 4.81/4.85 [1]E(x11,x11)
% 4.81/4.85 [2]E(x22,x21)+~E(x21,x22)
% 4.81/4.85 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 4.81/4.85 [4]~E(x41,x42)+E(f4(x41),f4(x42))
% 4.81/4.85 [5]~E(x51,x52)+E(f3(x51),f3(x52))
% 4.81/4.85 [6]~E(x61,x62)+E(f5(x61,x63),f5(x62,x63))
% 4.81/4.85 [7]~E(x71,x72)+E(f5(x73,x71),f5(x73,x72))
% 4.81/4.85 [8]~P1(x81)+P1(x82)+~E(x81,x82)
% 4.81/4.85 [9]P2(x92,x93,x94)+~E(x91,x92)+~P2(x91,x93,x94)
% 4.81/4.85 [10]P2(x103,x102,x104)+~E(x101,x102)+~P2(x103,x101,x104)
% 4.81/4.85 [11]P2(x113,x114,x112)+~E(x111,x112)+~P2(x113,x114,x111)
% 4.81/4.85
% 4.81/4.85 %-------------------------------------------
% 4.81/4.85 cnf(28,plain,
% 4.81/4.85 (E(x281,f5(x281,a2))),
% 4.81/4.85 inference(scs_inference,[],[13,17,25])).
% 4.81/4.85 cnf(29,plain,
% 4.81/4.85 (P2(x291,x292,f5(x291,x292))),
% 4.81/4.85 inference(rename_variables,[],[17])).
% 4.81/4.85 cnf(35,plain,
% 4.81/4.85 (P2(a2,x351,x351)),
% 4.81/4.85 inference(rename_variables,[],[14])).
% 4.81/4.85 cnf(38,plain,
% 4.81/4.85 (P1(f5(a1,f4(a1)))),
% 4.81/4.85 inference(scs_inference,[],[13,14,35,17,29,12,25,8,9,10,11,24])).
% 4.81/4.85 cnf(48,plain,
% 4.81/4.85 (E(x481,f5(x481,a2))),
% 4.81/4.85 inference(rename_variables,[],[28])).
% 4.81/4.85 cnf(50,plain,
% 4.81/4.85 (P2(f4(x501),x501,a2)),
% 4.81/4.85 inference(rename_variables,[],[16])).
% 4.81/4.85 cnf(51,plain,
% 4.81/4.86 (P2(x511,a2,x511)),
% 4.81/4.86 inference(rename_variables,[],[13])).
% 4.81/4.86 cnf(54,plain,
% 4.81/4.86 (P2(x541,a2,x541)),
% 4.81/4.86 inference(rename_variables,[],[13])).
% 4.81/4.86 cnf(60,plain,
% 4.81/4.86 (P2(x601,f4(x601),a2)),
% 4.81/4.86 inference(rename_variables,[],[15])).
% 4.81/4.86 cnf(62,plain,
% 4.81/4.86 (P1(a2)),
% 4.81/4.86 inference(scs_inference,[],[18,28,48,13,51,54,15,60,16,50,38,2,3,11,25,9,10,26,24])).
% 4.81/4.86 cnf(903,plain,
% 4.81/4.86 (~P2(a1,a2,a2)),
% 4.81/4.86 inference(scs_inference,[],[18,13,2,25])).
% 4.81/4.86 cnf(904,plain,
% 4.81/4.86 ($false),
% 4.81/4.86 inference(scs_inference,[],[903,62,21]),
% 4.81/4.86 ['proof']).
% 4.81/4.86 % SZS output end Proof
% 4.81/4.86 % Total time :4.240000s
%------------------------------------------------------------------------------