TSTP Solution File: GRP126-2.004 by CSE---1.6
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : GRP126-2.004 : TPTP v8.1.2. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% Computer : n017.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 : Thu Aug 31 00:11:05 EDT 2023
% Result : Unsatisfiable 0.65s 0.78s
% Output : CNFRefutation 0.65s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP126-2.004 : TPTP v8.1.2. Released v1.2.0.
% 0.06/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.11/0.34 % Computer : n017.cluster.edu
% 0.11/0.34 % Model : x86_64 x86_64
% 0.11/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.34 % Memory : 8042.1875MB
% 0.11/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.34 % CPULimit : 300
% 0.11/0.34 % WCLimit : 300
% 0.11/0.34 % DateTime : Mon Aug 28 22:59:43 EDT 2023
% 0.11/0.34 % CPUTime :
% 0.18/0.59 start to proof:theBenchmark
% 0.65/0.77 %-------------------------------------------
% 0.65/0.77 % File :CSE---1.6
% 0.65/0.77 % Problem :theBenchmark
% 0.65/0.77 % Transform :cnf
% 0.65/0.77 % Format :tptp:raw
% 0.65/0.77 % Command :java -jar mcs_scs.jar %d %s
% 0.65/0.77
% 0.65/0.77 % Result :Theorem 0.130000s
% 0.65/0.77 % Output :CNFRefutation 0.130000s
% 0.65/0.77 %-------------------------------------------
% 0.65/0.78 %--------------------------------------------------------------------------
% 0.65/0.78 % File : GRP126-2.004 : TPTP v8.1.2. Released v1.2.0.
% 0.65/0.78 % Domain : Group Theory (Quasigroups)
% 0.65/0.78 % Problem : (a.b).(b.a) = b
% 0.65/0.78 % Version : [Sla93] axioms : Augmented.
% 0.65/0.78 % English : Generate the multiplication table for the specified quasi-
% 0.65/0.78 % group with 4 elements.
% 0.65/0.78
% 0.65/0.78 % Refs : [FSB93] Fujita et al. (1993), Automatic Generation of Some Res
% 0.65/0.78 % : [Sla93] Slaney (1993), Email to G. Sutcliffe
% 0.65/0.78 % : [SFS95] Slaney et al. (1995), Automated Reasoning and Exhausti
% 0.65/0.78 % Source : [TPTP]
% 0.65/0.78 % Names :
% 0.65/0.78
% 0.65/0.78 % Status : Unsatisfiable
% 0.65/0.78 % Rating : 0.00 v2.4.0, 0.00 v2.1.0
% 0.65/0.78 % Syntax : Number of clauses : 32 ( 26 unt; 1 nHn; 31 RR)
% 0.65/0.78 % Number of literals : 47 ( 0 equ; 25 neg)
% 0.65/0.78 % Maximal clause size : 6 ( 1 avg)
% 0.65/0.78 % Maximal term depth : 1 ( 1 avg)
% 0.65/0.78 % Number of predicates : 5 ( 5 usr; 0 prp; 1-3 aty)
% 0.65/0.78 % Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% 0.65/0.78 % Number of variables : 22 ( 0 sgn)
% 0.65/0.78 % SPC : CNF_UNS_EPR_NEQ_NHN
% 0.65/0.78
% 0.65/0.78 % Comments : [SFS93]'s axiomatization has been modified for this.
% 0.65/0.78 % : Substitution axioms are not needed, as any positive equality
% 0.65/0.78 % literals should resolve on negative ones directly.
% 0.65/0.78 % : Version 2 has simple isomorphism avoidance (as mentioned in
% 0.65/0.78 % [FSB93])
% 0.65/0.78 % : tptp2X: -f tptp -s4 GRP126-2.g
% 0.65/0.78 %--------------------------------------------------------------------------
% 0.65/0.78 cnf(e_1_then_e_2,axiom,
% 0.65/0.78 next(e_1,e_2) ).
% 0.65/0.78
% 0.65/0.78 cnf(e_2_then_e_3,axiom,
% 0.65/0.78 next(e_2,e_3) ).
% 0.65/0.78
% 0.65/0.78 cnf(e_3_then_e_4,axiom,
% 0.65/0.78 next(e_3,e_4) ).
% 0.65/0.78
% 0.65/0.78 cnf(e_2_greater_e_1,axiom,
% 0.65/0.78 greater(e_2,e_1) ).
% 0.65/0.78
% 0.65/0.78 cnf(e_3_greater_e_1,axiom,
% 0.65/0.78 greater(e_3,e_1) ).
% 0.65/0.78
% 0.65/0.78 cnf(e_4_greater_e_1,axiom,
% 0.65/0.78 greater(e_4,e_1) ).
% 0.65/0.78
% 0.65/0.78 cnf(e_3_greater_e_2,axiom,
% 0.65/0.78 greater(e_3,e_2) ).
% 0.65/0.78
% 0.65/0.78 cnf(e_4_greater_e_2,axiom,
% 0.65/0.78 greater(e_4,e_2) ).
% 0.65/0.78
% 0.65/0.78 cnf(e_4_greater_e_3,axiom,
% 0.65/0.78 greater(e_4,e_3) ).
% 0.65/0.78
% 0.65/0.78 cnf(no_redundancy,axiom,
% 0.65/0.78 ( ~ product(X,e_1,Y)
% 0.65/0.78 | ~ next(X,X1)
% 0.65/0.78 | ~ greater(Y,X1) ) ).
% 0.65/0.78
% 0.65/0.78 cnf(element_1,axiom,
% 0.65/0.78 group_element(e_1) ).
% 0.65/0.78
% 0.65/0.78 cnf(element_2,axiom,
% 0.65/0.78 group_element(e_2) ).
% 0.65/0.78
% 0.65/0.78 cnf(element_3,axiom,
% 0.65/0.78 group_element(e_3) ).
% 0.65/0.78
% 0.65/0.78 cnf(element_4,axiom,
% 0.65/0.78 group_element(e_4) ).
% 0.65/0.78
% 0.65/0.78 cnf(e_1_is_not_e_2,axiom,
% 0.65/0.78 ~ equalish(e_1,e_2) ).
% 0.65/0.78
% 0.65/0.78 cnf(e_1_is_not_e_3,axiom,
% 0.65/0.78 ~ equalish(e_1,e_3) ).
% 0.65/0.78
% 0.65/0.78 cnf(e_1_is_not_e_4,axiom,
% 0.65/0.78 ~ equalish(e_1,e_4) ).
% 0.65/0.78
% 0.65/0.78 cnf(e_2_is_not_e_1,axiom,
% 0.65/0.78 ~ equalish(e_2,e_1) ).
% 0.65/0.78
% 0.65/0.78 cnf(e_2_is_not_e_3,axiom,
% 0.65/0.78 ~ equalish(e_2,e_3) ).
% 0.65/0.78
% 0.65/0.78 cnf(e_2_is_not_e_4,axiom,
% 0.65/0.78 ~ equalish(e_2,e_4) ).
% 0.65/0.78
% 0.65/0.78 cnf(e_3_is_not_e_1,axiom,
% 0.65/0.78 ~ equalish(e_3,e_1) ).
% 0.65/0.78
% 0.65/0.78 cnf(e_3_is_not_e_2,axiom,
% 0.65/0.78 ~ equalish(e_3,e_2) ).
% 0.65/0.78
% 0.65/0.78 cnf(e_3_is_not_e_4,axiom,
% 0.65/0.78 ~ equalish(e_3,e_4) ).
% 0.65/0.78
% 0.65/0.78 cnf(e_4_is_not_e_1,axiom,
% 0.65/0.78 ~ equalish(e_4,e_1) ).
% 0.65/0.78
% 0.65/0.78 cnf(e_4_is_not_e_2,axiom,
% 0.65/0.78 ~ equalish(e_4,e_2) ).
% 0.65/0.78
% 0.65/0.78 cnf(e_4_is_not_e_3,axiom,
% 0.65/0.78 ~ equalish(e_4,e_3) ).
% 0.65/0.78
% 0.65/0.78 cnf(product_total_function1,axiom,
% 0.65/0.78 ( ~ group_element(X)
% 0.65/0.78 | ~ group_element(Y)
% 0.65/0.78 | product(X,Y,e_1)
% 0.65/0.78 | product(X,Y,e_2)
% 0.65/0.78 | product(X,Y,e_3)
% 0.65/0.78 | product(X,Y,e_4) ) ).
% 0.65/0.78
% 0.65/0.78 cnf(product_total_function2,axiom,
% 0.65/0.78 ( ~ product(X,Y,W)
% 0.65/0.78 | ~ product(X,Y,Z)
% 0.65/0.78 | equalish(W,Z) ) ).
% 0.65/0.78
% 0.65/0.78 cnf(product_right_cancellation,axiom,
% 0.65/0.78 ( ~ product(X,W,Y)
% 0.65/0.78 | ~ product(X,Z,Y)
% 0.65/0.78 | equalish(W,Z) ) ).
% 0.65/0.78
% 0.65/0.78 cnf(product_left_cancellation,axiom,
% 0.65/0.78 ( ~ product(W,Y,X)
% 0.65/0.78 | ~ product(Z,Y,X)
% 0.65/0.78 | equalish(W,Z) ) ).
% 0.65/0.78
% 0.65/0.78 cnf(product_idempotence,axiom,
% 0.65/0.78 product(X,X,X) ).
% 0.65/0.78
% 0.65/0.78 cnf(qg4,negated_conjecture,
% 0.65/0.78 ( ~ product(X,Y,Z1)
% 0.65/0.78 | ~ product(Y,X,Z2)
% 0.65/0.78 | product(Z1,Z2,Y) ) ).
% 0.65/0.78
% 0.65/0.78 %--------------------------------------------------------------------------
% 0.65/0.78 %-------------------------------------------
% 0.65/0.78 % Proof found
% 0.65/0.78 % SZS status Theorem for theBenchmark
% 0.65/0.78 % SZS output start Proof
% 0.65/0.78 %ClaNum:32(EqnAxiom:0)
% 0.65/0.78 %VarNum:52(SingletonVarNum:22)
% 0.65/0.78 %MaxLitNum:6
% 0.65/0.78 %MaxfuncDepth:0
% 0.65/0.78 %SharedTerms:29
% 0.65/0.78 %goalClause: 31
% 0.65/0.78 [1]P1(a1)
% 0.65/0.78 [2]P1(a2)
% 0.65/0.78 [3]P1(a3)
% 0.65/0.78 [4]P1(a4)
% 0.65/0.78 [5]P4(a1,a2)
% 0.65/0.78 [6]P4(a2,a3)
% 0.65/0.78 [7]P4(a3,a4)
% 0.65/0.78 [8]P2(a2,a1)
% 0.65/0.78 [9]P2(a3,a1)
% 0.65/0.78 [10]P2(a3,a2)
% 0.65/0.78 [11]P2(a4,a1)
% 0.65/0.78 [12]P2(a4,a2)
% 0.65/0.78 [13]P2(a4,a3)
% 0.65/0.78 [15]~P3(a1,a2)
% 0.65/0.78 [16]~P3(a1,a3)
% 0.65/0.78 [17]~P3(a1,a4)
% 0.65/0.78 [18]~P3(a2,a1)
% 0.65/0.78 [19]~P3(a2,a3)
% 0.65/0.78 [20]~P3(a2,a4)
% 0.65/0.78 [21]~P3(a3,a1)
% 0.65/0.78 [22]~P3(a3,a2)
% 0.65/0.78 [23]~P3(a3,a4)
% 0.65/0.78 [24]~P3(a4,a1)
% 0.65/0.78 [25]~P3(a4,a2)
% 0.65/0.78 [26]~P3(a4,a3)
% 0.65/0.78 [14]P5(x141,x141,x141)
% 0.65/0.78 [27]~P4(x271,x272)+~P2(x273,x272)+~P5(x271,a1,x273)
% 0.65/0.79 [28]~P5(x283,x284,x281)+P3(x281,x282)+~P5(x283,x284,x282)
% 0.65/0.79 [29]~P5(x293,x291,x294)+P3(x291,x292)+~P5(x293,x292,x294)
% 0.65/0.79 [30]~P5(x301,x303,x304)+P3(x301,x302)+~P5(x302,x303,x304)
% 0.65/0.79 [31]~P5(x314,x313,x311)+P5(x311,x312,x313)+~P5(x313,x314,x312)
% 0.65/0.79 [32]~P1(x322)+~P1(x321)+P5(x321,x322,a2)+P5(x321,x322,a3)+P5(x321,x322,a4)+P5(x321,x322,a1)
% 0.65/0.79 %EqnAxiom
% 0.65/0.79
% 0.65/0.79 %-------------------------------------------
% 0.65/0.79 cnf(35,plain,
% 0.65/0.79 (P5(x351,x351,x351)),
% 0.65/0.79 inference(rename_variables,[],[14])).
% 0.65/0.79 cnf(37,plain,
% 0.65/0.79 (~P5(a1,a2,a1)),
% 0.65/0.79 inference(scs_inference,[],[14,35,5,15,30,27,29])).
% 0.65/0.79 cnf(46,plain,
% 0.65/0.79 (P5(x461,x461,x461)),
% 0.65/0.79 inference(rename_variables,[],[14])).
% 0.65/0.79 cnf(49,plain,
% 0.65/0.79 (P5(x491,x491,x491)),
% 0.65/0.79 inference(rename_variables,[],[14])).
% 0.65/0.79 cnf(51,plain,
% 0.65/0.79 (~P5(a2,a1,a4)),
% 0.65/0.79 inference(scs_inference,[],[6,13,16,14,46,28,30,27])).
% 0.65/0.79 cnf(56,plain,
% 0.65/0.79 (P5(a1,a2,a4)+P5(a1,a2,a3)+P5(a1,a2,a2)),
% 0.65/0.79 inference(scs_inference,[],[1,2,6,13,16,14,46,49,37,28,30,27,29,32])).
% 0.65/0.79 cnf(62,plain,
% 0.65/0.79 (~P5(a1,a4,a4)),
% 0.65/0.79 inference(scs_inference,[],[17,14,29,30])).
% 0.65/0.79 cnf(74,plain,
% 0.65/0.79 (P5(x741,x741,x741)),
% 0.65/0.79 inference(rename_variables,[],[14])).
% 0.65/0.79 cnf(77,plain,
% 0.65/0.79 (P5(x771,x771,x771)),
% 0.65/0.79 inference(rename_variables,[],[14])).
% 0.65/0.79 cnf(80,plain,
% 0.65/0.79 (P5(x801,x801,x801)),
% 0.65/0.79 inference(rename_variables,[],[14])).
% 0.65/0.79 cnf(82,plain,
% 0.65/0.79 (~P5(a1,a2,a2)),
% 0.65/0.79 inference(scs_inference,[],[18,5,14,74,77,80,62,28,29,27,31,30])).
% 0.65/0.79 cnf(85,plain,
% 0.65/0.79 (P5(a2,a1,a1)+P5(a2,a1,a3)),
% 0.65/0.79 inference(scs_inference,[],[2,18,5,14,74,77,80,51,62,1,28,29,27,31,30,32])).
% 0.65/0.79 cnf(88,plain,
% 0.65/0.79 (P5(a1,a2,a3)+P5(a1,a2,a4)),
% 0.65/0.79 inference(scs_inference,[],[82,56])).
% 0.65/0.79 cnf(90,plain,
% 0.65/0.79 (~P5(a2,a2,a3)),
% 0.65/0.79 inference(scs_inference,[],[19,14,28])).
% 0.65/0.79 cnf(91,plain,
% 0.65/0.79 (P5(x911,x911,x911)),
% 0.65/0.79 inference(rename_variables,[],[14])).
% 0.65/0.79 cnf(94,plain,
% 0.65/0.79 (P5(x941,x941,x941)),
% 0.65/0.79 inference(rename_variables,[],[14])).
% 0.65/0.79 cnf(98,plain,
% 0.65/0.79 (~P5(a2,a3,a3)),
% 0.65/0.79 inference(scs_inference,[],[12,19,5,14,91,94,28,29,27,30])).
% 0.65/0.79 cnf(115,plain,
% 0.65/0.79 (~P5(a3,a3,a2)),
% 0.65/0.79 inference(scs_inference,[],[14,98,29,31])).
% 0.65/0.79 cnf(116,plain,
% 0.65/0.79 (P5(x1161,x1161,x1161)),
% 0.65/0.79 inference(rename_variables,[],[14])).
% 0.65/0.79 cnf(118,plain,
% 0.65/0.79 (~P5(a1,a3,a3)),
% 0.65/0.79 inference(scs_inference,[],[21,14,116,98,29,31,30])).
% 0.65/0.79 cnf(197,plain,
% 0.65/0.79 (P5(x1971,x1971,x1971)),
% 0.65/0.79 inference(rename_variables,[],[14])).
% 0.65/0.79 cnf(199,plain,
% 0.65/0.79 (~P5(a1,a3,a1)),
% 0.65/0.79 inference(scs_inference,[],[21,23,14,197,28,30,29])).
% 0.65/0.79 cnf(223,plain,
% 0.65/0.79 (P5(a2,a1,a3)),
% 0.65/0.79 inference(scs_inference,[],[8,15,14,29,30,27,85])).
% 0.65/0.79 cnf(224,plain,
% 0.65/0.79 (~P5(a1,a2,a3)),
% 0.65/0.79 inference(scs_inference,[],[8,15,14,115,29,30,27,85,31])).
% 0.65/0.79 cnf(226,plain,
% 0.65/0.79 (P5(a1,a2,a4)),
% 0.65/0.79 inference(scs_inference,[],[224,88])).
% 0.65/0.79 cnf(253,plain,
% 0.65/0.79 (P5(a4,a3,a2)),
% 0.65/0.79 inference(scs_inference,[],[226,223,31])).
% 0.65/0.79 cnf(270,plain,
% 0.65/0.79 (~P5(a1,a3,a4)),
% 0.65/0.79 inference(scs_inference,[],[22,25,14,90,253,226,31,30,29])).
% 0.65/0.79 cnf(294,plain,
% 0.65/0.79 ($false),
% 0.65/0.79 inference(scs_inference,[],[17,199,270,118,6,253,3,223,1,30,27,32]),
% 0.65/0.79 ['proof']).
% 0.65/0.79 % SZS output end Proof
% 0.65/0.79 % Total time :0.130000s
%------------------------------------------------------------------------------