TSTP Solution File: GRP353-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : GRP353-1 : TPTP v8.1.2. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n003.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 00:18:37 EDT 2023
% Result : Unsatisfiable 0.53s 0.65s
% Output : CNFRefutation 0.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 35
% Syntax : Number of formulae : 150 ( 17 unt; 10 typ; 0 def)
% Number of atoms : 332 ( 331 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 270 ( 78 ~; 192 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 3 ( 2 >; 1 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 56 ( 0 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
identity: $i ).
tff(decl_23,type,
multiply: ( $i * $i ) > $i ).
tff(decl_24,type,
inverse: $i > $i ).
tff(decl_25,type,
sk_c6: $i ).
tff(decl_26,type,
sk_c5: $i ).
tff(decl_27,type,
sk_c7: $i ).
tff(decl_28,type,
sk_c2: $i ).
tff(decl_29,type,
sk_c3: $i ).
tff(decl_30,type,
sk_c4: $i ).
tff(decl_31,type,
sk_c1: $i ).
cnf(associativity,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',associativity) ).
cnf(left_inverse,axiom,
multiply(inverse(X1),X1) = identity,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
cnf(left_identity,axiom,
multiply(identity,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_identity) ).
cnf(prove_this_22,negated_conjecture,
( multiply(sk_c7,sk_c5) = sk_c6
| multiply(sk_c3,sk_c4) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_22) ).
cnf(prove_this_23,negated_conjecture,
( multiply(sk_c7,sk_c5) = sk_c6
| inverse(sk_c3) = sk_c4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_23) ).
cnf(prove_this_24,negated_conjecture,
( multiply(sk_c7,sk_c5) = sk_c6
| multiply(sk_c4,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_24) ).
cnf(prove_this_4,negated_conjecture,
( multiply(sk_c6,sk_c5) = sk_c7
| multiply(sk_c3,sk_c4) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
cnf(prove_this_21,negated_conjecture,
( multiply(sk_c7,sk_c5) = sk_c6
| multiply(sk_c2,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
cnf(prove_this_9,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| multiply(sk_c2,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).
cnf(prove_this_5,negated_conjecture,
( multiply(sk_c6,sk_c5) = sk_c7
| inverse(sk_c3) = sk_c4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
cnf(prove_this_7,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_7) ).
cnf(prove_this_19,negated_conjecture,
( multiply(sk_c7,sk_c5) = sk_c6
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_19) ).
cnf(prove_this_25,negated_conjecture,
( multiply(sk_c6,sk_c5) != sk_c7
| multiply(X1,sk_c7) != sk_c6
| inverse(X1) != sk_c7
| multiply(sk_c7,sk_c5) != sk_c6
| multiply(sk_c6,sk_c7) != sk_c5
| inverse(X2) != sk_c7
| multiply(X2,sk_c6) != sk_c7
| multiply(X3,X4) != sk_c6
| inverse(X3) != X4
| multiply(X4,sk_c7) != sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_25) ).
cnf(prove_this_8,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_8) ).
cnf(prove_this_13,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_13) ).
cnf(prove_this_14,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
cnf(prove_this_17,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c3) = sk_c4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_17) ).
cnf(prove_this_16,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c3,sk_c4) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_16) ).
cnf(prove_this_18,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c4,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).
cnf(prove_this_6,negated_conjecture,
( multiply(sk_c6,sk_c5) = sk_c7
| multiply(sk_c4,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
cnf(prove_this_15,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c2,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
cnf(prove_this_20,negated_conjecture,
( multiply(sk_c7,sk_c5) = sk_c6
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_20) ).
cnf(prove_this_10,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| multiply(sk_c3,sk_c4) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).
cnf(prove_this_11,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| inverse(sk_c3) = sk_c4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
cnf(prove_this_1,negated_conjecture,
( multiply(sk_c6,sk_c5) = sk_c7
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
cnf(c_0_25,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity ).
cnf(c_0_26,axiom,
multiply(inverse(X1),X1) = identity,
left_inverse ).
cnf(c_0_27,axiom,
multiply(identity,X1) = X1,
left_identity ).
cnf(c_0_28,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]) ).
cnf(c_0_29,plain,
multiply(inverse(inverse(X1)),X2) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_28,c_0_28]) ).
cnf(c_0_30,negated_conjecture,
( multiply(sk_c7,sk_c5) = sk_c6
| multiply(sk_c3,sk_c4) = sk_c6 ),
prove_this_22 ).
cnf(c_0_31,plain,
multiply(X1,identity) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_26]),c_0_29]) ).
cnf(c_0_32,negated_conjecture,
( multiply(inverse(sk_c3),sk_c6) = sk_c4
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(spm,[status(thm)],[c_0_28,c_0_30]) ).
cnf(c_0_33,negated_conjecture,
( multiply(sk_c7,sk_c5) = sk_c6
| inverse(sk_c3) = sk_c4 ),
prove_this_23 ).
cnf(c_0_34,negated_conjecture,
( multiply(sk_c7,sk_c5) = sk_c6
| multiply(sk_c4,sk_c7) = sk_c6 ),
prove_this_24 ).
cnf(c_0_35,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_31]),c_0_31]) ).
cnf(c_0_36,negated_conjecture,
( multiply(sk_c3,multiply(sk_c4,X1)) = multiply(sk_c6,X1)
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(spm,[status(thm)],[c_0_25,c_0_30]) ).
cnf(c_0_37,negated_conjecture,
( multiply(sk_c7,sk_c5) = sk_c6
| multiply(sk_c4,sk_c6) = sk_c4 ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_38,negated_conjecture,
( multiply(inverse(sk_c4),sk_c6) = sk_c7
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(spm,[status(thm)],[c_0_28,c_0_34]) ).
cnf(c_0_39,negated_conjecture,
( multiply(sk_c7,sk_c5) = sk_c6
| inverse(sk_c4) = sk_c3 ),
inference(spm,[status(thm)],[c_0_35,c_0_33]) ).
cnf(c_0_40,negated_conjecture,
( multiply(sk_c6,sk_c5) = sk_c7
| multiply(sk_c3,sk_c4) = sk_c6 ),
prove_this_4 ).
cnf(c_0_41,negated_conjecture,
( multiply(sk_c7,sk_c5) = sk_c6
| multiply(sk_c2,sk_c6) = sk_c7 ),
prove_this_21 ).
cnf(c_0_42,negated_conjecture,
( multiply(sk_c3,sk_c4) = multiply(sk_c6,sk_c6)
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_43,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| multiply(sk_c2,sk_c6) = sk_c7 ),
prove_this_9 ).
cnf(c_0_44,negated_conjecture,
( multiply(sk_c3,sk_c6) = multiply(sk_c6,sk_c7)
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(spm,[status(thm)],[c_0_36,c_0_34]) ).
cnf(c_0_45,negated_conjecture,
( multiply(sk_c7,sk_c5) = sk_c6
| multiply(sk_c3,sk_c6) = sk_c7 ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_46,negated_conjecture,
( multiply(inverse(sk_c3),sk_c6) = sk_c4
| multiply(sk_c6,sk_c5) = sk_c7 ),
inference(spm,[status(thm)],[c_0_28,c_0_40]) ).
cnf(c_0_47,negated_conjecture,
( multiply(sk_c6,sk_c5) = sk_c7
| inverse(sk_c3) = sk_c4 ),
prove_this_5 ).
cnf(c_0_48,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| multiply(sk_c6,sk_c7) = sk_c5 ),
prove_this_7 ).
cnf(c_0_49,negated_conjecture,
( multiply(sk_c2,multiply(sk_c6,X1)) = multiply(sk_c7,X1)
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(spm,[status(thm)],[c_0_25,c_0_41]) ).
cnf(c_0_50,negated_conjecture,
( multiply(sk_c6,sk_c6) = sk_c6
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(spm,[status(thm)],[c_0_30,c_0_42]) ).
cnf(c_0_51,negated_conjecture,
( multiply(inverse(sk_c2),sk_c7) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(spm,[status(thm)],[c_0_28,c_0_43]) ).
cnf(c_0_52,negated_conjecture,
( multiply(sk_c7,sk_c5) = sk_c6
| multiply(sk_c6,sk_c7) = sk_c5 ),
prove_this_19 ).
cnf(c_0_53,negated_conjecture,
( multiply(sk_c7,sk_c5) = sk_c6
| multiply(sk_c6,sk_c7) = sk_c7 ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_54,negated_conjecture,
( multiply(sk_c6,sk_c5) != sk_c7
| multiply(X1,sk_c7) != sk_c6
| inverse(X1) != sk_c7
| multiply(sk_c7,sk_c5) != sk_c6
| multiply(sk_c6,sk_c7) != sk_c5
| inverse(X2) != sk_c7
| multiply(X2,sk_c6) != sk_c7
| multiply(X3,X4) != sk_c6
| inverse(X3) != X4
| multiply(X4,sk_c7) != sk_c6 ),
prove_this_25 ).
cnf(c_0_55,negated_conjecture,
( multiply(sk_c6,sk_c5) = sk_c7
| multiply(sk_c4,sk_c6) = sk_c4 ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_56,negated_conjecture,
( multiply(inverse(sk_c1),sk_c6) = sk_c7
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(spm,[status(thm)],[c_0_28,c_0_48]) ).
cnf(c_0_57,negated_conjecture,
( multiply(sk_c2,sk_c6) = multiply(sk_c7,sk_c6)
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_58,negated_conjecture,
( multiply(inverse(inverse(sk_c2)),sk_c6) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(spm,[status(thm)],[c_0_28,c_0_51]) ).
cnf(c_0_59,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| inverse(sk_c2) = sk_c7 ),
prove_this_8 ).
cnf(c_0_60,negated_conjecture,
( multiply(sk_c7,sk_c5) = sk_c6
| sk_c5 = sk_c7 ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_61,negated_conjecture,
( multiply(inverse(X1),sk_c7) != sk_c6
| multiply(sk_c6,sk_c5) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| multiply(sk_c7,sk_c5) != sk_c6
| multiply(X1,inverse(X1)) != sk_c6
| multiply(X2,sk_c6) != sk_c7
| multiply(X3,sk_c7) != sk_c6
| inverse(X2) != sk_c7
| inverse(X3) != sk_c7 ),
inference(er,[status(thm)],[c_0_54]) ).
cnf(c_0_62,negated_conjecture,
( multiply(sk_c6,sk_c5) = sk_c7
| sk_c6 = identity ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_55]),c_0_26]) ).
cnf(c_0_63,negated_conjecture,
( multiply(inverse(inverse(sk_c1)),sk_c7) = sk_c6
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(spm,[status(thm)],[c_0_28,c_0_56]) ).
cnf(c_0_64,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c6,sk_c7) = sk_c5 ),
prove_this_13 ).
cnf(c_0_65,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c7
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(spm,[status(thm)],[c_0_41,c_0_57]) ).
cnf(c_0_66,negated_conjecture,
( multiply(inverse(sk_c7),sk_c6) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_67,negated_conjecture,
( multiply(inverse(sk_c7),sk_c6) = sk_c5
| sk_c5 = sk_c7 ),
inference(spm,[status(thm)],[c_0_28,c_0_60]) ).
cnf(c_0_68,negated_conjecture,
( sk_c6 = identity
| multiply(inverse(X1),sk_c7) != sk_c6
| multiply(sk_c6,sk_c7) != sk_c5
| multiply(sk_c7,sk_c5) != sk_c6
| multiply(X1,inverse(X1)) != sk_c6
| multiply(X2,sk_c6) != sk_c7
| multiply(X3,sk_c7) != sk_c6
| inverse(X2) != sk_c7
| inverse(X3) != sk_c7 ),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_69,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| sk_c6 = identity ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_26]) ).
cnf(c_0_70,negated_conjecture,
( multiply(sk_c7,sk_c5) = sk_c6
| sk_c6 = identity ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_37]),c_0_26]) ).
cnf(c_0_71,negated_conjecture,
( multiply(inverse(sk_c7),sk_c6) = sk_c5
| multiply(sk_c7,sk_c6) = sk_c7 ),
inference(spm,[status(thm)],[c_0_28,c_0_65]) ).
cnf(c_0_72,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| sk_c5 = sk_c7 ),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
cnf(c_0_73,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c2) = sk_c7 ),
prove_this_14 ).
cnf(c_0_74,negated_conjecture,
( multiply(sk_c4,multiply(sk_c3,X1)) = X1
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(spm,[status(thm)],[c_0_28,c_0_33]) ).
cnf(c_0_75,negated_conjecture,
( sk_c6 = identity
| multiply(inverse(X1),sk_c7) != sk_c6
| multiply(X1,inverse(X1)) != sk_c6
| multiply(X2,sk_c6) != sk_c7
| multiply(X3,sk_c7) != sk_c6
| inverse(X2) != sk_c7
| inverse(X3) != sk_c7 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_70]) ).
cnf(c_0_76,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c3) = sk_c4 ),
prove_this_17 ).
cnf(c_0_77,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c3,sk_c4) = sk_c6 ),
prove_this_16 ).
cnf(c_0_78,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c4,sk_c7) = sk_c6 ),
prove_this_18 ).
cnf(c_0_79,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6
| sk_c5 = sk_c7 ),
inference(spm,[status(thm)],[c_0_66,c_0_71]) ).
cnf(c_0_80,negated_conjecture,
( multiply(inverse(sk_c1),sk_c6) = sk_c7
| sk_c5 = sk_c7 ),
inference(spm,[status(thm)],[c_0_28,c_0_72]) ).
cnf(c_0_81,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c7) = sk_c2 ),
inference(spm,[status(thm)],[c_0_35,c_0_73]) ).
cnf(c_0_82,negated_conjecture,
( multiply(sk_c6,sk_c5) = sk_c7
| multiply(sk_c4,sk_c7) = sk_c6 ),
prove_this_6 ).
cnf(c_0_83,negated_conjecture,
( multiply(sk_c4,multiply(sk_c6,sk_c7)) = sk_c6
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(spm,[status(thm)],[c_0_74,c_0_44]) ).
cnf(c_0_84,negated_conjecture,
( inverse(sk_c1) = sk_c7
| sk_c6 = identity
| multiply(X1,sk_c6) != sk_c7
| multiply(X2,sk_c7) != sk_c6
| inverse(X1) != sk_c7
| inverse(X2) != sk_c7 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_77]),c_0_78]) ).
cnf(c_0_85,negated_conjecture,
( multiply(inverse(sk_c1),sk_c6) = sk_c7
| multiply(sk_c7,sk_c6) = sk_c7
| sk_c5 = sk_c7 ),
inference(spm,[status(thm)],[c_0_28,c_0_79]) ).
cnf(c_0_86,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c2,sk_c6) = sk_c7 ),
prove_this_15 ).
cnf(c_0_87,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c7
| inverse(sk_c7) = sk_c2
| sk_c5 = sk_c7 ),
inference(spm,[status(thm)],[c_0_80,c_0_81]) ).
cnf(c_0_88,negated_conjecture,
( multiply(inverse(sk_c4),sk_c6) = sk_c7
| multiply(sk_c6,sk_c5) = sk_c7 ),
inference(spm,[status(thm)],[c_0_28,c_0_82]) ).
cnf(c_0_89,negated_conjecture,
( multiply(sk_c6,sk_c5) = sk_c7
| inverse(sk_c4) = sk_c3 ),
inference(spm,[status(thm)],[c_0_35,c_0_47]) ).
cnf(c_0_90,negated_conjecture,
( multiply(sk_c7,sk_c5) = sk_c6
| multiply(sk_c4,sk_c5) = sk_c6 ),
inference(spm,[status(thm)],[c_0_83,c_0_52]) ).
cnf(c_0_91,negated_conjecture,
( inverse(sk_c1) = sk_c7
| sk_c6 = identity
| inverse(inverse(inverse(X1))) != sk_c7
| multiply(X1,sk_c6) != sk_c7
| multiply(X2,sk_c7) != sk_c6
| inverse(X2) != sk_c7 ),
inference(spm,[status(thm)],[c_0_84,c_0_29]) ).
cnf(c_0_92,negated_conjecture,
( multiply(sk_c2,sk_c6) = sk_c7
| multiply(sk_c7,sk_c6) = sk_c7
| sk_c5 = sk_c7 ),
inference(spm,[status(thm)],[c_0_85,c_0_86]) ).
cnf(c_0_93,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c7
| multiply(sk_c2,sk_c6) = sk_c5
| sk_c5 = sk_c7 ),
inference(spm,[status(thm)],[c_0_71,c_0_87]) ).
cnf(c_0_94,negated_conjecture,
( multiply(sk_c6,sk_c5) = sk_c7
| multiply(sk_c3,sk_c6) = sk_c7 ),
inference(spm,[status(thm)],[c_0_88,c_0_89]) ).
cnf(c_0_95,negated_conjecture,
( multiply(sk_c3,sk_c6) = multiply(sk_c6,sk_c5)
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(spm,[status(thm)],[c_0_36,c_0_90]) ).
cnf(c_0_96,negated_conjecture,
( inverse(sk_c1) = sk_c7
| sk_c6 = identity
| inverse(inverse(sk_c7)) != sk_c7
| multiply(X1,sk_c7) != sk_c6
| inverse(X1) != sk_c7 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_73]),c_0_86]) ).
cnf(c_0_97,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c7
| sk_c5 = sk_c7 ),
inference(spm,[status(thm)],[c_0_92,c_0_93]) ).
cnf(c_0_98,negated_conjecture,
( multiply(sk_c7,sk_c5) = sk_c6
| multiply(sk_c6,sk_c5) = sk_c7 ),
inference(spm,[status(thm)],[c_0_94,c_0_95]) ).
cnf(c_0_99,negated_conjecture,
( inverse(sk_c1) = sk_c7
| sk_c6 = identity
| multiply(X1,sk_c7) != sk_c6
| inverse(X1) != sk_c7 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_96,c_0_35])]) ).
cnf(c_0_100,negated_conjecture,
( sk_c5 = sk_c7
| sk_c6 = identity ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_97]),c_0_26]) ).
cnf(c_0_101,negated_conjecture,
( multiply(sk_c2,sk_c7) = multiply(sk_c7,sk_c7)
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(spm,[status(thm)],[c_0_49,c_0_53]) ).
cnf(c_0_102,negated_conjecture,
( multiply(sk_c2,sk_c7) = multiply(sk_c7,sk_c5)
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(spm,[status(thm)],[c_0_49,c_0_98]) ).
cnf(c_0_103,negated_conjecture,
( multiply(inverse(sk_c2),sk_c7) = sk_c6
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(spm,[status(thm)],[c_0_28,c_0_41]) ).
cnf(c_0_104,negated_conjecture,
( multiply(sk_c7,sk_c5) = sk_c6
| inverse(sk_c2) = sk_c7 ),
prove_this_20 ).
cnf(c_0_105,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| multiply(sk_c3,sk_c4) = sk_c6 ),
prove_this_10 ).
cnf(c_0_106,negated_conjecture,
( inverse(sk_c1) = sk_c7
| sk_c6 = identity
| multiply(X1,multiply(X2,sk_c7)) != sk_c6
| inverse(multiply(X1,X2)) != sk_c7 ),
inference(spm,[status(thm)],[c_0_99,c_0_25]) ).
cnf(c_0_107,negated_conjecture,
( multiply(sk_c7,sk_c7) = sk_c6
| sk_c6 = identity ),
inference(spm,[status(thm)],[c_0_70,c_0_100]) ).
cnf(c_0_108,negated_conjecture,
( multiply(inverse(sk_c6),sk_c7) = sk_c5
| sk_c6 = identity ),
inference(spm,[status(thm)],[c_0_28,c_0_62]) ).
cnf(c_0_109,negated_conjecture,
( multiply(sk_c7,sk_c5) = multiply(sk_c7,sk_c7)
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(spm,[status(thm)],[c_0_101,c_0_102]) ).
cnf(c_0_110,negated_conjecture,
( multiply(sk_c7,sk_c5) = sk_c6
| multiply(sk_c7,sk_c7) = sk_c6 ),
inference(spm,[status(thm)],[c_0_103,c_0_104]) ).
cnf(c_0_111,negated_conjecture,
( multiply(inverse(sk_c3),sk_c6) = sk_c4
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(spm,[status(thm)],[c_0_28,c_0_105]) ).
cnf(c_0_112,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| inverse(sk_c3) = sk_c4 ),
prove_this_11 ).
cnf(c_0_113,negated_conjecture,
( inverse(sk_c1) = sk_c7
| sk_c6 = identity
| inverse(multiply(X1,sk_c7)) != sk_c7
| multiply(X1,sk_c6) != sk_c6 ),
inference(spm,[status(thm)],[c_0_106,c_0_107]) ).
cnf(c_0_114,negated_conjecture,
( multiply(inverse(sk_c6),multiply(sk_c7,X1)) = multiply(sk_c5,X1)
| sk_c6 = identity ),
inference(spm,[status(thm)],[c_0_25,c_0_108]) ).
cnf(c_0_115,negated_conjecture,
multiply(sk_c7,sk_c5) = sk_c6,
inference(csr,[status(thm)],[inference(ef,[status(thm)],[c_0_109]),c_0_110]) ).
cnf(c_0_116,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| multiply(sk_c4,sk_c6) = sk_c4 ),
inference(spm,[status(thm)],[c_0_111,c_0_112]) ).
cnf(c_0_117,negated_conjecture,
( inverse(sk_c1) = sk_c7
| sk_c6 = identity
| inverse(multiply(X1,multiply(X2,sk_c7))) != sk_c7
| multiply(X1,multiply(X2,sk_c6)) != sk_c6 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_25]),c_0_25]) ).
cnf(c_0_118,negated_conjecture,
( multiply(sk_c5,sk_c7) = identity
| sk_c6 = identity ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_107]),c_0_26]) ).
cnf(c_0_119,negated_conjecture,
multiply(inverse(sk_c7),sk_c6) = sk_c5,
inference(spm,[status(thm)],[c_0_28,c_0_115]) ).
cnf(c_0_120,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c7) = sk_c1 ),
inference(spm,[status(thm)],[c_0_35,c_0_64]) ).
cnf(c_0_121,negated_conjecture,
( multiply(sk_c1,multiply(sk_c7,X1)) = multiply(sk_c6,X1)
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(spm,[status(thm)],[c_0_25,c_0_48]) ).
cnf(c_0_122,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| sk_c6 = identity ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_116]),c_0_26]) ).
cnf(c_0_123,negated_conjecture,
( inverse(sk_c1) = sk_c7
| sk_c6 = identity
| multiply(X1,multiply(sk_c5,sk_c6)) != sk_c6
| inverse(X1) != sk_c7 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_118]),c_0_31]) ).
cnf(c_0_124,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c1,sk_c6) = sk_c5 ),
inference(spm,[status(thm)],[c_0_119,c_0_120]) ).
cnf(c_0_125,negated_conjecture,
( multiply(sk_c1,sk_c6) = multiply(sk_c6,sk_c5)
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(spm,[status(thm)],[c_0_121,c_0_115]) ).
cnf(c_0_126,negated_conjecture,
( multiply(inverse(sk_c1),sk_c6) = sk_c7
| sk_c6 = identity ),
inference(spm,[status(thm)],[c_0_28,c_0_122]) ).
cnf(c_0_127,negated_conjecture,
( inverse(sk_c1) = sk_c7
| sk_c6 = identity ),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_28]),c_0_35]),c_0_100]) ).
cnf(c_0_128,negated_conjecture,
( multiply(sk_c6,sk_c5) = sk_c7
| multiply(sk_c6,sk_c7) = sk_c5 ),
prove_this_1 ).
cnf(c_0_129,negated_conjecture,
( multiply(sk_c6,sk_c5) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(spm,[status(thm)],[c_0_124,c_0_125]) ).
cnf(c_0_130,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c7
| sk_c6 = identity ),
inference(spm,[status(thm)],[c_0_126,c_0_127]) ).
cnf(c_0_131,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| sk_c5 = sk_c7 ),
inference(spm,[status(thm)],[c_0_128,c_0_129]) ).
cnf(c_0_132,negated_conjecture,
sk_c6 = identity,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_130]),c_0_26])]) ).
cnf(c_0_133,negated_conjecture,
sk_c5 = sk_c7,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_131,c_0_132]),c_0_27])]) ).
cnf(c_0_134,negated_conjecture,
( multiply(inverse(X1),sk_c7) != sk_c6
| multiply(sk_c6,sk_c5) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| multiply(X1,inverse(X1)) != sk_c6
| multiply(X2,sk_c6) != sk_c7
| multiply(X3,sk_c7) != sk_c6
| inverse(X2) != sk_c7
| inverse(X3) != sk_c7 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_61,c_0_115])]) ).
cnf(c_0_135,negated_conjecture,
inverse(sk_c7) = sk_c7,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_119,c_0_132]),c_0_31]),c_0_133]) ).
cnf(c_0_136,negated_conjecture,
( multiply(inverse(X1),sk_c7) != identity
| multiply(X1,inverse(X1)) != identity
| multiply(X2,sk_c7) != identity
| inverse(X2) != sk_c7 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_134,c_0_132]),c_0_132]),c_0_27]),c_0_132]),c_0_27]),c_0_132]),c_0_132]),c_0_31]),c_0_132])])]),c_0_133]),c_0_135])]) ).
cnf(c_0_137,negated_conjecture,
multiply(sk_c7,sk_c7) = identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_115,c_0_132]),c_0_133]) ).
cnf(c_0_138,negated_conjecture,
( multiply(X1,sk_c7) != identity
| inverse(X1) != sk_c7 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_136,c_0_135]),c_0_137])]) ).
cnf(c_0_139,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_138,c_0_135]),c_0_137])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP353-1 : TPTP v8.1.2. Released v2.5.0.
% 0.13/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n003.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Aug 28 22:25:55 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.40/0.56 start to proof: theBenchmark
% 0.53/0.65 % Version : CSE_E---1.5
% 0.53/0.65 % Problem : theBenchmark.p
% 0.53/0.65 % Proof found
% 0.53/0.65 % SZS status Theorem for theBenchmark.p
% 0.53/0.65 % SZS output start Proof
% See solution above
% 0.53/0.65 % Total time : 0.074000 s
% 0.53/0.65 % SZS output end Proof
% 0.53/0.65 % Total time : 0.078000 s
%------------------------------------------------------------------------------