%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP317-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:39:16 PM UTC 2026
% Result : Unsatisfiable 0.74s 0.54s
% Output : CNFRefutation 0.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 21
% Syntax : Number of clauses : 94 ( 21 unt; 64 nHn; 79 RR)
% Number of literals : 290 ( 289 equ; 137 neg)
% Maximal clause size : 15 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% 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 : 78 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
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_27,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c2,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_27) ).
cnf(prove_this_33,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_33) ).
cnf(prove_this_55,negated_conjecture,
( inverse(X6) != sk_c9
| multiply(X6,sk_c9) != sk_c7
| inverse(X5) != sk_c8
| multiply(X5,sk_c8) != sk_c9
| inverse(sk_c8) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c9
| multiply(X3,sk_c9) != X4
| inverse(X4) != sk_c9
| inverse(X3) != X4
| inverse(X2) != sk_c8
| multiply(X2,sk_c8) != sk_c9
| multiply(sk_c9,sk_c7) != sk_c8
| inverse(X1) != sk_c9
| multiply(X1,sk_c9) != sk_c8
| multiply(sk_c8,sk_c9) != sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_55) ).
cnf(prove_this_28,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c2,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_28) ).
cnf(prove_this_5,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| multiply(sk_c8,sk_c9) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
cnf(prove_this_23,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| multiply(sk_c9,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_23) ).
cnf(prove_this_8,negated_conjecture,
( inverse(sk_c8) = sk_c7
| multiply(sk_c1,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_8) ).
cnf(prove_this_7,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_7) ).
cnf(prove_this_6,negated_conjecture,
( inverse(sk_c6) = sk_c9
| multiply(sk_c8,sk_c9) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
cnf(prove_this_24,negated_conjecture,
( inverse(sk_c6) = sk_c9
| multiply(sk_c9,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_24) ).
cnf(prove_this_34,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_34) ).
cnf(prove_this_12,negated_conjecture,
( inverse(sk_c6) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_12) ).
cnf(prove_this_11,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| multiply(sk_c1,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
cnf(prove_this_10,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c1,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).
cnf(prove_this_9,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).
cnf(prove_this_17,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_17) ).
cnf(prove_this_18,negated_conjecture,
( inverse(sk_c6) = sk_c9
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).
cnf(prove_this_1,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c9
| multiply(sk_c8,sk_c9) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
cnf(c_0_21,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity ).
cnf(c_0_22,axiom,
multiply(inverse(X1),X1) = identity,
left_inverse ).
cnf(c_0_23,axiom,
multiply(identity,X1) = X1,
left_identity ).
cnf(c_0_24,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]) ).
cnf(c_0_25,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c2,sk_c8) = sk_c9 ),
prove_this_27 ).
cnf(c_0_26,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(inverse(sk_c2),sk_c9) = sk_c8 ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_27,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| inverse(sk_c2) = sk_c8 ),
prove_this_33 ).
cnf(c_0_28,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c8
| multiply(sk_c5,sk_c8) = sk_c9 ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_29,negated_conjecture,
( inverse(X6) != sk_c9
| multiply(X6,sk_c9) != sk_c7
| inverse(X5) != sk_c8
| multiply(X5,sk_c8) != sk_c9
| inverse(sk_c8) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c9
| multiply(X3,sk_c9) != X4
| inverse(X4) != sk_c9
| inverse(X3) != X4
| inverse(X2) != sk_c8
| multiply(X2,sk_c8) != sk_c9
| multiply(sk_c9,sk_c7) != sk_c8
| inverse(X1) != sk_c9
| multiply(X1,sk_c9) != sk_c8
| multiply(sk_c8,sk_c9) != sk_c7 ),
inference(fof_simplification,[status(thm)],[prove_this_55]) ).
cnf(c_0_30,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c8
| multiply(inverse(sk_c5),sk_c9) = sk_c8 ),
inference(spm,[status(thm)],[c_0_24,c_0_28]) ).
cnf(c_0_31,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c2,sk_c8) = sk_c9 ),
prove_this_28 ).
cnf(c_0_32,negated_conjecture,
( inverse(X6) != sk_c9
| multiply(X6,sk_c9) != sk_c7
| inverse(X5) != sk_c8
| multiply(X5,sk_c8) != sk_c9
| inverse(sk_c8) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c9
| multiply(X3,sk_c9) != X4
| inverse(X4) != sk_c9
| inverse(X3) != X4
| inverse(X2) != sk_c8
| multiply(X2,sk_c8) != sk_c9
| multiply(sk_c9,sk_c7) != sk_c8
| inverse(X1) != sk_c9
| multiply(X1,sk_c9) != sk_c8
| multiply(sk_c8,sk_c9) != sk_c7 ),
c_0_29 ).
cnf(c_0_33,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| multiply(sk_c8,sk_c9) = sk_c7 ),
prove_this_5 ).
cnf(c_0_34,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| multiply(sk_c9,sk_c7) = sk_c8 ),
prove_this_23 ).
cnf(c_0_35,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c8
| multiply(sk_c2,sk_c8) = sk_c9 ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_36,negated_conjecture,
( inverse(X5) != sk_c9
| inverse(X4) != sk_c8
| inverse(X3) != sk_c8
| inverse(X2) != sk_c9
| inverse(sk_c8) != sk_c7
| multiply(X5,sk_c9) != sk_c8
| multiply(X4,sk_c8) != sk_c9
| multiply(X3,sk_c8) != sk_c9
| multiply(X2,sk_c9) != sk_c7
| inverse(X1) != multiply(X1,sk_c9)
| multiply(sk_c9,sk_c7) != sk_c8
| multiply(sk_c8,sk_c7) != sk_c9
| multiply(sk_c8,sk_c9) != sk_c7
| inverse(multiply(X1,sk_c9)) != sk_c9 ),
inference(er,[status(thm)],[c_0_32]) ).
cnf(c_0_37,negated_conjecture,
( inverse(sk_c8) = sk_c7
| multiply(sk_c1,sk_c9) = sk_c8 ),
prove_this_8 ).
cnf(c_0_38,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c8 ),
prove_this_7 ).
cnf(c_0_39,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c7
| multiply(inverse(sk_c6),sk_c7) = sk_c9 ),
inference(spm,[status(thm)],[c_0_24,c_0_33]) ).
cnf(c_0_40,negated_conjecture,
( inverse(sk_c6) = sk_c9
| multiply(sk_c8,sk_c9) = sk_c7 ),
prove_this_6 ).
cnf(c_0_41,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c8
| multiply(inverse(sk_c6),sk_c7) = sk_c9 ),
inference(spm,[status(thm)],[c_0_24,c_0_34]) ).
cnf(c_0_42,negated_conjecture,
( inverse(sk_c6) = sk_c9
| multiply(sk_c9,sk_c7) = sk_c8 ),
prove_this_24 ).
cnf(c_0_43,plain,
multiply(inverse(identity),X1) = X1,
inference(spm,[status(thm)],[c_0_24,c_0_23]) ).
cnf(c_0_44,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c8
| multiply(inverse(sk_c2),sk_c9) = sk_c8 ),
inference(spm,[status(thm)],[c_0_24,c_0_35]) ).
cnf(c_0_45,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c2) = sk_c8 ),
prove_this_34 ).
cnf(c_0_46,negated_conjecture,
( inverse(X5) != sk_c9
| inverse(X4) != sk_c8
| inverse(X3) != sk_c8
| inverse(X2) != sk_c9
| multiply(X5,sk_c9) != sk_c8
| multiply(X4,sk_c8) != sk_c9
| multiply(X3,sk_c8) != sk_c9
| multiply(X2,sk_c9) != sk_c7
| inverse(X1) != multiply(X1,sk_c9)
| multiply(sk_c9,sk_c7) != sk_c8
| multiply(sk_c8,sk_c9) != sk_c7
| inverse(multiply(X1,sk_c9)) != sk_c9
| multiply(sk_c1,sk_c9) = sk_c8 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38]) ).
cnf(c_0_47,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c9
| multiply(sk_c8,sk_c9) = sk_c7 ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_48,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c9
| multiply(sk_c9,sk_c7) = sk_c8 ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_49,plain,
multiply(inverse(inverse(identity)),X1) = X1,
inference(spm,[status(thm)],[c_0_24,c_0_43]) ).
cnf(c_0_50,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c8,sk_c9) = sk_c8 ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_51,negated_conjecture,
( inverse(X5) != sk_c9
| inverse(X4) != sk_c8
| inverse(X3) != sk_c8
| inverse(X2) != sk_c9
| multiply(X5,sk_c9) != sk_c8
| multiply(X4,sk_c8) != sk_c9
| multiply(X3,sk_c8) != sk_c9
| multiply(X2,sk_c9) != sk_c7
| inverse(X1) != multiply(X1,sk_c9)
| inverse(multiply(X1,sk_c9)) != sk_c9
| multiply(sk_c1,sk_c9) = sk_c8
| multiply(sk_c9,sk_c7) = sk_c9 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_48]) ).
cnf(c_0_52,plain,
inverse(identity) = identity,
inference(spm,[status(thm)],[c_0_22,c_0_49]) ).
cnf(c_0_53,negated_conjecture,
multiply(sk_c8,sk_c9) = sk_c8,
inference(spm,[status(thm)],[c_0_30,c_0_50]) ).
cnf(c_0_54,negated_conjecture,
( identity != sk_c9
| inverse(X4) != sk_c9
| inverse(X3) != sk_c8
| inverse(X2) != sk_c8
| inverse(X1) != sk_c9
| inverse(sk_c9) != sk_c9
| multiply(X4,sk_c9) != sk_c8
| multiply(X3,sk_c8) != sk_c9
| multiply(X2,sk_c8) != sk_c9
| multiply(X1,sk_c9) != sk_c7
| multiply(sk_c9,sk_c7) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c8 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_23]),c_0_23]) ).
cnf(c_0_55,negated_conjecture,
identity = sk_c9,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_53]),c_0_22]) ).
cnf(c_0_56,negated_conjecture,
( inverse(X4) != sk_c9
| inverse(X3) != sk_c8
| inverse(X2) != sk_c8
| inverse(X1) != sk_c9
| inverse(sk_c9) != sk_c9
| multiply(X4,sk_c9) != sk_c8
| multiply(X3,sk_c8) != sk_c9
| multiply(X2,sk_c8) != sk_c9
| multiply(X1,sk_c9) != sk_c7
| multiply(sk_c1,sk_c9) = sk_c8
| multiply(sk_c9,sk_c7) = sk_c9 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_54,c_0_55])]) ).
cnf(c_0_57,plain,
inverse(sk_c9) = sk_c9,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_52,c_0_55]),c_0_55]) ).
cnf(c_0_58,negated_conjecture,
( inverse(X4) != sk_c9
| inverse(X3) != sk_c8
| inverse(X2) != sk_c8
| inverse(X1) != sk_c9
| multiply(X4,sk_c9) != sk_c8
| multiply(X3,sk_c8) != sk_c9
| multiply(X2,sk_c8) != sk_c9
| multiply(X1,sk_c9) != sk_c7
| multiply(sk_c9,sk_c7) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c8 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_56,c_0_57])]) ).
cnf(c_0_59,negated_conjecture,
( inverse(sk_c6) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c8 ),
prove_this_12 ).
cnf(c_0_60,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| multiply(sk_c1,sk_c9) = sk_c8 ),
prove_this_11 ).
cnf(c_0_61,negated_conjecture,
( inverse(X3) != sk_c9
| inverse(X2) != sk_c8
| inverse(X1) != sk_c8
| multiply(X3,sk_c9) != sk_c8
| multiply(X2,sk_c8) != sk_c9
| multiply(X1,sk_c8) != sk_c9
| multiply(sk_c1,sk_c9) = sk_c8
| multiply(sk_c9,sk_c7) = sk_c9 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_60]) ).
cnf(c_0_62,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c1,sk_c9) = sk_c8 ),
prove_this_10 ).
cnf(c_0_63,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c8 ),
prove_this_9 ).
cnf(c_0_64,negated_conjecture,
( inverse(X2) != sk_c9
| inverse(X1) != sk_c8
| multiply(X2,sk_c9) != sk_c8
| multiply(X1,sk_c8) != sk_c9
| multiply(sk_c9,sk_c7) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c8 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_63]) ).
cnf(c_0_65,negated_conjecture,
( inverse(X1) != sk_c9
| multiply(X1,sk_c9) != sk_c8
| multiply(sk_c1,sk_c9) = sk_c8
| multiply(sk_c9,sk_c7) = sk_c9 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_62]),c_0_63]) ).
cnf(c_0_66,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| multiply(inverse(sk_c1),sk_c8) = sk_c9 ),
inference(spm,[status(thm)],[c_0_24,c_0_60]) ).
cnf(c_0_67,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| inverse(sk_c1) = sk_c9 ),
prove_this_17 ).
cnf(c_0_68,negated_conjecture,
( multiply(sk_c6,sk_c9) != sk_c8
| multiply(sk_c9,sk_c7) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c8 ),
inference(spm,[status(thm)],[c_0_65,c_0_59]) ).
cnf(c_0_69,negated_conjecture,
( multiply(sk_c9,sk_c8) = sk_c9
| multiply(sk_c6,sk_c9) = sk_c7 ),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
cnf(c_0_70,negated_conjecture,
( sk_c7 = sk_c8
| multiply(sk_c9,sk_c7) = sk_c9 ),
inference(spm,[status(thm)],[c_0_47,c_0_53]) ).
cnf(c_0_71,negated_conjecture,
( multiply(sk_c9,sk_c9) != sk_c8
| multiply(sk_c9,sk_c7) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c8 ),
inference(spm,[status(thm)],[c_0_65,c_0_57]) ).
cnf(c_0_72,plain,
multiply(sk_c9,X1) = X1,
inference(rw,[status(thm)],[c_0_23,c_0_55]) ).
cnf(c_0_73,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c8
| multiply(sk_c9,sk_c7) = sk_c9
| multiply(sk_c9,sk_c8) = sk_c9 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_70]) ).
cnf(c_0_74,negated_conjecture,
( sk_c8 != sk_c9
| sk_c7 = sk_c9
| multiply(sk_c1,sk_c9) = sk_c8 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_71,c_0_72]),c_0_72]) ).
cnf(c_0_75,negated_conjecture,
( sk_c7 = sk_c9
| multiply(sk_c1,sk_c9) = sk_c8 ),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_73,c_0_72]),c_0_72]),c_0_74]) ).
cnf(c_0_76,negated_conjecture,
( sk_c8 != sk_c9
| multiply(sk_c9,sk_c7) = sk_c9 ),
inference(ef,[status(thm)],[c_0_48]) ).
cnf(c_0_77,negated_conjecture,
( sk_c7 = sk_c9
| multiply(inverse(sk_c1),sk_c8) = sk_c9 ),
inference(spm,[status(thm)],[c_0_24,c_0_75]) ).
cnf(c_0_78,negated_conjecture,
( inverse(sk_c6) = sk_c9
| inverse(sk_c1) = sk_c9 ),
prove_this_18 ).
cnf(c_0_79,negated_conjecture,
( sk_c8 != sk_c9
| sk_c7 = sk_c9 ),
inference(rw,[status(thm)],[c_0_76,c_0_72]) ).
cnf(c_0_80,negated_conjecture,
( sk_c7 = sk_c9
| inverse(sk_c6) = sk_c9 ),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_72]),c_0_79]) ).
cnf(c_0_81,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c9
| multiply(sk_c8,sk_c9) = sk_c7 ),
prove_this_1 ).
cnf(c_0_82,negated_conjecture,
( sk_c7 = sk_c9
| multiply(sk_c6,X1) = X1 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_80]),c_0_72]) ).
cnf(c_0_83,negated_conjecture,
( sk_c8 = sk_c9
| multiply(sk_c6,sk_c9) = sk_c7 ),
inference(rw,[status(thm)],[c_0_69,c_0_72]) ).
cnf(c_0_84,negated_conjecture,
( sk_c7 = sk_c8
| multiply(sk_c8,sk_c7) = sk_c9 ),
inference(rw,[status(thm)],[c_0_81,c_0_53]) ).
cnf(c_0_85,negated_conjecture,
sk_c7 = sk_c9,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_79]) ).
cnf(c_0_86,plain,
multiply(inverse(inverse(X1)),identity) = X1,
inference(spm,[status(thm)],[c_0_24,c_0_22]) ).
cnf(c_0_87,negated_conjecture,
sk_c8 = sk_c9,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_84,c_0_85]),c_0_53]),c_0_85])]) ).
cnf(c_0_88,plain,
multiply(inverse(inverse(X1)),sk_c9) = X1,
inference(rw,[status(thm)],[c_0_86,c_0_55]) ).
cnf(c_0_89,plain,
multiply(inverse(inverse(X1)),X2) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_24,c_0_24]) ).
cnf(c_0_90,negated_conjecture,
( inverse(X5) != sk_c9
| inverse(X4) != sk_c9
| inverse(X3) != sk_c9
| inverse(X2) != sk_c9
| multiply(X5,sk_c9) != sk_c9
| multiply(X4,sk_c9) != sk_c9
| multiply(X3,sk_c9) != sk_c9
| multiply(X2,sk_c9) != sk_c9
| inverse(X1) != multiply(X1,sk_c9)
| inverse(multiply(X1,sk_c9)) != sk_c9 ),
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)],[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_36,c_0_53]),c_0_85]),c_0_87]),c_0_87]),c_0_85]),c_0_72]),c_0_72]),c_0_85]),c_0_87]),c_0_85]),c_0_87]),c_0_87]),c_0_87]),c_0_87]),c_0_57]),c_0_85]),c_0_87]),c_0_87])]) ).
cnf(c_0_91,plain,
multiply(X1,sk_c9) = X1,
inference(rw,[status(thm)],[c_0_88,c_0_89]) ).
cnf(c_0_92,negated_conjecture,
( inverse(X1) != X1
| inverse(X1) != sk_c9 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[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_90,c_0_91]),c_0_91]),c_0_91]),c_0_91]),c_0_91]),c_0_91])])])])]),c_0_57])]) ).
cnf(c_0_93,negated_conjecture,
$false,
inference(spm,[status(thm)],[c_0_92,c_0_57]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP317-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n014.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 20 20:09:05 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.43 Running first-order theorem proving
% 0.14/0.43 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.74/0.54 % Version: 3.5.1
% 0.74/0.54 % Preprocessing class: FSMSSMSMSSSNFFN.
% 0.74/0.54 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.74/0.54 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 0.74/0.54 % Starting new_bool_3 with 300s (1) cores
% 0.74/0.54 % Starting new_bool_1 with 300s (1) cores
% 0.74/0.54 % Starting sh5l with 300s (1) cores
% 0.74/0.54 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with pid 2244381 completed with status 0
% 0.74/0.54 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI
% 0.74/0.54 % Preprocessing class: FSMSSMSMSSSNFFN.
% 0.74/0.54 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.74/0.54 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 0.74/0.54 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.74/0.54 % No SInE strategy applied
% 0.74/0.54 % Search class: FGHPS-FFMM21-SFFFFFNN
% 0.74/0.54 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.74/0.54 % Starting SubtermCWHack with 136s (1) cores
% 0.74/0.54 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 0.74/0.54 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.74/0.54 % Starting new_bool_3 with 136s (1) cores
% 0.74/0.54 % Starting new_bool_1 with 136s (1) cores
% 0.74/0.54 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with pid 2244386 completed with status 0
% 0.74/0.54 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI
% 0.74/0.54 % Preprocessing class: FSMSSMSMSSSNFFN.
% 0.74/0.54 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.74/0.54 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 0.74/0.54 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.74/0.54 % No SInE strategy applied
% 0.74/0.54 % Search class: FGHPS-FFMM21-SFFFFFNN
% 0.74/0.54 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.74/0.54 % Starting SubtermCWHack with 136s (1) cores
% 0.74/0.54 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 0.74/0.54 % Preprocessing time : 0.002 s
% 0.74/0.54 % Presaturation interreduction done
% 0.74/0.54
% 0.74/0.54 % Proof found!
% 0.74/0.54 % SZS status Unsatisfiable
% 0.74/0.54 % SZS output start CNFRefutation
% See solution above
% 0.74/0.54 % Parsed axioms : 58
% 0.74/0.54 % Removed by relevancy pruning/SinE : 0
% 0.74/0.54 % Initial clauses : 58
% 0.74/0.54 % Removed in clause preprocessing : 0
% 0.74/0.54 % Initial clauses in saturation : 58
% 0.74/0.54 % Processed clauses : 800
% 0.74/0.54 % ...of these trivial : 66
% 0.74/0.54 % ...subsumed : 267
% 0.74/0.54 % ...remaining for further processing : 467
% 0.74/0.54 % Other redundant clauses eliminated : 5
% 0.74/0.54 % Clauses deleted for lack of memory : 0
% 0.74/0.54 % Backward-subsumed : 48
% 0.74/0.54 % Backward-rewritten : 283
% 0.74/0.54 % Generated clauses : 2408
% 0.74/0.54 % ...of the previous two non-redundant : 2261
% 0.74/0.54 % ...aggressively subsumed : 0
% 0.74/0.54 % Contextual simplify-reflections : 24
% 0.74/0.54 % Paramodulations : 2400
% 0.74/0.54 % Factorizations : 3
% 0.74/0.54 % NegExts : 0
% 0.74/0.54 % Equation resolutions : 5
% 0.74/0.54 % Disequality decompositions : 0
% 0.74/0.54 % Total rewrite steps : 1576
% 0.74/0.54 % ...of those cached : 1505
% 0.74/0.54 % Propositional unsat checks : 0
% 0.74/0.54 % Propositional check models : 0
% 0.74/0.54 % Propositional check unsatisfiable : 0
% 0.74/0.54 % Propositional clauses : 0
% 0.74/0.54 % Propositional clauses after purity: 0
% 0.74/0.54 % Propositional unsat core size : 0
% 0.74/0.54 % Propositional preprocessing time : 0.000
% 0.74/0.54 % Propositional encoding time : 0.000
% 0.74/0.54 % Propositional solver time : 0.000
% 0.74/0.54 % Success case prop preproc time : 0.000
% 0.74/0.54 % Success case prop encoding time : 0.000
% 0.74/0.54 % Success case prop solver time : 0.000
% 0.74/0.54 % Current number of processed clauses : 77
% 0.74/0.54 % Positive orientable unit clauses : 10
% 0.74/0.54 % Positive unorientable unit clauses: 0
% 0.74/0.54 % Negative unit clauses : 0
% 0.74/0.54 % Non-unit-clauses : 67
% 0.74/0.54 % Current number of unprocessed clauses: 1472
% 0.74/0.54 % ...number of literals in the above : 8873
% 0.74/0.54 % Current number of archived formulas : 0
% 0.74/0.54 % Current number of archived clauses : 389
% 0.74/0.54 % Clause-clause subsumption calls (NU) : 3974
% 0.74/0.54 % Rec. Clause-clause subsumption calls : 2350
% 0.74/0.54 % Non-unit clause-clause subsumptions : 338
% 0.74/0.54 % Unit Clause-clause subsumption calls : 364
% 0.74/0.54 % Rewrite failures with RHS unbound : 0
% 0.74/0.54 % BW rewrite match attempts : 42
% 0.74/0.54 % BW rewrite match successes : 31
% 0.74/0.54 % Condensation attempts : 0
% 0.74/0.54 % Condensation successes : 0
% 0.74/0.54 % Termbank termtop insertions : 42932
% 0.74/0.54 % Search garbage collected termcells : 40
% 0.74/0.54
% 0.74/0.54 % -------------------------------------------------
% 0.74/0.54 % User time : 0.089 s
% 0.74/0.54 % System time : 0.008 s
% 0.74/0.54 % Total time : 0.097 s
% 0.74/0.54 % Maximum resident set size: 3660 pages
% 0.74/0.54
% 0.74/0.54 % -------------------------------------------------
% 0.74/0.54 % User time : 0.437 s
% 0.74/0.54 % System time : 0.032 s
% 0.74/0.54 % Total time : 0.469 s
% 0.74/0.54 % Maximum resident set size: 4608 pages
% 0.74/0.54 % E exiting
%------------------------------------------------------------------------------