%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP322-1 : 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 : n004.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 12:39:17 PM UTC 2026
% Result : Unsatisfiable 0.17s 0.54s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 24
% Syntax : Number of clauses : 114 ( 27 unt; 72 nHn; 100 RR)
% Number of literals : 291 ( 290 equ; 101 neg)
% Maximal clause size : 12 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 54 ( 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_23,negated_conjecture,
( multiply(sk_c5,sk_c9) = sk_c6
| multiply(sk_c9,sk_c3) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_23) ).
cnf(prove_this_24,negated_conjecture,
( inverse(sk_c5) = sk_c9
| multiply(sk_c9,sk_c3) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_24) ).
cnf(prove_this_28,negated_conjecture,
( multiply(sk_c9,sk_c6) = sk_c8
| multiply(sk_c2,sk_c9) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_28) ).
cnf(prove_this_22,negated_conjecture,
( multiply(sk_c9,sk_c6) = sk_c8
| multiply(sk_c9,sk_c3) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_22) ).
cnf(prove_this_34,negated_conjecture,
( multiply(sk_c9,sk_c6) = sk_c8
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_34) ).
cnf(prove_this_29,negated_conjecture,
( multiply(sk_c5,sk_c9) = sk_c6
| multiply(sk_c2,sk_c9) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_29) ).
cnf(prove_this_30,negated_conjecture,
( inverse(sk_c5) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_30) ).
cnf(prove_this_35,negated_conjecture,
( multiply(sk_c5,sk_c9) = sk_c6
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_35) ).
cnf(prove_this_37,negated_conjecture,
( inverse(X6) != sk_c9
| multiply(X6,sk_c9) != X5
| multiply(sk_c9,X5) != sk_c8
| inverse(X4) != sk_c9
| multiply(X4,sk_c9) != sk_c8
| multiply(sk_c9,sk_c8) != sk_c7
| inverse(X3) != sk_c9
| multiply(X3,sk_c9) != X2
| multiply(sk_c9,X2) != sk_c8
| inverse(X1) != sk_c8
| multiply(X1,sk_c8) != sk_c9
| multiply(sk_c8,sk_c9) != sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_37) ).
cnf(prove_this_33,negated_conjecture,
( inverse(sk_c4) = sk_c9
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_33) ).
cnf(prove_this_3,negated_conjecture,
( inverse(sk_c4) = sk_c9
| multiply(sk_c8,sk_c9) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
cnf(prove_this_36,negated_conjecture,
( inverse(sk_c5) = sk_c9
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_36) ).
cnf(prove_this_15,negated_conjecture,
( inverse(sk_c4) = sk_c9
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
cnf(prove_this_9,negated_conjecture,
( inverse(sk_c4) = sk_c9
| multiply(sk_c1,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).
cnf(prove_this_1,negated_conjecture,
( multiply(sk_c9,sk_c8) = sk_c7
| multiply(sk_c8,sk_c9) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
cnf(prove_this_27,negated_conjecture,
( inverse(sk_c4) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_27) ).
cnf(prove_this_21,negated_conjecture,
( inverse(sk_c4) = sk_c9
| multiply(sk_c9,sk_c3) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
cnf(prove_this_8,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_8) ).
cnf(prove_this_18,negated_conjecture,
( inverse(sk_c5) = sk_c9
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).
cnf(prove_this_13,negated_conjecture,
( multiply(sk_c9,sk_c8) = sk_c7
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_13) ).
cnf(prove_this_14,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
cnf(c_0_24,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity ).
cnf(c_0_25,axiom,
multiply(inverse(X1),X1) = identity,
left_inverse ).
cnf(c_0_26,axiom,
multiply(identity,X1) = X1,
left_identity ).
cnf(c_0_27,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]) ).
cnf(c_0_28,negated_conjecture,
( multiply(sk_c5,sk_c9) = sk_c6
| multiply(sk_c9,sk_c3) = sk_c8 ),
prove_this_23 ).
cnf(c_0_29,negated_conjecture,
( multiply(sk_c9,sk_c3) = sk_c8
| multiply(inverse(sk_c5),sk_c6) = sk_c9 ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_30,negated_conjecture,
( inverse(sk_c5) = sk_c9
| multiply(sk_c9,sk_c3) = sk_c8 ),
prove_this_24 ).
cnf(c_0_31,negated_conjecture,
( multiply(sk_c9,sk_c6) = sk_c8
| multiply(sk_c2,sk_c9) = sk_c3 ),
prove_this_28 ).
cnf(c_0_32,negated_conjecture,
( multiply(sk_c9,sk_c6) = sk_c8
| multiply(sk_c9,sk_c3) = sk_c8 ),
prove_this_22 ).
cnf(c_0_33,negated_conjecture,
( multiply(sk_c9,sk_c6) = sk_c9
| multiply(sk_c9,sk_c3) = sk_c8 ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_34,negated_conjecture,
( multiply(sk_c9,sk_c6) = sk_c8
| multiply(inverse(sk_c2),sk_c3) = sk_c9 ),
inference(spm,[status(thm)],[c_0_27,c_0_31]) ).
cnf(c_0_35,negated_conjecture,
( multiply(sk_c9,sk_c6) = sk_c8
| inverse(sk_c2) = sk_c9 ),
prove_this_34 ).
cnf(c_0_36,negated_conjecture,
( sk_c8 = sk_c9
| multiply(sk_c9,sk_c3) = sk_c8 ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_37,negated_conjecture,
( multiply(sk_c9,sk_c3) = sk_c9
| multiply(sk_c9,sk_c6) = sk_c8 ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_38,negated_conjecture,
( sk_c8 = sk_c9
| multiply(inverse(sk_c9),sk_c8) = sk_c3 ),
inference(spm,[status(thm)],[c_0_27,c_0_36]) ).
cnf(c_0_39,negated_conjecture,
( multiply(sk_c9,sk_c3) = sk_c9
| multiply(inverse(sk_c9),sk_c8) = sk_c6 ),
inference(spm,[status(thm)],[c_0_27,c_0_37]) ).
cnf(c_0_40,negated_conjecture,
( multiply(sk_c5,sk_c9) = sk_c6
| multiply(sk_c2,sk_c9) = sk_c3 ),
prove_this_29 ).
cnf(c_0_41,negated_conjecture,
( sk_c6 = sk_c3
| sk_c8 = sk_c9
| multiply(sk_c9,sk_c3) = sk_c9 ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_42,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c3
| multiply(inverse(sk_c5),sk_c6) = sk_c9 ),
inference(spm,[status(thm)],[c_0_27,c_0_40]) ).
cnf(c_0_43,negated_conjecture,
( sk_c8 = sk_c9
| sk_c6 = sk_c3 ),
inference(spm,[status(thm)],[c_0_36,c_0_41]) ).
cnf(c_0_44,negated_conjecture,
( sk_c8 = sk_c9
| multiply(sk_c2,sk_c9) = sk_c3
| multiply(inverse(sk_c5),sk_c3) = sk_c9 ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_45,negated_conjecture,
( inverse(sk_c5) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c3 ),
prove_this_30 ).
cnf(c_0_46,negated_conjecture,
( sk_c8 = sk_c9
| multiply(sk_c9,sk_c3) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c3 ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_47,negated_conjecture,
( sk_c8 = sk_c9
| multiply(sk_c9,sk_c3) = sk_c9
| multiply(inverse(sk_c2),sk_c3) = sk_c9 ),
inference(spm,[status(thm)],[c_0_27,c_0_46]) ).
cnf(c_0_48,negated_conjecture,
( multiply(sk_c5,sk_c9) = sk_c6
| inverse(sk_c2) = sk_c9 ),
prove_this_35 ).
cnf(c_0_49,negated_conjecture,
( inverse(X6) != sk_c9
| multiply(X6,sk_c9) != X5
| multiply(sk_c9,X5) != sk_c8
| inverse(X4) != sk_c9
| multiply(X4,sk_c9) != sk_c8
| multiply(sk_c9,sk_c8) != sk_c7
| inverse(X3) != sk_c9
| multiply(X3,sk_c9) != X2
| multiply(sk_c9,X2) != sk_c8
| inverse(X1) != sk_c8
| multiply(X1,sk_c8) != sk_c9
| multiply(sk_c8,sk_c9) != sk_c7 ),
inference(fof_simplification,[status(thm)],[prove_this_37]) ).
cnf(c_0_50,negated_conjecture,
( sk_c8 = sk_c9
| multiply(sk_c9,sk_c3) = sk_c9
| multiply(sk_c5,sk_c9) = sk_c6 ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_51,negated_conjecture,
( inverse(X6) != sk_c9
| multiply(X6,sk_c9) != X5
| multiply(sk_c9,X5) != sk_c8
| inverse(X4) != sk_c9
| multiply(X4,sk_c9) != sk_c8
| multiply(sk_c9,sk_c8) != sk_c7
| inverse(X3) != sk_c9
| multiply(X3,sk_c9) != X2
| multiply(sk_c9,X2) != sk_c8
| inverse(X1) != sk_c8
| multiply(X1,sk_c8) != sk_c9
| multiply(sk_c8,sk_c9) != sk_c7 ),
c_0_49 ).
cnf(c_0_52,negated_conjecture,
( sk_c8 = sk_c9
| multiply(sk_c9,sk_c3) = sk_c9
| multiply(inverse(sk_c5),sk_c6) = sk_c9 ),
inference(spm,[status(thm)],[c_0_27,c_0_50]) ).
cnf(c_0_53,negated_conjecture,
( inverse(X4) != sk_c8
| inverse(X2) != sk_c9
| inverse(X3) != sk_c9
| inverse(X1) != sk_c9
| multiply(X4,sk_c8) != sk_c9
| multiply(X3,sk_c9) != sk_c8
| multiply(sk_c9,sk_c8) != sk_c7
| multiply(sk_c8,sk_c9) != sk_c7
| multiply(sk_c9,multiply(X2,sk_c9)) != sk_c8
| multiply(sk_c9,multiply(X1,sk_c9)) != sk_c8 ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_51])]) ).
cnf(c_0_54,negated_conjecture,
( inverse(sk_c4) = sk_c9
| inverse(sk_c2) = sk_c9 ),
prove_this_33 ).
cnf(c_0_55,negated_conjecture,
( inverse(sk_c4) = sk_c9
| multiply(sk_c8,sk_c9) = sk_c7 ),
prove_this_3 ).
cnf(c_0_56,negated_conjecture,
( sk_c8 = sk_c9
| multiply(sk_c9,sk_c3) = sk_c9
| multiply(inverse(sk_c5),sk_c3) = sk_c9 ),
inference(spm,[status(thm)],[c_0_52,c_0_43]) ).
cnf(c_0_57,negated_conjecture,
( inverse(sk_c5) = sk_c9
| inverse(sk_c2) = sk_c9 ),
prove_this_36 ).
cnf(c_0_58,negated_conjecture,
( inverse(X3) != sk_c8
| inverse(X1) != sk_c9
| inverse(X2) != sk_c9
| multiply(X3,sk_c8) != sk_c9
| multiply(X2,sk_c9) != sk_c8
| multiply(sk_c9,sk_c8) != sk_c7
| multiply(sk_c9,multiply(X1,sk_c9)) != sk_c8
| multiply(sk_c9,multiply(sk_c2,sk_c9)) != sk_c8
| inverse(sk_c4) = sk_c9 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_55]) ).
cnf(c_0_59,negated_conjecture,
( inverse(sk_c4) = sk_c9
| inverse(sk_c1) = sk_c8 ),
prove_this_15 ).
cnf(c_0_60,negated_conjecture,
( sk_c8 = sk_c9
| inverse(sk_c2) = sk_c9
| multiply(sk_c9,sk_c3) = sk_c9 ),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_61,negated_conjecture,
( sk_c8 != sk_c9
| inverse(X2) != sk_c8
| inverse(X1) != sk_c9
| multiply(X2,sk_c8) != sk_c9
| multiply(sk_c1,sk_c9) != sk_c8
| multiply(sk_c9,sk_c8) != sk_c7
| multiply(sk_c9,multiply(X1,sk_c9)) != sk_c8
| multiply(sk_c9,multiply(sk_c2,sk_c9)) != sk_c8
| inverse(sk_c4) = sk_c9 ),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_62,negated_conjecture,
( sk_c8 = sk_c9
| multiply(sk_c9,sk_c3) = sk_c9 ),
inference(spm,[status(thm)],[c_0_47,c_0_60]) ).
cnf(c_0_63,negated_conjecture,
( sk_c8 != sk_c9
| inverse(X1) != sk_c8
| multiply(X1,sk_c8) != sk_c9
| multiply(sk_c1,sk_c9) != sk_c8
| multiply(sk_c9,sk_c8) != sk_c7
| multiply(sk_c9,multiply(sk_c2,sk_c9)) != sk_c8
| inverse(sk_c4) = sk_c9 ),
inference(spm,[status(thm)],[c_0_61,c_0_54]) ).
cnf(c_0_64,negated_conjecture,
( inverse(sk_c4) = sk_c9
| multiply(sk_c1,sk_c8) = sk_c9 ),
prove_this_9 ).
cnf(c_0_65,negated_conjecture,
( multiply(sk_c9,sk_c8) = sk_c7
| multiply(sk_c8,sk_c9) = sk_c7 ),
prove_this_1 ).
cnf(c_0_66,negated_conjecture,
sk_c8 = sk_c9,
inference(spm,[status(thm)],[c_0_36,c_0_62]) ).
cnf(c_0_67,negated_conjecture,
( sk_c8 != sk_c9
| multiply(sk_c1,sk_c9) != sk_c8
| multiply(sk_c9,sk_c8) != sk_c7
| multiply(sk_c9,multiply(sk_c2,sk_c9)) != sk_c8
| inverse(sk_c4) = sk_c9 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_59]),c_0_64]) ).
cnf(c_0_68,negated_conjecture,
multiply(sk_c9,sk_c9) = sk_c7,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_65,c_0_66]),c_0_66])]) ).
cnf(c_0_69,negated_conjecture,
( inverse(sk_c4) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c9 ),
inference(rw,[status(thm)],[c_0_64,c_0_66]) ).
cnf(c_0_70,negated_conjecture,
( inverse(sk_c4) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c3 ),
prove_this_27 ).
cnf(c_0_71,negated_conjecture,
( inverse(sk_c4) = sk_c9
| multiply(sk_c9,sk_c3) = sk_c8 ),
prove_this_21 ).
cnf(c_0_72,negated_conjecture,
( multiply(sk_c9,multiply(sk_c2,sk_c9)) != sk_c9
| inverse(sk_c4) = sk_c9 ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_67,c_0_66]),c_0_66]),c_0_66]),c_0_66])]),c_0_68])]),c_0_69]) ).
cnf(c_0_73,negated_conjecture,
( multiply(sk_c9,sk_c4) = identity
| multiply(sk_c2,sk_c9) = sk_c3 ),
inference(spm,[status(thm)],[c_0_25,c_0_70]) ).
cnf(c_0_74,negated_conjecture,
( inverse(sk_c4) = sk_c9
| multiply(sk_c9,sk_c3) = sk_c9 ),
inference(rw,[status(thm)],[c_0_71,c_0_66]) ).
cnf(c_0_75,negated_conjecture,
( inverse(sk_c4) = sk_c9
| multiply(sk_c9,sk_c4) = identity ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_74]) ).
cnf(c_0_76,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c9 ),
prove_this_8 ).
cnf(c_0_77,negated_conjecture,
multiply(sk_c9,sk_c4) = identity,
inference(spm,[status(thm)],[c_0_25,c_0_75]) ).
cnf(c_0_78,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c8
| multiply(inverse(sk_c1),sk_c9) = sk_c8 ),
inference(spm,[status(thm)],[c_0_27,c_0_76]) ).
cnf(c_0_79,negated_conjecture,
( inverse(sk_c5) = sk_c9
| inverse(sk_c1) = sk_c8 ),
prove_this_18 ).
cnf(c_0_80,negated_conjecture,
( multiply(sk_c9,sk_c8) = sk_c7
| inverse(sk_c1) = sk_c8 ),
prove_this_13 ).
cnf(c_0_81,negated_conjecture,
multiply(inverse(sk_c9),identity) = sk_c4,
inference(spm,[status(thm)],[c_0_27,c_0_77]) ).
cnf(c_0_82,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c8
| multiply(inverse(inverse(sk_c1)),sk_c8) = sk_c9 ),
inference(spm,[status(thm)],[c_0_27,c_0_78]) ).
cnf(c_0_83,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c8
| inverse(sk_c1) = sk_c8 ),
prove_this_14 ).
cnf(c_0_84,negated_conjecture,
( inverse(X3) != sk_c8
| inverse(X1) != sk_c9
| inverse(X2) != sk_c9
| multiply(X3,sk_c8) != sk_c9
| multiply(X2,sk_c9) != sk_c8
| multiply(sk_c8,sk_c9) != sk_c7
| multiply(sk_c9,multiply(X1,sk_c9)) != sk_c8
| multiply(sk_c9,multiply(sk_c5,sk_c9)) != sk_c8
| inverse(sk_c1) = sk_c8 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_79]),c_0_80]) ).
cnf(c_0_85,negated_conjecture,
multiply(inverse(sk_c9),X1) = multiply(sk_c4,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_81]),c_0_26]) ).
cnf(c_0_86,negated_conjecture,
( identity = sk_c9
| multiply(sk_c4,sk_c9) = sk_c8 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_25]) ).
cnf(c_0_87,negated_conjecture,
( inverse(X2) != sk_c8
| inverse(X1) != sk_c9
| multiply(X2,sk_c8) != sk_c9
| multiply(sk_c5,sk_c9) != sk_c8
| multiply(sk_c8,sk_c9) != sk_c7
| multiply(sk_c9,multiply(X1,sk_c9)) != sk_c8
| multiply(sk_c9,multiply(sk_c5,sk_c9)) != sk_c8
| inverse(sk_c1) = sk_c8 ),
inference(spm,[status(thm)],[c_0_84,c_0_79]) ).
cnf(c_0_88,negated_conjecture,
multiply(sk_c4,sk_c9) = identity,
inference(spm,[status(thm)],[c_0_25,c_0_85]) ).
cnf(c_0_89,negated_conjecture,
( identity = sk_c9
| multiply(sk_c4,sk_c9) = sk_c9 ),
inference(rw,[status(thm)],[c_0_86,c_0_66]) ).
cnf(c_0_90,negated_conjecture,
( inverse(X1) != sk_c8
| multiply(X1,sk_c8) != sk_c9
| multiply(sk_c5,sk_c9) != sk_c8
| multiply(sk_c8,sk_c9) != sk_c7
| multiply(sk_c9,multiply(sk_c5,sk_c9)) != sk_c8
| inverse(sk_c1) = sk_c8 ),
inference(spm,[status(thm)],[c_0_87,c_0_79]) ).
cnf(c_0_91,negated_conjecture,
identity = sk_c9,
inference(spm,[status(thm)],[c_0_88,c_0_89]) ).
cnf(c_0_92,negated_conjecture,
( sk_c8 != sk_c9
| multiply(sk_c5,sk_c8) != sk_c9
| multiply(sk_c5,sk_c9) != sk_c8
| multiply(sk_c8,sk_c9) != sk_c7
| multiply(sk_c9,multiply(sk_c5,sk_c9)) != sk_c8
| inverse(sk_c1) = sk_c8 ),
inference(spm,[status(thm)],[c_0_90,c_0_79]) ).
cnf(c_0_93,plain,
multiply(inverse(X1),X1) = sk_c9,
inference(rw,[status(thm)],[c_0_25,c_0_91]) ).
cnf(c_0_94,negated_conjecture,
( inverse(sk_c5) = sk_c9
| inverse(sk_c1) = sk_c9 ),
inference(rw,[status(thm)],[c_0_79,c_0_66]) ).
cnf(c_0_95,plain,
multiply(sk_c9,X1) = X1,
inference(rw,[status(thm)],[c_0_26,c_0_91]) ).
cnf(c_0_96,negated_conjecture,
( multiply(sk_c5,sk_c9) != sk_c9
| multiply(sk_c9,multiply(sk_c5,sk_c9)) != sk_c9
| inverse(sk_c1) = sk_c9 ),
inference(cn,[status(thm)],[inference(rw,[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)],[c_0_92,c_0_66]),c_0_66]),c_0_66]),c_0_66]),c_0_66]),c_0_66])]),c_0_68])]) ).
cnf(c_0_97,negated_conjecture,
( sk_c5 = sk_c9
| inverse(sk_c1) = sk_c9 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_94]),c_0_95]) ).
cnf(c_0_98,negated_conjecture,
multiply(sk_c4,identity) = sk_c4,
inference(rw,[status(thm)],[c_0_81,c_0_85]) ).
cnf(c_0_99,negated_conjecture,
( multiply(sk_c5,sk_c9) != sk_c9
| inverse(sk_c1) = sk_c9 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_96,c_0_95])]) ).
cnf(c_0_100,negated_conjecture,
( sk_c1 = sk_c9
| sk_c5 = sk_c9 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_97]),c_0_95]) ).
cnf(c_0_101,plain,
multiply(inverse(inverse(X1)),sk_c9) = X1,
inference(spm,[status(thm)],[c_0_27,c_0_93]) ).
cnf(c_0_102,negated_conjecture,
multiply(sk_c9,multiply(sk_c4,X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_77]),c_0_26]) ).
cnf(c_0_103,negated_conjecture,
( inverse(sk_c4) = sk_c9
| inverse(sk_c1) = sk_c9 ),
inference(rw,[status(thm)],[c_0_59,c_0_66]) ).
cnf(c_0_104,negated_conjecture,
sk_c4 = sk_c9,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_98,c_0_91]),c_0_88]),c_0_91]) ).
cnf(c_0_105,negated_conjecture,
( sk_c1 = sk_c9
| inverse(sk_c1) = sk_c9 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_100]),c_0_95])]) ).
cnf(c_0_106,plain,
multiply(inverse(inverse(X1)),X2) = multiply(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_101]),c_0_95]) ).
cnf(c_0_107,negated_conjecture,
multiply(sk_c9,identity) = sk_c9,
inference(spm,[status(thm)],[c_0_102,c_0_88]) ).
cnf(c_0_108,negated_conjecture,
( inverse(sk_c1) = sk_c9
| inverse(sk_c9) = sk_c9 ),
inference(rw,[status(thm)],[c_0_103,c_0_104]) ).
cnf(c_0_109,negated_conjecture,
sk_c1 = sk_c9,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_105]),c_0_95])]) ).
cnf(c_0_110,plain,
multiply(X1,sk_c9) = X1,
inference(rw,[status(thm)],[c_0_101,c_0_106]) ).
cnf(c_0_111,negated_conjecture,
sk_c7 = sk_c9,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_107,c_0_91]),c_0_68]) ).
cnf(c_0_112,negated_conjecture,
inverse(sk_c9) = sk_c9,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_108,c_0_109])]) ).
cnf(c_0_113,negated_conjecture,
$false,
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(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(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)],[c_0_53,c_0_66]),c_0_66]),c_0_66]),c_0_66]),c_0_66]),c_0_66]),c_0_66])]),c_0_110]),c_0_95]),c_0_110]),c_0_95]),c_0_95]),c_0_111]),c_0_110]),c_0_110])])])])])]),c_0_112])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP322-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n004.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 20 20:09:36 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 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
% 0.17/0.54 % Version: 3.5.1
% 0.17/0.54 % Preprocessing class: FSMSSMSMSSSNFFN.
% 0.17/0.54 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.54 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 0.17/0.54 % Starting new_bool_3 with 300s (1) cores
% 0.17/0.54 % Starting new_bool_1 with 300s (1) cores
% 0.17/0.54 % Starting sh5l with 300s (1) cores
% 0.17/0.54 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with pid 1383704 completed with status 0
% 0.17/0.54 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI
% 0.17/0.54 % Preprocessing class: FSMSSMSMSSSNFFN.
% 0.17/0.54 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.54 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 0.17/0.54 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.17/0.54 % No SInE strategy applied
% 0.17/0.54 % Search class: FGHPS-FFMM21-SFFFFFNN
% 0.17/0.54 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.17/0.54 % Starting SubtermCWHack with 136s (1) cores
% 0.17/0.54 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 0.17/0.54 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.17/0.54 % Starting new_bool_3 with 136s (1) cores
% 0.17/0.54 % Starting new_bool_1 with 136s (1) cores
% 0.17/0.54 % new_bool_1 with pid 1383715 completed with status 0
% 0.17/0.54 % Result found by new_bool_1
% 0.17/0.54 % Preprocessing class: FSMSSMSMSSSNFFN.
% 0.17/0.54 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.54 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 0.17/0.54 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.17/0.54 % No SInE strategy applied
% 0.17/0.54 % Search class: FGHPS-FFMM21-SFFFFFNN
% 0.17/0.54 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.17/0.54 % Starting SubtermCWHack with 136s (1) cores
% 0.17/0.54 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 0.17/0.54 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.17/0.54 % Starting new_bool_3 with 136s (1) cores
% 0.17/0.54 % Starting new_bool_1 with 136s (1) cores
% 0.17/0.54 % Preprocessing time : 0.001 s
% 0.17/0.54 % Presaturation interreduction done
% 0.17/0.54
% 0.17/0.54 % Proof found!
% 0.17/0.54 % SZS status Unsatisfiable
% 0.17/0.54 % SZS output start CNFRefutation
% See solution above
% 0.17/0.54 % Parsed axioms : 40
% 0.17/0.54 % Removed by relevancy pruning/SinE : 0
% 0.17/0.54 % Initial clauses : 40
% 0.17/0.54 % Removed in clause preprocessing : 0
% 0.17/0.54 % Initial clauses in saturation : 40
% 0.17/0.54 % Processed clauses : 1100
% 0.17/0.54 % ...of these trivial : 209
% 0.17/0.54 % ...subsumed : 322
% 0.17/0.54 % ...remaining for further processing : 569
% 0.17/0.54 % Other redundant clauses eliminated : 6
% 0.17/0.54 % Clauses deleted for lack of memory : 0
% 0.17/0.54 % Backward-subsumed : 77
% 0.17/0.54 % Backward-rewritten : 417
% 0.17/0.54 % Generated clauses : 3606
% 0.17/0.54 % ...of the previous two non-redundant : 3274
% 0.17/0.54 % ...aggressively subsumed : 0
% 0.17/0.54 % Contextual simplify-reflections : 84
% 0.17/0.54 % Paramodulations : 3599
% 0.17/0.54 % Factorizations : 5
% 0.17/0.54 % NegExts : 0
% 0.17/0.54 % Equation resolutions : 6
% 0.17/0.54 % Disequality decompositions : 0
% 0.17/0.54 % Total rewrite steps : 3812
% 0.17/0.54 % ...of those cached : 2945
% 0.17/0.54 % Propositional unsat checks : 0
% 0.17/0.54 % Propositional check models : 0
% 0.17/0.54 % Propositional check unsatisfiable : 0
% 0.17/0.54 % Propositional clauses : 0
% 0.17/0.54 % Propositional clauses after purity: 0
% 0.17/0.54 % Propositional unsat core size : 0
% 0.17/0.54 % Propositional preprocessing time : 0.000
% 0.17/0.54 % Propositional encoding time : 0.000
% 0.17/0.54 % Propositional solver time : 0.000
% 0.17/0.54 % Success case prop preproc time : 0.000
% 0.17/0.54 % Success case prop encoding time : 0.000
% 0.17/0.54 % Success case prop solver time : 0.000
% 0.17/0.54 % Current number of processed clauses : 33
% 0.17/0.54 % Positive orientable unit clauses : 32
% 0.17/0.54 % Positive unorientable unit clauses: 0
% 0.17/0.54 % Negative unit clauses : 0
% 0.17/0.54 % Non-unit-clauses : 1
% 0.17/0.54 % Current number of unprocessed clauses: 1743
% 0.17/0.54 % ...number of literals in the above : 8463
% 0.17/0.54 % Current number of archived formulas : 0
% 0.17/0.54 % Current number of archived clauses : 534
% 0.17/0.54 % Clause-clause subsumption calls (NU) : 8385
% 0.17/0.54 % Rec. Clause-clause subsumption calls : 3104
% 0.17/0.54 % Non-unit clause-clause subsumptions : 476
% 0.17/0.54 % Unit Clause-clause subsumption calls : 179
% 0.17/0.54 % Rewrite failures with RHS unbound : 0
% 0.17/0.54 % BW rewrite match attempts : 51
% 0.17/0.54 % BW rewrite match successes : 28
% 0.17/0.54 % Condensation attempts : 0
% 0.17/0.54 % Condensation successes : 0
% 0.17/0.54 % Termbank termtop insertions : 62909
% 0.17/0.54 % Search garbage collected termcells : 33
% 0.17/0.54
% 0.17/0.54 % -------------------------------------------------
% 0.17/0.54 % User time : 0.083 s
% 0.17/0.54 % System time : 0.007 s
% 0.17/0.54 % Total time : 0.090 s
% 0.17/0.54 % Maximum resident set size: 3652 pages
% 0.17/0.54
% 0.17/0.54 % -------------------------------------------------
% 0.17/0.54 % User time : 0.364 s
% 0.17/0.54 % System time : 0.034 s
% 0.17/0.54 % Total time : 0.399 s
% 0.17/0.54 % Maximum resident set size: 4864 pages
% 0.17/0.54 % E exiting
%------------------------------------------------------------------------------