%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP372-1 : 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 : n007.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 12:39:25 PM UTC 2026
% Result : Unsatisfiable 0.14s 5.46s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 23
% Syntax : Number of clauses : 110 ( 27 unt; 66 nHn; 95 RR)
% Number of literals : 282 ( 281 equ; 111 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 : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 66 ( 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_8,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_8) ).
cnf(prove_this_14,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
cnf(prove_this_7,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c6
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_7) ).
cnf(prove_this_13,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c6
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_13) ).
cnf(prove_this_9,negated_conjecture,
( inverse(sk_c3) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).
cnf(prove_this_25,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c6
| multiply(sk_c2,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_25) ).
cnf(prove_this_3,negated_conjecture,
( inverse(sk_c3) = sk_c8
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
cnf(prove_this_31,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c6
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_31) ).
cnf(prove_this_15,negated_conjecture,
( inverse(sk_c3) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
cnf(prove_this_37,negated_conjecture,
( inverse(X5) != sk_c8
| multiply(X5,sk_c8) != X4
| multiply(sk_c8,X4) != sk_c7
| inverse(X3) != sk_c8
| multiply(X3,sk_c8) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6
| inverse(X2) != sk_c7
| multiply(X2,sk_c7) != sk_c6
| multiply(sk_c8,sk_c6) != sk_c7
| inverse(X1) != sk_c8
| multiply(X1,sk_c8) != sk_c7
| inverse(sk_c8) != sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_37) ).
cnf(prove_this_23,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c5
| multiply(sk_c8,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_23) ).
cnf(prove_this_24,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c8,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_24) ).
cnf(prove_this_28,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c2,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_28) ).
cnf(prove_this_4,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
cnf(prove_this_22,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c8,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_22) ).
cnf(prove_this_34,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_34) ).
cnf(prove_this_10,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).
cnf(prove_this_16,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_16) ).
cnf(prove_this_5,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c5
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
cnf(prove_this_6,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
cnf(c_0_23,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity ).
cnf(c_0_24,axiom,
multiply(inverse(X1),X1) = identity,
left_inverse ).
cnf(c_0_25,axiom,
multiply(identity,X1) = X1,
left_identity ).
cnf(c_0_26,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]) ).
cnf(c_0_27,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
prove_this_8 ).
cnf(c_0_28,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| multiply(inverse(sk_c1),sk_c7) = sk_c8 ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_29,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| inverse(sk_c1) = sk_c8 ),
prove_this_14 ).
cnf(c_0_30,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c6
| multiply(sk_c1,sk_c8) = sk_c7 ),
prove_this_7 ).
cnf(c_0_31,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c8
| multiply(sk_c3,sk_c8) = sk_c7 ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_32,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c6
| multiply(inverse(sk_c1),sk_c7) = sk_c8 ),
inference(spm,[status(thm)],[c_0_26,c_0_30]) ).
cnf(c_0_33,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c6
| inverse(sk_c1) = sk_c8 ),
prove_this_13 ).
cnf(c_0_34,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c8
| multiply(inverse(sk_c3),sk_c7) = sk_c8 ),
inference(spm,[status(thm)],[c_0_26,c_0_31]) ).
cnf(c_0_35,negated_conjecture,
( inverse(sk_c3) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
prove_this_9 ).
cnf(c_0_36,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c6
| multiply(sk_c2,sk_c7) = sk_c6 ),
prove_this_25 ).
cnf(c_0_37,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c8
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_38,negated_conjecture,
( inverse(sk_c3) = sk_c8
| inverse(sk_c8) = sk_c7 ),
prove_this_3 ).
cnf(c_0_39,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_40,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c6
| multiply(inverse(sk_c2),sk_c6) = sk_c7 ),
inference(spm,[status(thm)],[c_0_26,c_0_36]) ).
cnf(c_0_41,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c6
| inverse(sk_c2) = sk_c7 ),
prove_this_31 ).
cnf(c_0_42,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c8
| multiply(inverse(sk_c8),sk_c6) = sk_c7 ),
inference(spm,[status(thm)],[c_0_26,c_0_37]) ).
cnf(c_0_43,negated_conjecture,
( inverse(sk_c8) = sk_c7
| multiply(sk_c8,sk_c7) = sk_c8 ),
inference(spm,[status(thm)],[c_0_34,c_0_38]) ).
cnf(c_0_44,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c8
| multiply(inverse(sk_c1),sk_c7) = sk_c8 ),
inference(spm,[status(thm)],[c_0_26,c_0_39]) ).
cnf(c_0_45,negated_conjecture,
( inverse(sk_c3) = sk_c8
| inverse(sk_c1) = sk_c8 ),
prove_this_15 ).
cnf(c_0_46,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c7
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_47,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c7
| multiply(sk_c8,sk_c7) = sk_c8 ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_48,negated_conjecture,
( inverse(sk_c3) = sk_c8
| multiply(sk_c8,sk_c7) = sk_c8 ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_49,negated_conjecture,
( inverse(X5) != sk_c8
| multiply(X5,sk_c8) != X4
| multiply(sk_c8,X4) != sk_c7
| inverse(X3) != sk_c8
| multiply(X3,sk_c8) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6
| inverse(X2) != sk_c7
| multiply(X2,sk_c7) != sk_c6
| multiply(sk_c8,sk_c6) != sk_c7
| inverse(X1) != sk_c8
| multiply(X1,sk_c8) != sk_c7
| inverse(sk_c8) != sk_c7 ),
inference(fof_simplification,[status(thm)],[prove_this_37]) ).
cnf(c_0_50,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c5
| multiply(sk_c8,sk_c6) = sk_c7 ),
prove_this_23 ).
cnf(c_0_51,negated_conjecture,
( identity = sk_c6
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_46]),c_0_24]) ).
cnf(c_0_52,negated_conjecture,
( identity = sk_c6
| multiply(sk_c8,sk_c7) = sk_c8 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_47]),c_0_24]) ).
cnf(c_0_53,negated_conjecture,
multiply(sk_c8,sk_c7) = sk_c8,
inference(spm,[status(thm)],[c_0_34,c_0_48]) ).
cnf(c_0_54,negated_conjecture,
( inverse(X5) != sk_c8
| multiply(X5,sk_c8) != X4
| multiply(sk_c8,X4) != sk_c7
| inverse(X3) != sk_c8
| multiply(X3,sk_c8) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6
| inverse(X2) != sk_c7
| multiply(X2,sk_c7) != sk_c6
| multiply(sk_c8,sk_c6) != sk_c7
| inverse(X1) != sk_c8
| multiply(X1,sk_c8) != sk_c7
| inverse(sk_c8) != sk_c7 ),
c_0_49 ).
cnf(c_0_55,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| multiply(inverse(sk_c4),sk_c5) = sk_c8 ),
inference(spm,[status(thm)],[c_0_26,c_0_50]) ).
cnf(c_0_56,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c8,sk_c6) = sk_c7 ),
prove_this_24 ).
cnf(c_0_57,negated_conjecture,
( sk_c6 = sk_c8
| identity = sk_c6 ),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_58,negated_conjecture,
identity = sk_c7,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_53]),c_0_24]) ).
cnf(c_0_59,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c2,sk_c7) = sk_c6 ),
prove_this_28 ).
cnf(c_0_60,negated_conjecture,
( inverse(X4) != sk_c8
| inverse(X3) != sk_c7
| inverse(X2) != sk_c8
| inverse(X1) != sk_c8
| inverse(sk_c8) != sk_c7
| multiply(X4,sk_c8) != sk_c7
| multiply(X3,sk_c7) != sk_c6
| multiply(X2,sk_c8) != sk_c7
| multiply(sk_c8,sk_c6) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6
| multiply(sk_c8,multiply(X1,sk_c8)) != sk_c7 ),
inference(er,[status(thm)],[c_0_54]) ).
cnf(c_0_61,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| inverse(sk_c8) = sk_c7 ),
prove_this_4 ).
cnf(c_0_62,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c8,sk_c6) = sk_c7 ),
prove_this_22 ).
cnf(c_0_63,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c8
| multiply(sk_c8,sk_c6) = sk_c7 ),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_64,negated_conjecture,
( sk_c6 = sk_c7
| sk_c6 = sk_c8 ),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_65,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(inverse(sk_c2),sk_c6) = sk_c7 ),
inference(spm,[status(thm)],[c_0_26,c_0_59]) ).
cnf(c_0_66,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| inverse(sk_c2) = sk_c7 ),
prove_this_34 ).
cnf(c_0_67,plain,
multiply(inverse(identity),X1) = X1,
inference(spm,[status(thm)],[c_0_26,c_0_25]) ).
cnf(c_0_68,negated_conjecture,
( inverse(X4) != sk_c8
| inverse(X3) != sk_c7
| inverse(X2) != sk_c8
| inverse(X1) != sk_c8
| multiply(X4,sk_c8) != sk_c7
| multiply(X3,sk_c7) != sk_c6
| multiply(X2,sk_c8) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6
| multiply(sk_c8,multiply(X1,sk_c8)) != sk_c7
| multiply(sk_c8,sk_c5) = sk_c7 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_62]) ).
cnf(c_0_69,negated_conjecture,
( sk_c6 != sk_c8
| multiply(sk_c8,sk_c7) = sk_c8 ),
inference(ef,[status(thm)],[c_0_37]) ).
cnf(c_0_70,negated_conjecture,
( sk_c7 = sk_c8
| multiply(sk_c8,sk_c6) = sk_c7 ),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_71,negated_conjecture,
( sk_c7 != sk_c8
| sk_c6 = sk_c8 ),
inference(ef,[status(thm)],[c_0_64]) ).
cnf(c_0_72,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c7
| multiply(sk_c8,sk_c5) = sk_c7 ),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_73,plain,
multiply(inverse(inverse(identity)),X1) = X1,
inference(spm,[status(thm)],[c_0_26,c_0_67]) ).
cnf(c_0_74,negated_conjecture,
( sk_c6 != sk_c8
| inverse(X4) != sk_c8
| inverse(X3) != sk_c7
| inverse(X2) != sk_c8
| inverse(X1) != sk_c8
| multiply(X4,sk_c8) != sk_c7
| multiply(X3,sk_c7) != sk_c6
| multiply(X2,sk_c8) != sk_c7
| multiply(sk_c8,multiply(X1,sk_c8)) != sk_c7
| multiply(sk_c8,sk_c5) = sk_c7 ),
inference(spm,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_75,negated_conjecture,
sk_c6 = sk_c8,
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_64]),c_0_53])]),c_0_71]) ).
cnf(c_0_76,negated_conjecture,
( identity = sk_c6
| multiply(sk_c8,sk_c5) = sk_c7 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_72]),c_0_24]) ).
cnf(c_0_77,plain,
inverse(identity) = identity,
inference(spm,[status(thm)],[c_0_24,c_0_73]) ).
cnf(c_0_78,negated_conjecture,
( sk_c6 != sk_c8
| identity = sk_c7 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_69]),c_0_24]) ).
cnf(c_0_79,negated_conjecture,
( inverse(X4) != sk_c8
| inverse(X3) != sk_c7
| inverse(X2) != sk_c8
| inverse(X1) != sk_c8
| multiply(X4,sk_c8) != sk_c7
| multiply(X3,sk_c7) != sk_c8
| multiply(X2,sk_c8) != sk_c7
| multiply(sk_c8,multiply(X1,sk_c8)) != sk_c7
| multiply(sk_c8,sk_c5) = sk_c7 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_74,c_0_75]),c_0_75])]) ).
cnf(c_0_80,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
prove_this_10 ).
cnf(c_0_81,negated_conjecture,
( sk_c7 = sk_c8
| multiply(sk_c8,sk_c5) = sk_c7 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_76,c_0_58]),c_0_75]) ).
cnf(c_0_82,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| inverse(sk_c1) = sk_c8 ),
prove_this_16 ).
cnf(c_0_83,negated_conjecture,
( sk_c6 != sk_c8
| inverse(sk_c7) = sk_c7 ),
inference(spm,[status(thm)],[c_0_77,c_0_78]) ).
cnf(c_0_84,negated_conjecture,
( inverse(X3) != sk_c8
| inverse(X2) != sk_c7
| inverse(X1) != sk_c8
| multiply(X3,sk_c8) != sk_c7
| multiply(X2,sk_c7) != sk_c8
| multiply(X1,sk_c8) != sk_c7
| multiply(sk_c8,sk_c5) = sk_c7 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_53]),c_0_81]),c_0_82]) ).
cnf(c_0_85,plain,
inverse(sk_c7) = sk_c7,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_77,c_0_58]),c_0_58]) ).
cnf(c_0_86,negated_conjecture,
( sk_c6 != sk_c8
| multiply(sk_c7,sk_c7) = identity ),
inference(spm,[status(thm)],[c_0_24,c_0_83]) ).
cnf(c_0_87,negated_conjecture,
( inverse(X2) != sk_c8
| inverse(X1) != sk_c7
| multiply(X2,sk_c8) != sk_c7
| multiply(X1,sk_c7) != sk_c8
| multiply(sk_c8,sk_c5) = sk_c7 ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_73]),c_0_58]),c_0_85]),c_0_85]),c_0_85])]),c_0_81]) ).
cnf(c_0_88,negated_conjecture,
multiply(sk_c7,sk_c7) = sk_c7,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_86,c_0_58]),c_0_75])]) ).
cnf(c_0_89,negated_conjecture,
( inverse(X1) != sk_c8
| multiply(X1,sk_c8) != sk_c7
| multiply(sk_c8,sk_c5) = sk_c7 ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_88]),c_0_85])]),c_0_81]) ).
cnf(c_0_90,negated_conjecture,
multiply(sk_c8,sk_c5) = sk_c7,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_82]),c_0_80]) ).
cnf(c_0_91,negated_conjecture,
multiply(inverse(sk_c8),sk_c7) = sk_c5,
inference(spm,[status(thm)],[c_0_26,c_0_90]) ).
cnf(c_0_92,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c5
| inverse(sk_c8) = sk_c7 ),
prove_this_5 ).
cnf(c_0_93,negated_conjecture,
( sk_c5 = sk_c7
| multiply(sk_c4,sk_c8) = sk_c5 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_88]) ).
cnf(c_0_94,negated_conjecture,
( sk_c5 = sk_c7
| multiply(inverse(sk_c4),sk_c5) = sk_c8 ),
inference(spm,[status(thm)],[c_0_26,c_0_93]) ).
cnf(c_0_95,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c8) = sk_c7 ),
prove_this_6 ).
cnf(c_0_96,negated_conjecture,
multiply(inverse(inverse(sk_c8)),sk_c5) = sk_c7,
inference(spm,[status(thm)],[c_0_26,c_0_91]) ).
cnf(c_0_97,negated_conjecture,
( sk_c7 = sk_c8
| sk_c5 = sk_c7
| inverse(sk_c8) = sk_c7 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_95]),c_0_90]) ).
cnf(c_0_98,plain,
multiply(sk_c7,X1) = X1,
inference(rw,[status(thm)],[c_0_25,c_0_58]) ).
cnf(c_0_99,negated_conjecture,
( sk_c5 = sk_c7
| sk_c7 = sk_c8 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_97]),c_0_85]),c_0_98])]) ).
cnf(c_0_100,plain,
multiply(inverse(inverse(X1)),identity) = X1,
inference(spm,[status(thm)],[c_0_26,c_0_24]) ).
cnf(c_0_101,negated_conjecture,
sk_c7 = sk_c8,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_99]),c_0_53])]) ).
cnf(c_0_102,plain,
multiply(inverse(inverse(X1)),sk_c8) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_100,c_0_58]),c_0_101]) ).
cnf(c_0_103,plain,
multiply(sk_c8,X1) = X1,
inference(rw,[status(thm)],[c_0_98,c_0_101]) ).
cnf(c_0_104,negated_conjecture,
( sk_c6 != sk_c8
| inverse(X4) != sk_c8
| inverse(X3) != sk_c7
| inverse(X2) != sk_c8
| inverse(X1) != sk_c8
| inverse(sk_c8) != sk_c7
| multiply(X4,sk_c8) != sk_c7
| multiply(X3,sk_c7) != sk_c6
| multiply(X2,sk_c8) != sk_c7
| multiply(sk_c8,sk_c6) != sk_c7
| multiply(sk_c8,multiply(X1,sk_c8)) != sk_c7 ),
inference(rw,[status(thm)],[c_0_60,c_0_53]) ).
cnf(c_0_105,plain,
multiply(inverse(inverse(X1)),X2) = multiply(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_102]),c_0_103]) ).
cnf(c_0_106,negated_conjecture,
( inverse(X4) != sk_c8
| inverse(X3) != sk_c7
| inverse(X2) != sk_c8
| inverse(X1) != sk_c8
| inverse(sk_c8) != sk_c7
| multiply(X4,sk_c8) != sk_c7
| multiply(X3,sk_c7) != sk_c8
| multiply(X2,sk_c8) != sk_c7
| multiply(sk_c8,sk_c8) != sk_c7
| multiply(sk_c8,multiply(X1,sk_c8)) != sk_c7 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_104,c_0_75]),c_0_75]),c_0_75])]) ).
cnf(c_0_107,plain,
multiply(X1,sk_c8) = X1,
inference(rw,[status(thm)],[c_0_102,c_0_105]) ).
cnf(c_0_108,plain,
inverse(sk_c8) = sk_c8,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_85,c_0_101]),c_0_101]) ).
cnf(c_0_109,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(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_106,c_0_101]),c_0_101]),c_0_101]),c_0_101]),c_0_101]),c_0_101]),c_0_101]),c_0_103]),c_0_107]),c_0_103]),c_0_107]),c_0_107]),c_0_107]),c_0_108])])])])])]),c_0_108])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP372-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/5.37 % Computer : n007.cluster.edu
% 0.09/5.37 % Model : x86_64 x86_64
% 0.09/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.37 % Memory : 8046.5625MB
% 0.09/5.37 % OS : Linux 6.8.0-71-generic
% 0.09/5.37 % CPULimit : 300
% 0.09/5.37 % WCLimit : 300
% 0.09/5.37 % DateTime : Sun Sep 20 20:08:11 UTC 2026
% 0.09/5.37 % CPUTime :
% 0.09/5.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/5.42 Running first-order theorem proving
% 0.14/5.42 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
% 0.14/5.46 % Version: 3.5.1
% 0.14/5.46 % Preprocessing class: FSMSSMSMSSSNFFN.
% 0.14/5.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/5.46 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 0.14/5.46 % Starting new_bool_3 with 300s (1) cores
% 0.14/5.46 % Starting new_bool_1 with 300s (1) cores
% 0.14/5.46 % Starting sh5l with 300s (1) cores
% 0.14/5.46 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with pid 3478588 completed with status 0
% 0.14/5.46 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI
% 0.14/5.46 % Preprocessing class: FSMSSMSMSSSNFFN.
% 0.14/5.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/5.46 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 0.14/5.46 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.14/5.46 % No SInE strategy applied
% 0.14/5.46 % Search class: FGHPS-FFMM21-SFFFFFNN
% 0.14/5.46 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/5.46 % Starting SubtermCWHack with 136s (1) cores
% 0.14/5.46 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 0.14/5.46 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.14/5.46 % Starting new_bool_3 with 136s (1) cores
% 0.14/5.46 % Starting new_bool_1 with 136s (1) cores
% 0.14/5.46 % G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with pid 3478595 completed with status 0
% 0.14/5.46 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN
% 0.14/5.46 % Preprocessing class: FSMSSMSMSSSNFFN.
% 0.14/5.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/5.46 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 0.14/5.46 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.14/5.46 % No SInE strategy applied
% 0.14/5.46 % Search class: FGHPS-FFMM21-SFFFFFNN
% 0.14/5.46 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/5.46 % Starting SubtermCWHack with 136s (1) cores
% 0.14/5.46 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 0.14/5.46 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.14/5.46 % Preprocessing time : 0.001 s
% 0.14/5.46 % Presaturation interreduction done
% 0.14/5.46
% 0.14/5.46 % Proof found!
% 0.14/5.46 % SZS status Unsatisfiable
% 0.14/5.46 % SZS output start CNFRefutation
% See solution above
% 0.14/5.46 % Parsed axioms : 40
% 0.14/5.46 % Removed by relevancy pruning/SinE : 0
% 0.14/5.46 % Initial clauses : 40
% 0.14/5.46 % Removed in clause preprocessing : 0
% 0.14/5.46 % Initial clauses in saturation : 40
% 0.14/5.46 % Processed clauses : 578
% 0.14/5.46 % ...of these trivial : 108
% 0.14/5.46 % ...subsumed : 100
% 0.14/5.46 % ...remaining for further processing : 370
% 0.14/5.46 % Other redundant clauses eliminated : 25
% 0.14/5.46 % Clauses deleted for lack of memory : 0
% 0.14/5.46 % Backward-subsumed : 44
% 0.14/5.46 % Backward-rewritten : 260
% 0.14/5.46 % Generated clauses : 1577
% 0.14/5.46 % ...of the previous two non-redundant : 1406
% 0.14/5.46 % ...aggressively subsumed : 0
% 0.14/5.46 % Contextual simplify-reflections : 18
% 0.14/5.46 % Paramodulations : 1550
% 0.14/5.46 % Factorizations : 5
% 0.14/5.46 % NegExts : 0
% 0.14/5.46 % Equation resolutions : 25
% 0.14/5.46 % Disequality decompositions : 0
% 0.14/5.46 % Total rewrite steps : 1715
% 0.14/5.46 % ...of those cached : 1589
% 0.14/5.46 % Propositional unsat checks : 0
% 0.14/5.46 % Propositional check models : 0
% 0.14/5.46 % Propositional check unsatisfiable : 0
% 0.14/5.46 % Propositional clauses : 0
% 0.14/5.46 % Propositional clauses after purity: 0
% 0.14/5.46 % Propositional unsat core size : 0
% 0.14/5.46 % Propositional preprocessing time : 0.000
% 0.14/5.46 % Propositional encoding time : 0.000
% 0.14/5.46 % Propositional solver time : 0.000
% 0.14/5.46 % Success case prop preproc time : 0.000
% 0.14/5.46 % Success case prop encoding time : 0.000
% 0.14/5.46 % Success case prop solver time : 0.000
% 0.14/5.46 % Current number of processed clauses : 24
% 0.14/5.46 % Positive orientable unit clauses : 20
% 0.14/5.46 % Positive unorientable unit clauses: 0
% 0.14/5.46 % Negative unit clauses : 0
% 0.14/5.46 % Non-unit-clauses : 4
% 0.14/5.46 % Current number of unprocessed clauses: 245
% 0.14/5.46 % ...number of literals in the above : 2139
% 0.14/5.46 % Current number of archived formulas : 0
% 0.14/5.46 % Current number of archived clauses : 344
% 0.14/5.46 % Clause-clause subsumption calls (NU) : 3453
% 0.14/5.46 % Rec. Clause-clause subsumption calls : 908
% 0.14/5.46 % Non-unit clause-clause subsumptions : 151
% 0.14/5.46 % Unit Clause-clause subsumption calls : 271
% 0.14/5.46 % Rewrite failures with RHS unbound : 0
% 0.14/5.46 % BW rewrite match attempts : 39
% 0.14/5.46 % BW rewrite match successes : 30
% 0.14/5.46 % Condensation attempts : 0
% 0.14/5.46 % Condensation successes : 0
% 0.14/5.46 % Termbank termtop insertions : 24645
% 0.14/5.46 % Search garbage collected termcells : 32
% 0.14/5.46
% 0.14/5.46 % -------------------------------------------------
% 0.14/5.46 % User time : 0.026 s
% 0.14/5.46 % System time : 0.003 s
% 0.14/5.46 % Total time : 0.028 s
% 0.14/5.46 % Maximum resident set size: 3652 pages
% 0.14/5.46
% 0.14/5.46 % -------------------------------------------------
% 0.14/5.46 % User time : 0.098 s
% 0.14/5.46 % System time : 0.017 s
% 0.14/5.46 % Total time : 0.115 s
% 0.14/5.46 % Maximum resident set size: 4864 pages
% 0.14/5.46 % E exiting
%------------------------------------------------------------------------------