%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP486-1 : TPTP v9.2.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n020.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 : Tue May 5 04:26:14 PM UTC 2026
% Result : Unsatisfiable 1.33s 1.75s
% Output : CNFRefutation 1.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 5
% Syntax : Number of clauses : 69 ( 69 unt; 0 nHn; 5 RR)
% Number of literals : 69 ( 68 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 105 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
double_divide(double_divide(X1,double_divide(double_divide(double_divide(X1,X2),X3),double_divide(X2,identity))),double_divide(identity,identity)) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
cnf(inverse,axiom,
inverse(X1) = double_divide(X1,identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse) ).
cnf(multiply,axiom,
multiply(X1,X2) = double_divide(double_divide(X2,X1),identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply) ).
cnf(identity,axiom,
identity = double_divide(X1,inverse(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity) ).
cnf(prove_these_axioms_3,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms_3) ).
cnf(c_0_5,axiom,
double_divide(double_divide(X1,double_divide(double_divide(double_divide(X1,X2),X3),double_divide(X2,identity))),double_divide(identity,identity)) = X3,
single_axiom ).
cnf(c_0_6,axiom,
inverse(X1) = double_divide(X1,identity),
inverse ).
cnf(c_0_7,axiom,
multiply(X1,X2) = double_divide(double_divide(X2,X1),identity),
multiply ).
cnf(c_0_8,plain,
double_divide(double_divide(X1,double_divide(double_divide(double_divide(X1,X2),X3),inverse(X2))),inverse(identity)) = X3,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5,c_0_6]),c_0_6]) ).
cnf(c_0_9,axiom,
identity = double_divide(X1,inverse(X1)),
identity ).
cnf(c_0_10,plain,
inverse(double_divide(X1,X2)) = multiply(X2,X1),
inference(rw,[status(thm)],[c_0_7,c_0_6]) ).
cnf(c_0_11,plain,
double_divide(double_divide(X1,double_divide(identity,inverse(X2))),inverse(identity)) = multiply(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_9]),c_0_10]) ).
cnf(c_0_12,plain,
double_divide(inverse(X1),inverse(identity)) = multiply(identity,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_9]),c_0_6]) ).
cnf(c_0_13,plain,
inverse(inverse(X1)) = multiply(identity,X1),
inference(spm,[status(thm)],[c_0_10,c_0_6]) ).
cnf(c_0_14,plain,
multiply(inverse(identity),inverse(X1)) = inverse(multiply(identity,X1)),
inference(spm,[status(thm)],[c_0_10,c_0_12]) ).
cnf(c_0_15,plain,
multiply(identity,double_divide(X1,X2)) = inverse(multiply(X2,X1)),
inference(spm,[status(thm)],[c_0_13,c_0_10]) ).
cnf(c_0_16,plain,
double_divide(double_divide(X1,multiply(X2,inverse(X1))),inverse(identity)) = double_divide(identity,inverse(X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_11]),c_0_6]) ).
cnf(c_0_17,plain,
multiply(inverse(identity),multiply(X1,X2)) = multiply(identity,multiply(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_10]),c_0_15]),c_0_13]) ).
cnf(c_0_18,plain,
multiply(X1,multiply(identity,X2)) = multiply(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_16]),c_0_11]),c_0_6]),c_0_13]) ).
cnf(c_0_19,plain,
multiply(inverse(X1),X1) = inverse(identity),
inference(spm,[status(thm)],[c_0_10,c_0_9]) ).
cnf(c_0_20,plain,
multiply(inverse(identity),X1) = multiply(identity,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_18]) ).
cnf(c_0_21,plain,
double_divide(inverse(X1),multiply(identity,X1)) = identity,
inference(spm,[status(thm)],[c_0_9,c_0_13]) ).
cnf(c_0_22,plain,
inverse(identity) = multiply(identity,identity),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_23,plain,
double_divide(inverse(multiply(identity,X1)),multiply(identity,X1)) = identity,
inference(spm,[status(thm)],[c_0_21,c_0_18]) ).
cnf(c_0_24,plain,
double_divide(inverse(X1),multiply(identity,identity)) = multiply(identity,X1),
inference(rw,[status(thm)],[c_0_12,c_0_22]) ).
cnf(c_0_25,plain,
multiply(inverse(X1),X1) = multiply(identity,identity),
inference(rw,[status(thm)],[c_0_19,c_0_22]) ).
cnf(c_0_26,plain,
multiply(identity,identity) = identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_18]) ).
cnf(c_0_27,plain,
multiply(inverse(X1),X1) = identity,
inference(rw,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_28,plain,
multiply(X1,inverse(multiply(X2,X3))) = multiply(X1,double_divide(X3,X2)),
inference(spm,[status(thm)],[c_0_18,c_0_15]) ).
cnf(c_0_29,plain,
multiply(inverse(multiply(identity,X1)),X1) = identity,
inference(spm,[status(thm)],[c_0_18,c_0_27]) ).
cnf(c_0_30,plain,
multiply(X1,double_divide(X2,inverse(multiply(identity,X2)))) = multiply(X1,identity),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_22]),c_0_26]) ).
cnf(c_0_31,plain,
multiply(multiply(X1,inverse(X2)),X2) = double_divide(identity,inverse(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_16,c_0_22]),c_0_26]),c_0_6]),c_0_10]) ).
cnf(c_0_32,plain,
double_divide(identity,inverse(X1)) = multiply(multiply(X1,identity),identity),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_10]),c_0_29]) ).
cnf(c_0_33,plain,
multiply(multiply(X1,inverse(X2)),X2) = multiply(multiply(X1,identity),identity),
inference(rw,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_34,plain,
multiply(multiply(X1,X2),inverse(X2)) = multiply(multiply(X1,identity),identity),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_13]),c_0_18]) ).
cnf(c_0_35,plain,
multiply(identity,inverse(X1)) = inverse(multiply(identity,X1)),
inference(spm,[status(thm)],[c_0_13,c_0_13]) ).
cnf(c_0_36,plain,
multiply(multiply(inverse(X1),identity),identity) = double_divide(identity,multiply(identity,X1)),
inference(spm,[status(thm)],[c_0_32,c_0_13]) ).
cnf(c_0_37,plain,
double_divide(identity,multiply(identity,X1)) = inverse(multiply(identity,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_29]),c_0_35]),c_0_36]),c_0_18]) ).
cnf(c_0_38,plain,
inverse(multiply(multiply(X1,identity),identity)) = multiply(inverse(X1),identity),
inference(spm,[status(thm)],[c_0_10,c_0_32]) ).
cnf(c_0_39,plain,
inverse(multiply(identity,multiply(X1,X2))) = inverse(multiply(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_28]),c_0_15]) ).
cnf(c_0_40,plain,
multiply(multiply(identity,X1),identity) = multiply(identity,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_37]),c_0_13]),c_0_18]) ).
cnf(c_0_41,plain,
multiply(identity,multiply(inverse(X1),identity)) = multiply(inverse(X1),identity),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_38]),c_0_39]),c_0_38]) ).
cnf(c_0_42,plain,
multiply(inverse(X1),identity) = inverse(multiply(identity,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_36]),c_0_37]) ).
cnf(c_0_43,plain,
multiply(multiply(X1,X2),identity) = multiply(identity,multiply(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_10]),c_0_15]),c_0_13]) ).
cnf(c_0_44,plain,
double_divide(identity,inverse(X1)) = multiply(identity,multiply(X1,identity)),
inference(rw,[status(thm)],[c_0_32,c_0_43]) ).
cnf(c_0_45,plain,
multiply(identity,multiply(X1,identity)) = multiply(identity,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_44]),c_0_18]),c_0_42]),c_0_13]),c_0_18]) ).
cnf(c_0_46,plain,
multiply(X1,multiply(X2,identity)) = multiply(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_45]),c_0_18]) ).
cnf(c_0_47,plain,
multiply(multiply(X1,X2),inverse(X2)) = multiply(identity,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_43]),c_0_46]) ).
cnf(c_0_48,plain,
multiply(multiply(identity,X1),X2) = multiply(identity,multiply(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_47]),c_0_13]),c_0_18]) ).
cnf(c_0_49,plain,
multiply(identity,multiply(X1,X2)) = multiply(X1,X2),
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_11,c_0_22]),c_0_32]),c_0_43]),c_0_46]),c_0_26]),c_0_6]),c_0_10]),c_0_48]) ).
cnf(c_0_50,plain,
multiply(double_divide(double_divide(double_divide(X1,X2),X3),inverse(X2)),X1) = X3,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_8,c_0_22]),c_0_26]),c_0_6]),c_0_10]) ).
cnf(c_0_51,plain,
double_divide(identity,inverse(X1)) = multiply(identity,X1),
inference(rw,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_52,plain,
multiply(identity,X1) = X1,
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_53,plain,
multiply(multiply(X1,X2),identity) = multiply(X1,X2),
inference(rw,[status(thm)],[c_0_43,c_0_49]) ).
cnf(c_0_54,plain,
double_divide(identity,inverse(X1)) = X1,
inference(rw,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_55,plain,
multiply(X1,identity) = X1,
inference(spm,[status(thm)],[c_0_53,c_0_50]) ).
cnf(c_0_56,plain,
double_divide(double_divide(X1,X2),X1) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_54]),c_0_13]),c_0_52]),c_0_55]) ).
cnf(c_0_57,plain,
double_divide(X1,double_divide(X2,X1)) = X2,
inference(spm,[status(thm)],[c_0_56,c_0_56]) ).
cnf(c_0_58,plain,
multiply(multiply(X1,X2),inverse(X2)) = X1,
inference(rw,[status(thm)],[c_0_47,c_0_52]) ).
cnf(c_0_59,plain,
multiply(double_divide(X1,X2),X2) = inverse(X1),
inference(spm,[status(thm)],[c_0_10,c_0_57]) ).
cnf(c_0_60,plain,
multiply(inverse(X1),inverse(X2)) = double_divide(X1,X2),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_61,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[c_0_13,c_0_52]) ).
cnf(c_0_62,plain,
double_divide(X1,inverse(X2)) = multiply(inverse(X1),X2),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_63,plain,
multiply(multiply(X1,inverse(X2)),X2) = multiply(identity,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_43]),c_0_46]) ).
cnf(c_0_64,plain,
multiply(multiply(multiply(X1,double_divide(X2,X3)),X3),X2) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_50,c_0_62]),c_0_10]) ).
cnf(c_0_65,plain,
multiply(multiply(X1,inverse(X2)),X2) = X1,
inference(rw,[status(thm)],[c_0_63,c_0_52]) ).
cnf(c_0_66,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
prove_these_axioms_3 ).
cnf(c_0_67,plain,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_10]) ).
cnf(c_0_68,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_66,c_0_67])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP486-1 : TPTP v9.2.1. Released v2.6.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33 % Computer : n020.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Mon May 4 18:38:34 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.33/1.75 % Version : CSE_E---1.7
% 1.33/1.75 % Problem : theBenchmark.p
% 1.33/1.75 % SZS status Unsatisfiable for theBenchmark.p
% 1.33/1.75 % SZS output start CNFRefutation
% See solution above
% 1.33/1.75 % Total time : 1.372s
%------------------------------------------------------------------------------