%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP101-1 : TPTP v9.2.1. Bugfixed v2.7.0.
% 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 : n002.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 04:23:48 PM UTC 2026
% Result : Unsatisfiable 1.87s 1.93s
% Output : CNFRefutation 1.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 5
% Syntax : Number of clauses : 56 ( 49 unt; 0 nHn; 11 RR)
% Number of literals : 73 ( 72 equ; 25 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 84 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(identity,axiom,
identity = double_divide(X1,inverse(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity) ).
cnf(inverse,axiom,
inverse(X1) = double_divide(X1,identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse) ).
cnf(single_axiom,axiom,
double_divide(double_divide(X1,double_divide(double_divide(X2,double_divide(X3,X1)),double_divide(X3,identity))),double_divide(identity,identity)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
cnf(prove_these_axioms,negated_conjecture,
( multiply(inverse(a1),a1) != identity
| multiply(identity,a2) != a2
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(a4,b4) != multiply(b4,a4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms) ).
cnf(multiply,axiom,
multiply(X1,X2) = double_divide(double_divide(X2,X1),identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply) ).
cnf(c_0_5,axiom,
identity = double_divide(X1,inverse(X1)),
identity ).
cnf(c_0_6,axiom,
inverse(X1) = double_divide(X1,identity),
inverse ).
cnf(c_0_7,axiom,
double_divide(double_divide(X1,double_divide(double_divide(X2,double_divide(X3,X1)),double_divide(X3,identity))),double_divide(identity,identity)) = X2,
single_axiom ).
cnf(c_0_8,plain,
identity = double_divide(X1,double_divide(X1,identity)),
inference(rw,[status(thm)],[c_0_5,c_0_6]) ).
cnf(c_0_9,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(X1,identity))),double_divide(identity,identity)) = X1,
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_10,plain,
double_divide(double_divide(identity,identity),double_divide(identity,identity)) = identity,
inference(spm,[status(thm)],[c_0_9,c_0_8]) ).
cnf(c_0_11,plain,
double_divide(identity,identity) = identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_10]),c_0_8]),c_0_10]) ).
cnf(c_0_12,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(X1,identity))),identity) = X1,
inference(rw,[status(thm)],[c_0_9,c_0_11]) ).
cnf(c_0_13,plain,
double_divide(double_divide(X1,double_divide(double_divide(X2,double_divide(X3,X1)),double_divide(X3,identity))),identity) = X2,
inference(rw,[status(thm)],[c_0_7,c_0_11]) ).
cnf(c_0_14,plain,
double_divide(double_divide(identity,double_divide(identity,X1)),identity) = double_divide(identity,double_divide(identity,double_divide(X1,identity))),
inference(spm,[status(thm)],[c_0_12,c_0_12]) ).
cnf(c_0_15,plain,
double_divide(double_divide(identity,double_divide(double_divide(X1,X2),X2)),identity) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_13]),c_0_13]) ).
cnf(c_0_16,plain,
double_divide(identity,double_divide(identity,double_divide(double_divide(X1,identity),identity))) = X1,
inference(rw,[status(thm)],[c_0_12,c_0_14]) ).
cnf(c_0_17,plain,
double_divide(double_divide(identity,X1),identity) = double_divide(identity,double_divide(identity,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_14]),c_0_14]),c_0_16]) ).
cnf(c_0_18,plain,
double_divide(X1,identity) = double_divide(identity,X1),
inference(spm,[status(thm)],[c_0_17,c_0_16]) ).
cnf(c_0_19,plain,
double_divide(X1,double_divide(identity,X1)) = identity,
inference(spm,[status(thm)],[c_0_8,c_0_18]) ).
cnf(c_0_20,plain,
double_divide(identity,double_divide(identity,double_divide(double_divide(X1,X2),X2))) = X1,
inference(rw,[status(thm)],[c_0_15,c_0_17]) ).
cnf(c_0_21,plain,
double_divide(double_divide(identity,double_divide(double_divide(X1,X2),X2)),X1) = identity,
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_22,plain,
double_divide(identity,double_divide(double_divide(X1,X2),X2)) = double_divide(identity,double_divide(identity,double_divide(identity,X1))),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_23,plain,
double_divide(identity,double_divide(identity,double_divide(identity,double_divide(identity,X1)))) = X1,
inference(rw,[status(thm)],[c_0_20,c_0_22]) ).
cnf(c_0_24,plain,
double_divide(identity,double_divide(double_divide(X1,identity),X1)) = identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_18]),c_0_8]),c_0_11]) ).
cnf(c_0_25,plain,
double_divide(double_divide(X1,identity),X1) = identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_8]),c_0_11]) ).
cnf(c_0_26,plain,
double_divide(identity,double_divide(identity,double_divide(identity,double_divide(X1,identity)))) = X1,
inference(rw,[status(thm)],[c_0_16,c_0_18]) ).
cnf(c_0_27,plain,
double_divide(identity,double_divide(identity,X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_25]),c_0_26]) ).
cnf(c_0_28,plain,
double_divide(identity,double_divide(X1,double_divide(double_divide(X2,double_divide(X3,X1)),double_divide(X3,identity)))) = X2,
inference(rw,[status(thm)],[c_0_13,c_0_18]) ).
cnf(c_0_29,plain,
double_divide(identity,double_divide(X1,identity)) = X1,
inference(rw,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_30,plain,
double_divide(identity,double_divide(double_divide(X1,X2),X2)) = double_divide(identity,X1),
inference(rw,[status(thm)],[c_0_22,c_0_27]) ).
cnf(c_0_31,plain,
double_divide(identity,double_divide(X1,X2)) = double_divide(identity,double_divide(X2,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_25]),c_0_29]),c_0_18]) ).
cnf(c_0_32,plain,
double_divide(double_divide(X1,X2),X2) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_30]),c_0_27]) ).
cnf(c_0_33,plain,
double_divide(X1,X2) = double_divide(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_31]),c_0_27]) ).
cnf(c_0_34,plain,
double_divide(X1,double_divide(X2,X1)) = X2,
inference(rw,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_35,plain,
double_divide(X1,double_divide(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_34]),c_0_33]) ).
cnf(c_0_36,plain,
double_divide(X1,double_divide(double_divide(X2,double_divide(X3,X1)),double_divide(X3,identity))) = double_divide(identity,X2),
inference(spm,[status(thm)],[c_0_35,c_0_28]) ).
cnf(c_0_37,plain,
double_divide(double_divide(X1,double_divide(X2,X3)),double_divide(X2,identity)) = double_divide(X3,double_divide(identity,X1)),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_38,plain,
double_divide(identity,double_divide(X1,double_divide(identity,X2))) = double_divide(X2,double_divide(identity,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_11]),c_0_33]) ).
cnf(c_0_39,negated_conjecture,
( multiply(inverse(a1),a1) != identity
| multiply(identity,a2) != a2
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(a4,b4) != multiply(b4,a4) ),
prove_these_axioms ).
cnf(c_0_40,axiom,
multiply(X1,X2) = double_divide(double_divide(X2,X1),identity),
multiply ).
cnf(c_0_41,plain,
double_divide(double_divide(identity,X1),X2) = double_divide(identity,double_divide(X1,double_divide(identity,X2))),
inference(spm,[status(thm)],[c_0_33,c_0_38]) ).
cnf(c_0_42,negated_conjecture,
( double_divide(double_divide(a2,identity),identity) != a2
| double_divide(double_divide(a1,double_divide(a1,identity)),identity) != identity
| double_divide(double_divide(b4,a4),identity) != double_divide(double_divide(a4,b4),identity)
| double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity) != double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),identity) ),
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_39,c_0_6]),c_0_40]),c_0_40]),c_0_40]),c_0_40]),c_0_40]),c_0_40]),c_0_40]),c_0_40]) ).
cnf(c_0_43,plain,
double_divide(double_divide(X1,identity),X2) = double_divide(identity,double_divide(X1,double_divide(identity,X2))),
inference(spm,[status(thm)],[c_0_41,c_0_33]) ).
cnf(c_0_44,negated_conjecture,
( double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),identity) != double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity)
| double_divide(double_divide(a4,b4),identity) != double_divide(double_divide(b4,a4),identity)
| double_divide(double_divide(a2,identity),identity) != a2
| double_divide(identity,identity) != identity ),
inference(rw,[status(thm)],[c_0_42,c_0_8]) ).
cnf(c_0_45,plain,
double_divide(identity,double_divide(X1,double_divide(identity,double_divide(double_divide(X1,X2),X3)))) = double_divide(X2,double_divide(identity,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_33]),c_0_33]),c_0_43]) ).
cnf(c_0_46,negated_conjecture,
( double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),identity) != double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity)
| double_divide(double_divide(a4,b4),identity) != double_divide(double_divide(b4,a4),identity)
| double_divide(double_divide(a2,identity),identity) != a2 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_44,c_0_11])]) ).
cnf(c_0_47,plain,
double_divide(X1,double_divide(identity,double_divide(double_divide(X1,X2),X3))) = double_divide(identity,double_divide(X2,double_divide(identity,X3))),
inference(spm,[status(thm)],[c_0_35,c_0_45]) ).
cnf(c_0_48,negated_conjecture,
( double_divide(identity,double_divide(double_divide(identity,double_divide(c3,b3)),a3)) != double_divide(identity,double_divide(c3,double_divide(identity,double_divide(b3,a3))))
| double_divide(identity,double_divide(a4,b4)) != double_divide(identity,double_divide(b4,a4))
| double_divide(identity,double_divide(a2,identity)) != a2 ),
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_46,c_0_18]),c_0_18]),c_0_18]),c_0_18]),c_0_18]),c_0_18]),c_0_18]) ).
cnf(c_0_49,plain,
double_divide(identity,double_divide(double_divide(X1,X2),X3)) = double_divide(X1,double_divide(identity,double_divide(X2,double_divide(identity,X3)))),
inference(spm,[status(thm)],[c_0_35,c_0_47]) ).
cnf(c_0_50,negated_conjecture,
( double_divide(identity,double_divide(double_divide(identity,double_divide(c3,b3)),a3)) != double_divide(identity,double_divide(c3,double_divide(identity,double_divide(b3,a3))))
| double_divide(identity,double_divide(a4,b4)) != double_divide(identity,double_divide(b4,a4)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_48,c_0_29])]) ).
cnf(c_0_51,plain,
double_divide(identity,double_divide(X1,double_divide(identity,double_divide(X2,double_divide(X1,X3))))) = double_divide(X3,double_divide(identity,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_33]),c_0_38]) ).
cnf(c_0_52,plain,
double_divide(double_divide(X1,X2),X3) = double_divide(identity,double_divide(X1,double_divide(identity,double_divide(X2,double_divide(identity,X3))))),
inference(spm,[status(thm)],[c_0_35,c_0_49]) ).
cnf(c_0_53,negated_conjecture,
double_divide(identity,double_divide(a3,double_divide(identity,double_divide(b3,c3)))) != double_divide(identity,double_divide(c3,double_divide(identity,double_divide(a3,b3)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_50,c_0_31]),c_0_31]),c_0_31]),c_0_31])]) ).
cnf(c_0_54,plain,
double_divide(identity,double_divide(X1,double_divide(identity,double_divide(X2,X3)))) = double_divide(identity,double_divide(X3,double_divide(identity,double_divide(X1,X2)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_34]),c_0_52]),c_0_35]) ).
cnf(c_0_55,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_53,c_0_54])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GRP101-1 : TPTP v9.2.1. Bugfixed v2.7.0.
% 0.00/0.11 % 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
% 0.14/0.32 % Computer : n002.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Mon May 4 18:20:01 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 1.87/1.93 % Version : CSE_E---1.7
% 1.87/1.93 % Problem : theBenchmark.p
% 1.87/1.93 % SZS status Unsatisfiable for theBenchmark.p
% 1.87/1.93 % SZS output start CNFRefutation
% See solution above
% 1.87/1.93 % Total time : 1.370s
%------------------------------------------------------------------------------