%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP078-1 : TPTP v9.2.1. Bugfixed v2.3.0.
% 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 : n007.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 04:23:45 PM UTC 2026
% Result : Unsatisfiable 1.30s 1.74s
% Output : CNFRefutation 1.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 5
% Syntax : Number of clauses : 34 ( 28 unt; 0 nHn; 9 RR)
% Number of literals : 45 ( 44 equ; 18 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 42 ( 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(identity,X1),double_divide(identity,double_divide(double_divide(double_divide(X1,X2),identity),double_divide(X3,X2)))) = X3,
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)) ),
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(identity,X1),double_divide(identity,double_divide(double_divide(double_divide(X1,X2),identity),double_divide(X3,X2)))) = X3,
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,X1),double_divide(identity,identity)) = double_divide(double_divide(X1,identity),identity),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_10,plain,
double_divide(double_divide(X1,identity),double_divide(double_divide(identity,X1),double_divide(identity,identity))) = identity,
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_11,plain,
double_divide(double_divide(identity,X1),double_divide(identity,identity)) = double_divide(identity,double_divide(X1,double_divide(identity,identity))),
inference(spm,[status(thm)],[c_0_7,c_0_10]) ).
cnf(c_0_12,plain,
double_divide(double_divide(X1,identity),double_divide(identity,double_divide(X1,double_divide(identity,identity)))) = identity,
inference(rw,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_13,plain,
double_divide(identity,identity) = identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_8]),c_0_11]),c_0_8]) ).
cnf(c_0_14,plain,
double_divide(double_divide(identity,X1),identity) = double_divide(identity,double_divide(X1,identity)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_11,c_0_13]),c_0_13]) ).
cnf(c_0_15,plain,
double_divide(identity,double_divide(identity,double_divide(identity,double_divide(X1,identity)))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_13]),c_0_13]),c_0_13]) ).
cnf(c_0_16,plain,
double_divide(double_divide(X1,identity),identity) = double_divide(identity,double_divide(X1,double_divide(identity,identity))),
inference(rw,[status(thm)],[c_0_9,c_0_11]) ).
cnf(c_0_17,plain,
double_divide(X1,identity) = double_divide(identity,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_14]),c_0_14]),c_0_16]),c_0_13]),c_0_15]) ).
cnf(c_0_18,plain,
double_divide(double_divide(identity,X1),double_divide(identity,double_divide(double_divide(identity,double_divide(X1,X2)),double_divide(X3,X2)))) = X3,
inference(rw,[status(thm)],[c_0_7,c_0_17]) ).
cnf(c_0_19,negated_conjecture,
( multiply(inverse(a1),a1) != identity
| multiply(identity,a2) != a2
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ),
prove_these_axioms ).
cnf(c_0_20,axiom,
multiply(X1,X2) = double_divide(double_divide(X2,X1),identity),
multiply ).
cnf(c_0_21,plain,
double_divide(double_divide(identity,X1),X1) = identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_13]),c_0_14]),c_0_17]),c_0_15]) ).
cnf(c_0_22,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(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)],[c_0_19,c_0_6]),c_0_20]),c_0_20]),c_0_20]),c_0_20]),c_0_20]),c_0_20]) ).
cnf(c_0_23,plain,
double_divide(identity,double_divide(identity,X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_21]),c_0_13]),c_0_17]) ).
cnf(c_0_24,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(a2,identity),identity) != a2
| double_divide(identity,identity) != identity ),
inference(rw,[status(thm)],[c_0_22,c_0_8]) ).
cnf(c_0_25,plain,
double_divide(X1,double_divide(X2,X1)) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_23]),c_0_13]),c_0_23]) ).
cnf(c_0_26,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(identity,double_divide(a2,double_divide(identity,identity))) != a2
| double_divide(identity,identity) != identity ),
inference(rw,[status(thm)],[c_0_24,c_0_16]) ).
cnf(c_0_27,plain,
double_divide(X1,double_divide(identity,double_divide(double_divide(identity,X2),double_divide(X3,double_divide(identity,double_divide(double_divide(identity,double_divide(X1,X4)),double_divide(X2,X4))))))) = X3,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_18]),c_0_23]) ).
cnf(c_0_28,plain,
double_divide(double_divide(X1,X2),X1) = X2,
inference(spm,[status(thm)],[c_0_25,c_0_25]) ).
cnf(c_0_29,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(a2,identity)) != a2 ),
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)],[c_0_26,c_0_13]),c_0_13])]),c_0_17]),c_0_17]),c_0_17]),c_0_17]) ).
cnf(c_0_30,plain,
double_divide(double_divide(identity,double_divide(X1,X2)),double_divide(X3,X2)) = double_divide(X1,double_divide(identity,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_21]),c_0_28]),c_0_23]) ).
cnf(c_0_31,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)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_25])]) ).
cnf(c_0_32,plain,
double_divide(double_divide(identity,double_divide(X1,X2)),X3) = double_divide(X1,double_divide(identity,double_divide(X2,X3))),
inference(spm,[status(thm)],[c_0_30,c_0_28]) ).
cnf(c_0_33,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_32])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP078-1 : TPTP v9.2.1. Bugfixed v2.3.0.
% 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 : n007.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 18:18:53 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.30/1.74 % Version : CSE_E---1.7
% 1.30/1.74 % Problem : theBenchmark.p
% 1.30/1.74 % SZS status Unsatisfiable for theBenchmark.p
% 1.30/1.74 % SZS output start CNFRefutation
% See solution above
% 1.30/1.74 % Total time : 1.373s
%------------------------------------------------------------------------------