%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP105-1 : 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 : n014.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 04:23:51 PM UTC 2026
% Result : Unsatisfiable 1.46s 1.79s
% Output : CNFRefutation 1.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 3
% Syntax : Number of clauses : 49 ( 43 unt; 0 nHn; 9 RR)
% Number of literals : 63 ( 62 equ; 22 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 9 con; 0-2 aty)
% Number of variables : 99 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
double_divide(inverse(double_divide(double_divide(X1,X2),inverse(double_divide(X1,inverse(X3))))),X2) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
cnf(prove_these_axioms,negated_conjecture,
( multiply(inverse(a1),a1) != multiply(inverse(b1),b1)
| multiply(multiply(inverse(b2),b2),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) = inverse(double_divide(X2,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply) ).
cnf(c_0_3,axiom,
double_divide(inverse(double_divide(double_divide(X1,X2),inverse(double_divide(X1,inverse(X3))))),X2) = X3,
single_axiom ).
cnf(c_0_4,plain,
double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(X1,inverse(X2)),inverse(double_divide(X1,inverse(X3))))),X4),inverse(X3))),X4) = X2,
inference(spm,[status(thm)],[c_0_3,c_0_3]) ).
cnf(c_0_5,plain,
double_divide(inverse(double_divide(X1,inverse(X1))),inverse(X2)) = X2,
inference(spm,[status(thm)],[c_0_4,c_0_3]) ).
cnf(c_0_6,plain,
double_divide(inverse(double_divide(X1,inverse(X2))),inverse(X1)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_3,c_0_5]),c_0_5]) ).
cnf(c_0_7,plain,
double_divide(inverse(X1),inverse(inverse(double_divide(X2,inverse(X1))))) = X2,
inference(spm,[status(thm)],[c_0_6,c_0_6]) ).
cnf(c_0_8,plain,
double_divide(inverse(X1),inverse(inverse(X2))) = inverse(double_divide(X1,inverse(X2))),
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
cnf(c_0_9,plain,
inverse(double_divide(X1,inverse(double_divide(X2,inverse(X1))))) = X2,
inference(rw,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_10,plain,
double_divide(inverse(X1),inverse(X2)) = inverse(double_divide(X1,X2)),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_11,plain,
inverse(double_divide(double_divide(X1,inverse(X1)),X2)) = X2,
inference(rw,[status(thm)],[c_0_5,c_0_10]) ).
cnf(c_0_12,plain,
inverse(double_divide(X1,inverse(double_divide(X2,inverse(X2))))) = X1,
inference(spm,[status(thm)],[c_0_9,c_0_11]) ).
cnf(c_0_13,plain,
double_divide(double_divide(X1,X2),X2) = X1,
inference(spm,[status(thm)],[c_0_3,c_0_12]) ).
cnf(c_0_14,plain,
inverse(double_divide(double_divide(X1,inverse(X2)),X1)) = X2,
inference(rw,[status(thm)],[c_0_6,c_0_10]) ).
cnf(c_0_15,plain,
inverse(double_divide(X1,inverse(X2))) = double_divide(X2,inverse(X1)),
inference(spm,[status(thm)],[c_0_9,c_0_13]) ).
cnf(c_0_16,plain,
inverse(inverse(X1)) = X1,
inference(spm,[status(thm)],[c_0_14,c_0_13]) ).
cnf(c_0_17,plain,
inverse(inverse(double_divide(double_divide(X1,X2),X1))) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_10]),c_0_10]) ).
cnf(c_0_18,plain,
double_divide(X1,X2) = double_divide(X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_10]),c_0_16]),c_0_16]) ).
cnf(c_0_19,plain,
double_divide(double_divide(X1,X2),X1) = X2,
inference(rw,[status(thm)],[c_0_17,c_0_16]) ).
cnf(c_0_20,plain,
double_divide(X1,double_divide(X2,inverse(double_divide(double_divide(double_divide(X3,inverse(X2)),double_divide(X4,inverse(X3))),X1)))) = X4,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4,c_0_15]),c_0_15]),c_0_15]),c_0_18]) ).
cnf(c_0_21,plain,
double_divide(X1,double_divide(X1,X2)) = X2,
inference(spm,[status(thm)],[c_0_19,c_0_13]) ).
cnf(c_0_22,plain,
inverse(double_divide(inverse(X1),X2)) = double_divide(X1,inverse(X2)),
inference(spm,[status(thm)],[c_0_10,c_0_16]) ).
cnf(c_0_23,plain,
double_divide(X1,double_divide(X2,double_divide(X3,inverse(X1)))) = double_divide(X3,inverse(X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]) ).
cnf(c_0_24,plain,
double_divide(X1,double_divide(double_divide(X2,inverse(X3)),inverse(double_divide(X2,X1)))) = X3,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_3,c_0_15]),c_0_18]) ).
cnf(c_0_25,negated_conjecture,
( multiply(inverse(a1),a1) != multiply(inverse(b1),b1)
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(a4,b4) != multiply(b4,a4) ),
prove_these_axioms ).
cnf(c_0_26,axiom,
multiply(X1,X2) = inverse(double_divide(X2,X1)),
multiply ).
cnf(c_0_27,plain,
double_divide(double_divide(X1,inverse(X2)),inverse(X3)) = double_divide(double_divide(X1,X3),X2),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_28,negated_conjecture,
( inverse(double_divide(b4,a4)) != inverse(double_divide(a4,b4))
| inverse(double_divide(a2,inverse(double_divide(b2,inverse(b2))))) != a2
| inverse(double_divide(b1,inverse(b1))) != inverse(double_divide(a1,inverse(a1)))
| inverse(double_divide(c3,inverse(double_divide(b3,a3)))) != inverse(double_divide(inverse(double_divide(c3,b3)),a3)) ),
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_25,c_0_26]),c_0_26]),c_0_26]),c_0_26]),c_0_26]),c_0_26]),c_0_26]),c_0_26]),c_0_26]),c_0_26]) ).
cnf(c_0_29,plain,
double_divide(X1,double_divide(X2,inverse(X3))) = inverse(double_divide(double_divide(X3,X1),X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_27]),c_0_15]) ).
cnf(c_0_30,plain,
double_divide(double_divide(inverse(X1),X2),X3) = inverse(double_divide(double_divide(X1,X3),X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_10]),c_0_10]) ).
cnf(c_0_31,negated_conjecture,
( inverse(double_divide(inverse(double_divide(c3,b3)),a3)) != inverse(double_divide(c3,inverse(double_divide(b3,a3))))
| inverse(double_divide(a1,inverse(a1))) != inverse(double_divide(b1,inverse(b1)))
| inverse(double_divide(a4,b4)) != inverse(double_divide(b4,a4)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_12])]) ).
cnf(c_0_32,plain,
double_divide(X1,inverse(double_divide(double_divide(X1,X2),X3))) = double_divide(X3,inverse(X2)),
inference(rw,[status(thm)],[c_0_23,c_0_29]) ).
cnf(c_0_33,plain,
double_divide(double_divide(X1,X2),X3) = double_divide(X3,double_divide(X2,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_16]),c_0_30]),c_0_16]) ).
cnf(c_0_34,negated_conjecture,
( inverse(double_divide(inverse(double_divide(c3,b3)),a3)) != double_divide(double_divide(b3,a3),inverse(c3))
| double_divide(a1,inverse(a1)) != double_divide(b1,inverse(b1))
| inverse(double_divide(a4,b4)) != inverse(double_divide(b4,a4)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_15]),c_0_15]),c_0_15]) ).
cnf(c_0_35,plain,
double_divide(X1,double_divide(X2,X1)) = X2,
inference(spm,[status(thm)],[c_0_19,c_0_19]) ).
cnf(c_0_36,plain,
double_divide(double_divide(X1,inverse(X1)),X2) = inverse(X2),
inference(spm,[status(thm)],[c_0_16,c_0_11]) ).
cnf(c_0_37,plain,
double_divide(inverse(X1),double_divide(X2,double_divide(X1,X3))) = double_divide(X3,inverse(X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_32]),c_0_15]),c_0_33]) ).
cnf(c_0_38,negated_conjecture,
( double_divide(inverse(c3),double_divide(a3,b3)) != double_divide(inverse(a3),double_divide(b3,c3))
| double_divide(a1,inverse(a1)) != double_divide(b1,inverse(b1)) ),
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_34,c_0_18]),c_0_18]),c_0_15]),c_0_18]),c_0_18]),c_0_18]),c_0_18])]) ).
cnf(c_0_39,plain,
double_divide(X1,inverse(X1)) = double_divide(X2,inverse(X2)),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_40,plain,
double_divide(double_divide(X1,X2),inverse(X3)) = double_divide(inverse(X1),double_divide(X3,X2)),
inference(spm,[status(thm)],[c_0_37,c_0_21]) ).
cnf(c_0_41,plain,
double_divide(double_divide(X1,inverse(X2)),X3) = inverse(double_divide(double_divide(X3,X2),X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_29]),c_0_16]),c_0_15]),c_0_29]) ).
cnf(c_0_42,plain,
double_divide(inverse(double_divide(X1,X2)),X3) = double_divide(X2,inverse(double_divide(X1,X3))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_10]),c_0_15]) ).
cnf(c_0_43,negated_conjecture,
double_divide(inverse(c3),double_divide(a3,b3)) != double_divide(inverse(a3),double_divide(b3,c3)),
inference(sr,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_44,plain,
double_divide(inverse(X1),double_divide(X2,X3)) = double_divide(inverse(X3),double_divide(X2,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_35]),c_0_40]) ).
cnf(c_0_45,plain,
double_divide(X1,inverse(double_divide(X2,X3))) = double_divide(X2,inverse(double_divide(X3,X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_10]),c_0_15]),c_0_42]) ).
cnf(c_0_46,negated_conjecture,
double_divide(inverse(b3),double_divide(a3,c3)) != double_divide(inverse(a3),double_divide(b3,c3)),
inference(rw,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_47,plain,
double_divide(inverse(X1),double_divide(X2,X3)) = double_divide(inverse(X3),double_divide(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_45]),c_0_15]),c_0_40]),c_0_40]) ).
cnf(c_0_48,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_46,c_0_47]),c_0_18])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GRP105-1 : 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 : n014.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 18:20:51 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 1.46/1.79 % Version : CSE_E---1.7
% 1.46/1.79 % Problem : theBenchmark.p
% 1.46/1.79 % SZS status Unsatisfiable for theBenchmark.p
% 1.46/1.79 % SZS output start CNFRefutation
% See solution above
% 1.46/1.79 % Total time : 1.373s
%------------------------------------------------------------------------------