%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP083-1 : TPTP v9.2.1. Bugfixed v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n021.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 13.80s 8.95s
% Output : CNFRefutation 13.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 3
% Syntax : Number of clauses : 69 ( 55 unt; 0 nHn; 18 RR)
% Number of literals : 86 ( 85 equ; 34 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 13 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 183 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
double_divide(double_divide(X1,inverse(double_divide(X2,X3))),double_divide(inverse(X2),inverse(double_divide(X4,double_divide(X1,X4))))) = X3,
file('/export/starexec/sandbox2/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)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms) ).
cnf(multiply,axiom,
multiply(X1,X2) = inverse(double_divide(X2,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply) ).
cnf(c_0_3,axiom,
double_divide(double_divide(X1,inverse(double_divide(X2,X3))),double_divide(inverse(X2),inverse(double_divide(X4,double_divide(X1,X4))))) = X3,
single_axiom ).
cnf(c_0_4,plain,
double_divide(double_divide(X1,inverse(X2)),double_divide(inverse(double_divide(X3,inverse(double_divide(X4,X2)))),inverse(double_divide(X5,double_divide(X1,X5))))) = double_divide(inverse(X4),inverse(double_divide(X6,double_divide(X3,X6)))),
inference(spm,[status(thm)],[c_0_3,c_0_3]) ).
cnf(c_0_5,plain,
double_divide(inverse(X1),inverse(double_divide(X2,double_divide(X3,X2)))) = double_divide(inverse(X1),inverse(double_divide(X4,double_divide(X3,X4)))),
inference(spm,[status(thm)],[c_0_4,c_0_4]) ).
cnf(c_0_6,plain,
inverse(double_divide(X1,double_divide(X2,X1))) = inverse(double_divide(X3,double_divide(X2,X3))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_3,c_0_5]),c_0_3]) ).
cnf(c_0_7,plain,
double_divide(double_divide(X1,inverse(double_divide(X2,double_divide(X3,X2)))),double_divide(inverse(X4),inverse(double_divide(X5,double_divide(X1,X5))))) = double_divide(X3,X4),
inference(spm,[status(thm)],[c_0_3,c_0_6]) ).
cnf(c_0_8,plain,
double_divide(X1,double_divide(X2,inverse(double_divide(X3,double_divide(X4,double_divide(X1,X4)))))) = double_divide(inverse(X3),inverse(double_divide(X5,double_divide(X2,X5)))),
inference(spm,[status(thm)],[c_0_4,c_0_7]) ).
cnf(c_0_9,plain,
double_divide(inverse(double_divide(double_divide(X1,inverse(double_divide(X2,X3))),X1)),inverse(double_divide(X4,double_divide(inverse(X2),X4)))) = X3,
inference(spm,[status(thm)],[c_0_3,c_0_8]) ).
cnf(c_0_10,plain,
double_divide(double_divide(inverse(X1),inverse(double_divide(double_divide(double_divide(X2,inverse(double_divide(X1,X3))),X2),X4))),X3) = X4,
inference(spm,[status(thm)],[c_0_3,c_0_9]) ).
cnf(c_0_11,plain,
double_divide(inverse(X1),inverse(double_divide(X2,double_divide(inverse(double_divide(double_divide(X3,inverse(double_divide(X4,inverse(X4)))),X3)),X2)))) = X1,
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_12,plain,
double_divide(double_divide(X1,inverse(double_divide(double_divide(double_divide(X2,inverse(double_divide(X3,inverse(X3)))),X2),X4))),X1) = X4,
inference(spm,[status(thm)],[c_0_9,c_0_11]) ).
cnf(c_0_13,plain,
double_divide(double_divide(X1,inverse(double_divide(inverse(double_divide(double_divide(X2,inverse(double_divide(X3,inverse(X3)))),X2)),X4))),X1) = X4,
inference(spm,[status(thm)],[c_0_12,c_0_12]) ).
cnf(c_0_14,plain,
double_divide(double_divide(X1,inverse(inverse(X2))),X1) = inverse(double_divide(X3,double_divide(inverse(X2),X3))),
inference(spm,[status(thm)],[c_0_13,c_0_9]) ).
cnf(c_0_15,plain,
double_divide(double_divide(X1,inverse(inverse(X2))),X1) = double_divide(double_divide(X3,inverse(inverse(X2))),X3),
inference(spm,[status(thm)],[c_0_14,c_0_14]) ).
cnf(c_0_16,plain,
double_divide(double_divide(inverse(X1),inverse(double_divide(double_divide(X2,inverse(inverse(X3))),X2))),X4) = double_divide(inverse(inverse(X3)),inverse(double_divide(X1,X4))),
inference(spm,[status(thm)],[c_0_10,c_0_15]) ).
cnf(c_0_17,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)) ),
prove_these_axioms ).
cnf(c_0_18,axiom,
multiply(X1,X2) = inverse(double_divide(X2,X1)),
multiply ).
cnf(c_0_19,plain,
double_divide(inverse(inverse(X1)),inverse(double_divide(X2,inverse(X2)))) = double_divide(inverse(inverse(X1)),inverse(double_divide(X3,inverse(X3)))),
inference(spm,[status(thm)],[c_0_12,c_0_16]) ).
cnf(c_0_20,negated_conjecture,
( 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)],[c_0_17,c_0_18]),c_0_18]),c_0_18]),c_0_18]),c_0_18]),c_0_18]),c_0_18]),c_0_18]) ).
cnf(c_0_21,plain,
inverse(double_divide(X1,inverse(X1))) = inverse(double_divide(X2,inverse(X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_3,c_0_19]),c_0_3]) ).
cnf(c_0_22,negated_conjecture,
( inverse(double_divide(inverse(double_divide(c3,b3)),a3)) != inverse(double_divide(c3,inverse(double_divide(b3,a3))))
| inverse(double_divide(a2,inverse(double_divide(b2,inverse(b2))))) != a2 ),
inference(sr,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_23,plain,
double_divide(X1,inverse(X1)) = double_divide(X2,inverse(X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_21]),c_0_11]) ).
cnf(c_0_24,plain,
double_divide(X1,double_divide(X2,double_divide(X3,X2))) = double_divide(X1,double_divide(X4,double_divide(X3,X4))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_6]),c_0_7]) ).
cnf(c_0_25,negated_conjecture,
( inverse(double_divide(inverse(double_divide(c3,b3)),a3)) != inverse(double_divide(c3,inverse(double_divide(b3,a3))))
| inverse(double_divide(a2,inverse(double_divide(X1,inverse(X1))))) != a2 ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_26,plain,
double_divide(double_divide(X1,inverse(X1)),inverse(X2)) = inverse(double_divide(X3,double_divide(inverse(X2),X3))),
inference(spm,[status(thm)],[c_0_14,c_0_23]) ).
cnf(c_0_27,plain,
double_divide(X1,double_divide(X2,X1)) = double_divide(X3,double_divide(X2,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_3,c_0_24]),c_0_3]) ).
cnf(c_0_28,plain,
double_divide(double_divide(double_divide(X1,inverse(double_divide(X2,X3))),inverse(double_divide(X4,X5))),double_divide(inverse(X4),inverse(double_divide(double_divide(inverse(X2),inverse(double_divide(X6,double_divide(X1,X6)))),X3)))) = X5,
inference(spm,[status(thm)],[c_0_3,c_0_3]) ).
cnf(c_0_29,negated_conjecture,
( inverse(double_divide(inverse(double_divide(c3,b3)),a3)) != inverse(double_divide(c3,inverse(double_divide(b3,a3))))
| inverse(double_divide(a2,inverse(inverse(double_divide(X1,double_divide(inverse(double_divide(X2,inverse(X2))),X1)))))) != a2 ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_30,plain,
double_divide(X1,double_divide(X2,X1)) = double_divide(inverse(X2),double_divide(X3,inverse(X3))),
inference(spm,[status(thm)],[c_0_27,c_0_23]) ).
cnf(c_0_31,plain,
double_divide(double_divide(X1,inverse(X1)),inverse(X2)) = double_divide(double_divide(X3,inverse(inverse(X2))),X3),
inference(spm,[status(thm)],[c_0_15,c_0_23]) ).
cnf(c_0_32,plain,
double_divide(X1,double_divide(inverse(X2),inverse(double_divide(inverse(double_divide(X2,X3)),X1)))) = X3,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_10]),c_0_9]) ).
cnf(c_0_33,negated_conjecture,
( inverse(double_divide(a2,inverse(inverse(double_divide(double_divide(X1,inverse(X1)),double_divide(X2,double_divide(double_divide(X3,inverse(X3)),X2))))))) != a2
| inverse(double_divide(inverse(double_divide(c3,b3)),a3)) != inverse(double_divide(c3,inverse(double_divide(b3,a3)))) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_34,plain,
double_divide(X1,inverse(X1)) = double_divide(double_divide(X2,inverse(inverse(double_divide(X3,inverse(X3))))),X2),
inference(spm,[status(thm)],[c_0_23,c_0_31]) ).
cnf(c_0_35,plain,
double_divide(X1,double_divide(inverse(X2),inverse(double_divide(inverse(double_divide(X3,inverse(X3))),X1)))) = inverse(X2),
inference(spm,[status(thm)],[c_0_32,c_0_23]) ).
cnf(c_0_36,negated_conjecture,
( inverse(double_divide(a2,inverse(inverse(double_divide(double_divide(X1,inverse(X1)),double_divide(double_divide(X2,inverse(double_divide(X3,inverse(X3)))),X2)))))) != a2
| inverse(double_divide(inverse(double_divide(c3,b3)),a3)) != inverse(double_divide(c3,inverse(double_divide(b3,a3)))) ),
inference(spm,[status(thm)],[c_0_33,c_0_12]) ).
cnf(c_0_37,plain,
inverse(double_divide(X1,inverse(inverse(double_divide(X2,inverse(X2)))))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_34]),c_0_35]) ).
cnf(c_0_38,negated_conjecture,
( inverse(double_divide(a2,inverse(inverse(double_divide(double_divide(X1,inverse(X1)),double_divide(double_divide(X2,inverse(X2)),double_divide(X3,inverse(X3)))))))) != a2
| inverse(double_divide(inverse(double_divide(c3,b3)),a3)) != inverse(double_divide(c3,inverse(double_divide(b3,a3)))) ),
inference(spm,[status(thm)],[c_0_36,c_0_23]) ).
cnf(c_0_39,plain,
double_divide(double_divide(X1,inverse(X1)),X2) = double_divide(double_divide(X3,inverse(X2)),X3),
inference(spm,[status(thm)],[c_0_31,c_0_37]) ).
cnf(c_0_40,negated_conjecture,
( inverse(double_divide(inverse(double_divide(c3,b3)),a3)) != inverse(double_divide(c3,inverse(double_divide(b3,a3))))
| inverse(double_divide(a2,inverse(inverse(double_divide(X1,double_divide(double_divide(X2,inverse(X2)),X1)))))) != a2 ),
inference(spm,[status(thm)],[c_0_38,c_0_27]) ).
cnf(c_0_41,plain,
double_divide(inverse(X1),inverse(double_divide(X2,inverse(X2)))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_39]),c_0_13]) ).
cnf(c_0_42,plain,
double_divide(double_divide(X1,inverse(X2)),X1) = double_divide(double_divide(X3,inverse(X2)),X3),
inference(spm,[status(thm)],[c_0_15,c_0_37]) ).
cnf(c_0_43,negated_conjecture,
( inverse(double_divide(inverse(double_divide(c3,b3)),a3)) != inverse(double_divide(c3,inverse(double_divide(b3,a3))))
| inverse(double_divide(a2,inverse(inverse(double_divide(inverse(X1),inverse(double_divide(X2,double_divide(inverse(X1),X2)))))))) != a2 ),
inference(spm,[status(thm)],[c_0_40,c_0_26]) ).
cnf(c_0_44,plain,
double_divide(inverse(inverse(double_divide(X1,X2))),X1) = X2,
inference(spm,[status(thm)],[c_0_32,c_0_41]) ).
cnf(c_0_45,plain,
double_divide(inverse(double_divide(X1,inverse(X1))),X2) = inverse(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_41]),c_0_41]) ).
cnf(c_0_46,plain,
double_divide(double_divide(X1,X2),X1) = double_divide(double_divide(X3,X2),X3),
inference(spm,[status(thm)],[c_0_42,c_0_37]) ).
cnf(c_0_47,negated_conjecture,
( inverse(double_divide(inverse(double_divide(c3,b3)),a3)) != inverse(double_divide(c3,inverse(double_divide(b3,a3))))
| inverse(double_divide(a2,inverse(inverse(double_divide(double_divide(X1,inverse(double_divide(X2,inverse(X2)))),X1))))) != a2 ),
inference(spm,[status(thm)],[c_0_43,c_0_11]) ).
cnf(c_0_48,plain,
double_divide(double_divide(inverse(double_divide(double_divide(X1,inverse(double_divide(X2,inverse(X2)))),X1)),inverse(double_divide(X3,X4))),X3) = X4,
inference(spm,[status(thm)],[c_0_10,c_0_10]) ).
cnf(c_0_49,plain,
double_divide(X1,double_divide(X2,X1)) = double_divide(double_divide(inverse(X3),inverse(double_divide(inverse(double_divide(X3,X4)),X2))),X4),
inference(spm,[status(thm)],[c_0_27,c_0_32]) ).
cnf(c_0_50,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_41]) ).
cnf(c_0_51,plain,
double_divide(double_divide(X1,X2),X1) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_45]),c_0_41]) ).
cnf(c_0_52,negated_conjecture,
( inverse(double_divide(inverse(double_divide(c3,b3)),a3)) != inverse(double_divide(c3,inverse(double_divide(b3,a3))))
| inverse(double_divide(a2,inverse(inverse(inverse(double_divide(double_divide(X1,inverse(double_divide(X2,inverse(X2)))),X1)))))) != a2 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_35]) ).
cnf(c_0_53,plain,
double_divide(double_divide(inverse(inverse(double_divide(X1,inverse(X1)))),inverse(double_divide(double_divide(X2,double_divide(X3,X2)),X4))),X3) = X4,
inference(spm,[status(thm)],[c_0_10,c_0_49]) ).
cnf(c_0_54,plain,
inverse(double_divide(X1,double_divide(X2,inverse(X2)))) = X1,
inference(rw,[status(thm)],[c_0_37,c_0_50]) ).
cnf(c_0_55,plain,
double_divide(double_divide(inverse(X1),inverse(X2)),X3) = double_divide(X2,inverse(double_divide(X1,X3))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_16,c_0_50]),c_0_50]),c_0_51]) ).
cnf(c_0_56,negated_conjecture,
( inverse(double_divide(a2,inverse(inverse(inverse(inverse(double_divide(X1,double_divide(inverse(inverse(double_divide(X2,inverse(X2)))),X1)))))))) != a2
| inverse(double_divide(inverse(double_divide(c3,b3)),a3)) != inverse(double_divide(c3,inverse(double_divide(b3,a3)))) ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_57,plain,
double_divide(double_divide(X1,inverse(X1)),X2) = inverse(double_divide(X3,double_divide(X2,X3))),
inference(spm,[status(thm)],[c_0_26,c_0_37]) ).
cnf(c_0_58,plain,
double_divide(inverse(X1),inverse(X2)) = inverse(double_divide(X2,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_54]) ).
cnf(c_0_59,negated_conjecture,
inverse(double_divide(inverse(double_divide(c3,b3)),a3)) != inverse(double_divide(c3,inverse(double_divide(b3,a3)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_37]),c_0_37])]) ).
cnf(c_0_60,plain,
inverse(double_divide(inverse(X1),X2)) = double_divide(inverse(X2),X1),
inference(spm,[status(thm)],[c_0_58,c_0_50]) ).
cnf(c_0_61,plain,
double_divide(double_divide(inverse(X1),inverse(inverse(double_divide(X2,double_divide(inverse(X3),X2))))),X4) = double_divide(inverse(inverse(X3)),inverse(double_divide(X1,X4))),
inference(spm,[status(thm)],[c_0_10,c_0_14]) ).
cnf(c_0_62,plain,
double_divide(X1,double_divide(inverse(X2),X1)) = inverse(X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_45]),c_0_50]) ).
cnf(c_0_63,negated_conjecture,
inverse(double_divide(c3,inverse(double_divide(b3,a3)))) != double_divide(inverse(a3),double_divide(c3,b3)),
inference(rw,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_64,plain,
inverse(double_divide(X1,inverse(X2))) = double_divide(X2,inverse(X1)),
inference(spm,[status(thm)],[c_0_58,c_0_50]) ).
cnf(c_0_65,plain,
double_divide(inverse(double_divide(X1,X2)),X3) = double_divide(X1,inverse(double_divide(X2,X3))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_61,c_0_50]),c_0_50]),c_0_62]),c_0_58]) ).
cnf(c_0_66,negated_conjecture,
double_divide(double_divide(b3,a3),inverse(c3)) != double_divide(inverse(a3),double_divide(c3,b3)),
inference(rw,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_67,plain,
double_divide(double_divide(X1,X2),inverse(X3)) = double_divide(inverse(X2),double_divide(X3,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_65]),c_0_64]) ).
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 : GRP083-1 : TPTP v9.2.1. Bugfixed v2.3.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.14/0.33 % Computer : n021.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Mon May 4 18:21:10 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 13.80/8.95 % Version : CSE_E---1.7
% 13.80/8.95 % Problem : theBenchmark.p
% 13.80/8.95 % SZS status Unsatisfiable for theBenchmark.p
% 13.80/8.95 % SZS output start CNFRefutation
% See solution above
% 13.80/9.00 % Total time : 6.380s
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