%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP063-1 : 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 : n023.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 04:23:42 PM UTC 2026
% Result : Unsatisfiable 1.27s 1.77s
% Output : CNFRefutation 1.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 4
% Syntax : Number of clauses : 50 ( 46 unt; 0 nHn; 6 RR)
% Number of literals : 57 ( 56 equ; 12 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 7 ( 2 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 : 101 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(multiply,axiom,
multiply(X1,X2) = divide(X1,divide(divide(X3,X3),X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply) ).
cnf(inverse,axiom,
inverse(X1) = divide(divide(X2,X2),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse) ).
cnf(single_axiom,axiom,
divide(X1,divide(divide(divide(divide(X1,X1),X2),X3),divide(divide(divide(X1,X1),X1),X3))) = X2,
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(c_0_4,axiom,
multiply(X1,X2) = divide(X1,divide(divide(X3,X3),X2)),
multiply ).
cnf(c_0_5,axiom,
inverse(X1) = divide(divide(X2,X2),X1),
inverse ).
cnf(c_0_6,plain,
divide(X1,inverse(X2)) = multiply(X1,X2),
inference(rw,[status(thm)],[c_0_4,c_0_5]) ).
cnf(c_0_7,plain,
divide(inverse(divide(X1,X1)),X2) = inverse(X2),
inference(spm,[status(thm)],[c_0_5,c_0_5]) ).
cnf(c_0_8,axiom,
divide(X1,divide(divide(divide(divide(X1,X1),X2),X3),divide(divide(divide(X1,X1),X1),X3))) = X2,
single_axiom ).
cnf(c_0_9,plain,
multiply(inverse(divide(X1,X1)),X2) = inverse(inverse(X2)),
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
cnf(c_0_10,plain,
divide(multiply(inverse(X1),X1),X2) = inverse(X2),
inference(spm,[status(thm)],[c_0_5,c_0_6]) ).
cnf(c_0_11,plain,
divide(X1,divide(divide(inverse(X2),X3),divide(inverse(X1),X3))) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_8,c_0_5]),c_0_5]) ).
cnf(c_0_12,plain,
multiply(inverse(multiply(inverse(X1),X1)),X2) = inverse(inverse(X2)),
inference(spm,[status(thm)],[c_0_9,c_0_6]) ).
cnf(c_0_13,plain,
multiply(inverse(inverse(multiply(inverse(X1),X1))),X2) = inverse(inverse(X2)),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_14,plain,
multiply(X1,multiply(inverse(X1),X2)) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_5]),c_0_6]),c_0_6]) ).
cnf(c_0_15,plain,
multiply(inverse(inverse(inverse(multiply(inverse(X1),X1)))),X2) = inverse(inverse(X2)),
inference(spm,[status(thm)],[c_0_12,c_0_12]) ).
cnf(c_0_16,plain,
inverse(inverse(inverse(inverse(X1)))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]) ).
cnf(c_0_17,plain,
multiply(inverse(inverse(X1)),X2) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_14,c_0_14]) ).
cnf(c_0_18,plain,
multiply(X1,inverse(inverse(inverse(X2)))) = divide(X1,X2),
inference(spm,[status(thm)],[c_0_6,c_0_16]) ).
cnf(c_0_19,plain,
inverse(multiply(divide(inverse(X1),X2),X2)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_11]),c_0_7]),c_0_6]) ).
cnf(c_0_20,plain,
divide(inverse(inverse(X1)),X2) = divide(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_18]) ).
cnf(c_0_21,plain,
inverse(multiply(divide(X1,X2),X2)) = inverse(X1),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_22,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[c_0_19,c_0_21]) ).
cnf(c_0_23,plain,
multiply(divide(X1,X2),X2) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_21]),c_0_11]) ).
cnf(c_0_24,plain,
multiply(X1,inverse(X2)) = divide(X1,X2),
inference(rw,[status(thm)],[c_0_18,c_0_22]) ).
cnf(c_0_25,plain,
divide(multiply(X1,X2),X2) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_6]),c_0_24]) ).
cnf(c_0_26,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(spm,[status(thm)],[c_0_14,c_0_17]) ).
cnf(c_0_27,plain,
multiply(multiply(inverse(X1),X1),X2) = inverse(inverse(X2)),
inference(spm,[status(thm)],[c_0_6,c_0_10]) ).
cnf(c_0_28,plain,
divide(X1,multiply(X2,X1)) = inverse(X2),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_29,plain,
multiply(multiply(X1,inverse(X1)),X2) = inverse(inverse(X2)),
inference(spm,[status(thm)],[c_0_27,c_0_17]) ).
cnf(c_0_30,plain,
inverse(divide(X1,X2)) = divide(X2,X1),
inference(spm,[status(thm)],[c_0_28,c_0_23]) ).
cnf(c_0_31,plain,
multiply(divide(X1,X1),X2) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_22]),c_0_24]) ).
cnf(c_0_32,plain,
inverse(multiply(X1,X2)) = divide(inverse(X2),X1),
inference(spm,[status(thm)],[c_0_30,c_0_6]) ).
cnf(c_0_33,plain,
divide(X1,X1) = divide(X2,X2),
inference(spm,[status(thm)],[c_0_25,c_0_31]) ).
cnf(c_0_34,plain,
divide(X1,divide(X2,divide(inverse(X1),divide(divide(inverse(X2),X3),divide(X4,X3))))) = X4,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_11]),c_0_22]) ).
cnf(c_0_35,plain,
divide(X1,divide(inverse(X2),X3)) = multiply(X1,multiply(X3,X2)),
inference(spm,[status(thm)],[c_0_6,c_0_32]) ).
cnf(c_0_36,plain,
divide(X1,divide(X2,X2)) = X1,
inference(spm,[status(thm)],[c_0_11,c_0_33]) ).
cnf(c_0_37,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_38,plain,
divide(X1,multiply(X2,multiply(divide(divide(inverse(X2),X3),divide(X4,X3)),X1))) = X4,
inference(rw,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_39,plain,
multiply(X1,multiply(inverse(X2),X3)) = divide(X1,multiply(inverse(X3),X2)),
inference(spm,[status(thm)],[c_0_35,c_0_6]) ).
cnf(c_0_40,plain,
divide(X1,multiply(inverse(X2),X2)) = X1,
inference(spm,[status(thm)],[c_0_36,c_0_6]) ).
cnf(c_0_41,plain,
multiply(X1,divide(X2,X3)) = divide(X1,divide(X3,X2)),
inference(spm,[status(thm)],[c_0_6,c_0_30]) ).
cnf(c_0_42,negated_conjecture,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1)
| inverse(inverse(a2)) != a2 ),
inference(rw,[status(thm)],[c_0_37,c_0_27]) ).
cnf(c_0_43,plain,
divide(multiply(divide(X1,X2),multiply(X2,X3)),X3) = 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_10,c_0_38]),c_0_39]),c_0_40]),c_0_41]),c_0_35]),c_0_30]) ).
cnf(c_0_44,negated_conjecture,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_22])]) ).
cnf(c_0_45,plain,
multiply(inverse(X1),X1) = multiply(inverse(X2),X2),
inference(spm,[status(thm)],[c_0_23,c_0_10]) ).
cnf(c_0_46,plain,
multiply(divide(X1,X2),multiply(X2,X3)) = multiply(X1,X3),
inference(spm,[status(thm)],[c_0_23,c_0_43]) ).
cnf(c_0_47,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
inference(sr,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_48,plain,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_26]),c_0_6]) ).
cnf(c_0_49,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_47,c_0_48])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.15 % Problem : GRP063-1 : TPTP v9.2.1. Bugfixed v2.3.0.
% 0.10/0.15 % 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
% 0.17/0.36 % Computer : n023.cluster.edu
% 0.17/0.36 % Model : x86_64 x86_64
% 0.17/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.36 % Memory : 8042.1875MB
% 0.17/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.36 % CPULimit : 300
% 0.17/0.36 % WCLimit : 300
% 0.17/0.36 % DateTime : Mon May 4 18:19:53 EDT 2026
% 0.20/0.36 % CPUTime :
% 0.20/0.37 % start to proof: theBenchmark
% 1.27/1.77 % Version : CSE_E---1.7
% 1.27/1.77 % Problem : theBenchmark.p
% 1.27/1.77 % SZS status Unsatisfiable for theBenchmark.p
% 1.27/1.77 % SZS output start CNFRefutation
% See solution above
% 1.27/1.77 % Total time : 1.368s
%------------------------------------------------------------------------------