%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP069-1 : 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 : n031.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 04:23:43 PM UTC 2026
% Result : Unsatisfiable 1.25s 1.72s
% Output : CNFRefutation 1.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of clauses : 25 ( 21 unt; 0 nHn; 6 RR)
% Number of literals : 32 ( 31 equ; 12 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 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 : 38 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
divide(X1,divide(divide(divide(divide(X1,X1),X2),X3),divide(divide(identity,X1),X3))) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
cnf(identity,axiom,
identity = divide(X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity) ).
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/sandbox2/benchmark/theBenchmark.p',prove_these_axioms) ).
cnf(inverse,axiom,
inverse(X1) = divide(identity,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse) ).
cnf(multiply,axiom,
multiply(X1,X2) = divide(X1,divide(identity,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply) ).
cnf(c_0_5,axiom,
divide(X1,divide(divide(divide(divide(X1,X1),X2),X3),divide(divide(identity,X1),X3))) = X2,
single_axiom ).
cnf(c_0_6,axiom,
identity = divide(X1,X1),
identity ).
cnf(c_0_7,plain,
divide(X1,divide(divide(divide(identity,X2),X3),divide(divide(identity,X1),X3))) = X2,
inference(rw,[status(thm)],[c_0_5,c_0_6]) ).
cnf(c_0_8,plain,
divide(X1,identity) = X1,
inference(spm,[status(thm)],[c_0_7,c_0_6]) ).
cnf(c_0_9,plain,
divide(X1,divide(divide(identity,X2),divide(identity,X1))) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_8]),c_0_8]) ).
cnf(c_0_10,plain,
divide(divide(identity,X1),divide(divide(identity,X2),X1)) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_9]),c_0_6]),c_0_8]) ).
cnf(c_0_11,plain,
divide(divide(identity,X1),divide(X2,X1)) = divide(identity,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_9]),c_0_6]),c_0_8]) ).
cnf(c_0_12,plain,
divide(identity,divide(identity,X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_8]),c_0_8]) ).
cnf(c_0_13,plain,
divide(divide(identity,divide(X1,X2)),divide(identity,X1)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_11]),c_0_12]) ).
cnf(c_0_14,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_15,axiom,
inverse(X1) = divide(identity,X1),
inverse ).
cnf(c_0_16,axiom,
multiply(X1,X2) = divide(X1,divide(identity,X2)),
multiply ).
cnf(c_0_17,plain,
divide(divide(identity,divide(divide(identity,X1),X2)),X1) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_9]),c_0_6]),c_0_8]) ).
cnf(c_0_18,negated_conjecture,
( divide(identity,divide(identity,a2)) != a2
| divide(divide(identity,a1),divide(identity,a1)) != identity
| divide(divide(a3,divide(identity,b3)),divide(identity,c3)) != divide(a3,divide(identity,divide(b3,divide(identity,c3)))) ),
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_14,c_0_15]),c_0_16]),c_0_16]),c_0_16]),c_0_16]),c_0_16]),c_0_16]) ).
cnf(c_0_19,plain,
divide(divide(divide(identity,X1),X2),divide(X3,X2)) = divide(divide(identity,X1),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_7]),c_0_12]) ).
cnf(c_0_20,negated_conjecture,
( divide(divide(a3,divide(identity,b3)),divide(identity,c3)) != divide(a3,divide(identity,divide(b3,divide(identity,c3))))
| divide(identity,divide(identity,a2)) != a2 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_18,c_0_6])]) ).
cnf(c_0_21,plain,
divide(divide(X1,X2),divide(X3,X2)) = divide(X1,X3),
inference(spm,[status(thm)],[c_0_19,c_0_12]) ).
cnf(c_0_22,negated_conjecture,
divide(divide(a3,divide(identity,b3)),divide(identity,c3)) != divide(a3,divide(identity,divide(b3,divide(identity,c3)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_12])]) ).
cnf(c_0_23,plain,
divide(divide(X1,divide(identity,X2)),X3) = divide(X1,divide(identity,divide(X2,X3))),
inference(spm,[status(thm)],[c_0_21,c_0_13]) ).
cnf(c_0_24,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_23])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP069-1 : 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
% 0.15/0.33 % Computer : n031.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 18:21:23 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.25/1.72 % Version : CSE_E---1.7
% 1.25/1.72 % Problem : theBenchmark.p
% 1.25/1.72 % SZS status Unsatisfiable for theBenchmark.p
% 1.25/1.72 % SZS output start CNFRefutation
% See solution above
% 1.25/1.72 % Total time : 1.372s
%------------------------------------------------------------------------------