%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP092-1 : 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 : 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 04:23:46 PM UTC 2026
% Result : Unsatisfiable 1.55s 1.80s
% Output : CNFRefutation 1.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 5
% Syntax : Number of clauses : 37 ( 33 unt; 0 nHn; 6 RR)
% Number of literals : 48 ( 47 equ; 16 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 10 con; 0-2 aty)
% Number of variables : 68 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(multiply,axiom,
multiply(X1,X2) = divide(X1,divide(divide(X3,X3),X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply) ).
cnf(identity,axiom,
identity = divide(X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity) ).
cnf(single_axiom,axiom,
divide(divide(X1,X2),divide(divide(X1,X3),X2)) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
cnf(inverse,axiom,
inverse(X1) = divide(divide(X2,X2),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse) ).
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(c_0_5,axiom,
multiply(X1,X2) = divide(X1,divide(divide(X3,X3),X2)),
multiply ).
cnf(c_0_6,axiom,
identity = divide(X1,X1),
identity ).
cnf(c_0_7,plain,
divide(X1,divide(identity,X2)) = multiply(X1,X2),
inference(rw,[status(thm)],[c_0_5,c_0_6]) ).
cnf(c_0_8,axiom,
divide(divide(X1,X2),divide(divide(X1,X3),X2)) = X3,
single_axiom ).
cnf(c_0_9,plain,
divide(X1,identity) = multiply(X1,identity),
inference(spm,[status(thm)],[c_0_7,c_0_6]) ).
cnf(c_0_10,plain,
multiply(divide(X1,divide(X1,X2)),identity) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_6]),c_0_9]) ).
cnf(c_0_11,plain,
multiply(X1,identity) = X1,
inference(spm,[status(thm)],[c_0_10,c_0_8]) ).
cnf(c_0_12,plain,
multiply(divide(X1,X2),X2) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_6]),c_0_7]) ).
cnf(c_0_13,plain,
divide(X1,divide(X1,X2)) = X2,
inference(rw,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_14,plain,
multiply(X1,divide(divide(X2,X1),X3)) = divide(X2,X3),
inference(spm,[status(thm)],[c_0_12,c_0_8]) ).
cnf(c_0_15,plain,
divide(divide(X1,X2),divide(X3,X2)) = divide(X1,X3),
inference(spm,[status(thm)],[c_0_8,c_0_13]) ).
cnf(c_0_16,plain,
multiply(X1,divide(X2,X1)) = X2,
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_17,plain,
multiply(X1,divide(identity,X2)) = divide(X1,X2),
inference(spm,[status(thm)],[c_0_14,c_0_6]) ).
cnf(c_0_18,plain,
divide(X1,divide(X2,X3)) = multiply(X3,divide(X1,X2)),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_19,plain,
multiply(X1,multiply(X2,divide(identity,X1))) = X2,
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_20,plain,
multiply(X1,X2) = multiply(X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7,c_0_18]),c_0_9]),c_0_11]) ).
cnf(c_0_21,axiom,
inverse(X1) = divide(divide(X2,X2),X1),
inverse ).
cnf(c_0_22,plain,
multiply(X1,multiply(divide(identity,X1),X2)) = X2,
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_23,plain,
divide(X1,multiply(X2,divide(X3,X4))) = multiply(divide(X4,X2),divide(X1,X3)),
inference(spm,[status(thm)],[c_0_18,c_0_18]) ).
cnf(c_0_24,plain,
divide(X1,identity) = X1,
inference(rw,[status(thm)],[c_0_9,c_0_11]) ).
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,plain,
inverse(X1) = divide(identity,X1),
inference(rw,[status(thm)],[c_0_21,c_0_6]) ).
cnf(c_0_27,plain,
multiply(X1,divide(X2,multiply(X1,X3))) = divide(X2,X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]) ).
cnf(c_0_28,negated_conjecture,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(divide(identity,a1),a1) != multiply(divide(identity,b1),b1)
| multiply(multiply(divide(identity,b2),b2),a2) != a2
| multiply(a4,b4) != multiply(b4,a4) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_26]),c_0_26]),c_0_26]) ).
cnf(c_0_29,plain,
multiply(divide(identity,X1),X1) = identity,
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
cnf(c_0_30,plain,
multiply(multiply(X1,X2),divide(X3,X4)) = multiply(X1,multiply(X2,divide(X3,X4))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_27]),c_0_18]),c_0_18]) ).
cnf(c_0_31,negated_conjecture,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(a4,b4) != multiply(b4,a4)
| multiply(identity,a2) != a2 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_29]),c_0_29]),c_0_29])]) ).
cnf(c_0_32,plain,
multiply(identity,X1) = X1,
inference(spm,[status(thm)],[c_0_12,c_0_6]) ).
cnf(c_0_33,plain,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
inference(spm,[status(thm)],[c_0_30,c_0_24]) ).
cnf(c_0_34,negated_conjecture,
multiply(c3,multiply(a3,b3)) != multiply(a3,multiply(b3,c3)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_32])]),c_0_20]),c_0_20])]) ).
cnf(c_0_35,plain,
multiply(X1,multiply(X2,X3)) = multiply(X3,multiply(X1,X2)),
inference(spm,[status(thm)],[c_0_20,c_0_33]) ).
cnf(c_0_36,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_35])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GRP092-1 : 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
% 0.15/0.32 % Computer : n007.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Mon May 4 18:19:24 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.33 % start to proof: theBenchmark
% 1.55/1.80 % Version : CSE_E---1.7
% 1.55/1.80 % Problem : theBenchmark.p
% 1.55/1.80 % SZS status Unsatisfiable for theBenchmark.p
% 1.55/1.80 % SZS output start CNFRefutation
% See solution above
% 1.55/1.81 % Total time : 1.372s
%------------------------------------------------------------------------------