%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP098-1 : 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 04:23:47 PM UTC 2026
% Result : Unsatisfiable 1.64s 1.82s
% Output : CNFRefutation 1.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 3
% Syntax : Number of clauses : 35 ( 28 unt; 0 nHn; 10 RR)
% Number of literals : 49 ( 48 equ; 23 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 7 ( 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 : 59 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
divide(divide(divide(X1,inverse(X2)),X3),divide(X1,X3)) = X2,
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) = divide(X1,inverse(X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply) ).
cnf(c_0_3,axiom,
divide(divide(divide(X1,inverse(X2)),X3),divide(X1,X3)) = X2,
single_axiom ).
cnf(c_0_4,plain,
divide(divide(divide(divide(divide(X1,inverse(X2)),X3),inverse(X4)),divide(X1,X3)),X2) = X4,
inference(spm,[status(thm)],[c_0_3,c_0_3]) ).
cnf(c_0_5,plain,
divide(divide(X1,inverse(X2)),X1) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_4,c_0_4]),c_0_3]) ).
cnf(c_0_6,plain,
divide(X1,divide(X2,X2)) = X1,
inference(spm,[status(thm)],[c_0_3,c_0_5]) ).
cnf(c_0_7,plain,
divide(X1,divide(divide(X2,inverse(X1)),divide(X2,inverse(X3)))) = X3,
inference(spm,[status(thm)],[c_0_3,c_0_3]) ).
cnf(c_0_8,plain,
divide(divide(X1,X1),inverse(X2)) = X2,
inference(spm,[status(thm)],[c_0_5,c_0_6]) ).
cnf(c_0_9,plain,
divide(X1,divide(X1,X2)) = 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(X1,X1),X2) = inverse(X2),
inference(spm,[status(thm)],[c_0_9,c_0_8]) ).
cnf(c_0_11,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_12,axiom,
multiply(X1,X2) = divide(X1,inverse(X2)),
multiply ).
cnf(c_0_13,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[c_0_8,c_0_10]) ).
cnf(c_0_14,negated_conjecture,
( divide(b4,inverse(a4)) != divide(a4,inverse(b4))
| divide(divide(inverse(b2),inverse(b2)),inverse(a2)) != a2
| divide(inverse(b1),inverse(b1)) != divide(inverse(a1),inverse(a1))
| divide(divide(a3,inverse(b3)),inverse(c3)) != divide(a3,inverse(divide(b3,inverse(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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_11,c_0_12]),c_0_12]),c_0_12]),c_0_12]),c_0_12]),c_0_12]),c_0_12]),c_0_12]),c_0_12]),c_0_12]) ).
cnf(c_0_15,plain,
divide(divide(X1,X2),X1) = inverse(X2),
inference(spm,[status(thm)],[c_0_5,c_0_13]) ).
cnf(c_0_16,negated_conjecture,
( divide(divide(a3,inverse(b3)),inverse(c3)) != divide(a3,inverse(divide(b3,inverse(c3))))
| divide(inverse(a1),inverse(a1)) != divide(inverse(b1),inverse(b1))
| divide(a4,inverse(b4)) != divide(b4,inverse(a4)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_8])]) ).
cnf(c_0_17,plain,
divide(X1,X1) = divide(X2,X2),
inference(spm,[status(thm)],[c_0_9,c_0_6]) ).
cnf(c_0_18,plain,
divide(divide(X1,X2),inverse(X2)) = X1,
inference(spm,[status(thm)],[c_0_9,c_0_15]) ).
cnf(c_0_19,negated_conjecture,
( divide(divide(a3,inverse(b3)),inverse(c3)) != divide(a3,inverse(divide(b3,inverse(c3))))
| divide(a4,inverse(b4)) != divide(b4,inverse(a4)) ),
inference(sr,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_20,plain,
inverse(divide(X1,X2)) = divide(X2,X1),
inference(spm,[status(thm)],[c_0_15,c_0_9]) ).
cnf(c_0_21,plain,
divide(divide(X1,inverse(X2)),X2) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_4,c_0_17]),c_0_10]),c_0_13]),c_0_9]) ).
cnf(c_0_22,plain,
divide(inverse(X1),inverse(X2)) = divide(X2,X1),
inference(spm,[status(thm)],[c_0_18,c_0_15]) ).
cnf(c_0_23,negated_conjecture,
( divide(divide(a3,inverse(b3)),inverse(c3)) != divide(a3,divide(inverse(c3),b3))
| divide(a4,inverse(b4)) != divide(b4,inverse(a4)) ),
inference(rw,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_24,plain,
divide(inverse(X1),X2) = divide(inverse(X2),X1),
inference(spm,[status(thm)],[c_0_21,c_0_15]) ).
cnf(c_0_25,plain,
divide(X1,inverse(X2)) = divide(X2,inverse(X1)),
inference(spm,[status(thm)],[c_0_22,c_0_13]) ).
cnf(c_0_26,plain,
divide(divide(divide(X1,inverse(X2)),X3),X2) = divide(X1,X3),
inference(spm,[status(thm)],[c_0_9,c_0_3]) ).
cnf(c_0_27,negated_conjecture,
( divide(divide(a3,inverse(b3)),inverse(c3)) != divide(a3,divide(inverse(b3),c3))
| divide(a4,inverse(b4)) != divide(b4,inverse(a4)) ),
inference(rw,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_28,plain,
divide(X1,divide(X2,divide(X3,X1))) = divide(X3,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_13]),c_0_20]) ).
cnf(c_0_29,negated_conjecture,
divide(c3,divide(inverse(a3),b3)) != divide(a3,divide(inverse(b3),c3)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_25]),c_0_20]),c_0_24]),c_0_25])]) ).
cnf(c_0_30,plain,
divide(X1,divide(X2,X3)) = divide(X3,divide(X2,X1)),
inference(spm,[status(thm)],[c_0_9,c_0_28]) ).
cnf(c_0_31,plain,
divide(divide(X1,inverse(X2)),X3) = divide(X2,divide(X3,X1)),
inference(spm,[status(thm)],[c_0_28,c_0_21]) ).
cnf(c_0_32,negated_conjecture,
divide(b3,divide(inverse(a3),c3)) != divide(a3,divide(inverse(b3),c3)),
inference(rw,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_33,plain,
divide(X1,divide(inverse(X2),X3)) = divide(X2,divide(inverse(X1),X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_31]),c_0_20]) ).
cnf(c_0_34,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_33])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GRP098-1 : 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 18:19:08 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.33 % start to proof: theBenchmark
% 1.64/1.82 % Version : CSE_E---1.7
% 1.64/1.82 % Problem : theBenchmark.p
% 1.64/1.82 % SZS status Unsatisfiable for theBenchmark.p
% 1.64/1.82 % SZS output start CNFRefutation
% See solution above
% 1.64/1.83 % Total time : 1.371s
%------------------------------------------------------------------------------