%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP093-1 : 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 : n027.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 1.29s 1.73s
% Output : CNFRefutation 1.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 5
% Syntax : Number of clauses : 46 ( 41 unt; 0 nHn; 9 RR)
% Number of literals : 58 ( 57 equ; 20 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 10 ( 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 : 75 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
divide(divide(identity,divide(divide(divide(X1,X2),X3),X1)),X3) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
cnf(identity,axiom,
identity = divide(X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity) ).
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(inverse,axiom,
inverse(X1) = divide(identity,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse) ).
cnf(multiply,axiom,
multiply(X1,X2) = divide(X1,divide(identity,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply) ).
cnf(c_0_5,axiom,
divide(divide(identity,divide(divide(divide(X1,X2),X3),X1)),X3) = X2,
single_axiom ).
cnf(c_0_6,axiom,
identity = divide(X1,X1),
identity ).
cnf(c_0_7,plain,
divide(divide(identity,divide(divide(identity,X1),X2)),X1) = X2,
inference(spm,[status(thm)],[c_0_5,c_0_6]) ).
cnf(c_0_8,plain,
divide(divide(identity,divide(identity,X1)),identity) = X1,
inference(spm,[status(thm)],[c_0_7,c_0_6]) ).
cnf(c_0_9,plain,
divide(divide(identity,divide(X1,identity)),identity) = divide(identity,X1),
inference(spm,[status(thm)],[c_0_5,c_0_8]) ).
cnf(c_0_10,plain,
divide(identity,divide(identity,divide(X1,identity))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_9]),c_0_8]) ).
cnf(c_0_11,plain,
divide(divide(identity,X1),identity) = divide(identity,divide(X1,identity)),
inference(spm,[status(thm)],[c_0_8,c_0_10]) ).
cnf(c_0_12,plain,
divide(divide(X1,identity),identity) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_11]),c_0_11]),c_0_10]) ).
cnf(c_0_13,plain,
divide(divide(identity,divide(identity,X1)),divide(X1,X2)) = X2,
inference(spm,[status(thm)],[c_0_5,c_0_6]) ).
cnf(c_0_14,plain,
divide(identity,divide(identity,X1)) = divide(X1,identity),
inference(spm,[status(thm)],[c_0_10,c_0_12]) ).
cnf(c_0_15,plain,
divide(identity,divide(identity,X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_6]),c_0_6]) ).
cnf(c_0_16,plain,
divide(X1,identity) = X1,
inference(rw,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_17,plain,
divide(X1,divide(X1,X2)) = X2,
inference(rw,[status(thm)],[c_0_13,c_0_15]) ).
cnf(c_0_18,plain,
divide(identity,divide(divide(X1,X2),X1)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_16]),c_0_16]) ).
cnf(c_0_19,plain,
divide(divide(X1,X2),X1) = divide(identity,X2),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_20,plain,
divide(divide(identity,X1),divide(X2,X1)) = divide(identity,X2),
inference(spm,[status(thm)],[c_0_19,c_0_19]) ).
cnf(c_0_21,plain,
divide(X1,X2) = divide(identity,divide(X2,X1)),
inference(spm,[status(thm)],[c_0_19,c_0_17]) ).
cnf(c_0_22,plain,
divide(divide(identity,X1),divide(identity,X2)) = divide(X2,X1),
inference(spm,[status(thm)],[c_0_17,c_0_20]) ).
cnf(c_0_23,plain,
divide(divide(X1,X2),divide(identity,X2)) = X1,
inference(spm,[status(thm)],[c_0_17,c_0_19]) ).
cnf(c_0_24,plain,
divide(divide(identity,X1),divide(identity,X2)) = divide(identity,divide(X1,X2)),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_25,plain,
divide(X1,divide(identity,divide(X2,X1))) = X2,
inference(spm,[status(thm)],[c_0_23,c_0_17]) ).
cnf(c_0_26,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_27,axiom,
inverse(X1) = divide(identity,X1),
inverse ).
cnf(c_0_28,axiom,
multiply(X1,X2) = divide(X1,divide(identity,X2)),
multiply ).
cnf(c_0_29,plain,
divide(divide(divide(X1,X2),X3),X1) = divide(divide(identity,X3),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_5]),c_0_17]) ).
cnf(c_0_30,plain,
divide(divide(identity,X1),X2) = divide(identity,divide(X1,divide(identity,X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_16]) ).
cnf(c_0_31,negated_conjecture,
( divide(b4,divide(identity,a4)) != divide(a4,divide(identity,b4))
| divide(divide(divide(identity,b2),divide(identity,b2)),divide(identity,a2)) != a2
| divide(divide(identity,b1),divide(identity,b1)) != divide(divide(identity,a1),divide(identity,a1))
| 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)],[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_26,c_0_27]),c_0_27]),c_0_27]),c_0_28]),c_0_28]),c_0_28]),c_0_28]),c_0_28]),c_0_28]),c_0_28]),c_0_28]),c_0_28]),c_0_28]) ).
cnf(c_0_32,plain,
divide(identity,divide(X1,divide(divide(X1,X2),X3))) = divide(identity,divide(X3,divide(identity,X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_21]),c_0_30]) ).
cnf(c_0_33,negated_conjecture,
( divide(divide(a3,divide(identity,b3)),divide(identity,c3)) != divide(a3,divide(identity,divide(b3,divide(identity,c3))))
| divide(b4,divide(identity,a4)) != divide(a4,divide(identity,b4))
| divide(identity,divide(identity,a2)) != a2 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_6]),c_0_6]),c_0_6])]) ).
cnf(c_0_34,plain,
divide(X1,divide(X2,divide(identity,X1))) = divide(identity,X2),
inference(spm,[status(thm)],[c_0_20,c_0_17]) ).
cnf(c_0_35,plain,
divide(X1,divide(divide(X1,X2),divide(identity,X3))) = divide(X2,X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_32]),c_0_17]),c_0_24]),c_0_17]) ).
cnf(c_0_36,negated_conjecture,
( divide(divide(a3,divide(identity,b3)),divide(identity,c3)) != divide(a3,divide(identity,divide(b3,divide(identity,c3))))
| divide(b4,divide(identity,a4)) != divide(a4,divide(identity,b4)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_14]),c_0_16])]) ).
cnf(c_0_37,plain,
divide(X1,divide(identity,X2)) = divide(X2,divide(identity,X1)),
inference(spm,[status(thm)],[c_0_17,c_0_34]) ).
cnf(c_0_38,plain,
divide(X1,divide(divide(X1,X2),X3)) = divide(X2,divide(identity,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_25]),c_0_16]) ).
cnf(c_0_39,negated_conjecture,
divide(a3,divide(identity,divide(c3,divide(identity,b3)))) != divide(c3,divide(identity,divide(b3,divide(identity,a3)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_37]),c_0_37]),c_0_37]),c_0_37])]) ).
cnf(c_0_40,plain,
divide(divide(X1,X2),X3) = divide(X1,divide(X2,divide(identity,X3))),
inference(spm,[status(thm)],[c_0_17,c_0_38]) ).
cnf(c_0_41,negated_conjecture,
divide(a3,divide(identity,divide(c3,divide(X1,divide(b3,divide(identity,X1)))))) != divide(c3,divide(identity,divide(b3,divide(identity,a3)))),
inference(spm,[status(thm)],[c_0_39,c_0_34]) ).
cnf(c_0_42,plain,
divide(X1,divide(X2,divide(X3,divide(X1,X2)))) = X3,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_40]),c_0_17]) ).
cnf(c_0_43,negated_conjecture,
divide(a3,divide(identity,divide(c3,divide(X1,divide(X2,divide(identity,divide(b3,divide(identity,divide(X1,X2))))))))) != divide(c3,divide(identity,divide(b3,divide(identity,a3)))),
inference(spm,[status(thm)],[c_0_41,c_0_40]) ).
cnf(c_0_44,plain,
divide(X1,divide(X2,divide(X3,divide(X1,divide(X2,X4))))) = divide(X3,X4),
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_40,c_0_42]),c_0_40]),c_0_17]),c_0_40]),c_0_40]),c_0_17]) ).
cnf(c_0_45,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_16])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GRP093-1 : 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
% 0.14/0.32 % Computer : n027.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Mon May 4 18:20:19 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 1.29/1.73 % Version : CSE_E---1.7
% 1.29/1.73 % Problem : theBenchmark.p
% 1.29/1.73 % SZS status Unsatisfiable for theBenchmark.p
% 1.29/1.73 % SZS output start CNFRefutation
% See solution above
% 1.29/1.73 % Total time : 1.371s
%------------------------------------------------------------------------------