%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : HEN009-5 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 01:37:09 PM UTC 2026
% Result : Unsatisfiable 4.22s 0.91s
% Output : Proof 4.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 38 ( 26 unt; 0 def)
% Number of atoms : 54 ( 53 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 38 ( 22 ~; 16 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-4 aty)
% Number of variables : 67 ( 7 sgn 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f6,axiom,
( divide(divide(X,Z),Y) = zero
| divide(divide(X,Y),Z) != zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',property_of_divide1) ).
fof(f6_nnf,plain,
! [X,Y,Z] :
( divide(divide(X,Z),Y) = zero
| divide(divide(X,Y),Z) != zero ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [X,Y,Z] :
( divide(divide(X,Z),Y) = zero
| divide(divide(X,Y),Z) != zero ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
( divide(divide(X0,X2),X1) = zero
| divide(divide(X0,X1),X2) != zero ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(hi6,axiom,
ifeq(divide(divide(X0,X1),X2),zero,divide(divide(X0,X2),X1),zero) = zero,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(f0,axiom,
divide(divide(X,Y),X) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quotient_smaller_than_numerator) ).
fof(f0_nnf,plain,
! [X,Y] : divide(divide(X,Y),X) = zero,
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X,Y] : divide(divide(X,Y),X) = zero,
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
divide(divide(X0,X1),X0) = zero,
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi0,axiom,
divide(divide(X0,X1),X0) = zero,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(h4,plain,
divide(divide(V0,V0),V1) = zero,
inference(hyper_resolution,[status(thm)],[hi6,hi0]) ).
cnf(f3,axiom,
( X = Y
| divide(Y,X) != zero
| divide(X,Y) != zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',divide_and_equal) ).
fof(f3_nnf,plain,
! [X,Y] :
( X = Y
| divide(Y,X) != zero
| divide(X,Y) != zero ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [X,Y] :
( X = Y
| divide(Y,X) != zero
| divide(X,Y) != zero ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
( X0 = X1
| divide(X1,X0) != zero
| divide(X0,X1) != zero ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(hi3,axiom,
ifeq(divide(X0,X1),zero,ifeq(divide(X1,X0),zero,X0,X1),X1) = X1,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(f2,axiom,
divide(zero,X) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',zero_is_smallest) ).
fof(f2_nnf,plain,
! [X] : divide(zero,X) = zero,
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X] : divide(zero,X) = zero,
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
divide(zero,X0) = zero,
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi2,axiom,
divide(zero,X0) = zero,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(h15,plain,
zero = divide(V0,V0),
inference(hyper_resolution,[status(thm)],[hi3,hi2,h4]) ).
cnf(h17,plain,
divide(divide(V0,divide(V0,V1)),V1) = zero,
inference(hyper_resolution,[status(thm)],[hi6,h15]) ).
cnf(f7,axiom,
( divide(divide(Z,Y),divide(Z,X)) = zero
| divide(X,Y) != zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',property_of_divide2) ).
fof(f7_nnf,plain,
! [X,Y,Z] :
( divide(divide(Z,Y),divide(Z,X)) = zero
| divide(X,Y) != zero ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [X,Y,Z] :
( divide(divide(Z,Y),divide(Z,X)) = zero
| divide(X,Y) != zero ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
( divide(divide(X2,X1),divide(X2,X0)) = zero
| divide(X0,X1) != zero ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(hi7,axiom,
ifeq(divide(X0,X1),zero,divide(divide(X2,X1),divide(X2,X0)),zero) = zero,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(h55,plain,
divide(divide(V0,V1),divide(V0,divide(V2,divide(V2,V1)))) = zero,
inference(hyper_resolution,[status(thm)],[hi7,h17]) ).
cnf(t26,plain,
divide(X1,divide(X1,divide(X1,X2))) = divide(X1,X2),
inference(hyper_resolution,[status(thm)],[hi3,h17,h55]) ).
cnf(t264,plain,
divide(X1,divide(X1,divide(X1,X2))) = divide(X1,X2),
inference(orient,[status(thm)],[t26]) ).
cnf(f8,negated_conjecture,
divide(identity,a) != divide(identity,divide(identity,divide(identity,a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
fof(f8_nnf,plain,
divide(identity,a) != divide(identity,divide(identity,divide(identity,a))),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
divide(identity,a) != divide(identity,divide(identity,divide(identity,a))),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
divide(identity,a) != divide(identity,divide(identity,divide(identity,a))),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(goal_0,negated_conjecture,
divide(identity,divide(identity,divide(identity,a))) != divide(identity,a),
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(g0_0,plain,
divide(identity,a) != divide(identity,a),
inference(rw,[status(thm)],[goal_0,t264]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : HEN009-5 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.02 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.03/0.30 % Computer : n012.cluster.edu
% 0.03/0.30 % Model : x86_64 x86_64
% 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30 % Memory : 8046.5625MB
% 0.03/0.30 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Wed Sep 23 16:15:35 UTC 2026
% 0.03/0.31 % CPUTime :
% 0.03/0.31 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 4.22/0.91 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.22/0.91 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------