%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : HEN008-5 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n003.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 01:37:08 PM UTC 2026
% Result : Unsatisfiable 7.13s 1.65s
% Output : Proof 7.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of formulae : 41 ( 37 unt; 0 def)
% Number of atoms : 49 ( 48 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 22 ( 14 ~; 8 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-4 aty)
% Number of variables : 51 ( 6 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(t6,plain,
ifeq(divide(X1,X2),zero,ifeq(divide(X2,X1),zero,X1,X2),X2) = X2,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t8,plain,
ifeq(divide(X1,X2),zero,ifeq(divide(X2,X1),zero,X1,X2),X2) = X2,
inference(orient,[status(thm)],[t6]) ).
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(t2,plain,
divide(zero,X1) = zero,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t31,plain,
divide(zero,X1) = zero,
inference(orient,[status(thm)],[t2]) ).
cnf(t33,plain,
zero = ifeq(divide(X1,zero),zero,ifeq(zero,zero,X1,zero),zero),
inference(cp,[status(thm)],[t8,t31]) ).
cnf(t4,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t7,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t4]) ).
cnf(t110,plain,
zero = ifeq(divide(X1,zero),zero,X1,zero),
inference(step,[status(thm)],[t33,t7]) ).
cnf(t43,plain,
ifeq(divide(X1,zero),zero,X1,zero) = zero,
inference(orient,[status(thm)],[t110]) ).
cnf(f1,axiom,
divide(divide(divide(X,Z),divide(Y,Z)),divide(divide(X,Y),Z)) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quotient_property) ).
fof(f1_nnf,plain,
! [X,Z,Y] : divide(divide(divide(X,Z),divide(Y,Z)),divide(divide(X,Y),Z)) = zero,
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X,Z,Y] : divide(divide(divide(X,Z),divide(Y,Z)),divide(divide(X,Y),Z)) = zero,
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
divide(divide(divide(X0,X1),divide(X2,X1)),divide(divide(X0,X2),X1)) = zero,
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(t5,plain,
divide(divide(divide(X1,X2),divide(X3,X2)),divide(divide(X1,X3),X2)) = zero,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t17,plain,
divide(divide(divide(X1,X2),divide(X3,X2)),divide(divide(X1,X3),X2)) = zero,
inference(orient,[status(thm)],[t5]) ).
cnf(f5,hypothesis,
divide(a,b) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_divide_b_is_zero) ).
fof(f5_nnf,plain,
divide(a,b) = zero,
inference(nnf_transformation,[status(thm)],[f5]) ).
cnf(c5,plain,
divide(a,b) = zero,
inference(cnf_transformation,[status(esa)],[f5_nnf]) ).
cnf(t1,plain,
divide(a,b) = zero,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t35,plain,
divide(a,b) = zero,
inference(orient,[status(thm)],[t1]) ).
cnf(t39,plain,
zero = divide(divide(divide(a,X1),divide(b,X1)),divide(zero,X1)),
inference(cp,[status(thm)],[t17,t35]) ).
cnf(t117,plain,
zero = divide(divide(divide(a,X1),divide(b,X1)),zero),
inference(step,[status(thm)],[t39,t31]) ).
cnf(t93,plain,
divide(divide(divide(a,X1),divide(b,X1)),zero) = zero,
inference(orient,[status(thm)],[t117]) ).
cnf(t94,plain,
zero = ifeq(zero,zero,divide(divide(a,X1),divide(b,X1)),zero),
inference(cp,[status(thm)],[t43,t93]) ).
cnf(t118,plain,
zero = divide(divide(a,X1),divide(b,X1)),
inference(step,[status(thm)],[t94,t7]) ).
cnf(t101,plain,
divide(divide(a,X1),divide(b,X1)) = zero,
inference(orient,[status(thm)],[t118]) ).
cnf(f6,negated_conjecture,
divide(divide(a,c),divide(b,c)) != zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_property_of_divide3) ).
fof(f6_nnf,plain,
divide(divide(a,c),divide(b,c)) != zero,
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
divide(divide(a,c),divide(b,c)) != zero,
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
divide(divide(a,c),divide(b,c)) != zero,
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(goal_0,negated_conjecture,
divide(divide(a,c),divide(b,c)) != zero,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(g0_0,plain,
zero != zero,
inference(rw,[status(thm)],[goal_0,t101]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN008-5 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.37 % Computer : n003.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Wed Sep 23 16:16:19 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 7.13/1.65 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.13/1.65 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------