%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : HEN004-5 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n011.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 01:36:58 PM UTC 2026
% Result : Unsatisfiable 5.83s 16.28s
% Output : Proof 5.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 7
% Syntax : Number of formulae : 57 ( 53 unt; 0 def)
% Number of atoms : 65 ( 64 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 : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-4 aty)
% Number of variables : 80 ( 10 sgn 18 !; 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(t36,plain,
divide(zero,X1) = zero,
inference(orient,[status(thm)],[t2]) ).
cnf(t38,plain,
zero = ifeq(divide(X1,zero),zero,ifeq(zero,zero,X1,zero),zero),
inference(cp,[status(thm)],[t8,t36]) ).
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(t152,plain,
zero = ifeq(divide(X1,zero),zero,X1,zero),
inference(step,[status(thm)],[t38,t7]) ).
cnf(t43,plain,
ifeq(divide(X1,zero),zero,X1,zero) = zero,
inference(orient,[status(thm)],[t152]) ).
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(t19,plain,
divide(divide(divide(X1,X2),divide(X3,X2)),divide(divide(X1,X3),X2)) = zero,
inference(orient,[status(thm)],[t5]) ).
cnf(t39,plain,
zero = divide(divide(divide(X1,X2),zero),divide(divide(X1,zero),X2)),
inference(cp,[status(thm)],[t19,t36]) ).
cnf(t67,plain,
divide(divide(divide(X1,X2),zero),divide(divide(X1,zero),X2)) = zero,
inference(orient,[status(thm)],[t39]) ).
cnf(f5,axiom,
divide(X,X) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_divide_x_is_zero) ).
fof(f5_nnf,plain,
! [X] : divide(X,X) = zero,
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [X] : divide(X,X) = zero,
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
divide(X0,X0) = zero,
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(t0,plain,
divide(X1,X1) = zero,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t9,plain,
divide(X1,X1) = zero,
inference(orient,[status(thm)],[t0]) ).
cnf(t70,plain,
zero = divide(divide(divide(X1,divide(X1,zero)),zero),zero),
inference(cp,[status(thm)],[t67,t9]) ).
cnf(t115,plain,
divide(divide(divide(X1,divide(X1,zero)),zero),zero) = zero,
inference(orient,[status(thm)],[t70]) ).
cnf(t116,plain,
zero = ifeq(zero,zero,divide(divide(X1,divide(X1,zero)),zero),zero),
inference(cp,[status(thm)],[t43,t115]) ).
cnf(t159,plain,
zero = divide(divide(X1,divide(X1,zero)),zero),
inference(step,[status(thm)],[t116,t7]) ).
cnf(t125,plain,
divide(divide(X1,divide(X1,zero)),zero) = zero,
inference(orient,[status(thm)],[t159]) ).
cnf(t126,plain,
zero = ifeq(zero,zero,divide(X1,divide(X1,zero)),zero),
inference(cp,[status(thm)],[t43,t125]) ).
cnf(t160,plain,
zero = divide(X1,divide(X1,zero)),
inference(step,[status(thm)],[t126,t7]) ).
cnf(t135,plain,
divide(X1,divide(X1,zero)) = zero,
inference(orient,[status(thm)],[t160]) ).
cnf(t136,plain,
divide(X1,zero) = ifeq(zero,zero,ifeq(divide(divide(X1,zero),X1),zero,X1,divide(X1,zero)),divide(X1,zero)),
inference(cp,[status(thm)],[t8,t135]) ).
cnf(t161,plain,
divide(X1,zero) = ifeq(divide(divide(X1,zero),X1),zero,X1,divide(X1,zero)),
inference(step,[status(thm)],[t136,t7]) ).
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(t3,plain,
divide(divide(X1,X2),X1) = zero,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t13,plain,
divide(divide(X1,X2),X1) = zero,
inference(orient,[status(thm)],[t3]) ).
cnf(t162,plain,
divide(X1,zero) = ifeq(zero,zero,X1,divide(X1,zero)),
inference(step,[status(thm)],[t161,t13]) ).
cnf(t163,plain,
divide(X1,zero) = X1,
inference(step,[status(thm)],[t162,t7]) ).
cnf(t143,plain,
divide(X1,zero) = X1,
inference(orient,[status(thm)],[t163]) ).
cnf(f6,negated_conjecture,
divide(a,zero) != a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_x_divide_zero_is_x) ).
fof(f6_nnf,plain,
divide(a,zero) != a,
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
divide(a,zero) != a,
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
divide(a,zero) != a,
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(goal_0,negated_conjecture,
divide(a,zero) != a,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(g0_0,plain,
a != a,
inference(rw,[status(thm)],[goal_0,t143]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN004-5 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.34 % Computer : n011.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/15.42 % CPULimit : 300
% 0.08/15.42 % WCLimit : 300
% 0.08/15.43 % DateTime : Wed Sep 23 16:13:04 UTC 2026
% 0.08/15.43 % CPUTime :
% 0.08/15.43 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 5.83/16.28 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.83/16.28 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------