%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : HEN004-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n018.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 0.13s 5.85s
% Output : Proof 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 46
% Number of leaves : 8
% Syntax : Number of formulae : 94 ( 82 unt; 0 def)
% Number of atoms : 110 ( 81 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 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-4 aty)
% Number of variables : 135 ( 18 sgn 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f5,axiom,
( X = Y
| ~ less_equal(Y,X)
| ~ less_equal(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_equal_and_equal) ).
fof(f5_nnf,plain,
! [X,Y] :
( X = Y
| ~ less_equal(Y,X)
| ~ less_equal(X,Y) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [X,Y] :
( X = Y
| ~ less_equal(Y,X)
| ~ less_equal(X,Y) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
( X0 = X1
| ~ less_equal(X1,X0)
| ~ less_equal(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(t10,plain,
ifeq(less_equal(X1,X2),true,ifeq(less_equal(X2,X1),true,X1,X2),X2) = X2,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t13,plain,
ifeq(less_equal(X1,X2),true,ifeq(less_equal(X2,X1),true,X1,X2),X2) = X2,
inference(orient,[status(thm)],[t10]) ).
cnf(f1,axiom,
( less_equal(X,Y)
| divide(X,Y) != zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quotient_less_equal2) ).
fof(f1_nnf,plain,
! [X,Y] :
( less_equal(X,Y)
| divide(X,Y) != zero ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X,Y] :
( less_equal(X,Y)
| divide(X,Y) != zero ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( less_equal(X0,X1)
| divide(X0,X1) != zero ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(t7,plain,
ifeq(divide(X1,X2),zero,less_equal(X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t68,plain,
ifeq(divide(X1,X2),zero,less_equal(X1,X2),true) = true,
inference(orient,[status(thm)],[t7]) ).
cnf(f4,axiom,
less_equal(zero,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',zero_is_smallest) ).
fof(f4_nnf,plain,
! [X] : less_equal(zero,X),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [X] : less_equal(zero,X),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
less_equal(zero,X0),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(t3,plain,
less_equal(zero,X1) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t65,plain,
less_equal(zero,X1) = true,
inference(orient,[status(thm)],[t3]) ).
cnf(t67,plain,
zero = ifeq(less_equal(X1,zero),true,ifeq(true,true,X1,zero),zero),
inference(cp,[status(thm)],[t13,t65]) ).
cnf(t5,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t12,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t5]) ).
cnf(t237,plain,
zero = ifeq(less_equal(X1,zero),true,X1,zero),
inference(step,[status(thm)],[t67,t12]) ).
cnf(t72,plain,
ifeq(less_equal(X1,zero),true,X1,zero) = zero,
inference(orient,[status(thm)],[t237]) ).
cnf(f0,axiom,
( divide(X,Y) = zero
| ~ less_equal(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quotient_less_equal1) ).
fof(f0_nnf,plain,
! [X,Y] :
( divide(X,Y) = zero
| ~ less_equal(X,Y) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X,Y] :
( divide(X,Y) = zero
| ~ less_equal(X,Y) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( divide(X0,X1) = zero
| ~ less_equal(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi0,axiom,
ifeq(less_equal(X0,X1),true,divide(X0,X1),zero) = zero,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(f3,axiom,
less_equal(divide(divide(X,Z),divide(Y,Z)),divide(divide(X,Y),Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quotient_property) ).
fof(f3_nnf,plain,
! [X,Z,Y] : less_equal(divide(divide(X,Z),divide(Y,Z)),divide(divide(X,Y),Z)),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [X,Z,Y] : less_equal(divide(divide(X,Z),divide(Y,Z)),divide(divide(X,Y),Z)),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
less_equal(divide(divide(X0,X1),divide(X2,X1)),divide(divide(X0,X2),X1)),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(hi3,axiom,
less_equal(divide(divide(X0,X1),divide(X2,X1)),divide(divide(X0,X2),X1)) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t9,plain,
divide(divide(divide(X1,X2),divide(X3,X2)),divide(divide(X1,X3),X2)) = zero,
inference(hyper_resolution,[status(thm)],[hi0,hi3]) ).
cnf(t18,plain,
divide(divide(divide(X1,X2),divide(X3,X2)),divide(divide(X1,X3),X2)) = zero,
inference(orient,[status(thm)],[t9]) ).
cnf(hi4,axiom,
less_equal(zero,X0) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t1,plain,
divide(zero,X1) = zero,
inference(hyper_resolution,[status(thm)],[hi0,hi4]) ).
cnf(t30,plain,
divide(zero,X1) = zero,
inference(orient,[status(thm)],[t1]) ).
cnf(t31,plain,
zero = divide(divide(divide(X1,X2),zero),divide(divide(X1,zero),X2)),
inference(cp,[status(thm)],[t18,t30]) ).
cnf(t137,plain,
divide(divide(divide(X1,X2),zero),divide(divide(X1,zero),X2)) = zero,
inference(orient,[status(thm)],[t31]) ).
cnf(f2,axiom,
less_equal(divide(X,Y),X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quotient_smaller_than_numerator) ).
fof(f2_nnf,plain,
! [X,Y] : less_equal(divide(X,Y),X),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X,Y] : less_equal(divide(X,Y),X),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
less_equal(divide(X0,X1),X0),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi2,axiom,
less_equal(divide(X0,X1),X0) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t4,plain,
divide(divide(X1,X2),X1) = zero,
inference(hyper_resolution,[status(thm)],[hi0,hi2]) ).
cnf(t15,plain,
divide(divide(X1,X2),X1) = zero,
inference(orient,[status(thm)],[t4]) ).
cnf(t22,plain,
zero = divide(divide(divide(X1,X1),divide(X2,X1)),zero),
inference(cp,[status(thm)],[t18,t15]) ).
cnf(t73,plain,
divide(divide(divide(X1,X1),divide(X2,X1)),zero) = zero,
inference(orient,[status(thm)],[t22]) ).
cnf(t74,plain,
zero = divide(divide(divide(X1,X1),zero),zero),
inference(cp,[status(thm)],[t73,t30]) ).
cnf(t85,plain,
divide(divide(divide(X1,X1),zero),zero) = zero,
inference(orient,[status(thm)],[t74]) ).
cnf(t86,plain,
true = ifeq(zero,zero,less_equal(divide(divide(X1,X1),zero),zero),true),
inference(cp,[status(thm)],[t68,t85]) ).
cnf(t238,plain,
true = less_equal(divide(divide(X1,X1),zero),zero),
inference(step,[status(thm)],[t86,t12]) ).
cnf(t92,plain,
less_equal(divide(divide(X1,X1),zero),zero) = true,
inference(orient,[status(thm)],[t238]) ).
cnf(t93,plain,
zero = ifeq(true,true,divide(divide(X1,X1),zero),zero),
inference(cp,[status(thm)],[t72,t92]) ).
cnf(t239,plain,
zero = divide(divide(X1,X1),zero),
inference(step,[status(thm)],[t93,t12]) ).
cnf(t97,plain,
divide(divide(X1,X1),zero) = zero,
inference(orient,[status(thm)],[t239]) ).
cnf(t98,plain,
true = ifeq(zero,zero,less_equal(divide(X1,X1),zero),true),
inference(cp,[status(thm)],[t68,t97]) ).
cnf(t240,plain,
true = less_equal(divide(X1,X1),zero),
inference(step,[status(thm)],[t98,t12]) ).
cnf(t105,plain,
less_equal(divide(X1,X1),zero) = true,
inference(orient,[status(thm)],[t240]) ).
cnf(t106,plain,
zero = ifeq(true,true,divide(X1,X1),zero),
inference(cp,[status(thm)],[t72,t105]) ).
cnf(t241,plain,
zero = divide(X1,X1),
inference(step,[status(thm)],[t106,t12]) ).
cnf(t110,plain,
divide(X1,X1) = zero,
inference(orient,[status(thm)],[t241]) ).
cnf(t139,plain,
zero = divide(divide(divide(X1,divide(X1,zero)),zero),zero),
inference(cp,[status(thm)],[t137,t110]) ).
cnf(t157,plain,
divide(divide(divide(X1,divide(X1,zero)),zero),zero) = zero,
inference(orient,[status(thm)],[t139]) ).
cnf(t158,plain,
true = ifeq(zero,zero,less_equal(divide(divide(X1,divide(X1,zero)),zero),zero),true),
inference(cp,[status(thm)],[t68,t157]) ).
cnf(t252,plain,
true = less_equal(divide(divide(X1,divide(X1,zero)),zero),zero),
inference(step,[status(thm)],[t158,t12]) ).
cnf(t200,plain,
less_equal(divide(divide(X1,divide(X1,zero)),zero),zero) = true,
inference(orient,[status(thm)],[t252]) ).
cnf(t201,plain,
zero = ifeq(true,true,divide(divide(X1,divide(X1,zero)),zero),zero),
inference(cp,[status(thm)],[t72,t200]) ).
cnf(t253,plain,
zero = divide(divide(X1,divide(X1,zero)),zero),
inference(step,[status(thm)],[t201,t12]) ).
cnf(t205,plain,
divide(divide(X1,divide(X1,zero)),zero) = zero,
inference(orient,[status(thm)],[t253]) ).
cnf(t206,plain,
true = ifeq(zero,zero,less_equal(divide(X1,divide(X1,zero)),zero),true),
inference(cp,[status(thm)],[t68,t205]) ).
cnf(t254,plain,
true = less_equal(divide(X1,divide(X1,zero)),zero),
inference(step,[status(thm)],[t206,t12]) ).
cnf(t214,plain,
less_equal(divide(X1,divide(X1,zero)),zero) = true,
inference(orient,[status(thm)],[t254]) ).
cnf(t215,plain,
zero = ifeq(true,true,divide(X1,divide(X1,zero)),zero),
inference(cp,[status(thm)],[t72,t214]) ).
cnf(t255,plain,
zero = divide(X1,divide(X1,zero)),
inference(step,[status(thm)],[t215,t12]) ).
cnf(t219,plain,
divide(X1,divide(X1,zero)) = zero,
inference(orient,[status(thm)],[t255]) ).
cnf(t220,plain,
true = ifeq(zero,zero,less_equal(X1,divide(X1,zero)),true),
inference(cp,[status(thm)],[t68,t219]) ).
cnf(t256,plain,
true = less_equal(X1,divide(X1,zero)),
inference(step,[status(thm)],[t220,t12]) ).
cnf(t229,plain,
less_equal(X1,divide(X1,zero)) = true,
inference(orient,[status(thm)],[t256]) ).
cnf(t230,plain,
divide(X1,zero) = ifeq(true,true,ifeq(less_equal(divide(X1,zero),X1),true,X1,divide(X1,zero)),divide(X1,zero)),
inference(cp,[status(thm)],[t13,t229]) ).
cnf(t257,plain,
divide(X1,zero) = ifeq(less_equal(divide(X1,zero),X1),true,X1,divide(X1,zero)),
inference(step,[status(thm)],[t230,t12]) ).
cnf(t6,plain,
less_equal(divide(X1,X2),X1) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t40,plain,
less_equal(divide(X1,X2),X1) = true,
inference(orient,[status(thm)],[t6]) ).
cnf(t258,plain,
divide(X1,zero) = ifeq(true,true,X1,divide(X1,zero)),
inference(step,[status(thm)],[t257,t40]) ).
cnf(t259,plain,
divide(X1,zero) = X1,
inference(step,[status(thm)],[t258,t12]) ).
cnf(t232,plain,
divide(X1,zero) = X1,
inference(orient,[status(thm)],[t259]) ).
cnf(f7,negated_conjecture,
divide(a,zero) != a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_x_divide_zero_is_x) ).
fof(f7_nnf,plain,
divide(a,zero) != a,
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
divide(a,zero) != a,
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
divide(a,zero) != a,
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(goal_0,negated_conjecture,
divide(a,zero) != a,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(g0_0,plain,
a != a,
inference(rw,[status(thm)],[goal_0,t232]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : HEN004-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/5.36 % Computer : n018.cluster.edu
% 0.10/5.36 % Model : x86_64 x86_64
% 0.10/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.36 % Memory : 8046.5625MB
% 0.10/5.36 % OS : Linux 6.8.0-71-generic
% 0.10/5.36 % CPULimit : 300
% 0.10/5.36 % WCLimit : 300
% 0.10/5.36 % DateTime : Wed Sep 23 16:12:38 UTC 2026
% 0.10/5.36 % CPUTime :
% 0.10/5.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.13/5.85 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/5.85 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------