%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : HEN006-6 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n005.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 01:37:03 PM UTC 2026
% Result : Unsatisfiable 6.47s 1.34s
% Output : Proof 6.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% Number of leaves : 11
% Syntax : Number of formulae : 110 ( 98 unt; 0 def)
% Number of atoms : 126 ( 90 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 : 7 ( 7 usr; 5 con; 0-4 aty)
% Number of variables : 141 ( 20 sgn 28 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f1,axiom,
( less_equal(X,Y)
| divide(X,Y) != zero ),
file('/export/starexec/sandbox2/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(t11,plain,
ifeq(divide(X1,X2),zero,less_equal(X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t90,plain,
ifeq(divide(X1,X2),zero,less_equal(X1,X2),true) = true,
inference(orient,[status(thm)],[t11]) ).
cnf(f0,axiom,
( divide(X,Y) = zero
| ~ less_equal(X,Y) ),
file('/export/starexec/sandbox2/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/sandbox2/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(t13,plain,
divide(divide(divide(X1,X2),divide(X3,X2)),divide(divide(X1,X3),X2)) = zero,
inference(hyper_resolution,[status(thm)],[hi0,hi3]) ).
cnf(t24,plain,
divide(divide(divide(X1,X2),divide(X3,X2)),divide(divide(X1,X3),X2)) = zero,
inference(orient,[status(thm)],[t13]) ).
cnf(f2,axiom,
less_equal(divide(X,Y),X),
file('/export/starexec/sandbox2/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(t6,plain,
divide(divide(X1,X2),X1) = zero,
inference(hyper_resolution,[status(thm)],[hi0,hi2]) ).
cnf(t20,plain,
divide(divide(X1,X2),X1) = zero,
inference(orient,[status(thm)],[t6]) ).
cnf(t29,plain,
zero = divide(divide(divide(X1,X2),zero),divide(divide(X1,divide(X2,X3)),X2)),
inference(cp,[status(thm)],[t24,t20]) ).
cnf(f5,axiom,
( X = Y
| ~ less_equal(Y,X)
| ~ less_equal(X,Y) ),
file('/export/starexec/sandbox2/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(t14,plain,
ifeq(less_equal(X1,X2),true,ifeq(less_equal(X2,X1),true,X1,X2),X2) = X2,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t17,plain,
ifeq(less_equal(X1,X2),true,ifeq(less_equal(X2,X1),true,X1,X2),X2) = X2,
inference(orient,[status(thm)],[t14]) ).
cnf(f4,axiom,
less_equal(zero,X),
file('/export/starexec/sandbox2/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(t5,plain,
less_equal(zero,X1) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t87,plain,
less_equal(zero,X1) = true,
inference(orient,[status(thm)],[t5]) ).
cnf(t89,plain,
zero = ifeq(less_equal(X1,zero),true,ifeq(true,true,X1,zero),zero),
inference(cp,[status(thm)],[t17,t87]) ).
cnf(t8,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t16,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t8]) ).
cnf(t314,plain,
zero = ifeq(less_equal(X1,zero),true,X1,zero),
inference(step,[status(thm)],[t89,t16]) ).
cnf(t94,plain,
ifeq(less_equal(X1,zero),true,X1,zero) = zero,
inference(orient,[status(thm)],[t314]) ).
cnf(f8,axiom,
divide(zero,X) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',zero_divide_anything_is_zero) ).
fof(f8_nnf,plain,
! [X] : divide(zero,X) = zero,
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [X] : divide(zero,X) = zero,
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
divide(zero,X0) = zero,
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(t2,plain,
divide(zero,X1) = zero,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t45,plain,
divide(zero,X1) = zero,
inference(orient,[status(thm)],[t2]) ).
cnf(t46,plain,
zero = divide(divide(divide(X1,X2),zero),divide(divide(X1,zero),X2)),
inference(cp,[status(thm)],[t24,t45]) ).
cnf(t149,plain,
divide(divide(divide(X1,X2),zero),divide(divide(X1,zero),X2)) = zero,
inference(orient,[status(thm)],[t46]) ).
cnf(f9,axiom,
divide(X,X) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_divide_x_is_zero) ).
fof(f9_nnf,plain,
! [X] : divide(X,X) = zero,
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [X] : divide(X,X) = zero,
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
divide(X0,X0) = zero,
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(t0,plain,
divide(X1,X1) = zero,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(t18,plain,
divide(X1,X1) = zero,
inference(orient,[status(thm)],[t0]) ).
cnf(t152,plain,
zero = divide(divide(divide(X1,divide(X1,zero)),zero),zero),
inference(cp,[status(thm)],[t149,t18]) ).
cnf(t170,plain,
divide(divide(divide(X1,divide(X1,zero)),zero),zero) = zero,
inference(orient,[status(thm)],[t152]) ).
cnf(t171,plain,
true = ifeq(zero,zero,less_equal(divide(divide(X1,divide(X1,zero)),zero),zero),true),
inference(cp,[status(thm)],[t90,t170]) ).
cnf(t326,plain,
true = less_equal(divide(divide(X1,divide(X1,zero)),zero),zero),
inference(step,[status(thm)],[t171,t16]) ).
cnf(t213,plain,
less_equal(divide(divide(X1,divide(X1,zero)),zero),zero) = true,
inference(orient,[status(thm)],[t326]) ).
cnf(t214,plain,
zero = ifeq(true,true,divide(divide(X1,divide(X1,zero)),zero),zero),
inference(cp,[status(thm)],[t94,t213]) ).
cnf(t327,plain,
zero = divide(divide(X1,divide(X1,zero)),zero),
inference(step,[status(thm)],[t214,t16]) ).
cnf(t218,plain,
divide(divide(X1,divide(X1,zero)),zero) = zero,
inference(orient,[status(thm)],[t327]) ).
cnf(t219,plain,
true = ifeq(zero,zero,less_equal(divide(X1,divide(X1,zero)),zero),true),
inference(cp,[status(thm)],[t90,t218]) ).
cnf(t328,plain,
true = less_equal(divide(X1,divide(X1,zero)),zero),
inference(step,[status(thm)],[t219,t16]) ).
cnf(t227,plain,
less_equal(divide(X1,divide(X1,zero)),zero) = true,
inference(orient,[status(thm)],[t328]) ).
cnf(t228,plain,
zero = ifeq(true,true,divide(X1,divide(X1,zero)),zero),
inference(cp,[status(thm)],[t94,t227]) ).
cnf(t329,plain,
zero = divide(X1,divide(X1,zero)),
inference(step,[status(thm)],[t228,t16]) ).
cnf(t232,plain,
divide(X1,divide(X1,zero)) = zero,
inference(orient,[status(thm)],[t329]) ).
cnf(t233,plain,
true = ifeq(zero,zero,less_equal(X1,divide(X1,zero)),true),
inference(cp,[status(thm)],[t90,t232]) ).
cnf(t330,plain,
true = less_equal(X1,divide(X1,zero)),
inference(step,[status(thm)],[t233,t16]) ).
cnf(t242,plain,
less_equal(X1,divide(X1,zero)) = true,
inference(orient,[status(thm)],[t330]) ).
cnf(t243,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)],[t17,t242]) ).
cnf(t331,plain,
divide(X1,zero) = ifeq(less_equal(divide(X1,zero),X1),true,X1,divide(X1,zero)),
inference(step,[status(thm)],[t243,t16]) ).
cnf(t9,plain,
less_equal(divide(X1,X2),X1) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t58,plain,
less_equal(divide(X1,X2),X1) = true,
inference(orient,[status(thm)],[t9]) ).
cnf(t332,plain,
divide(X1,zero) = ifeq(true,true,X1,divide(X1,zero)),
inference(step,[status(thm)],[t331,t58]) ).
cnf(t333,plain,
divide(X1,zero) = X1,
inference(step,[status(thm)],[t332,t16]) ).
cnf(t245,plain,
divide(X1,zero) = X1,
inference(orient,[status(thm)],[t333]) ).
cnf(t341,plain,
zero = divide(divide(X1,X2),divide(divide(X1,divide(X2,X3)),X2)),
inference(step,[status(thm)],[t29,t245]) ).
cnf(t286,plain,
divide(divide(X1,X2),divide(divide(X1,divide(X2,X3)),X2)) = zero,
inference(orient,[status(thm)],[t341]) ).
cnf(t15,plain,
less_equal(divide(divide(X1,X2),divide(X3,X2)),divide(divide(X1,X3),X2)) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t66,plain,
less_equal(divide(divide(X1,X2),divide(X3,X2)),divide(divide(X1,X3),X2)) = true,
inference(orient,[status(thm)],[t15]) ).
cnf(f10,hypothesis,
less_equal(divide(a,b),d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_divide_b_LE_d) ).
fof(f10_nnf,plain,
less_equal(divide(a,b),d),
inference(nnf_transformation,[status(thm)],[f10]) ).
cnf(c10,plain,
less_equal(divide(a,b),d),
inference(cnf_transformation,[status(esa)],[f10_nnf]) ).
cnf(hi10,axiom,
less_equal(divide(a,b),d) = true,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(t7,plain,
divide(divide(a,b),d) = zero,
inference(hyper_resolution,[status(thm)],[hi0,hi10]) ).
cnf(t39,plain,
divide(divide(a,b),d) = zero,
inference(orient,[status(thm)],[t7]) ).
cnf(t75,plain,
true = less_equal(divide(divide(a,d),divide(b,d)),zero),
inference(cp,[status(thm)],[t66,t39]) ).
cnf(t104,plain,
less_equal(divide(divide(a,d),divide(b,d)),zero) = true,
inference(orient,[status(thm)],[t75]) ).
cnf(t105,plain,
zero = ifeq(true,true,divide(divide(a,d),divide(b,d)),zero),
inference(cp,[status(thm)],[t94,t104]) ).
cnf(t315,plain,
zero = divide(divide(a,d),divide(b,d)),
inference(step,[status(thm)],[t105,t16]) ).
cnf(t109,plain,
divide(divide(a,d),divide(b,d)) = zero,
inference(orient,[status(thm)],[t315]) ).
cnf(t288,plain,
zero = divide(divide(divide(a,d),b),divide(zero,b)),
inference(cp,[status(thm)],[t286,t109]) ).
cnf(t342,plain,
zero = divide(divide(divide(a,d),b),zero),
inference(step,[status(thm)],[t288,t45]) ).
cnf(t343,plain,
zero = divide(divide(a,d),b),
inference(step,[status(thm)],[t342,t245]) ).
cnf(t300,plain,
divide(divide(a,d),b) = zero,
inference(orient,[status(thm)],[t343]) ).
cnf(t301,plain,
true = ifeq(zero,zero,less_equal(divide(a,d),b),true),
inference(cp,[status(thm)],[t90,t300]) ).
cnf(t344,plain,
true = less_equal(divide(a,d),b),
inference(step,[status(thm)],[t301,t16]) ).
cnf(t308,plain,
less_equal(divide(a,d),b) = true,
inference(orient,[status(thm)],[t344]) ).
cnf(f11,negated_conjecture,
~ less_equal(divide(a,d),b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_a_divide_d_LE_b) ).
fof(f11_nnf,plain,
~ less_equal(divide(a,d),b),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
~ less_equal(divide(a,d),b),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
~ less_equal(divide(a,d),b),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(goal_0,negated_conjecture,
less_equal(divide(a,d),b) != true,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t308]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN006-6 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n005.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Wed Sep 23 16:12:32 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 6.47/1.34 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.47/1.34 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------