%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : HEN009-6 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n020.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 16.13s 2.49s
% Output : Proof 16.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% Number of leaves : 13
% Syntax : Number of formulae : 132 ( 112 unt; 0 def)
% Number of atoms : 156 ( 115 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 58 ( 34 ~; 24 |; 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 : 10 ( 10 usr; 8 con; 0-4 aty)
% Number of variables : 131 ( 42 sgn 28 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f12,hypothesis,
divide(identity,a) != divide(identity,divide(identity,divide(identity,a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',part_of_theorem) ).
fof(f12_nnf,plain,
divide(identity,a) != divide(identity,divide(identity,divide(identity,a))),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
divide(identity,a) != divide(identity,divide(identity,divide(identity,a))),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c12,plain,
divide(identity,a) != divide(identity,divide(identity,divide(identity,a))),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(t13,plain,
ifeq(divide(identity,a),divide(identity,divide(identity,divide(identity,a))),false,true) = true,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(f13,hypothesis,
divide(identity,a) = b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id_divide_a_is_b) ).
fof(f13_nnf,plain,
divide(identity,a) = b,
inference(nnf_transformation,[status(thm)],[f13]) ).
cnf(c13,plain,
divide(identity,a) = b,
inference(cnf_transformation,[status(esa)],[f13_nnf]) ).
cnf(t2,plain,
divide(identity,a) = b,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(t23,plain,
divide(identity,a) = b,
inference(orient,[status(thm)],[t2]) ).
cnf(t645,plain,
ifeq(b,divide(identity,divide(identity,divide(identity,a))),false,true) = true,
inference(step,[status(thm)],[t13,t23]) ).
cnf(t646,plain,
ifeq(b,divide(identity,divide(identity,b)),false,true) = true,
inference(step,[status(thm)],[t645,t23]) ).
cnf(f14,hypothesis,
divide(identity,b) = c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id_divide_b_is_c) ).
fof(f14_nnf,plain,
divide(identity,b) = c,
inference(nnf_transformation,[status(thm)],[f14]) ).
cnf(c14,plain,
divide(identity,b) = c,
inference(cnf_transformation,[status(esa)],[f14_nnf]) ).
cnf(t3,plain,
divide(identity,b) = c,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(t22,plain,
divide(identity,b) = c,
inference(orient,[status(thm)],[t3]) ).
cnf(t647,plain,
ifeq(b,divide(identity,c),false,true) = true,
inference(step,[status(thm)],[t646,t22]) ).
cnf(f15,hypothesis,
divide(identity,c) = d,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id_divide_c_is_d) ).
fof(f15_nnf,plain,
divide(identity,c) = d,
inference(nnf_transformation,[status(thm)],[f15]) ).
cnf(c15,plain,
divide(identity,c) = d,
inference(cnf_transformation,[status(esa)],[f15_nnf]) ).
cnf(t4,plain,
divide(identity,c) = d,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(t24,plain,
divide(identity,c) = d,
inference(orient,[status(thm)],[t4]) ).
cnf(t648,plain,
ifeq(b,d,false,true) = true,
inference(step,[status(thm)],[t647,t24]) ).
cnf(t68,plain,
ifeq(b,d,false,true) = true,
inference(orient,[status(thm)],[t648]) ).
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(t19,plain,
ifeq(less_equal(X1,X2),true,ifeq(less_equal(X2,X1),true,X1,X2),X2) = X2,
inference(orient,[status(thm)],[t14]) ).
cnf(f10,axiom,
( less_equal(divide(X,Z),Y)
| ~ less_equal(divide(X,Y),Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',property_of_divide1) ).
fof(f10_nnf,plain,
! [X,Y,Z] :
( less_equal(divide(X,Z),Y)
| ~ less_equal(divide(X,Y),Z) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [X,Y,Z] :
( less_equal(divide(X,Z),Y)
| ~ less_equal(divide(X,Y),Z) ),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
( less_equal(divide(X0,X2),X1)
| ~ less_equal(divide(X0,X1),X2) ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(t16,plain,
ifeq(less_equal(divide(X1,X2),X3),true,less_equal(divide(X1,X3),X2),true) = true,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(t84,plain,
ifeq(less_equal(divide(X1,X2),X3),true,less_equal(divide(X1,X3),X2),true) = true,
inference(orient,[status(thm)],[t16]) ).
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(t61,plain,
ifeq(divide(X1,X2),zero,less_equal(X1,X2),true) = true,
inference(orient,[status(thm)],[t11]) ).
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(t7,plain,
less_equal(zero,X1) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t58,plain,
less_equal(zero,X1) = true,
inference(orient,[status(thm)],[t7]) ).
cnf(t60,plain,
zero = ifeq(less_equal(X1,zero),true,ifeq(true,true,X1,zero),zero),
inference(cp,[status(thm)],[t19,t58]) ).
cnf(t8,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t18,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t8]) ).
cnf(t677,plain,
zero = ifeq(less_equal(X1,zero),true,X1,zero),
inference(step,[status(thm)],[t60,t18]) ).
cnf(t257,plain,
ifeq(less_equal(X1,zero),true,X1,zero) = zero,
inference(orient,[status(thm)],[t677]) ).
cnf(f11,axiom,
( less_equal(divide(X,Z),divide(Y,Z))
| ~ less_equal(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',property_of_divide3) ).
fof(f11_nnf,plain,
! [X,Y,Z] :
( less_equal(divide(X,Z),divide(Y,Z))
| ~ less_equal(X,Y) ),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [X,Y,Z] :
( less_equal(divide(X,Z),divide(Y,Z))
| ~ less_equal(X,Y) ),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
( less_equal(divide(X0,X2),divide(X1,X2))
| ~ less_equal(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(t15,plain,
ifeq(less_equal(X1,X2),true,less_equal(divide(X1,X3),divide(X2,X3)),true) = true,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(t69,plain,
ifeq(less_equal(X1,X2),true,less_equal(divide(X1,X3),divide(X2,X3)),true) = true,
inference(orient,[status(thm)],[t15]) ).
cnf(t81,plain,
true = ifeq(less_equal(X1,identity),true,less_equal(divide(X1,c),d),true),
inference(cp,[status(thm)],[t69,t24]) ).
cnf(f6,axiom,
less_equal(X,identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_is_largest) ).
fof(f6_nnf,plain,
! [X] : less_equal(X,identity),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [X] : less_equal(X,identity),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
less_equal(X0,identity),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(t6,plain,
less_equal(X1,identity) = true,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t26,plain,
less_equal(X1,identity) = true,
inference(orient,[status(thm)],[t6]) ).
cnf(t650,plain,
true = ifeq(true,true,less_equal(divide(X1,c),d),true),
inference(step,[status(thm)],[t81,t26]) ).
cnf(t651,plain,
true = less_equal(divide(X1,c),d),
inference(step,[status(thm)],[t650,t18]) ).
cnf(t103,plain,
less_equal(divide(X1,c),d) = true,
inference(orient,[status(thm)],[t651]) ).
cnf(t108,plain,
true = ifeq(true,true,less_equal(divide(X1,d),c),true),
inference(cp,[status(thm)],[t84,t103]) ).
cnf(t658,plain,
true = less_equal(divide(X1,d),c),
inference(step,[status(thm)],[t108,t18]) ).
cnf(t142,plain,
less_equal(divide(X1,d),c) = true,
inference(orient,[status(thm)],[t658]) ).
cnf(t147,plain,
true = ifeq(true,true,less_equal(divide(divide(X1,d),X2),divide(c,X2)),true),
inference(cp,[status(thm)],[t69,t142]) ).
cnf(t739,plain,
true = less_equal(divide(divide(X1,d),X2),divide(c,X2)),
inference(step,[status(thm)],[t147,t18]) ).
cnf(t580,plain,
less_equal(divide(divide(X1,d),X2),divide(c,X2)) = true,
inference(orient,[status(thm)],[t739]) ).
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(t12,plain,
ifeq(less_equal(X1,X2),true,divide(X1,X2),zero) = zero,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t93,plain,
ifeq(less_equal(X1,X2),true,divide(X1,X2),zero) = zero,
inference(orient,[status(thm)],[t12]) ).
cnf(t83,plain,
true = ifeq(less_equal(X1,identity),true,less_equal(divide(X1,a),b),true),
inference(cp,[status(thm)],[t69,t23]) ).
cnf(t654,plain,
true = ifeq(true,true,less_equal(divide(X1,a),b),true),
inference(step,[status(thm)],[t83,t26]) ).
cnf(t655,plain,
true = less_equal(divide(X1,a),b),
inference(step,[status(thm)],[t654,t18]) ).
cnf(t119,plain,
less_equal(divide(X1,a),b) = true,
inference(orient,[status(thm)],[t655]) ).
cnf(t124,plain,
true = ifeq(true,true,less_equal(divide(X1,b),a),true),
inference(cp,[status(thm)],[t84,t119]) ).
cnf(t663,plain,
true = less_equal(divide(X1,b),a),
inference(step,[status(thm)],[t124,t18]) ).
cnf(t184,plain,
less_equal(divide(X1,b),a) = true,
inference(orient,[status(thm)],[t663]) ).
cnf(t185,plain,
true = less_equal(c,a),
inference(cp,[status(thm)],[t184,t22]) ).
cnf(t191,plain,
less_equal(c,a) = true,
inference(orient,[status(thm)],[t185]) ).
cnf(t192,plain,
zero = ifeq(true,true,divide(c,a),zero),
inference(cp,[status(thm)],[t93,t191]) ).
cnf(t664,plain,
zero = divide(c,a),
inference(step,[status(thm)],[t192,t18]) ).
cnf(t197,plain,
divide(c,a) = zero,
inference(orient,[status(thm)],[t664]) ).
cnf(t581,plain,
true = less_equal(divide(divide(X1,d),a),zero),
inference(cp,[status(thm)],[t580,t197]) ).
cnf(t589,plain,
less_equal(divide(divide(X1,d),a),zero) = true,
inference(orient,[status(thm)],[t581]) ).
cnf(t591,plain,
zero = ifeq(true,true,divide(divide(X1,d),a),zero),
inference(cp,[status(thm)],[t257,t589]) ).
cnf(t741,plain,
zero = divide(divide(X1,d),a),
inference(step,[status(thm)],[t591,t18]) ).
cnf(t599,plain,
divide(divide(X1,d),a) = zero,
inference(orient,[status(thm)],[t741]) ).
cnf(t601,plain,
true = ifeq(zero,zero,less_equal(divide(X1,d),a),true),
inference(cp,[status(thm)],[t61,t599]) ).
cnf(t742,plain,
true = less_equal(divide(X1,d),a),
inference(step,[status(thm)],[t601,t18]) ).
cnf(t609,plain,
less_equal(divide(X1,d),a) = true,
inference(orient,[status(thm)],[t742]) ).
cnf(t612,plain,
true = ifeq(true,true,less_equal(divide(X1,a),d),true),
inference(cp,[status(thm)],[t84,t609]) ).
cnf(t743,plain,
true = less_equal(divide(X1,a),d),
inference(step,[status(thm)],[t612,t18]) ).
cnf(t614,plain,
less_equal(divide(X1,a),d) = true,
inference(orient,[status(thm)],[t743]) ).
cnf(t615,plain,
true = less_equal(b,d),
inference(cp,[status(thm)],[t614,t23]) ).
cnf(t621,plain,
less_equal(b,d) = true,
inference(orient,[status(thm)],[t615]) ).
cnf(t624,plain,
d = ifeq(true,true,ifeq(less_equal(d,b),true,b,d),d),
inference(cp,[status(thm)],[t19,t621]) ).
cnf(t748,plain,
d = ifeq(less_equal(d,b),true,b,d),
inference(step,[status(thm)],[t624,t18]) ).
cnf(t82,plain,
true = ifeq(less_equal(X1,identity),true,less_equal(divide(X1,b),c),true),
inference(cp,[status(thm)],[t69,t22]) ).
cnf(t652,plain,
true = ifeq(true,true,less_equal(divide(X1,b),c),true),
inference(step,[status(thm)],[t82,t26]) ).
cnf(t653,plain,
true = less_equal(divide(X1,b),c),
inference(step,[status(thm)],[t652,t18]) ).
cnf(t111,plain,
less_equal(divide(X1,b),c) = true,
inference(orient,[status(thm)],[t653]) ).
cnf(t116,plain,
true = ifeq(true,true,less_equal(divide(X1,c),b),true),
inference(cp,[status(thm)],[t84,t111]) ).
cnf(t660,plain,
true = less_equal(divide(X1,c),b),
inference(step,[status(thm)],[t116,t18]) ).
cnf(t156,plain,
less_equal(divide(X1,c),b) = true,
inference(orient,[status(thm)],[t660]) ).
cnf(t157,plain,
true = less_equal(d,b),
inference(cp,[status(thm)],[t156,t24]) ).
cnf(t163,plain,
less_equal(d,b) = true,
inference(orient,[status(thm)],[t157]) ).
cnf(t749,plain,
d = ifeq(true,true,b,d),
inference(step,[status(thm)],[t748,t163]) ).
cnf(t750,plain,
d = b,
inference(step,[status(thm)],[t749,t18]) ).
cnf(t629,plain,
b = d,
inference(orient,[status(thm)],[t750]) ).
cnf(t753,plain,
ifeq(d,d,false,true) = true,
inference(step,[status(thm)],[t68,t629]) ).
cnf(t754,plain,
false = true,
inference(step,[status(thm)],[t753,t18]) ).
cnf(t632,plain,
false = true,
inference(rw,[status(thm)],[t754]) ).
cnf(t644,plain,
false = true,
inference(orient,[status(thm)],[t632]) ).
cnf(f16,negated_conjecture,
b != d,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_b_equals_d) ).
fof(f16_nnf,plain,
b != d,
inference(nnf_transformation,[status(thm)],[f16]) ).
fof(f16_sk,plain,
b != d,
inference(skolemisation,[status(esa)],[f16_nnf]) ).
cnf(c16,plain,
b != d,
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c12,c16]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t644]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : HEN009-6 : 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 : n020.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
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Wed Sep 23 16:16:47 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 16.13/2.49 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 16.13/2.49 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------