%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : HEN005-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n016.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 01:37:00 PM UTC 2026
% Result : Unsatisfiable 4.43s 11.14s
% Output : Proof 4.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 9
% Syntax : Number of formulae : 77 ( 65 unt; 0 def)
% Number of atoms : 93 ( 58 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 : 4 ( 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 : 76 ( 9 sgn 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(t11,plain,
ifeq(divide(X1,X2),zero,less_equal(X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t94,plain,
ifeq(divide(X1,X2),zero,less_equal(X1,X2),true) = true,
inference(orient,[status(thm)],[t11]) ).
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(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/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(t7,plain,
less_equal(zero,X1) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t85,plain,
less_equal(zero,X1) = true,
inference(orient,[status(thm)],[t7]) ).
cnf(t87,plain,
zero = ifeq(less_equal(X1,zero),true,ifeq(true,true,X1,zero),zero),
inference(cp,[status(thm)],[t17,t85]) ).
cnf(t9,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t16,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t9]) ).
cnf(t222,plain,
zero = ifeq(less_equal(X1,zero),true,X1,zero),
inference(step,[status(thm)],[t87,t16]) ).
cnf(t98,plain,
ifeq(less_equal(X1,zero),true,X1,zero) = zero,
inference(orient,[status(thm)],[t222]) ).
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(t13,plain,
divide(divide(divide(X1,X2),divide(X3,X2)),divide(divide(X1,X3),X2)) = zero,
inference(hyper_resolution,[status(thm)],[hi0,hi3]) ).
cnf(t22,plain,
divide(divide(divide(X1,X2),divide(X3,X2)),divide(divide(X1,X3),X2)) = zero,
inference(orient,[status(thm)],[t13]) ).
cnf(f7,hypothesis,
less_equal(a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_LE_b) ).
fof(f7_nnf,plain,
less_equal(a,b),
inference(nnf_transformation,[status(thm)],[f7]) ).
cnf(c7,plain,
less_equal(a,b),
inference(cnf_transformation,[status(esa)],[f7_nnf]) ).
cnf(hi7,axiom,
less_equal(a,b) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t1,plain,
divide(a,b) = zero,
inference(hyper_resolution,[status(thm)],[hi0,hi7]) ).
cnf(t39,plain,
divide(a,b) = zero,
inference(orient,[status(thm)],[t1]) ).
cnf(t41,plain,
zero = divide(divide(divide(a,X1),divide(b,X1)),divide(zero,X1)),
inference(cp,[status(thm)],[t22,t39]) ).
cnf(hi4,axiom,
less_equal(zero,X0) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t3,plain,
divide(zero,X1) = zero,
inference(hyper_resolution,[status(thm)],[hi0,hi4]) ).
cnf(t34,plain,
divide(zero,X1) = zero,
inference(orient,[status(thm)],[t3]) ).
cnf(t233,plain,
zero = divide(divide(divide(a,X1),divide(b,X1)),zero),
inference(step,[status(thm)],[t41,t34]) ).
cnf(t173,plain,
divide(divide(divide(a,X1),divide(b,X1)),zero) = zero,
inference(orient,[status(thm)],[t233]) ).
cnf(f8,hypothesis,
less_equal(b,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_LE_c) ).
fof(f8_nnf,plain,
less_equal(b,c),
inference(nnf_transformation,[status(thm)],[f8]) ).
cnf(c8,plain,
less_equal(b,c),
inference(cnf_transformation,[status(esa)],[f8_nnf]) ).
cnf(hi8,axiom,
less_equal(b,c) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t2,plain,
divide(b,c) = zero,
inference(hyper_resolution,[status(thm)],[hi0,hi8]) ).
cnf(t36,plain,
divide(b,c) = zero,
inference(orient,[status(thm)],[t2]) ).
cnf(t174,plain,
zero = divide(divide(divide(a,c),zero),zero),
inference(cp,[status(thm)],[t173,t36]) ).
cnf(t183,plain,
divide(divide(divide(a,c),zero),zero) = zero,
inference(orient,[status(thm)],[t174]) ).
cnf(t184,plain,
true = ifeq(zero,zero,less_equal(divide(divide(a,c),zero),zero),true),
inference(cp,[status(thm)],[t94,t183]) ).
cnf(t234,plain,
true = less_equal(divide(divide(a,c),zero),zero),
inference(step,[status(thm)],[t184,t16]) ).
cnf(t190,plain,
less_equal(divide(divide(a,c),zero),zero) = true,
inference(orient,[status(thm)],[t234]) ).
cnf(t191,plain,
zero = ifeq(true,true,divide(divide(a,c),zero),zero),
inference(cp,[status(thm)],[t98,t190]) ).
cnf(t235,plain,
zero = divide(divide(a,c),zero),
inference(step,[status(thm)],[t191,t16]) ).
cnf(t195,plain,
divide(divide(a,c),zero) = zero,
inference(orient,[status(thm)],[t235]) ).
cnf(t196,plain,
true = ifeq(zero,zero,less_equal(divide(a,c),zero),true),
inference(cp,[status(thm)],[t94,t195]) ).
cnf(t236,plain,
true = less_equal(divide(a,c),zero),
inference(step,[status(thm)],[t196,t16]) ).
cnf(t204,plain,
less_equal(divide(a,c),zero) = true,
inference(orient,[status(thm)],[t236]) ).
cnf(t205,plain,
zero = ifeq(true,true,divide(a,c),zero),
inference(cp,[status(thm)],[t98,t204]) ).
cnf(t237,plain,
zero = divide(a,c),
inference(step,[status(thm)],[t205,t16]) ).
cnf(t209,plain,
divide(a,c) = zero,
inference(orient,[status(thm)],[t237]) ).
cnf(t210,plain,
true = ifeq(zero,zero,less_equal(a,c),true),
inference(cp,[status(thm)],[t94,t209]) ).
cnf(t238,plain,
true = less_equal(a,c),
inference(step,[status(thm)],[t210,t16]) ).
cnf(t216,plain,
less_equal(a,c) = true,
inference(orient,[status(thm)],[t238]) ).
cnf(f9,negated_conjecture,
~ less_equal(a,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_a_LE_c) ).
fof(f9_nnf,plain,
~ less_equal(a,c),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
~ less_equal(a,c),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
~ less_equal(a,c),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(goal_0,negated_conjecture,
less_equal(a,c) != true,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t216]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : HEN005-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/10.36 % Computer : n016.cluster.edu
% 0.08/10.36 % Model : x86_64 x86_64
% 0.08/10.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/10.36 % Memory : 8046.5625MB
% 0.08/10.36 % OS : Linux 6.8.0-71-generic
% 0.08/10.36 % CPULimit : 300
% 0.08/10.36 % WCLimit : 300
% 0.08/10.36 % DateTime : Wed Sep 23 16:16:21 UTC 2026
% 0.08/10.37 % CPUTime :
% 0.08/10.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 4.43/11.14 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.43/11.14 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------