%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : HEN006-4 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n004.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 01:37:02 PM UTC 2026
% Result : Unsatisfiable 15.98s 2.43s
% Output : Proof 15.98s
% Verified :
% Comments :
%------------------------------------------------------------------------------
cnf(t14,axiom,
sFlat0 = divide(a,d),
introduced(definition) ).
cnf(t69,plain,
divide(a,d) = sFlat0,
inference(orient,[status(thm)],[t14]) ).
cnf(t15,axiom,
sFlat1 = less_equal(divide(a,d),b),
introduced(definition) ).
cnf(t422,plain,
sFlat1 = less_equal(sFlat0,b),
inference(step,[status(thm)],[t15,t69]) ).
cnf(t75,plain,
less_equal(sFlat0,b) = sFlat1,
inference(orient,[status(thm)],[t422]) ).
cnf(f11,axiom,
( less_equal(X,Z)
| ~ less_equal(Y,Z)
| ~ less_equal(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_of_less_equal) ).
fof(f11_nnf,plain,
! [X,Y,Z] :
( less_equal(X,Z)
| ~ less_equal(Y,Z)
| ~ less_equal(X,Y) ),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [X,Y,Z] :
( less_equal(X,Z)
| ~ less_equal(Y,Z)
| ~ less_equal(X,Y) ),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
( less_equal(X0,X2)
| ~ less_equal(X1,X2)
| ~ less_equal(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(t13,plain,
ifeq(less_equal(X1,X2),true,ifeq(less_equal(X2,X3),true,less_equal(X1,X3),true),true) = true,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(t39,plain,
ifeq(less_equal(X1,X2),true,ifeq(less_equal(X2,X3),true,less_equal(X1,X3),true),true) = true,
inference(orient,[status(thm)],[t13]) ).
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(t7,plain,
less_equal(divide(X1,X2),X1) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t21,plain,
less_equal(divide(X1,X2),X1) = true,
inference(orient,[status(thm)],[t7]) ).
cnf(t48,plain,
true = ifeq(less_equal(X1,divide(X2,X3)),true,ifeq(true,true,less_equal(X1,X2),true),true),
inference(cp,[status(thm)],[t39,t21]) ).
cnf(t6,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t16,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t6]) ).
cnf(t478,plain,
true = ifeq(less_equal(X1,divide(X2,X3)),true,less_equal(X1,X2),true),
inference(step,[status(thm)],[t48,t16]) ).
cnf(t339,plain,
ifeq(less_equal(X1,divide(X2,X3)),true,less_equal(X1,X2),true) = true,
inference(orient,[status(thm)],[t478]) ).
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(t9,plain,
ifeq(divide(X1,X2),zero,less_equal(X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t33,plain,
ifeq(divide(X1,X2),zero,less_equal(X1,X2),true) = true,
inference(orient,[status(thm)],[t9]) ).
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(t11,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)],[t11]) ).
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(t5,plain,
less_equal(zero,X1) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t30,plain,
less_equal(zero,X1) = true,
inference(orient,[status(thm)],[t5]) ).
cnf(t32,plain,
zero = ifeq(less_equal(X1,zero),true,ifeq(true,true,X1,zero),zero),
inference(cp,[status(thm)],[t17,t30]) ).
cnf(t430,plain,
zero = ifeq(less_equal(X1,zero),true,X1,zero),
inference(step,[status(thm)],[t32,t16]) ).
cnf(t115,plain,
ifeq(less_equal(X1,zero),true,X1,zero) = zero,
inference(orient,[status(thm)],[t430]) ).
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(t12,plain,
less_equal(divide(divide(X1,X2),divide(X3,X2)),divide(divide(X1,X3),X2)) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t24,plain,
less_equal(divide(divide(X1,X2),divide(X3,X2)),divide(divide(X1,X3),X2)) = true,
inference(orient,[status(thm)],[t12]) ).
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(t10,plain,
ifeq(less_equal(X1,X2),true,divide(X1,X2),zero) = zero,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t82,plain,
ifeq(less_equal(X1,X2),true,divide(X1,X2),zero) = zero,
inference(orient,[status(thm)],[t10]) ).
cnf(f12,hypothesis,
less_equal(divide(a,b),d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_divide_b_LE_d) ).
fof(f12_nnf,plain,
less_equal(divide(a,b),d),
inference(nnf_transformation,[status(thm)],[f12]) ).
cnf(c12,plain,
less_equal(divide(a,b),d),
inference(cnf_transformation,[status(esa)],[f12_nnf]) ).
cnf(t8,plain,
less_equal(divide(a,b),d) = true,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(t27,plain,
less_equal(divide(a,b),d) = true,
inference(orient,[status(thm)],[t8]) ).
cnf(t84,plain,
zero = ifeq(true,true,divide(divide(a,b),d),zero),
inference(cp,[status(thm)],[t82,t27]) ).
cnf(t425,plain,
zero = divide(divide(a,b),d),
inference(step,[status(thm)],[t84,t16]) ).
cnf(t105,plain,
divide(divide(a,b),d) = zero,
inference(orient,[status(thm)],[t425]) ).
cnf(t107,plain,
true = less_equal(divide(divide(a,d),divide(b,d)),zero),
inference(cp,[status(thm)],[t24,t105]) ).
cnf(t435,plain,
true = less_equal(divide(sFlat0,divide(b,d)),zero),
inference(step,[status(thm)],[t107,t69]) ).
cnf(t126,plain,
less_equal(divide(sFlat0,divide(b,d)),zero) = true,
inference(orient,[status(thm)],[t435]) ).
cnf(t127,plain,
zero = ifeq(true,true,divide(sFlat0,divide(b,d)),zero),
inference(cp,[status(thm)],[t115,t126]) ).
cnf(t436,plain,
zero = divide(sFlat0,divide(b,d)),
inference(step,[status(thm)],[t127,t16]) ).
cnf(t135,plain,
divide(sFlat0,divide(b,d)) = zero,
inference(orient,[status(thm)],[t436]) ).
cnf(t137,plain,
true = ifeq(zero,zero,less_equal(sFlat0,divide(b,d)),true),
inference(cp,[status(thm)],[t33,t135]) ).
cnf(t437,plain,
true = less_equal(sFlat0,divide(b,d)),
inference(step,[status(thm)],[t137,t16]) ).
cnf(t140,plain,
less_equal(sFlat0,divide(b,d)) = true,
inference(orient,[status(thm)],[t437]) ).
cnf(t342,plain,
true = ifeq(true,true,less_equal(sFlat0,b),true),
inference(cp,[status(thm)],[t339,t140]) ).
cnf(t479,plain,
true = less_equal(sFlat0,b),
inference(step,[status(thm)],[t342,t16]) ).
cnf(t480,plain,
true = sFlat1,
inference(step,[status(thm)],[t479,t75]) ).
cnf(t346,plain,
true = sFlat1,
inference(orient,[status(thm)],[t480]) ).
cnf(f13,negated_conjecture,
~ less_equal(divide(a,d),b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_a_divide_d_LE_b) ).
fof(f13_nnf,plain,
~ less_equal(divide(a,d),b),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
~ less_equal(divide(a,d),b),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c13,plain,
~ less_equal(divide(a,d),b),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(goal_0,negated_conjecture,
less_equal(divide(a,d),b) != true,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(g0_0,plain,
less_equal(sFlat0,b) != true,
inference(rw,[status(thm)],[goal_0,t69]) ).
cnf(g0_1,plain,
sFlat1 != true,
inference(rw,[status(thm)],[g0_0,t75]) ).
cnf(g0_2,plain,
sFlat1 != sFlat1,
inference(rw,[status(thm)],[g0_1,t346]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN006-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.35 % Computer : n004.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Wed Sep 23 16:12:35 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 15.98/2.43 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 15.98/2.43 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------