%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : HEN008-4 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n002.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 01:37:07 PM UTC 2026
% Result : Unsatisfiable 20.03s 8.52s
% Output : Proof 20.03s
% Verified :
% Comments :
%------------------------------------------------------------------------------
cnf(t16,axiom,
sFlat0 = divide(a,c),
introduced(definition) ).
cnf(t96,plain,
divide(a,c) = sFlat0,
inference(orient,[status(thm)],[t16]) ).
cnf(t17,axiom,
sFlat1 = divide(b,c),
introduced(definition) ).
cnf(t106,plain,
divide(b,c) = sFlat1,
inference(orient,[status(thm)],[t17]) ).
cnf(t18,axiom,
sFlat2 = less_equal(divide(a,c),divide(b,c)),
introduced(definition) ).
cnf(t948,plain,
sFlat2 = less_equal(sFlat0,divide(b,c)),
inference(step,[status(thm)],[t18,t96]) ).
cnf(t949,plain,
sFlat2 = less_equal(sFlat0,sFlat1),
inference(step,[status(thm)],[t948,t106]) ).
cnf(t116,plain,
less_equal(sFlat0,sFlat1) = sFlat2,
inference(orient,[status(thm)],[t949]) ).
cnf(f12,axiom,
( less_equal(divide(X,Z),Y)
| ~ less_equal(divide(X,Y),Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',property_of_divide1) ).
fof(f12_nnf,plain,
! [X,Y,Z] :
( less_equal(divide(X,Z),Y)
| ~ less_equal(divide(X,Y),Z) ),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [X,Y,Z] :
( less_equal(divide(X,Z),Y)
| ~ less_equal(divide(X,Y),Z) ),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c12,plain,
( less_equal(divide(X0,X2),X1)
| ~ less_equal(divide(X0,X1),X2) ),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(t13,plain,
ifeq(less_equal(divide(X1,X2),X3),true,less_equal(divide(X1,X3),X2),true) = true,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(t66,plain,
ifeq(less_equal(divide(X1,X2),X3),true,less_equal(divide(X1,X3),X2),true) = true,
inference(orient,[status(thm)],[t13]) ).
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(t14,plain,
less_equal(divide(divide(X1,X2),divide(X3,X2)),divide(divide(X1,X3),X2)) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t27,plain,
less_equal(divide(divide(X1,X2),divide(X3,X2)),divide(divide(X1,X3),X2)) = true,
inference(orient,[status(thm)],[t14]) ).
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(t10,plain,
ifeq(less_equal(X1,X2),true,divide(X1,X2),zero) = zero,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t124,plain,
ifeq(less_equal(X1,X2),true,divide(X1,X2),zero) = zero,
inference(orient,[status(thm)],[t10]) ).
cnf(f14,hypothesis,
less_equal(a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_LE_b) ).
fof(f14_nnf,plain,
less_equal(a,b),
inference(nnf_transformation,[status(thm)],[f14]) ).
cnf(c14,plain,
less_equal(a,b),
inference(cnf_transformation,[status(esa)],[f14_nnf]) ).
cnf(t5,plain,
less_equal(a,b) = true,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(t33,plain,
less_equal(a,b) = true,
inference(orient,[status(thm)],[t5]) ).
cnf(t126,plain,
zero = ifeq(true,true,divide(a,b),zero),
inference(cp,[status(thm)],[t124,t33]) ).
cnf(t7,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t19,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t7]) ).
cnf(t951,plain,
zero = divide(a,b),
inference(step,[status(thm)],[t126,t19]) ).
cnf(t157,plain,
divide(a,b) = zero,
inference(orient,[status(thm)],[t951]) ).
cnf(t163,plain,
true = less_equal(divide(divide(a,X1),divide(b,X1)),divide(zero,X1)),
inference(cp,[status(thm)],[t27,t157]) ).
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(t3,plain,
divide(zero,X1) = zero,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t84,plain,
divide(zero,X1) = zero,
inference(orient,[status(thm)],[t3]) ).
cnf(t1064,plain,
true = less_equal(divide(divide(a,X1),divide(b,X1)),zero),
inference(step,[status(thm)],[t163,t84]) ).
cnf(t803,plain,
less_equal(divide(divide(a,X1),divide(b,X1)),zero) = true,
inference(orient,[status(thm)],[t1064]) ).
cnf(t804,plain,
true = less_equal(divide(sFlat0,divide(b,c)),zero),
inference(cp,[status(thm)],[t803,t96]) ).
cnf(t1065,plain,
true = less_equal(divide(sFlat0,sFlat1),zero),
inference(step,[status(thm)],[t804,t106]) ).
cnf(t818,plain,
less_equal(divide(sFlat0,sFlat1),zero) = true,
inference(orient,[status(thm)],[t1065]) ).
cnf(t827,plain,
true = ifeq(true,true,less_equal(divide(sFlat0,zero),sFlat1),true),
inference(cp,[status(thm)],[t66,t818]) ).
cnf(t1066,plain,
true = less_equal(divide(sFlat0,zero),sFlat1),
inference(step,[status(thm)],[t827,t19]) ).
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(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(t20,plain,
ifeq(less_equal(X1,X2),true,ifeq(less_equal(X2,X1),true,X1,X2),X2) = X2,
inference(orient,[status(thm)],[t11]) ).
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(t9,plain,
ifeq(divide(X1,X2),zero,less_equal(X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t36,plain,
ifeq(divide(X1,X2),zero,less_equal(X1,X2),true) = true,
inference(orient,[status(thm)],[t9]) ).
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(t6,plain,
less_equal(zero,X1) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t30,plain,
less_equal(zero,X1) = true,
inference(orient,[status(thm)],[t6]) ).
cnf(t32,plain,
zero = ifeq(less_equal(X1,zero),true,ifeq(true,true,X1,zero),zero),
inference(cp,[status(thm)],[t20,t30]) ).
cnf(t971,plain,
zero = ifeq(less_equal(X1,zero),true,X1,zero),
inference(step,[status(thm)],[t32,t19]) ).
cnf(t269,plain,
ifeq(less_equal(X1,zero),true,X1,zero) = zero,
inference(orient,[status(thm)],[t971]) ).
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(t74,plain,
divide(X1,X1) = zero,
inference(orient,[status(thm)],[t0]) ).
cnf(t75,plain,
true = ifeq(zero,zero,less_equal(X1,X1),true),
inference(cp,[status(thm)],[t36,t74]) ).
cnf(t950,plain,
true = less_equal(X1,X1),
inference(step,[status(thm)],[t75,t19]) ).
cnf(t133,plain,
less_equal(X1,X1) = true,
inference(orient,[status(thm)],[t950]) ).
cnf(t134,plain,
true = ifeq(true,true,less_equal(divide(X1,divide(X1,X2)),X2),true),
inference(cp,[status(thm)],[t66,t133]) ).
cnf(t980,plain,
true = less_equal(divide(X1,divide(X1,X2)),X2),
inference(step,[status(thm)],[t134,t19]) ).
cnf(t326,plain,
less_equal(divide(X1,divide(X1,X2)),X2) = true,
inference(orient,[status(thm)],[t980]) ).
cnf(t335,plain,
zero = ifeq(true,true,divide(X1,divide(X1,zero)),zero),
inference(cp,[status(thm)],[t269,t326]) ).
cnf(t981,plain,
zero = divide(X1,divide(X1,zero)),
inference(step,[status(thm)],[t335,t19]) ).
cnf(t360,plain,
divide(X1,divide(X1,zero)) = zero,
inference(orient,[status(thm)],[t981]) ).
cnf(t362,plain,
true = ifeq(zero,zero,less_equal(X1,divide(X1,zero)),true),
inference(cp,[status(thm)],[t36,t360]) ).
cnf(t984,plain,
true = less_equal(X1,divide(X1,zero)),
inference(step,[status(thm)],[t362,t19]) ).
cnf(t380,plain,
less_equal(X1,divide(X1,zero)) = true,
inference(orient,[status(thm)],[t984]) ).
cnf(t383,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)],[t20,t380]) ).
cnf(t986,plain,
divide(X1,zero) = ifeq(less_equal(divide(X1,zero),X1),true,X1,divide(X1,zero)),
inference(step,[status(thm)],[t383,t19]) ).
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(t8,plain,
less_equal(divide(X1,X2),X1) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t24,plain,
less_equal(divide(X1,X2),X1) = true,
inference(orient,[status(thm)],[t8]) ).
cnf(t987,plain,
divide(X1,zero) = ifeq(true,true,X1,divide(X1,zero)),
inference(step,[status(thm)],[t986,t24]) ).
cnf(t988,plain,
divide(X1,zero) = X1,
inference(step,[status(thm)],[t987,t19]) ).
cnf(t396,plain,
divide(X1,zero) = X1,
inference(orient,[status(thm)],[t988]) ).
cnf(t1067,plain,
true = less_equal(sFlat0,sFlat1),
inference(step,[status(thm)],[t1066,t396]) ).
cnf(t1068,plain,
true = sFlat2,
inference(step,[status(thm)],[t1067,t116]) ).
cnf(t831,plain,
true = sFlat2,
inference(orient,[status(thm)],[t1068]) ).
cnf(f15,negated_conjecture,
~ less_equal(divide(a,c),divide(b,c)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_a_divide_c_LE_b_divide_c) ).
fof(f15_nnf,plain,
~ less_equal(divide(a,c),divide(b,c)),
inference(nnf_transformation,[status(thm)],[f15]) ).
fof(f15_sk,plain,
~ less_equal(divide(a,c),divide(b,c)),
inference(skolemisation,[status(esa)],[f15_nnf]) ).
cnf(c15,plain,
~ less_equal(divide(a,c),divide(b,c)),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(goal_0,negated_conjecture,
less_equal(divide(a,c),divide(b,c)) != true,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(g0_0,plain,
less_equal(sFlat0,divide(b,c)) != true,
inference(rw,[status(thm)],[goal_0,t96]) ).
cnf(g0_1,plain,
less_equal(sFlat0,sFlat1) != true,
inference(rw,[status(thm)],[g0_0,t106]) ).
cnf(g0_2,plain,
sFlat2 != true,
inference(rw,[status(thm)],[g0_1,t116]) ).
cnf(g0_3,plain,
sFlat2 != sFlat2,
inference(rw,[status(thm)],[g0_2,t831]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : HEN008-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/5.58 % Computer : n002.cluster.edu
% 0.11/5.58 % Model : x86_64 x86_64
% 0.11/5.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.58 % Memory : 8046.5625MB
% 0.11/5.58 % OS : Linux 6.8.0-71-generic
% 0.11/5.58 % CPULimit : 300
% 0.11/5.58 % WCLimit : 300
% 0.11/5.58 % DateTime : Wed Sep 23 16:17:10 UTC 2026
% 0.11/5.59 % CPUTime :
% 0.11/5.59 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 20.03/8.52 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 20.03/8.52 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------