%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : HEN007-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n018.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 01:37:04 PM UTC 2026
% Result : Unsatisfiable 8.08s 1.77s
% Output : Proof 8.08s
% Verified :
% Comments :
%------------------------------------------------------------------------------
cnf(t9,axiom,
sFlat0 = divide(c,b),
introduced(definition) ).
cnf(t14,plain,
divide(c,b) = sFlat0,
inference(orient,[status(thm)],[t9]) ).
cnf(t10,axiom,
sFlat1 = divide(c,a),
introduced(definition) ).
cnf(t15,plain,
divide(c,a) = sFlat1,
inference(orient,[status(thm)],[t10]) ).
cnf(t11,axiom,
sFlat2 = less_equal(divide(c,b),divide(c,a)),
introduced(definition) ).
cnf(t444,plain,
sFlat2 = less_equal(sFlat0,divide(c,a)),
inference(step,[status(thm)],[t11,t14]) ).
cnf(t445,plain,
sFlat2 = less_equal(sFlat0,sFlat1),
inference(step,[status(thm)],[t444,t15]) ).
cnf(t47,plain,
less_equal(sFlat0,sFlat1) = sFlat2,
inference(orient,[status(thm)],[t445]) ).
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(t4,plain,
less_equal(divide(X1,X2),X1) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t19,plain,
less_equal(divide(X1,X2),X1) = true,
inference(orient,[status(thm)],[t4]) ).
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(t7,plain,
ifeq(less_equal(X1,X2),true,ifeq(less_equal(X2,X1),true,X1,X2),X2) = X2,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t13,plain,
ifeq(less_equal(X1,X2),true,ifeq(less_equal(X2,X1),true,X1,X2),X2) = X2,
inference(orient,[status(thm)],[t7]) ).
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(t5,plain,
ifeq(divide(X1,X2),zero,less_equal(X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t39,plain,
ifeq(divide(X1,X2),zero,less_equal(X1,X2),true) = true,
inference(orient,[status(thm)],[t5]) ).
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(t2,plain,
less_equal(zero,X1) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t33,plain,
less_equal(zero,X1) = true,
inference(orient,[status(thm)],[t2]) ).
cnf(t35,plain,
zero = ifeq(less_equal(X1,zero),true,ifeq(true,true,X1,zero),zero),
inference(cp,[status(thm)],[t13,t33]) ).
cnf(t3,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t12,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t3]) ).
cnf(t455,plain,
zero = ifeq(less_equal(X1,zero),true,X1,zero),
inference(step,[status(thm)],[t35,t12]) ).
cnf(t91,plain,
ifeq(less_equal(X1,zero),true,X1,zero) = zero,
inference(orient,[status(thm)],[t455]) ).
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(t8,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)],[t8]) ).
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(t6,plain,
ifeq(less_equal(X1,X2),true,divide(X1,X2),zero) = zero,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t51,plain,
ifeq(less_equal(X1,X2),true,divide(X1,X2),zero) = zero,
inference(orient,[status(thm)],[t6]) ).
cnf(t25,plain,
true = less_equal(divide(sFlat0,divide(X1,b)),divide(divide(c,X1),b)),
inference(cp,[status(thm)],[t24,t14]) ).
cnf(t269,plain,
less_equal(divide(sFlat0,divide(X1,b)),divide(divide(c,X1),b)) = true,
inference(orient,[status(thm)],[t25]) ).
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(t1,plain,
less_equal(a,b) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t36,plain,
less_equal(a,b) = true,
inference(orient,[status(thm)],[t1]) ).
cnf(t54,plain,
zero = ifeq(true,true,divide(a,b),zero),
inference(cp,[status(thm)],[t51,t36]) ).
cnf(t447,plain,
zero = divide(a,b),
inference(step,[status(thm)],[t54,t12]) ).
cnf(t72,plain,
divide(a,b) = zero,
inference(orient,[status(thm)],[t447]) ).
cnf(t273,plain,
true = less_equal(divide(sFlat0,zero),divide(divide(c,a),b)),
inference(cp,[status(thm)],[t269,t72]) ).
cnf(t486,plain,
true = less_equal(divide(sFlat0,zero),divide(sFlat1,b)),
inference(step,[status(thm)],[t273,t15]) ).
cnf(t286,plain,
less_equal(divide(sFlat0,zero),divide(sFlat1,b)) = true,
inference(orient,[status(thm)],[t486]) ).
cnf(t287,plain,
zero = ifeq(true,true,divide(divide(sFlat0,zero),divide(sFlat1,b)),zero),
inference(cp,[status(thm)],[t51,t286]) ).
cnf(t491,plain,
zero = divide(divide(sFlat0,zero),divide(sFlat1,b)),
inference(step,[status(thm)],[t287,t12]) ).
cnf(t310,plain,
divide(divide(sFlat0,zero),divide(sFlat1,b)) = zero,
inference(orient,[status(thm)],[t491]) ).
cnf(t312,plain,
true = less_equal(divide(divide(sFlat0,divide(sFlat1,b)),divide(zero,divide(sFlat1,b))),zero),
inference(cp,[status(thm)],[t24,t310]) ).
cnf(t55,plain,
zero = ifeq(true,true,divide(zero,X1),zero),
inference(cp,[status(thm)],[t51,t33]) ).
cnf(t448,plain,
zero = divide(zero,X1),
inference(step,[status(thm)],[t55,t12]) ).
cnf(t76,plain,
divide(zero,X1) = zero,
inference(orient,[status(thm)],[t448]) ).
cnf(t500,plain,
true = less_equal(divide(divide(sFlat0,divide(sFlat1,b)),zero),zero),
inference(step,[status(thm)],[t312,t76]) ).
cnf(t353,plain,
less_equal(divide(divide(sFlat0,divide(sFlat1,b)),zero),zero) = true,
inference(orient,[status(thm)],[t500]) ).
cnf(t354,plain,
zero = ifeq(true,true,divide(divide(sFlat0,divide(sFlat1,b)),zero),zero),
inference(cp,[status(thm)],[t91,t353]) ).
cnf(t501,plain,
zero = divide(divide(sFlat0,divide(sFlat1,b)),zero),
inference(step,[status(thm)],[t354,t12]) ).
cnf(t360,plain,
divide(divide(sFlat0,divide(sFlat1,b)),zero) = zero,
inference(orient,[status(thm)],[t501]) ).
cnf(t362,plain,
true = ifeq(zero,zero,less_equal(divide(sFlat0,divide(sFlat1,b)),zero),true),
inference(cp,[status(thm)],[t39,t360]) ).
cnf(t502,plain,
true = less_equal(divide(sFlat0,divide(sFlat1,b)),zero),
inference(step,[status(thm)],[t362,t12]) ).
cnf(t366,plain,
less_equal(divide(sFlat0,divide(sFlat1,b)),zero) = true,
inference(orient,[status(thm)],[t502]) ).
cnf(t367,plain,
zero = ifeq(true,true,divide(sFlat0,divide(sFlat1,b)),zero),
inference(cp,[status(thm)],[t91,t366]) ).
cnf(t503,plain,
zero = divide(sFlat0,divide(sFlat1,b)),
inference(step,[status(thm)],[t367,t12]) ).
cnf(t371,plain,
divide(sFlat0,divide(sFlat1,b)) = zero,
inference(orient,[status(thm)],[t503]) ).
cnf(t373,plain,
true = ifeq(zero,zero,less_equal(sFlat0,divide(sFlat1,b)),true),
inference(cp,[status(thm)],[t39,t371]) ).
cnf(t504,plain,
true = less_equal(sFlat0,divide(sFlat1,b)),
inference(step,[status(thm)],[t373,t12]) ).
cnf(t376,plain,
less_equal(sFlat0,divide(sFlat1,b)) = true,
inference(orient,[status(thm)],[t504]) ).
cnf(t377,plain,
divide(sFlat1,b) = ifeq(true,true,ifeq(less_equal(divide(sFlat1,b),sFlat0),true,sFlat0,divide(sFlat1,b)),divide(sFlat1,b)),
inference(cp,[status(thm)],[t13,t376]) ).
cnf(t505,plain,
divide(sFlat1,b) = ifeq(less_equal(divide(sFlat1,b),sFlat0),true,sFlat0,divide(sFlat1,b)),
inference(step,[status(thm)],[t377,t12]) ).
cnf(t21,plain,
true = less_equal(sFlat1,c),
inference(cp,[status(thm)],[t19,t15]) ).
cnf(t65,plain,
less_equal(sFlat1,c) = true,
inference(orient,[status(thm)],[t21]) ).
cnf(t66,plain,
zero = ifeq(true,true,divide(sFlat1,c),zero),
inference(cp,[status(thm)],[t51,t65]) ).
cnf(t450,plain,
zero = divide(sFlat1,c),
inference(step,[status(thm)],[t66,t12]) ).
cnf(t81,plain,
divide(sFlat1,c) = zero,
inference(orient,[status(thm)],[t450]) ).
cnf(t83,plain,
true = less_equal(divide(divide(sFlat1,X1),divide(c,X1)),divide(zero,X1)),
inference(cp,[status(thm)],[t24,t81]) ).
cnf(t467,plain,
true = less_equal(divide(divide(sFlat1,X1),divide(c,X1)),zero),
inference(step,[status(thm)],[t83,t76]) ).
cnf(t137,plain,
less_equal(divide(divide(sFlat1,X1),divide(c,X1)),zero) = true,
inference(orient,[status(thm)],[t467]) ).
cnf(t138,plain,
true = less_equal(divide(divide(sFlat1,b),sFlat0),zero),
inference(cp,[status(thm)],[t137,t14]) ).
cnf(t145,plain,
less_equal(divide(divide(sFlat1,b),sFlat0),zero) = true,
inference(orient,[status(thm)],[t138]) ).
cnf(t146,plain,
zero = ifeq(true,true,divide(divide(sFlat1,b),sFlat0),zero),
inference(cp,[status(thm)],[t91,t145]) ).
cnf(t468,plain,
zero = divide(divide(sFlat1,b),sFlat0),
inference(step,[status(thm)],[t146,t12]) ).
cnf(t152,plain,
divide(divide(sFlat1,b),sFlat0) = zero,
inference(orient,[status(thm)],[t468]) ).
cnf(t154,plain,
true = ifeq(zero,zero,less_equal(divide(sFlat1,b),sFlat0),true),
inference(cp,[status(thm)],[t39,t152]) ).
cnf(t469,plain,
true = less_equal(divide(sFlat1,b),sFlat0),
inference(step,[status(thm)],[t154,t12]) ).
cnf(t158,plain,
less_equal(divide(sFlat1,b),sFlat0) = true,
inference(orient,[status(thm)],[t469]) ).
cnf(t506,plain,
divide(sFlat1,b) = ifeq(true,true,sFlat0,divide(sFlat1,b)),
inference(step,[status(thm)],[t505,t158]) ).
cnf(t507,plain,
divide(sFlat1,b) = sFlat0,
inference(step,[status(thm)],[t506,t12]) ).
cnf(t379,plain,
divide(sFlat1,b) = sFlat0,
inference(orient,[status(thm)],[t507]) ).
cnf(t380,plain,
true = less_equal(sFlat0,sFlat1),
inference(cp,[status(thm)],[t19,t379]) ).
cnf(t508,plain,
true = sFlat2,
inference(step,[status(thm)],[t380,t47]) ).
cnf(t389,plain,
true = sFlat2,
inference(orient,[status(thm)],[t508]) ).
cnf(f8,negated_conjecture,
~ less_equal(divide(c,b),divide(c,a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_c_divide_b_LE_c_divide_a) ).
fof(f8_nnf,plain,
~ less_equal(divide(c,b),divide(c,a)),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
~ less_equal(divide(c,b),divide(c,a)),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
~ less_equal(divide(c,b),divide(c,a)),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(goal_0,negated_conjecture,
less_equal(divide(c,b),divide(c,a)) != true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(g0_0,plain,
less_equal(sFlat0,divide(c,a)) != true,
inference(rw,[status(thm)],[goal_0,t14]) ).
cnf(g0_1,plain,
less_equal(sFlat0,sFlat1) != true,
inference(rw,[status(thm)],[g0_0,t15]) ).
cnf(g0_2,plain,
sFlat2 != true,
inference(rw,[status(thm)],[g0_1,t47]) ).
cnf(g0_3,plain,
sFlat2 != sFlat2,
inference(rw,[status(thm)],[g0_2,t389]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN007-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.12/0.59 % Computer : n018.cluster.edu
% 0.12/0.59 % Model : x86_64 x86_64
% 0.12/0.59 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.59 % Memory : 8046.5625MB
% 0.12/0.59 % OS : Linux 6.8.0-71-generic
% 0.12/0.59 % CPULimit : 300
% 0.12/0.59 % WCLimit : 300
% 0.12/0.59 % DateTime : Wed Sep 23 16:15:03 UTC 2026
% 0.12/0.59 % CPUTime :
% 0.12/0.59 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 8.08/1.77 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.08/1.77 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------