%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : HEN012-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n005.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 01:37:12 PM UTC 2026
% Result : Unsatisfiable 7.60s 1.46s
% Output : Proof 7.60s
% Verified :
% Comments :
%------------------------------------------------------------------------------
cnf(t12,axiom,
sFlat0 = less_equal(a,a),
introduced(definition) ).
cnf(t70,plain,
less_equal(a,a) = sFlat0,
inference(orient,[status(thm)],[t12]) ).
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(t10,plain,
ifeq(less_equal(X1,X2),true,ifeq(less_equal(X2,X1),true,X1,X2),X2) = X2,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t14,plain,
ifeq(less_equal(X1,X2),true,ifeq(less_equal(X2,X1),true,X1,X2),X2) = X2,
inference(orient,[status(thm)],[t10]) ).
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(t3,plain,
less_equal(zero,X1) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t66,plain,
less_equal(zero,X1) = true,
inference(orient,[status(thm)],[t3]) ).
cnf(t68,plain,
zero = ifeq(less_equal(X1,zero),true,ifeq(true,true,X1,zero),zero),
inference(cp,[status(thm)],[t14,t66]) ).
cnf(t5,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t13,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t5]) ).
cnf(t130,plain,
zero = ifeq(less_equal(X1,zero),true,X1,zero),
inference(step,[status(thm)],[t68,t13]) ).
cnf(t78,plain,
ifeq(less_equal(X1,zero),true,X1,zero) = zero,
inference(orient,[status(thm)],[t130]) ).
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(t7,plain,
ifeq(divide(X1,X2),zero,less_equal(X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t69,plain,
ifeq(divide(X1,X2),zero,less_equal(X1,X2),true) = true,
inference(orient,[status(thm)],[t7]) ).
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(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/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(hi3,axiom,
less_equal(divide(divide(X0,X1),divide(X2,X1)),divide(divide(X0,X2),X1)) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t9,plain,
divide(divide(divide(X1,X2),divide(X3,X2)),divide(divide(X1,X3),X2)) = zero,
inference(hyper_resolution,[status(thm)],[hi0,hi3]) ).
cnf(t19,plain,
divide(divide(divide(X1,X2),divide(X3,X2)),divide(divide(X1,X3),X2)) = zero,
inference(orient,[status(thm)],[t9]) ).
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(hi2,axiom,
less_equal(divide(X0,X1),X0) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t4,plain,
divide(divide(X1,X2),X1) = zero,
inference(hyper_resolution,[status(thm)],[hi0,hi2]) ).
cnf(t16,plain,
divide(divide(X1,X2),X1) = zero,
inference(orient,[status(thm)],[t4]) ).
cnf(t23,plain,
zero = divide(divide(divide(X1,X1),divide(X2,X1)),zero),
inference(cp,[status(thm)],[t19,t16]) ).
cnf(t81,plain,
divide(divide(divide(X1,X1),divide(X2,X1)),zero) = zero,
inference(orient,[status(thm)],[t23]) ).
cnf(hi4,axiom,
less_equal(zero,X0) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t1,plain,
divide(zero,X1) = zero,
inference(hyper_resolution,[status(thm)],[hi0,hi4]) ).
cnf(t31,plain,
divide(zero,X1) = zero,
inference(orient,[status(thm)],[t1]) ).
cnf(t82,plain,
zero = divide(divide(divide(X1,X1),zero),zero),
inference(cp,[status(thm)],[t81,t31]) ).
cnf(t93,plain,
divide(divide(divide(X1,X1),zero),zero) = zero,
inference(orient,[status(thm)],[t82]) ).
cnf(t94,plain,
true = ifeq(zero,zero,less_equal(divide(divide(X1,X1),zero),zero),true),
inference(cp,[status(thm)],[t69,t93]) ).
cnf(t131,plain,
true = less_equal(divide(divide(X1,X1),zero),zero),
inference(step,[status(thm)],[t94,t13]) ).
cnf(t100,plain,
less_equal(divide(divide(X1,X1),zero),zero) = true,
inference(orient,[status(thm)],[t131]) ).
cnf(t101,plain,
zero = ifeq(true,true,divide(divide(X1,X1),zero),zero),
inference(cp,[status(thm)],[t78,t100]) ).
cnf(t132,plain,
zero = divide(divide(X1,X1),zero),
inference(step,[status(thm)],[t101,t13]) ).
cnf(t105,plain,
divide(divide(X1,X1),zero) = zero,
inference(orient,[status(thm)],[t132]) ).
cnf(t106,plain,
true = ifeq(zero,zero,less_equal(divide(X1,X1),zero),true),
inference(cp,[status(thm)],[t69,t105]) ).
cnf(t133,plain,
true = less_equal(divide(X1,X1),zero),
inference(step,[status(thm)],[t106,t13]) ).
cnf(t113,plain,
less_equal(divide(X1,X1),zero) = true,
inference(orient,[status(thm)],[t133]) ).
cnf(t114,plain,
zero = ifeq(true,true,divide(X1,X1),zero),
inference(cp,[status(thm)],[t78,t113]) ).
cnf(t134,plain,
zero = divide(X1,X1),
inference(step,[status(thm)],[t114,t13]) ).
cnf(t118,plain,
divide(X1,X1) = zero,
inference(orient,[status(thm)],[t134]) ).
cnf(f7,negated_conjecture,
~ less_equal(a,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_a_LE_a) ).
fof(f7_nnf,plain,
~ less_equal(a,a),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
~ less_equal(a,a),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
~ less_equal(a,a),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(goal_0,negated_conjecture,
less_equal(a,a) != true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(g0_0,plain,
sFlat0 != true,
inference(rw,[status(thm)],[goal_0,t70]) ).
cnf(g0_1,plain,
sFlat0 != ifeq(divide(a,a),zero,sFlat0,true),
inference(rw,[status(thm)],[g0_0]) ).
cnf(g0_2,plain,
sFlat0 != ifeq(zero,zero,sFlat0,true),
inference(rw,[status(thm)],[g0_1,t118]) ).
cnf(g0_3,plain,
sFlat0 != sFlat0,
inference(rw,[status(thm)],[g0_2,t13]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN012-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.36 % Computer : n005.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Wed Sep 23 16:18:02 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 7.60/1.46 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.60/1.46 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------