%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : HEN005-4 : 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 01:37:00 PM UTC 2026
% Result : Unsatisfiable 6.35s 1.31s
% Output : Proof 6.35s
% Verified :
% Comments :
%------------------------------------------------------------------------------
cnf(t21,axiom,
sFlat0 = less_equal(a,c),
introduced(definition) ).
cnf(t107,plain,
less_equal(a,c) = sFlat0,
inference(orient,[status(thm)],[t21]) ).
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(t16,plain,
ifeq(divide(X1,X2),zero,less_equal(X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t105,plain,
ifeq(divide(X1,X2),zero,less_equal(X1,X2),true) = true,
inference(orient,[status(thm)],[t16]) ).
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(t18,plain,
divide(divide(divide(X1,X2),divide(X3,X2)),divide(divide(X1,X3),X2)) = zero,
inference(hyper_resolution,[status(thm)],[hi0,hi3]) ).
cnf(t32,plain,
divide(divide(divide(X1,X2),divide(X3,X2)),divide(divide(X1,X3),X2)) = zero,
inference(orient,[status(thm)],[t18]) ).
cnf(f11,hypothesis,
less_equal(a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_LE_b) ).
fof(f11_nnf,plain,
less_equal(a,b),
inference(nnf_transformation,[status(thm)],[f11]) ).
cnf(c11,plain,
less_equal(a,b),
inference(cnf_transformation,[status(esa)],[f11_nnf]) ).
cnf(hi11,axiom,
less_equal(a,b) = true,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(t3,plain,
divide(a,b) = zero,
inference(hyper_resolution,[status(thm)],[hi0,hi11]) ).
cnf(t52,plain,
divide(a,b) = zero,
inference(orient,[status(thm)],[t3]) ).
cnf(t54,plain,
zero = divide(divide(divide(a,X1),divide(b,X1)),divide(zero,X1)),
inference(cp,[status(thm)],[t32,t52]) ).
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(t5,plain,
divide(zero,X1) = zero,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t48,plain,
divide(zero,X1) = zero,
inference(orient,[status(thm)],[t5]) ).
cnf(t158,plain,
zero = divide(divide(divide(a,X1),divide(b,X1)),zero),
inference(step,[status(thm)],[t54,t48]) ).
cnf(f10,axiom,
divide(X,zero) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_divide_zero_is_x) ).
fof(f10_nnf,plain,
! [X] : divide(X,zero) = X,
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [X] : divide(X,zero) = X,
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
divide(X0,zero) = X0,
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(t2,plain,
divide(X1,zero) = X1,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(t22,plain,
divide(X1,zero) = X1,
inference(orient,[status(thm)],[t2]) ).
cnf(t159,plain,
zero = divide(divide(a,X1),divide(b,X1)),
inference(step,[status(thm)],[t158,t22]) ).
cnf(t121,plain,
divide(divide(a,X1),divide(b,X1)) = zero,
inference(orient,[status(thm)],[t159]) ).
cnf(f12,hypothesis,
less_equal(b,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_LE_c) ).
fof(f12_nnf,plain,
less_equal(b,c),
inference(nnf_transformation,[status(thm)],[f12]) ).
cnf(c12,plain,
less_equal(b,c),
inference(cnf_transformation,[status(esa)],[f12_nnf]) ).
cnf(hi12,axiom,
less_equal(b,c) = true,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(t4,plain,
divide(b,c) = zero,
inference(hyper_resolution,[status(thm)],[hi0,hi12]) ).
cnf(t49,plain,
divide(b,c) = zero,
inference(orient,[status(thm)],[t4]) ).
cnf(t122,plain,
zero = divide(divide(a,c),zero),
inference(cp,[status(thm)],[t121,t49]) ).
cnf(t160,plain,
zero = divide(a,c),
inference(step,[status(thm)],[t122,t22]) ).
cnf(t131,plain,
divide(a,c) = zero,
inference(orient,[status(thm)],[t160]) ).
cnf(t132,plain,
true = ifeq(zero,zero,less_equal(a,c),true),
inference(cp,[status(thm)],[t105,t131]) ).
cnf(t14,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t23,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t14]) ).
cnf(t161,plain,
true = less_equal(a,c),
inference(step,[status(thm)],[t132,t23]) ).
cnf(t162,plain,
true = sFlat0,
inference(step,[status(thm)],[t161,t107]) ).
cnf(t138,plain,
true = sFlat0,
inference(orient,[status(thm)],[t162]) ).
cnf(f13,negated_conjecture,
~ less_equal(a,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_a_LE_c) ).
fof(f13_nnf,plain,
~ less_equal(a,c),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
~ less_equal(a,c),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c13,plain,
~ less_equal(a,c),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(goal_0,negated_conjecture,
less_equal(a,c) != true,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(g0_0,plain,
sFlat0 != true,
inference(rw,[status(thm)],[goal_0,t107]) ).
cnf(g0_1,plain,
sFlat0 != sFlat0,
inference(rw,[status(thm)],[g0_0,t138]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN005-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.12/0.36 % Computer : n002.cluster.edu
% 0.12/0.36 % Model : x86_64 x86_64
% 0.12/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.36 % Memory : 8046.5625MB
% 0.12/0.36 % OS : Linux 6.8.0-71-generic
% 0.12/0.36 % CPULimit : 300
% 0.12/0.36 % WCLimit : 300
% 0.12/0.36 % DateTime : Wed Sep 23 16:14:18 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 6.35/1.31 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.35/1.31 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------