%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : HEN008-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n003.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 0.76s 6.17s
% Output : Proof 0.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of formulae : 53 ( 41 unt; 0 def)
% Number of atoms : 89 ( 15 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 78 ( 42 ~; 36 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-4 aty)
% Number of variables : 95 ( 3 sgn 38 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f0,axiom,
( quotient(X,Y,zero)
| ~ less_equal(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quotient_less_equal) ).
fof(f0_nnf,plain,
! [X,Y] :
( quotient(X,Y,zero)
| ~ less_equal(X,Y) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X,Y] :
( quotient(X,Y,zero)
| ~ less_equal(X,Y) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( quotient(X0,X1,zero)
| ~ less_equal(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi0,axiom,
ifeq(less_equal(X0,X1),true,quotient(X0,X1,zero),true) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(f16,hypothesis,
less_equal(a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aLEb) ).
fof(f16_nnf,plain,
less_equal(a,b),
inference(nnf_transformation,[status(thm)],[f16]) ).
cnf(c16,plain,
less_equal(a,b),
inference(cnf_transformation,[status(esa)],[f16_nnf]) ).
cnf(hi16,axiom,
less_equal(a,b) = true,
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(h0,plain,
quotient(a,b,zero) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi16]) ).
cnf(f3,axiom,
( less_equal(V4,V5)
| ~ quotient(V1,Z,V5)
| ~ quotient(V3,V2,V4)
| ~ quotient(X,Z,V3)
| ~ quotient(Y,Z,V2)
| ~ quotient(X,Y,V1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quotient_property) ).
fof(f3_nnf,plain,
! [X,Y,V1,Z,V2,V3,V4,V5] :
( less_equal(V4,V5)
| ~ quotient(V1,Z,V5)
| ~ quotient(V3,V2,V4)
| ~ quotient(X,Z,V3)
| ~ quotient(Y,Z,V2)
| ~ quotient(X,Y,V1) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [X,Y,V1,Z,V2,V3,V4,V5] :
( less_equal(V4,V5)
| ~ quotient(V1,Z,V5)
| ~ quotient(V3,V2,V4)
| ~ quotient(X,Z,V3)
| ~ quotient(Y,Z,V2)
| ~ quotient(X,Y,V1) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
( less_equal(X6,X7)
| ~ quotient(X2,X3,X7)
| ~ quotient(X5,X4,X6)
| ~ quotient(X0,X3,X5)
| ~ quotient(X1,X3,X4)
| ~ quotient(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(hi3,axiom,
ifeq(quotient(X0,X1,X2),true,ifeq(quotient(X1,X3,X4),true,ifeq(quotient(X0,X3,X5),true,ifeq(quotient(X5,X4,X6),true,ifeq(quotient(X2,X3,X7),true,less_equal(X6,X7),true),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(f18,hypothesis,
quotient(b,c,bQc),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bQc) ).
fof(f18_nnf,plain,
quotient(b,c,bQc),
inference(nnf_transformation,[status(thm)],[f18]) ).
cnf(c18,plain,
quotient(b,c,bQc),
inference(cnf_transformation,[status(esa)],[f18_nnf]) ).
cnf(hi18,axiom,
quotient(b,c,bQc) = true,
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(f17,hypothesis,
quotient(a,c,aQc),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aQc) ).
fof(f17_nnf,plain,
quotient(a,c,aQc),
inference(nnf_transformation,[status(thm)],[f17]) ).
cnf(c17,plain,
quotient(a,c,aQc),
inference(cnf_transformation,[status(esa)],[f17_nnf]) ).
cnf(hi17,axiom,
quotient(a,c,aQc) = true,
inference(equality_encoding,[status(esa)],[c17]) ).
cnf(f7,axiom,
quotient(X,Y,divide(X,Y)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure) ).
fof(f7_nnf,plain,
! [X,Y] : quotient(X,Y,divide(X,Y)),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [X,Y] : quotient(X,Y,divide(X,Y)),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
quotient(X0,X1,divide(X0,X1)),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(hi7,axiom,
quotient(X0,X1,divide(X0,X1)) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(f10,axiom,
quotient(zero,X,zero),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',zero_divide_anything_is_zero) ).
fof(f10_nnf,plain,
! [X] : quotient(zero,X,zero),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [X] : quotient(zero,X,zero),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
quotient(zero,X0,zero),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(hi10,axiom,
quotient(zero,X0,zero) = true,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(h113,plain,
less_equal(divide(aQc,bQc),zero) = true,
inference(hyper_resolution,[status(thm)],[hi3,h0,hi18,hi17,hi7,hi10]) ).
cnf(f14,axiom,
( less_equal(W2,Y)
| ~ quotient(X,Z,W2)
| ~ less_equal(W1,Z)
| ~ quotient(X,Y,W1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xQyLEz_implies_xQzLEy) ).
fof(f14_nnf,plain,
! [X,Y,W1,Z,W2] :
( less_equal(W2,Y)
| ~ quotient(X,Z,W2)
| ~ less_equal(W1,Z)
| ~ quotient(X,Y,W1) ),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [X,Y,W1,Z,W2] :
( less_equal(W2,Y)
| ~ quotient(X,Z,W2)
| ~ less_equal(W1,Z)
| ~ quotient(X,Y,W1) ),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c14,plain,
( less_equal(X4,X1)
| ~ quotient(X0,X3,X4)
| ~ less_equal(X2,X3)
| ~ quotient(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(hi14,axiom,
ifeq(quotient(X0,X1,X2),true,ifeq(less_equal(X2,X3),true,ifeq(quotient(X0,X3,X4),true,less_equal(X4,X1),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(f12,axiom,
quotient(X,zero,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_divde_zero_is_x) ).
fof(f12_nnf,plain,
! [X] : quotient(X,zero,X),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [X] : quotient(X,zero,X),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c12,plain,
quotient(X0,zero,X0),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(hi12,axiom,
quotient(X0,zero,X0) = true,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(t17,plain,
less_equal(aQc,bQc) = true,
inference(hyper_resolution,[status(thm)],[hi14,hi7,h113,hi12]) ).
cnf(t444,plain,
less_equal(aQc,bQc) = true,
inference(orient,[status(thm)],[t17]) ).
cnf(f19,negated_conjecture,
~ less_equal(aQc,bQc),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_aQcLEbQc) ).
fof(f19_nnf,plain,
~ less_equal(aQc,bQc),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
~ less_equal(aQc,bQc),
inference(skolemisation,[status(esa)],[f19_nnf]) ).
cnf(c19,plain,
~ less_equal(aQc,bQc),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(goal_0,negated_conjecture,
less_equal(aQc,bQc) != true,
inference(equality_encoding,[status(esa)],[c19]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t444]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN008-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/5.58 % Computer : n003.cluster.edu
% 0.10/5.58 % Model : x86_64 x86_64
% 0.10/5.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.58 % Memory : 8046.5625MB
% 0.10/5.58 % OS : Linux 6.8.0-71-generic
% 0.10/5.58 % CPULimit : 300
% 0.10/5.58 % WCLimit : 300
% 0.10/5.58 % DateTime : Wed Sep 23 16:15:56 UTC 2026
% 0.10/5.58 % CPUTime :
% 0.10/5.58 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.76/6.17 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.76/6.17 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------