%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : HEN009-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n009.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 01:37:09 PM UTC 2026
% Result : Unsatisfiable 5.73s 6.31s
% Output : Proof 5.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 9
% Syntax : Number of formulae : 50 ( 34 unt; 0 def)
% Number of atoms : 86 ( 24 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 78 ( 42 ~; 36 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 7 con; 0-4 aty)
% Number of variables : 76 ( 0 sgn 30 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f1,axiom,
( less_equal(X,Y)
| ~ quotient(X,Y,zero) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_equal_quotient) ).
fof(f1_nnf,plain,
! [X,Y] :
( less_equal(X,Y)
| ~ quotient(X,Y,zero) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X,Y] :
( less_equal(X,Y)
| ~ quotient(X,Y,zero) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( less_equal(X0,X1)
| ~ quotient(X0,X1,zero) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(hi1,axiom,
ifeq(quotient(X0,X1,zero),true,less_equal(X0,X1),true) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(f11,axiom,
quotient(X,X,zero),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_divide_x_is_zero) ).
fof(f11_nnf,plain,
! [X] : quotient(X,X,zero),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [X] : quotient(X,X,zero),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
quotient(X0,X0,zero),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(hi11,axiom,
quotient(X0,X0,zero) = true,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(h106,plain,
less_equal(V0,V0) = true,
inference(hyper_resolution,[status(thm)],[hi1,hi11]) ).
cnf(f14,axiom,
( less_equal(W2,Y)
| ~ quotient(X,Z,W2)
| ~ less_equal(W1,Z)
| ~ quotient(X,Y,W1) ),
file('/export/starexec/sandbox/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(f17,hypothesis,
quotient(identity,a,idQa),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_divide_a) ).
fof(f17_nnf,plain,
quotient(identity,a,idQa),
inference(nnf_transformation,[status(thm)],[f17]) ).
cnf(c17,plain,
quotient(identity,a,idQa),
inference(cnf_transformation,[status(esa)],[f17_nnf]) ).
cnf(hi17,axiom,
quotient(identity,a,idQa) = true,
inference(equality_encoding,[status(esa)],[c17]) ).
cnf(f18,hypothesis,
quotient(identity,idQa,idQ_idQa),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_divide_idQa) ).
fof(f18_nnf,plain,
quotient(identity,idQa,idQ_idQa),
inference(nnf_transformation,[status(thm)],[f18]) ).
cnf(c18,plain,
quotient(identity,idQa,idQ_idQa),
inference(cnf_transformation,[status(esa)],[f18_nnf]) ).
cnf(hi18,axiom,
quotient(identity,idQa,idQ_idQa) = true,
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(h499,plain,
less_equal(idQ_idQa,a) = true,
inference(hyper_resolution,[status(thm)],[hi14,hi17,h106,hi18]) ).
cnf(f15,axiom,
( less_equal(W1,W2)
| ~ quotient(Z,X,W2)
| ~ quotient(Z,Y,W1)
| ~ less_equal(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',xLEy_implies_zQyLEzQx) ).
fof(f15_nnf,plain,
! [X,Y,Z,W1,W2] :
( less_equal(W1,W2)
| ~ quotient(Z,X,W2)
| ~ quotient(Z,Y,W1)
| ~ less_equal(X,Y) ),
inference(nnf_transformation,[status(thm)],[f15]) ).
fof(f15_sk,plain,
! [X,Y,Z,W1,W2] :
( less_equal(W1,W2)
| ~ quotient(Z,X,W2)
| ~ quotient(Z,Y,W1)
| ~ less_equal(X,Y) ),
inference(skolemisation,[status(esa)],[f15_nnf]) ).
cnf(c15,plain,
( less_equal(X3,X4)
| ~ quotient(X2,X0,X4)
| ~ quotient(X2,X1,X3)
| ~ less_equal(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(hi15,axiom,
ifeq(less_equal(X0,X1),true,ifeq(quotient(X2,X1,X3),true,ifeq(quotient(X2,X0,X4),true,less_equal(X3,X4),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(f19,hypothesis,
quotient(identity,idQ_idQa,idQ__idQ_idQa),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_divide_idQ_idQa) ).
fof(f19_nnf,plain,
quotient(identity,idQ_idQa,idQ__idQ_idQa),
inference(nnf_transformation,[status(thm)],[f19]) ).
cnf(c19,plain,
quotient(identity,idQ_idQa,idQ__idQ_idQa),
inference(cnf_transformation,[status(esa)],[f19_nnf]) ).
cnf(hi19,axiom,
quotient(identity,idQ_idQa,idQ__idQ_idQa) = true,
inference(equality_encoding,[status(esa)],[c19]) ).
cnf(h1454,plain,
less_equal(idQa,idQ__idQ_idQa) = true,
inference(hyper_resolution,[status(thm)],[hi15,h499,hi17,hi19]) ).
cnf(h497,plain,
less_equal(idQ__idQ_idQa,idQa) = true,
inference(hyper_resolution,[status(thm)],[hi14,hi18,h106,hi19]) ).
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(hi5,axiom,
ifeq(less_equal(X0,X1),true,ifeq(less_equal(X1,X0),true,X0,X1),X1) = X1,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t0,plain,
idQa = idQ__idQ_idQa,
inference(hyper_resolution,[status(thm)],[hi5,h497,h1454]) ).
cnf(t1012,plain,
idQ__idQ_idQa = idQa,
inference(orient,[status(thm)],[t0]) ).
cnf(f20,negated_conjecture,
idQa != idQ__idQ_idQa,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_one_inversion_equals_three) ).
fof(f20_nnf,plain,
idQa != idQ__idQ_idQa,
inference(nnf_transformation,[status(thm)],[f20]) ).
fof(f20_sk,plain,
idQa != idQ__idQ_idQa,
inference(skolemisation,[status(esa)],[f20_nnf]) ).
cnf(c20,plain,
idQa != idQ__idQ_idQa,
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(goal_0,negated_conjecture,
idQa != idQ__idQ_idQa,
inference(equality_encoding,[status(esa)],[c20]) ).
cnf(g0_0,plain,
idQa != idQa,
inference(rw,[status(thm)],[goal_0,t1012]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN009-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/5.37 % Computer : n009.cluster.edu
% 0.10/5.37 % Model : x86_64 x86_64
% 0.10/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.37 % Memory : 8046.5625MB
% 0.10/5.37 % OS : Linux 6.8.0-71-generic
% 0.10/5.37 % CPULimit : 300
% 0.10/5.37 % WCLimit : 300
% 0.10/5.37 % DateTime : Wed Sep 23 16:15:04 UTC 2026
% 0.10/5.38 % CPUTime :
% 0.10/5.38 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 5.73/6.31 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.73/6.31 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------