%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : HEN010-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n006.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 01:37:10 PM UTC 2026
% Result : Unsatisfiable 9.72s 1.88s
% Output : Proof 9.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 14
% Syntax : Number of formulae : 77 ( 53 unt; 0 def)
% Number of atoms : 141 ( 31 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 134 ( 70 ~; 64 |; 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 : 151 ( 3 sgn 60 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f1,axiom,
( less_equal(X,Y)
| ~ quotient(X,Y,zero) ),
file('/export/starexec/sandbox2/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/sandbox2/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(h0,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/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(f18,hypothesis,
quotient(identity,a,idQa),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_divide_a) ).
fof(f18_nnf,plain,
quotient(identity,a,idQa),
inference(nnf_transformation,[status(thm)],[f18]) ).
cnf(c18,plain,
quotient(identity,a,idQa),
inference(cnf_transformation,[status(esa)],[f18_nnf]) ).
cnf(hi18,axiom,
quotient(identity,a,idQa) = true,
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(f19,hypothesis,
quotient(identity,idQa,idQ_idQa),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_divide_idQa) ).
fof(f19_nnf,plain,
quotient(identity,idQa,idQ_idQa),
inference(nnf_transformation,[status(thm)],[f19]) ).
cnf(c19,plain,
quotient(identity,idQa,idQ_idQa),
inference(cnf_transformation,[status(esa)],[f19_nnf]) ).
cnf(hi19,axiom,
quotient(identity,idQa,idQ_idQa) = true,
inference(equality_encoding,[status(esa)],[c19]) ).
cnf(h1,plain,
less_equal(idQ_idQa,a) = true,
inference(hyper_resolution,[status(thm)],[hi14,hi18,h0,hi19]) ).
cnf(f15,axiom,
( less_equal(W1,W2)
| ~ quotient(Z,X,W2)
| ~ quotient(Z,Y,W1)
| ~ less_equal(X,Y) ),
file('/export/starexec/sandbox2/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(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(f20,hypothesis,
quotient(idQa,idQ_idQa,idQa_Q__idQ_idQa),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_divide_idQ_idQa) ).
fof(f20_nnf,plain,
quotient(idQa,idQ_idQa,idQa_Q__idQ_idQa),
inference(nnf_transformation,[status(thm)],[f20]) ).
cnf(c20,plain,
quotient(idQa,idQ_idQa,idQa_Q__idQ_idQa),
inference(cnf_transformation,[status(esa)],[f20_nnf]) ).
cnf(hi20,axiom,
quotient(idQa,idQ_idQa,idQa_Q__idQ_idQa) = true,
inference(equality_encoding,[status(esa)],[c20]) ).
cnf(h48,plain,
less_equal(divide(idQa,a),idQa_Q__idQ_idQa) = true,
inference(hyper_resolution,[status(thm)],[hi15,h1,hi7,hi20]) ).
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(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(h90,plain,
less_equal(idQa,divide(idQa,a)) = true,
inference(hyper_resolution,[status(thm)],[hi3,hi18,hi11,hi18,hi12,hi7]) ).
cnf(f13,axiom,
( less_equal(X,Z)
| ~ less_equal(Y,Z)
| ~ less_equal(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity_of_less_equal) ).
fof(f13_nnf,plain,
! [X,Y,Z] :
( less_equal(X,Z)
| ~ less_equal(Y,Z)
| ~ less_equal(X,Y) ),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [X,Y,Z] :
( less_equal(X,Z)
| ~ less_equal(Y,Z)
| ~ less_equal(X,Y) ),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c13,plain,
( less_equal(X0,X2)
| ~ less_equal(X1,X2)
| ~ less_equal(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(hi13,axiom,
ifeq(less_equal(X0,X1),true,ifeq(less_equal(X1,X2),true,less_equal(X0,X2),true),true) = true,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(h320,plain,
less_equal(idQa,idQa_Q__idQ_idQa) = true,
inference(hyper_resolution,[status(thm)],[hi13,h90,h48]) ).
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(hi4,axiom,
less_equal(zero,X0) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(h3,plain,
less_equal(idQa_Q__idQ_idQa,idQa) = true,
inference(hyper_resolution,[status(thm)],[hi15,hi4,hi20,hi12]) ).
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(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_Q__idQ_idQa = idQa,
inference(hyper_resolution,[status(thm)],[hi5,h3,h320]) ).
cnf(t1429,plain,
idQa = idQa_Q__idQ_idQa,
inference(orient,[status(thm)],[t0]) ).
cnf(f21,negated_conjecture,
idQa != idQa_Q__idQ_idQa,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_idQa_equals_idQa_Q__idQ_idQa) ).
fof(f21_nnf,plain,
idQa != idQa_Q__idQ_idQa,
inference(nnf_transformation,[status(thm)],[f21]) ).
fof(f21_sk,plain,
idQa != idQa_Q__idQ_idQa,
inference(skolemisation,[status(esa)],[f21_nnf]) ).
cnf(c21,plain,
idQa != idQa_Q__idQ_idQa,
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(goal_0,negated_conjecture,
idQa_Q__idQ_idQa != idQa,
inference(equality_encoding,[status(esa)],[c21]) ).
cnf(g0_0,plain,
idQa_Q__idQ_idQa != idQa_Q__idQ_idQa,
inference(rw,[status(thm)],[goal_0,t1429]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN010-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n006.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Wed Sep 23 16:16:11 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 9.72/1.88 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.72/1.88 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------