%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : HEN010-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n008.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 59.32s 8.28s
% Output : Proof 59.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 82
% Number of leaves : 14
% Syntax : Number of formulae : 275 ( 251 unt; 0 def)
% Number of atoms : 323 ( 237 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 102 ( 54 ~; 48 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 1 avg)
% Maximal term depth : 7 ( 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 : 321 ( 55 sgn 50 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(t235,plain,
ifeq(less_equal(X1,X2),true,ifeq(less_equal(X2,X1),true,X1,X2),X2) = X2,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t259,plain,
ifeq(less_equal(X1,X2),true,ifeq(less_equal(X2,X1),true,X1,X2),X2) = X2,
inference(orient,[status(thm)],[t235]) ).
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(t180,plain,
ifeq(quotient(X1,X2,zero),true,less_equal(X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t938,plain,
ifeq(quotient(X1,X2,zero),true,less_equal(X1,X2),true) = true,
inference(orient,[status(thm)],[t180]) ).
cnf(f7,axiom,
quotient(X,Y,divide(X,Y)),
file('/export/starexec/sandbox/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(t49,plain,
quotient(X1,X2,divide(X1,X2)) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t489,plain,
quotient(X1,X2,divide(X1,X2)) = true,
inference(orient,[status(thm)],[t49]) ).
cnf(f4,axiom,
less_equal(zero,X),
file('/export/starexec/sandbox/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(t10,plain,
less_equal(zero,X1) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t770,plain,
less_equal(zero,X1) = true,
inference(orient,[status(thm)],[t10]) ).
cnf(t771,plain,
X1 = ifeq(true,true,ifeq(less_equal(X1,zero),true,zero,X1),X1),
inference(cp,[status(thm)],[t259,t770]) ).
cnf(t48,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t256,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t48]) ).
cnf(t18479,plain,
X1 = ifeq(less_equal(X1,zero),true,zero,X1),
inference(step,[status(thm)],[t771,t256]) ).
cnf(t1261,plain,
ifeq(less_equal(X1,zero),true,zero,X1) = X1,
inference(orient,[status(thm)],[t18479]) ).
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/sandbox/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(t255,plain,
ifeq(quotient(X1,X2,X3),true,ifeq(quotient(X2,X4,X5),true,ifeq(quotient(X1,X4,X6),true,ifeq(quotient(X6,X5,X7),true,ifeq(quotient(X3,X4,X8),true,less_equal(X7,X8),true),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t794,plain,
ifeq(quotient(X1,X2,X3),true,ifeq(quotient(X2,X4,X5),true,ifeq(quotient(X1,X4,X6),true,ifeq(quotient(X6,X5,X7),true,ifeq(quotient(X3,X4,X8),true,less_equal(X7,X8),true),true),true),true),true) = true,
inference(orient,[status(thm)],[t255]) ).
cnf(t795,plain,
true = ifeq(true,true,ifeq(quotient(X1,X2,X3),true,ifeq(quotient(X4,X2,X5),true,ifeq(quotient(X5,X3,X6),true,ifeq(quotient(divide(X4,X1),X2,X7),true,less_equal(X6,X7),true),true),true),true),true),
inference(cp,[status(thm)],[t794,t489]) ).
cnf(t19006,plain,
true = ifeq(quotient(X1,X2,X3),true,ifeq(quotient(X4,X2,X5),true,ifeq(quotient(X5,X3,X6),true,ifeq(quotient(divide(X4,X1),X2,X7),true,less_equal(X6,X7),true),true),true),true),
inference(step,[status(thm)],[t795,t256]) ).
cnf(t5985,plain,
ifeq(quotient(X1,X2,X3),true,ifeq(quotient(X4,X2,X5),true,ifeq(quotient(X5,X3,X6),true,ifeq(quotient(divide(X4,X1),X2,X7),true,less_equal(X6,X7),true),true),true),true) = true,
inference(orient,[status(thm)],[t19006]) ).
cnf(f2,axiom,
( less_equal(Z,X)
| ~ quotient(X,Y,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',divisor_existence) ).
fof(f2_nnf,plain,
! [X,Y,Z] :
( less_equal(Z,X)
| ~ quotient(X,Y,Z) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X,Y,Z] :
( less_equal(Z,X)
| ~ quotient(X,Y,Z) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( less_equal(X2,X0)
| ~ quotient(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi2,axiom,
ifeq(quotient(X0,X1,X2),true,less_equal(X2,X0),true) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(f11,hypothesis,
quotient(idQa,idQ_idQa,idQa_Q__idQ_idQa),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_divide_idQ_idQa) ).
fof(f11_nnf,plain,
quotient(idQa,idQ_idQa,idQa_Q__idQ_idQa),
inference(nnf_transformation,[status(thm)],[f11]) ).
cnf(c11,plain,
quotient(idQa,idQ_idQa,idQa_Q__idQ_idQa),
inference(cnf_transformation,[status(esa)],[f11_nnf]) ).
cnf(hi11,axiom,
quotient(idQa,idQ_idQa,idQa_Q__idQ_idQa) = true,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(h28,plain,
less_equal(idQa_Q__idQ_idQa,idQa) = true,
inference(hyper_resolution,[status(thm)],[hi2,hi11]) ).
cnf(f0,axiom,
( quotient(X,Y,zero)
| ~ less_equal(X,Y) ),
file('/export/starexec/sandbox/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(h142,plain,
quotient(idQa_Q__idQ_idQa,idQa,zero) = true,
inference(hyper_resolution,[status(thm)],[hi0,h28]) ).
cnf(h285,plain,
less_equal(zero,idQa_Q__idQ_idQa) = true,
inference(hyper_resolution,[status(thm)],[hi2,h142]) ).
cnf(h298,plain,
quotient(zero,idQa_Q__idQ_idQa,zero) = true,
inference(hyper_resolution,[status(thm)],[hi0,h285]) ).
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(hi7,axiom,
quotient(X0,X1,divide(X0,X1)) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(f9,hypothesis,
quotient(identity,a,idQa),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_divide_a) ).
fof(f9_nnf,plain,
quotient(identity,a,idQa),
inference(nnf_transformation,[status(thm)],[f9]) ).
cnf(c9,plain,
quotient(identity,a,idQa),
inference(cnf_transformation,[status(esa)],[f9_nnf]) ).
cnf(hi9,axiom,
quotient(identity,a,idQa) = true,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(h7,plain,
less_equal(divide(idQa,divide(V0,a)),divide(divide(identity,V0),a)) = true,
inference(hyper_resolution,[status(thm)],[hi3,hi7,hi7,hi9,hi7,hi7]) ).
cnf(h134,plain,
quotient(divide(idQa,divide(V0,a)),divide(divide(identity,V0),a),zero) = true,
inference(hyper_resolution,[status(thm)],[hi0,h7]) ).
cnf(h810,plain,
less_equal(divide(divide(divide(idQa,divide(V0,a)),idQa_Q__idQ_idQa),divide(divide(divide(identity,V0),a),idQa_Q__idQ_idQa)),zero) = true,
inference(hyper_resolution,[status(thm)],[hi3,h134,hi7,hi7,hi7,h298]) ).
cnf(h3,plain,
less_equal(divide(V0,V1),V0) = true,
inference(hyper_resolution,[status(thm)],[hi2,hi7]) ).
cnf(h131,plain,
quotient(divide(V0,V1),V0,zero) = true,
inference(hyper_resolution,[status(thm)],[hi0,h3]) ).
cnf(h668,plain,
less_equal(zero,divide(V0,V1)) = true,
inference(hyper_resolution,[status(thm)],[hi2,h131]) ).
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(t241,plain,
divide(divide(divide(idQa,divide(X1,a)),idQa_Q__idQ_idQa),divide(divide(divide(identity,X1),a),idQa_Q__idQ_idQa)) = zero,
inference(hyper_resolution,[status(thm)],[hi5,h668,h810]) ).
cnf(t272,plain,
divide(divide(divide(idQa,divide(X1,a)),idQa_Q__idQ_idQa),divide(divide(divide(identity,X1),a),idQa_Q__idQ_idQa)) = zero,
inference(orient,[status(thm)],[t241]) ).
cnf(h26,plain,
less_equal(divide(divide(V0,idQ_idQa),idQa_Q__idQ_idQa),divide(divide(V0,idQa),idQ_idQa)) = true,
inference(hyper_resolution,[status(thm)],[hi3,hi7,hi11,hi7,hi7,hi7]) ).
cnf(h152,plain,
quotient(divide(divide(V0,idQ_idQa),idQa_Q__idQ_idQa),divide(divide(V0,idQa),idQ_idQa),zero) = true,
inference(hyper_resolution,[status(thm)],[hi0,h26]) ).
cnf(f8,axiom,
( Z = W
| ~ quotient(X,Y,W)
| ~ quotient(X,Y,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',well_defined) ).
fof(f8_nnf,plain,
! [X,Y,Z,W] :
( Z = W
| ~ quotient(X,Y,W)
| ~ quotient(X,Y,Z) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [X,Y,Z,W] :
( Z = W
| ~ quotient(X,Y,W)
| ~ quotient(X,Y,Z) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
( X2 = X3
| ~ quotient(X0,X1,X3)
| ~ quotient(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(hi8,axiom,
ifeq(quotient(X0,X1,X2),true,ifeq(quotient(X0,X1,X3),true,X2,X3),X3) = X3,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t206,plain,
divide(divide(divide(X1,idQ_idQa),idQa_Q__idQ_idQa),divide(divide(X1,idQa),idQ_idQa)) = zero,
inference(hyper_resolution,[status(thm)],[hi8,hi7,h152]) ).
cnf(t260,plain,
divide(divide(divide(X1,idQ_idQa),idQa_Q__idQ_idQa),divide(divide(X1,idQa),idQ_idQa)) = zero,
inference(orient,[status(thm)],[t206]) ).
cnf(f10,hypothesis,
quotient(identity,idQa,idQ_idQa),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_divide_idQa) ).
fof(f10_nnf,plain,
quotient(identity,idQa,idQ_idQa),
inference(nnf_transformation,[status(thm)],[f10]) ).
cnf(c10,plain,
quotient(identity,idQa,idQ_idQa),
inference(cnf_transformation,[status(esa)],[f10_nnf]) ).
cnf(hi10,axiom,
quotient(identity,idQa,idQ_idQa) = true,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(t5,plain,
divide(identity,idQa) = idQ_idQa,
inference(hyper_resolution,[status(thm)],[hi8,hi7,hi10]) ).
cnf(t475,plain,
divide(identity,idQa) = idQ_idQa,
inference(orient,[status(thm)],[t5]) ).
cnf(t476,plain,
zero = divide(divide(divide(identity,idQ_idQa),idQa_Q__idQ_idQa),divide(idQ_idQa,idQ_idQa)),
inference(cp,[status(thm)],[t260,t475]) ).
cnf(hi4,axiom,
less_equal(zero,X0) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(h0,plain,
quotient(zero,V0,zero) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi4]) ).
cnf(f6,axiom,
less_equal(X,identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_is_largest) ).
fof(f6_nnf,plain,
! [X] : less_equal(X,identity),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [X] : less_equal(X,identity),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
less_equal(X0,identity),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(hi6,axiom,
less_equal(X0,identity) = true,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(h1,plain,
quotient(V0,identity,zero) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi6]) ).
cnf(h124,plain,
less_equal(divide(idQ_idQa,divide(identity,idQa)),zero) = true,
inference(hyper_resolution,[status(thm)],[hi3,h1,hi7,hi10,hi7,h0]) ).
cnf(t30,plain,
divide(idQ_idQa,divide(identity,idQa)) = zero,
inference(hyper_resolution,[status(thm)],[hi5,hi4,h124]) ).
cnf(t471,plain,
divide(idQ_idQa,divide(identity,idQa)) = zero,
inference(orient,[status(thm)],[t30]) ).
cnf(t18425,plain,
divide(idQ_idQa,idQ_idQa) = zero,
inference(step,[status(thm)],[t471,t475]) ).
cnf(t480,plain,
divide(idQ_idQa,idQ_idQa) = zero,
inference(rw,[status(thm)],[t18425]) ).
cnf(t973,plain,
divide(idQ_idQa,idQ_idQa) = zero,
inference(orient,[status(thm)],[t480]) ).
cnf(t18525,plain,
zero = divide(divide(divide(identity,idQ_idQa),idQa_Q__idQ_idQa),zero),
inference(step,[status(thm)],[t476,t973]) ).
cnf(t1455,plain,
divide(divide(divide(identity,idQ_idQa),idQa_Q__idQ_idQa),zero) = zero,
inference(orient,[status(thm)],[t18525]) ).
cnf(t1456,plain,
true = quotient(divide(divide(identity,idQ_idQa),idQa_Q__idQ_idQa),zero,zero),
inference(cp,[status(thm)],[t489,t1455]) ).
cnf(t1457,plain,
quotient(divide(divide(identity,idQ_idQa),idQa_Q__idQ_idQa),zero,zero) = true,
inference(orient,[status(thm)],[t1456]) ).
cnf(t1459,plain,
true = ifeq(true,true,less_equal(divide(divide(identity,idQ_idQa),idQa_Q__idQ_idQa),zero),true),
inference(cp,[status(thm)],[t938,t1457]) ).
cnf(t18526,plain,
true = less_equal(divide(divide(identity,idQ_idQa),idQa_Q__idQ_idQa),zero),
inference(step,[status(thm)],[t1459,t256]) ).
cnf(t1467,plain,
less_equal(divide(divide(identity,idQ_idQa),idQa_Q__idQ_idQa),zero) = true,
inference(orient,[status(thm)],[t18526]) ).
cnf(t1468,plain,
divide(divide(identity,idQ_idQa),idQa_Q__idQ_idQa) = ifeq(true,true,zero,divide(divide(identity,idQ_idQa),idQa_Q__idQ_idQa)),
inference(cp,[status(thm)],[t1261,t1467]) ).
cnf(t18527,plain,
divide(divide(identity,idQ_idQa),idQa_Q__idQ_idQa) = zero,
inference(step,[status(thm)],[t1468,t256]) ).
cnf(t1474,plain,
divide(divide(identity,idQ_idQa),idQa_Q__idQ_idQa) = zero,
inference(orient,[status(thm)],[t18527]) ).
cnf(t1475,plain,
true = quotient(divide(identity,idQ_idQa),idQa_Q__idQ_idQa,zero),
inference(cp,[status(thm)],[t489,t1474]) ).
cnf(t1478,plain,
quotient(divide(identity,idQ_idQa),idQa_Q__idQ_idQa,zero) = true,
inference(orient,[status(thm)],[t1475]) ).
cnf(t1480,plain,
true = ifeq(true,true,less_equal(divide(identity,idQ_idQa),idQa_Q__idQ_idQa),true),
inference(cp,[status(thm)],[t938,t1478]) ).
cnf(t18528,plain,
true = less_equal(divide(identity,idQ_idQa),idQa_Q__idQ_idQa),
inference(step,[status(thm)],[t1480,t256]) ).
cnf(t1488,plain,
less_equal(divide(identity,idQ_idQa),idQa_Q__idQ_idQa) = true,
inference(orient,[status(thm)],[t18528]) ).
cnf(t1490,plain,
idQa_Q__idQ_idQa = ifeq(true,true,ifeq(less_equal(idQa_Q__idQ_idQa,divide(identity,idQ_idQa)),true,divide(identity,idQ_idQa),idQa_Q__idQ_idQa),idQa_Q__idQ_idQa),
inference(cp,[status(thm)],[t259,t1488]) ).
cnf(t18529,plain,
idQa_Q__idQ_idQa = ifeq(less_equal(idQa_Q__idQ_idQa,divide(identity,idQ_idQa)),true,divide(identity,idQ_idQa),idQa_Q__idQ_idQa),
inference(step,[status(thm)],[t1490,t256]) ).
cnf(h10,plain,
less_equal(idQa,identity) = true,
inference(hyper_resolution,[status(thm)],[hi2,hi9]) ).
cnf(h69,plain,
quotient(idQa,identity,zero) = true,
inference(hyper_resolution,[status(thm)],[hi0,h10]) ).
cnf(h203,plain,
less_equal(divide(divide(idQa,V0),divide(identity,V0)),zero) = true,
inference(hyper_resolution,[status(thm)],[hi3,h69,hi7,hi7,hi7,h0]) ).
cnf(t59,plain,
divide(divide(idQa,X1),divide(identity,X1)) = zero,
inference(hyper_resolution,[status(thm)],[hi5,h668,h203]) ).
cnf(t321,plain,
divide(divide(idQa,X1),divide(identity,X1)) = zero,
inference(orient,[status(thm)],[t59]) ).
cnf(t0,plain,
divide(idQa,idQ_idQa) = idQa_Q__idQ_idQa,
inference(hyper_resolution,[status(thm)],[hi8,hi7,hi11]) ).
cnf(t451,plain,
divide(idQa,idQ_idQa) = idQa_Q__idQ_idQa,
inference(orient,[status(thm)],[t0]) ).
cnf(t453,plain,
zero = divide(idQa_Q__idQ_idQa,divide(identity,idQ_idQa)),
inference(cp,[status(thm)],[t321,t451]) ).
cnf(t1059,plain,
divide(idQa_Q__idQ_idQa,divide(identity,idQ_idQa)) = zero,
inference(orient,[status(thm)],[t453]) ).
cnf(t1060,plain,
true = quotient(idQa_Q__idQ_idQa,divide(identity,idQ_idQa),zero),
inference(cp,[status(thm)],[t489,t1059]) ).
cnf(t1208,plain,
quotient(idQa_Q__idQ_idQa,divide(identity,idQ_idQa),zero) = true,
inference(orient,[status(thm)],[t1060]) ).
cnf(t1210,plain,
true = ifeq(true,true,less_equal(idQa_Q__idQ_idQa,divide(identity,idQ_idQa)),true),
inference(cp,[status(thm)],[t938,t1208]) ).
cnf(t18473,plain,
true = less_equal(idQa_Q__idQ_idQa,divide(identity,idQ_idQa)),
inference(step,[status(thm)],[t1210,t256]) ).
cnf(t1218,plain,
less_equal(idQa_Q__idQ_idQa,divide(identity,idQ_idQa)) = true,
inference(orient,[status(thm)],[t18473]) ).
cnf(t18530,plain,
idQa_Q__idQ_idQa = ifeq(true,true,divide(identity,idQ_idQa),idQa_Q__idQ_idQa),
inference(step,[status(thm)],[t18529,t1218]) ).
cnf(t18531,plain,
idQa_Q__idQ_idQa = divide(identity,idQ_idQa),
inference(step,[status(thm)],[t18530,t256]) ).
cnf(t1493,plain,
divide(identity,idQ_idQa) = idQa_Q__idQ_idQa,
inference(orient,[status(thm)],[t18531]) ).
cnf(t1496,plain,
zero = divide(divide(divide(idQa,divide(idQ_idQa,a)),idQa_Q__idQ_idQa),divide(divide(idQa_Q__idQ_idQa,a),idQa_Q__idQ_idQa)),
inference(cp,[status(thm)],[t272,t1493]) ).
cnf(t242,plain,
ifeq(quotient(X1,X2,X3),true,ifeq(quotient(X1,X2,X4),true,X3,X4),X4) = X4,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t257,plain,
ifeq(quotient(X1,X2,X3),true,ifeq(quotient(X1,X2,X4),true,X3,X4),X4) = X4,
inference(orient,[status(thm)],[t242]) ).
cnf(t547,plain,
X1 = ifeq(true,true,ifeq(quotient(X2,X3,X1),true,divide(X2,X3),X1),X1),
inference(cp,[status(thm)],[t257,t489]) ).
cnf(t18543,plain,
X1 = ifeq(quotient(X2,X3,X1),true,divide(X2,X3),X1),
inference(step,[status(thm)],[t547,t256]) ).
cnf(t1573,plain,
ifeq(quotient(X1,X2,X3),true,divide(X1,X2),X3) = X3,
inference(orient,[status(thm)],[t18543]) ).
cnf(t178,plain,
ifeq(less_equal(X1,X2),true,quotient(X1,X2,zero),true) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t956,plain,
ifeq(less_equal(X1,X2),true,quotient(X1,X2,zero),true) = true,
inference(orient,[status(thm)],[t178]) ).
cnf(t179,plain,
ifeq(quotient(X1,X2,X3),true,less_equal(X3,X1),true) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t776,plain,
ifeq(quotient(X1,X2,X3),true,less_equal(X3,X1),true) = true,
inference(orient,[status(thm)],[t179]) ).
cnf(t777,plain,
true = ifeq(true,true,less_equal(divide(X1,X2),X1),true),
inference(cp,[status(thm)],[t776,t489]) ).
cnf(t18459,plain,
true = less_equal(divide(X1,X2),X1),
inference(step,[status(thm)],[t777,t256]) ).
cnf(t1077,plain,
less_equal(divide(X1,X2),X1) = true,
inference(orient,[status(thm)],[t18459]) ).
cnf(t1078,plain,
true = ifeq(true,true,quotient(divide(X1,X2),X1,zero),true),
inference(cp,[status(thm)],[t956,t1077]) ).
cnf(t18474,plain,
true = quotient(divide(X1,X2),X1,zero),
inference(step,[status(thm)],[t1078,t256]) ).
cnf(t1231,plain,
quotient(divide(X1,X2),X1,zero) = true,
inference(orient,[status(thm)],[t18474]) ).
cnf(t1574,plain,
zero = ifeq(true,true,divide(divide(X1,X2),X1),zero),
inference(cp,[status(thm)],[t1573,t1231]) ).
cnf(t18544,plain,
zero = divide(divide(X1,X2),X1),
inference(step,[status(thm)],[t1574,t256]) ).
cnf(t1612,plain,
divide(divide(X1,X2),X1) = zero,
inference(orient,[status(thm)],[t18544]) ).
cnf(t18654,plain,
zero = divide(divide(divide(idQa,divide(idQ_idQa,a)),idQa_Q__idQ_idQa),zero),
inference(step,[status(thm)],[t1496,t1612]) ).
cnf(t2438,plain,
divide(divide(divide(idQa,divide(idQ_idQa,a)),idQa_Q__idQ_idQa),zero) = zero,
inference(orient,[status(thm)],[t18654]) ).
cnf(t2441,plain,
true = quotient(divide(divide(idQa,divide(idQ_idQa,a)),idQa_Q__idQ_idQa),zero,zero),
inference(cp,[status(thm)],[t489,t2438]) ).
cnf(t2442,plain,
quotient(divide(divide(idQa,divide(idQ_idQa,a)),idQa_Q__idQ_idQa),zero,zero) = true,
inference(orient,[status(thm)],[t2441]) ).
cnf(t2444,plain,
true = ifeq(true,true,less_equal(divide(divide(idQa,divide(idQ_idQa,a)),idQa_Q__idQ_idQa),zero),true),
inference(cp,[status(thm)],[t938,t2442]) ).
cnf(t18655,plain,
true = less_equal(divide(divide(idQa,divide(idQ_idQa,a)),idQa_Q__idQ_idQa),zero),
inference(step,[status(thm)],[t2444,t256]) ).
cnf(t2452,plain,
less_equal(divide(divide(idQa,divide(idQ_idQa,a)),idQa_Q__idQ_idQa),zero) = true,
inference(orient,[status(thm)],[t18655]) ).
cnf(t2453,plain,
divide(divide(idQa,divide(idQ_idQa,a)),idQa_Q__idQ_idQa) = ifeq(true,true,zero,divide(divide(idQa,divide(idQ_idQa,a)),idQa_Q__idQ_idQa)),
inference(cp,[status(thm)],[t1261,t2452]) ).
cnf(t18656,plain,
divide(divide(idQa,divide(idQ_idQa,a)),idQa_Q__idQ_idQa) = zero,
inference(step,[status(thm)],[t2453,t256]) ).
cnf(t2459,plain,
divide(divide(idQa,divide(idQ_idQa,a)),idQa_Q__idQ_idQa) = zero,
inference(orient,[status(thm)],[t18656]) ).
cnf(t2462,plain,
true = quotient(divide(idQa,divide(idQ_idQa,a)),idQa_Q__idQ_idQa,zero),
inference(cp,[status(thm)],[t489,t2459]) ).
cnf(t2464,plain,
quotient(divide(idQa,divide(idQ_idQa,a)),idQa_Q__idQ_idQa,zero) = true,
inference(orient,[status(thm)],[t2462]) ).
cnf(h13,plain,
less_equal(divide(idQ_idQa,divide(a,idQa)),divide(idQa,idQa)) = true,
inference(hyper_resolution,[status(thm)],[hi3,hi9,hi7,hi10,hi7,hi7]) ).
cnf(h139,plain,
quotient(divide(idQ_idQa,divide(a,idQa)),divide(idQa,idQa),zero) = true,
inference(hyper_resolution,[status(thm)],[hi0,h13]) ).
cnf(t126,plain,
divide(divide(idQ_idQa,divide(a,idQa)),divide(idQa,idQa)) = zero,
inference(hyper_resolution,[status(thm)],[hi8,hi7,h139]) ).
cnf(t358,plain,
divide(divide(idQ_idQa,divide(a,idQa)),divide(idQa,idQa)) = zero,
inference(orient,[status(thm)],[t126]) ).
cnf(h116,plain,
less_equal(divide(idQa,idQa),zero) = true,
inference(hyper_resolution,[status(thm)],[hi3,h1,hi9,hi9,hi7,h0]) ).
cnf(t1,plain,
divide(idQa,idQa) = zero,
inference(hyper_resolution,[status(thm)],[hi5,hi4,h116]) ).
cnf(t439,plain,
divide(idQa,idQa) = zero,
inference(orient,[status(thm)],[t1]) ).
cnf(t18419,plain,
divide(divide(idQ_idQa,divide(a,idQa)),zero) = zero,
inference(step,[status(thm)],[t358,t439]) ).
cnf(t447,plain,
divide(divide(idQ_idQa,divide(a,idQa)),zero) = zero,
inference(rw,[status(thm)],[t18419]) ).
cnf(t1253,plain,
divide(divide(idQ_idQa,divide(a,idQa)),zero) = zero,
inference(orient,[status(thm)],[t447]) ).
cnf(t1254,plain,
true = quotient(divide(idQ_idQa,divide(a,idQa)),zero,zero),
inference(cp,[status(thm)],[t489,t1253]) ).
cnf(t1411,plain,
quotient(divide(idQ_idQa,divide(a,idQa)),zero,zero) = true,
inference(orient,[status(thm)],[t1254]) ).
cnf(t1413,plain,
true = ifeq(true,true,less_equal(divide(idQ_idQa,divide(a,idQa)),zero),true),
inference(cp,[status(thm)],[t938,t1411]) ).
cnf(t18519,plain,
true = less_equal(divide(idQ_idQa,divide(a,idQa)),zero),
inference(step,[status(thm)],[t1413,t256]) ).
cnf(t1421,plain,
less_equal(divide(idQ_idQa,divide(a,idQa)),zero) = true,
inference(orient,[status(thm)],[t18519]) ).
cnf(t1422,plain,
divide(idQ_idQa,divide(a,idQa)) = ifeq(true,true,zero,divide(idQ_idQa,divide(a,idQa))),
inference(cp,[status(thm)],[t1261,t1421]) ).
cnf(t18520,plain,
divide(idQ_idQa,divide(a,idQa)) = zero,
inference(step,[status(thm)],[t1422,t256]) ).
cnf(t1428,plain,
divide(idQ_idQa,divide(a,idQa)) = zero,
inference(orient,[status(thm)],[t18520]) ).
cnf(t1429,plain,
true = quotient(idQ_idQa,divide(a,idQa),zero),
inference(cp,[status(thm)],[t489,t1428]) ).
cnf(t1436,plain,
quotient(idQ_idQa,divide(a,idQa),zero) = true,
inference(orient,[status(thm)],[t1429]) ).
cnf(t1438,plain,
true = ifeq(true,true,less_equal(idQ_idQa,divide(a,idQa)),true),
inference(cp,[status(thm)],[t938,t1436]) ).
cnf(t18522,plain,
true = less_equal(idQ_idQa,divide(a,idQa)),
inference(step,[status(thm)],[t1438,t256]) ).
cnf(t1446,plain,
less_equal(idQ_idQa,divide(a,idQa)) = true,
inference(orient,[status(thm)],[t18522]) ).
cnf(t1448,plain,
divide(a,idQa) = ifeq(true,true,ifeq(less_equal(divide(a,idQa),idQ_idQa),true,idQ_idQa,divide(a,idQa)),divide(a,idQa)),
inference(cp,[status(thm)],[t259,t1446]) ).
cnf(t18631,plain,
divide(a,idQa) = ifeq(less_equal(divide(a,idQa),idQ_idQa),true,idQ_idQa,divide(a,idQa)),
inference(step,[status(thm)],[t1448,t256]) ).
cnf(t2330,plain,
ifeq(less_equal(divide(a,idQa),idQ_idQa),true,idQ_idQa,divide(a,idQa)) = divide(a,idQa),
inference(orient,[status(thm)],[t18631]) ).
cnf(t14,plain,
quotient(identity,idQa,idQ_idQa) = true,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(t680,plain,
quotient(identity,idQa,idQ_idQa) = true,
inference(orient,[status(thm)],[t14]) ).
cnf(t821,plain,
true = ifeq(quotient(X1,identity,X2),true,ifeq(true,true,ifeq(quotient(X1,idQa,X3),true,ifeq(quotient(X3,idQ_idQa,X4),true,ifeq(quotient(X2,idQa,X5),true,less_equal(X4,X5),true),true),true),true),true),
inference(cp,[status(thm)],[t794,t680]) ).
cnf(t19389,plain,
true = ifeq(quotient(X1,identity,X2),true,ifeq(quotient(X1,idQa,X3),true,ifeq(quotient(X3,idQ_idQa,X4),true,ifeq(quotient(X2,idQa,X5),true,less_equal(X4,X5),true),true),true),true),
inference(step,[status(thm)],[t821,t256]) ).
cnf(t15217,plain,
ifeq(quotient(X1,identity,X2),true,ifeq(quotient(X1,idQa,X3),true,ifeq(quotient(X3,idQ_idQa,X4),true,ifeq(quotient(X2,idQa,X5),true,less_equal(X4,X5),true),true),true),true) = true,
inference(orient,[status(thm)],[t19389]) ).
cnf(t958,plain,
true = ifeq(true,true,quotient(zero,X1,zero),true),
inference(cp,[status(thm)],[t956,t770]) ).
cnf(t18457,plain,
true = quotient(zero,X1,zero),
inference(step,[status(thm)],[t958,t256]) ).
cnf(t1036,plain,
quotient(zero,X1,zero) = true,
inference(orient,[status(thm)],[t18457]) ).
cnf(t15324,plain,
true = ifeq(quotient(X1,identity,zero),true,ifeq(quotient(X1,idQa,X2),true,ifeq(quotient(X2,idQ_idQa,X3),true,ifeq(true,true,less_equal(X3,zero),true),true),true),true),
inference(cp,[status(thm)],[t15217,t1036]) ).
cnf(t8,plain,
less_equal(X1,identity) = true,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t686,plain,
less_equal(X1,identity) = true,
inference(orient,[status(thm)],[t8]) ).
cnf(t957,plain,
true = ifeq(true,true,quotient(X1,identity,zero),true),
inference(cp,[status(thm)],[t956,t686]) ).
cnf(t18456,plain,
true = quotient(X1,identity,zero),
inference(step,[status(thm)],[t957,t256]) ).
cnf(t1028,plain,
quotient(X1,identity,zero) = true,
inference(orient,[status(thm)],[t18456]) ).
cnf(t19390,plain,
true = ifeq(true,true,ifeq(quotient(X1,idQa,X2),true,ifeq(quotient(X2,idQ_idQa,X3),true,ifeq(true,true,less_equal(X3,zero),true),true),true),true),
inference(step,[status(thm)],[t15324,t1028]) ).
cnf(t19391,plain,
true = ifeq(quotient(X1,idQa,X2),true,ifeq(quotient(X2,idQ_idQa,X3),true,ifeq(true,true,less_equal(X3,zero),true),true),true),
inference(step,[status(thm)],[t19390,t256]) ).
cnf(t19392,plain,
true = ifeq(quotient(X1,idQa,X2),true,ifeq(quotient(X2,idQ_idQa,X3),true,less_equal(X3,zero),true),true),
inference(step,[status(thm)],[t19391,t256]) ).
cnf(t15485,plain,
ifeq(quotient(X1,idQa,X2),true,ifeq(quotient(X2,idQ_idQa,X3),true,less_equal(X3,zero),true),true) = true,
inference(orient,[status(thm)],[t19392]) ).
cnf(t15486,plain,
true = ifeq(true,true,ifeq(quotient(divide(X1,idQa),idQ_idQa,X2),true,less_equal(X2,zero),true),true),
inference(cp,[status(thm)],[t15485,t489]) ).
cnf(t19401,plain,
true = ifeq(quotient(divide(X1,idQa),idQ_idQa,X2),true,less_equal(X2,zero),true),
inference(step,[status(thm)],[t15486,t256]) ).
cnf(t15512,plain,
ifeq(quotient(divide(X1,idQa),idQ_idQa,X2),true,less_equal(X2,zero),true) = true,
inference(orient,[status(thm)],[t19401]) ).
cnf(t15513,plain,
true = ifeq(true,true,less_equal(divide(divide(X1,idQa),idQ_idQa),zero),true),
inference(cp,[status(thm)],[t15512,t489]) ).
cnf(t19402,plain,
true = less_equal(divide(divide(X1,idQa),idQ_idQa),zero),
inference(step,[status(thm)],[t15513,t256]) ).
cnf(t15518,plain,
less_equal(divide(divide(X1,idQa),idQ_idQa),zero) = true,
inference(orient,[status(thm)],[t19402]) ).
cnf(t15519,plain,
divide(divide(X1,idQa),idQ_idQa) = ifeq(true,true,zero,divide(divide(X1,idQa),idQ_idQa)),
inference(cp,[status(thm)],[t1261,t15518]) ).
cnf(t19403,plain,
divide(divide(X1,idQa),idQ_idQa) = zero,
inference(step,[status(thm)],[t15519,t256]) ).
cnf(t15540,plain,
divide(divide(X1,idQa),idQ_idQa) = zero,
inference(orient,[status(thm)],[t19403]) ).
cnf(t15543,plain,
true = quotient(divide(X1,idQa),idQ_idQa,zero),
inference(cp,[status(thm)],[t489,t15540]) ).
cnf(t15560,plain,
quotient(divide(X1,idQa),idQ_idQa,zero) = true,
inference(orient,[status(thm)],[t15543]) ).
cnf(t15562,plain,
true = ifeq(true,true,less_equal(divide(X1,idQa),idQ_idQa),true),
inference(cp,[status(thm)],[t938,t15560]) ).
cnf(t19410,plain,
true = less_equal(divide(X1,idQa),idQ_idQa),
inference(step,[status(thm)],[t15562,t256]) ).
cnf(t15584,plain,
less_equal(divide(X1,idQa),idQ_idQa) = true,
inference(orient,[status(thm)],[t19410]) ).
cnf(t19411,plain,
ifeq(true,true,idQ_idQa,divide(a,idQa)) = divide(a,idQa),
inference(step,[status(thm)],[t2330,t15584]) ).
cnf(t19412,plain,
idQ_idQa = divide(a,idQa),
inference(step,[status(thm)],[t19411,t256]) ).
cnf(t15600,plain,
idQ_idQa = divide(a,idQa),
inference(rw,[status(thm)],[t19412]) ).
cnf(t15602,plain,
divide(a,idQa) = idQ_idQa,
inference(orient,[status(thm)],[t15600]) ).
cnf(t15604,plain,
zero = divide(idQ_idQa,a),
inference(cp,[status(thm)],[t1612,t15602]) ).
cnf(t15664,plain,
divide(idQ_idQa,a) = zero,
inference(orient,[status(thm)],[t15604]) ).
cnf(t19416,plain,
quotient(divide(idQa,zero),idQa_Q__idQ_idQa,zero) = true,
inference(step,[status(thm)],[t2464,t15664]) ).
cnf(t15694,plain,
quotient(divide(idQa,zero),idQa_Q__idQ_idQa,zero) = true,
inference(rw,[status(thm)],[t19416]) ).
cnf(t15911,plain,
quotient(divide(idQa,zero),idQa_Q__idQ_idQa,zero) = true,
inference(orient,[status(thm)],[t15694]) ).
cnf(t15928,plain,
true = ifeq(quotient(zero,idQa_Q__idQ_idQa,X1),true,ifeq(quotient(idQa,idQa_Q__idQ_idQa,X2),true,ifeq(quotient(X2,X1,X3),true,ifeq(true,true,less_equal(X3,zero),true),true),true),true),
inference(cp,[status(thm)],[t5985,t15911]) ).
cnf(t19927,plain,
true = ifeq(quotient(zero,idQa_Q__idQ_idQa,X1),true,ifeq(quotient(idQa,idQa_Q__idQ_idQa,X2),true,ifeq(quotient(X2,X1,X3),true,less_equal(X3,zero),true),true),true),
inference(step,[status(thm)],[t15928,t256]) ).
cnf(t17907,plain,
ifeq(quotient(zero,idQa_Q__idQ_idQa,X1),true,ifeq(quotient(idQa,idQa_Q__idQ_idQa,X2),true,ifeq(quotient(X2,X1,X3),true,less_equal(X3,zero),true),true),true) = true,
inference(orient,[status(thm)],[t19927]) ).
cnf(t17908,plain,
true = ifeq(true,true,ifeq(quotient(idQa,idQa_Q__idQ_idQa,X1),true,ifeq(quotient(X1,zero,X2),true,less_equal(X2,zero),true),true),true),
inference(cp,[status(thm)],[t17907,t1036]) ).
cnf(t19928,plain,
true = ifeq(quotient(idQa,idQa_Q__idQ_idQa,X1),true,ifeq(quotient(X1,zero,X2),true,less_equal(X2,zero),true),true),
inference(step,[status(thm)],[t17908,t256]) ).
cnf(t17918,plain,
ifeq(quotient(idQa,idQa_Q__idQ_idQa,X1),true,ifeq(quotient(X1,zero,X2),true,less_equal(X2,zero),true),true) = true,
inference(orient,[status(thm)],[t19928]) ).
cnf(t17919,plain,
true = ifeq(true,true,ifeq(quotient(divide(idQa,idQa_Q__idQ_idQa),zero,X1),true,less_equal(X1,zero),true),true),
inference(cp,[status(thm)],[t17918,t489]) ).
cnf(t19929,plain,
true = ifeq(quotient(divide(idQa,idQa_Q__idQ_idQa),zero,X1),true,less_equal(X1,zero),true),
inference(step,[status(thm)],[t17919,t256]) ).
cnf(t17921,plain,
ifeq(quotient(divide(idQa,idQa_Q__idQ_idQa),zero,X1),true,less_equal(X1,zero),true) = true,
inference(orient,[status(thm)],[t19929]) ).
cnf(t17922,plain,
true = ifeq(true,true,less_equal(divide(divide(idQa,idQa_Q__idQ_idQa),zero),zero),true),
inference(cp,[status(thm)],[t17921,t489]) ).
cnf(t19930,plain,
true = less_equal(divide(divide(idQa,idQa_Q__idQ_idQa),zero),zero),
inference(step,[status(thm)],[t17922,t256]) ).
cnf(t17923,plain,
less_equal(divide(divide(idQa,idQa_Q__idQ_idQa),zero),zero) = true,
inference(orient,[status(thm)],[t19930]) ).
cnf(t17924,plain,
divide(divide(idQa,idQa_Q__idQ_idQa),zero) = ifeq(true,true,zero,divide(divide(idQa,idQa_Q__idQ_idQa),zero)),
inference(cp,[status(thm)],[t1261,t17923]) ).
cnf(t19931,plain,
divide(divide(idQa,idQa_Q__idQ_idQa),zero) = zero,
inference(step,[status(thm)],[t17924,t256]) ).
cnf(t17929,plain,
divide(divide(idQa,idQa_Q__idQ_idQa),zero) = zero,
inference(orient,[status(thm)],[t19931]) ).
cnf(t17932,plain,
true = quotient(divide(idQa,idQa_Q__idQ_idQa),zero,zero),
inference(cp,[status(thm)],[t489,t17929]) ).
cnf(t17935,plain,
quotient(divide(idQa,idQa_Q__idQ_idQa),zero,zero) = true,
inference(orient,[status(thm)],[t17932]) ).
cnf(t17937,plain,
true = ifeq(true,true,less_equal(divide(idQa,idQa_Q__idQ_idQa),zero),true),
inference(cp,[status(thm)],[t938,t17935]) ).
cnf(t19932,plain,
true = less_equal(divide(idQa,idQa_Q__idQ_idQa),zero),
inference(step,[status(thm)],[t17937,t256]) ).
cnf(t17950,plain,
less_equal(divide(idQa,idQa_Q__idQ_idQa),zero) = true,
inference(orient,[status(thm)],[t19932]) ).
cnf(t17951,plain,
divide(idQa,idQa_Q__idQ_idQa) = ifeq(true,true,zero,divide(idQa,idQa_Q__idQ_idQa)),
inference(cp,[status(thm)],[t1261,t17950]) ).
cnf(t19933,plain,
divide(idQa,idQa_Q__idQ_idQa) = zero,
inference(step,[status(thm)],[t17951,t256]) ).
cnf(t17955,plain,
divide(idQa,idQa_Q__idQ_idQa) = zero,
inference(orient,[status(thm)],[t19933]) ).
cnf(t17958,plain,
true = quotient(idQa,idQa_Q__idQ_idQa,zero),
inference(cp,[status(thm)],[t489,t17955]) ).
cnf(t17987,plain,
quotient(idQa,idQa_Q__idQ_idQa,zero) = true,
inference(orient,[status(thm)],[t17958]) ).
cnf(t17989,plain,
true = ifeq(true,true,less_equal(idQa,idQa_Q__idQ_idQa),true),
inference(cp,[status(thm)],[t938,t17987]) ).
cnf(t19934,plain,
true = less_equal(idQa,idQa_Q__idQ_idQa),
inference(step,[status(thm)],[t17989,t256]) ).
cnf(t18011,plain,
less_equal(idQa,idQa_Q__idQ_idQa) = true,
inference(orient,[status(thm)],[t19934]) ).
cnf(t18012,plain,
idQa_Q__idQ_idQa = ifeq(true,true,ifeq(less_equal(idQa_Q__idQ_idQa,idQa),true,idQa,idQa_Q__idQ_idQa),idQa_Q__idQ_idQa),
inference(cp,[status(thm)],[t259,t18011]) ).
cnf(t19939,plain,
idQa_Q__idQ_idQa = ifeq(less_equal(idQa_Q__idQ_idQa,idQa),true,idQa,idQa_Q__idQ_idQa),
inference(step,[status(thm)],[t18012,t256]) ).
cnf(t9,plain,
less_equal(idQa_Q__idQ_idQa,idQa) = true,
inference(hyper_resolution,[status(thm)],[hi2,hi11]) ).
cnf(t773,plain,
less_equal(idQa_Q__idQ_idQa,idQa) = true,
inference(orient,[status(thm)],[t9]) ).
cnf(t19940,plain,
idQa_Q__idQ_idQa = ifeq(true,true,idQa,idQa_Q__idQ_idQa),
inference(step,[status(thm)],[t19939,t773]) ).
cnf(t19941,plain,
idQa_Q__idQ_idQa = idQa,
inference(step,[status(thm)],[t19940,t256]) ).
cnf(t18016,plain,
idQa = idQa_Q__idQ_idQa,
inference(orient,[status(thm)],[t19941]) ).
cnf(f12,negated_conjecture,
idQa != idQa_Q__idQ_idQa,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_idQa_equals_idQa_Q__idQ_idQa) ).
fof(f12_nnf,plain,
idQa != idQa_Q__idQ_idQa,
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
idQa != idQa_Q__idQ_idQa,
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c12,plain,
idQa != idQa_Q__idQ_idQa,
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(goal_0,negated_conjecture,
idQa_Q__idQ_idQa != idQa,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(g0_0,plain,
idQa_Q__idQ_idQa != idQa_Q__idQ_idQa,
inference(rw,[status(thm)],[goal_0,t18016]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN010-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.37 % Computer : n008.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Wed Sep 23 16:16:38 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 59.32/8.28 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 59.32/8.28 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------