%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : ALG362-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n007.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 12:52:23 PM UTC 2026
% Result : Unsatisfiable 204.59s 27.22s
% Output : Proof 204.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 39
% Syntax : Number of formulae : 191 ( 71 unt; 0 def)
% Number of atoms : 347 ( 65 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 430 ( 274 ~; 156 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 1 prp; 0-3 aty)
% Number of functors : 18 ( 18 usr; 7 con; 0-4 aty)
% Number of variables : 316 ( 10 sgn 132 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f631,axiom,
( ~ c_lessequals(V_i,V_j,tc_RealDef_Oreal)
| ~ c_lessequals(V_j,V_k,tc_RealDef_Oreal)
| c_lessequals(V_i,V_k,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__le__trans_0) ).
fof(f631_nnf,plain,
! [V_i,V_k,V_j] :
( ~ c_lessequals(V_i,V_j,tc_RealDef_Oreal)
| ~ c_lessequals(V_j,V_k,tc_RealDef_Oreal)
| c_lessequals(V_i,V_k,tc_RealDef_Oreal) ),
inference(nnf_transformation,[status(thm)],[f631]) ).
fof(f631_sk,plain,
! [V_i,V_k,V_j] :
( ~ c_lessequals(V_i,V_j,tc_RealDef_Oreal)
| ~ c_lessequals(V_j,V_k,tc_RealDef_Oreal)
| c_lessequals(V_i,V_k,tc_RealDef_Oreal) ),
inference(skolemisation,[status(esa)],[f631_nnf]) ).
cnf(c631,plain,
( ~ c_lessequals(X0,X2,tc_RealDef_Oreal)
| ~ c_lessequals(X2,X1,tc_RealDef_Oreal)
| c_lessequals(X0,X1,tc_RealDef_Oreal) ),
inference(cnf_transformation,[status(esa)],[f631_sk]) ).
cnf(t190,plain,
ifeq(c_lessequals(X1,X2,tc_RealDef_Oreal),true,ifeq(c_lessequals(X3,X1,tc_RealDef_Oreal),true,c_lessequals(X3,X2,tc_RealDef_Oreal),true),true) = true,
inference(equality_encoding,[status(esa)],[c631]) ).
cnf(t626,plain,
ifeq(c_lessequals(X1,X2,tc_RealDef_Oreal),true,ifeq(c_lessequals(X3,X1,tc_RealDef_Oreal),true,c_lessequals(X3,X2,tc_RealDef_Oreal),true),true) = true,
inference(orient,[status(thm)],[t190]) ).
cnf(f654,axiom,
( ~ c_lessequals(V_x,V_y,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Oplus__class_Oplus(V_z,V_x,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(V_z,V_y,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__add__left__mono_0) ).
fof(f654_nnf,plain,
! [V_z,V_x,V_y] :
( ~ c_lessequals(V_x,V_y,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Oplus__class_Oplus(V_z,V_x,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(V_z,V_y,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(nnf_transformation,[status(thm)],[f654]) ).
fof(f654_sk,plain,
! [V_z,V_x,V_y] :
( ~ c_lessequals(V_x,V_y,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Oplus__class_Oplus(V_z,V_x,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(V_z,V_y,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(skolemisation,[status(esa)],[f654_nnf]) ).
cnf(c654,plain,
( ~ c_lessequals(X1,X2,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Oplus__class_Oplus(X0,X1,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X0,X2,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(cnf_transformation,[status(esa)],[f654_sk]) ).
cnf(t182,plain,
ifeq(c_lessequals(X1,X2,tc_RealDef_Oreal),true,c_lessequals(c_HOL_Oplus__class_Oplus(X3,X1,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X3,X2,tc_RealDef_Oreal),tc_RealDef_Oreal),true) = true,
inference(equality_encoding,[status(esa)],[c654]) ).
cnf(f638,axiom,
( c_HOL_Oplus__class_Oplus(V_a,V_c,T_a) = c_HOL_Oplus__class_Oplus(V_c,V_a,T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I24_J_0) ).
fof(f638_nnf,plain,
! [T_a,V_a,V_c] :
( c_HOL_Oplus__class_Oplus(V_a,V_c,T_a) = c_HOL_Oplus__class_Oplus(V_c,V_a,T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
inference(nnf_transformation,[status(thm)],[f638]) ).
fof(f638_sk,plain,
! [T_a,V_a,V_c] :
( c_HOL_Oplus__class_Oplus(V_a,V_c,T_a) = c_HOL_Oplus__class_Oplus(V_c,V_a,T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
inference(skolemisation,[status(esa)],[f638_nnf]) ).
cnf(c638,plain,
( c_HOL_Oplus__class_Oplus(X1,X2,X0) = c_HOL_Oplus__class_Oplus(X2,X1,X0)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[status(esa)],[f638_sk]) ).
cnf(hi610,axiom,
ifeq(class_Ring__and__Field_Ocomm__semiring__1(X0),true,c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Oplus__class_Oplus(X2,X1,X0)) = c_HOL_Oplus__class_Oplus(X2,X1,X0),
inference(equality_encoding,[status(esa)],[c638]) ).
cnf(f729,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__1) ).
fof(f729_nnf,plain,
class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal),
inference(nnf_transformation,[status(thm)],[f729]) ).
cnf(c729,plain,
class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal),
inference(cnf_transformation,[status(esa)],[f729_nnf]) ).
cnf(hi700,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal) = true,
inference(equality_encoding,[status(esa)],[c729]) ).
cnf(t42,plain,
c_HOL_Oplus__class_Oplus(X1,X2,tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(X2,X1,tc_RealDef_Oreal),
inference(hyper_resolution,[status(thm)],[hi610,hi700]) ).
cnf(t246,plain,
c_HOL_Oplus__class_Oplus(X1,X2,tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(X2,X1,tc_RealDef_Oreal),
inference(orient,[status(thm)],[t42]) ).
cnf(t77476,plain,
ifeq(c_lessequals(X1,X2,tc_RealDef_Oreal),true,c_lessequals(c_HOL_Oplus__class_Oplus(X1,X3,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X3,X2,tc_RealDef_Oreal),tc_RealDef_Oreal),true) = true,
inference(step,[status(thm)],[t182,t246]) ).
cnf(t77477,plain,
ifeq(c_lessequals(X1,X2,tc_RealDef_Oreal),true,c_lessequals(c_HOL_Oplus__class_Oplus(X1,X3,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X2,X3,tc_RealDef_Oreal),tc_RealDef_Oreal),true) = true,
inference(step,[status(thm)],[t77476,t246]) ).
cnf(t588,plain,
ifeq(c_lessequals(X1,X2,tc_RealDef_Oreal),true,c_lessequals(c_HOL_Oplus__class_Oplus(X1,X3,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X2,X3,tc_RealDef_Oreal),tc_RealDef_Oreal),true) = true,
inference(orient,[status(thm)],[t77477]) ).
cnf(f573,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oone__class_Oone(T_a),T_a)
| ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__one_0) ).
fof(f573_nnf,plain,
! [T_a] :
( c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oone__class_Oone(T_a),T_a)
| ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
inference(nnf_transformation,[status(thm)],[f573]) ).
fof(f573_sk,plain,
! [T_a] :
( c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oone__class_Oone(T_a),T_a)
| ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
inference(skolemisation,[status(esa)],[f573_nnf]) ).
cnf(c573,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oone__class_Oone(X0),X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) ),
inference(cnf_transformation,[status(esa)],[f573_sk]) ).
cnf(hi546,axiom,
ifeq(class_Ring__and__Field_Oordered__semidom(X0),true,c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oone__class_Oone(X0),X0),true) = true,
inference(equality_encoding,[status(esa)],[c573]) ).
cnf(f728,axiom,
class_Ring__and__Field_Oordered__semidom(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semidom) ).
fof(f728_nnf,plain,
class_Ring__and__Field_Oordered__semidom(tc_RealDef_Oreal),
inference(nnf_transformation,[status(thm)],[f728]) ).
cnf(c728,plain,
class_Ring__and__Field_Oordered__semidom(tc_RealDef_Oreal),
inference(cnf_transformation,[status(esa)],[f728_nnf]) ).
cnf(hi699,axiom,
class_Ring__and__Field_Oordered__semidom(tc_RealDef_Oreal) = true,
inference(equality_encoding,[status(esa)],[c728]) ).
cnf(t32,plain,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) = true,
inference(hyper_resolution,[status(thm)],[hi546,hi699]) ).
cnf(t501,plain,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) = true,
inference(orient,[status(thm)],[t32]) ).
cnf(t607,plain,
true = ifeq(true,true,c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X1,tc_RealDef_Oreal),tc_RealDef_Oreal),true),
inference(cp,[status(thm)],[t588,t501]) ).
cnf(t28,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t241,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t28]) ).
cnf(t77697,plain,
true = c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X1,tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(step,[status(thm)],[t607,t241]) ).
cnf(t77698,plain,
true = c_lessequals(c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X1,tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(step,[status(thm)],[t77697,t246]) ).
cnf(f403,axiom,
( c_HOL_Oplus__class_Oplus(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = V_a
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I6_J_0) ).
fof(f403_nnf,plain,
! [T_a,V_a] :
( c_HOL_Oplus__class_Oplus(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = V_a
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
inference(nnf_transformation,[status(thm)],[f403]) ).
fof(f403_sk,plain,
! [T_a,V_a] :
( c_HOL_Oplus__class_Oplus(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = V_a
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
inference(skolemisation,[status(esa)],[f403_nnf]) ).
cnf(c403,plain,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[status(esa)],[f403_sk]) ).
cnf(hi391,axiom,
ifeq(class_Ring__and__Field_Ocomm__semiring__1(X0),true,c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X0),X0),X1) = X1,
inference(equality_encoding,[status(esa)],[c403]) ).
cnf(t13,plain,
c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = X1,
inference(hyper_resolution,[status(thm)],[hi391,hi700]) ).
cnf(t202,plain,
c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = X1,
inference(orient,[status(thm)],[t13]) ).
cnf(t77699,plain,
true = c_lessequals(X1,c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X1,tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(step,[status(thm)],[t77698,t202]) ).
cnf(t77700,plain,
true = c_lessequals(X1,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(step,[status(thm)],[t77699,t246]) ).
cnf(t4906,plain,
c_lessequals(X1,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = true,
inference(orient,[status(thm)],[t77700]) ).
cnf(t4916,plain,
true = ifeq(true,true,ifeq(c_lessequals(X1,X2,tc_RealDef_Oreal),true,c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),true),true),
inference(cp,[status(thm)],[t626,t4906]) ).
cnf(t79517,plain,
true = ifeq(c_lessequals(X1,X2,tc_RealDef_Oreal),true,c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),true),
inference(step,[status(thm)],[t4916,t241]) ).
cnf(t76522,plain,
ifeq(c_lessequals(X1,X2,tc_RealDef_Oreal),true,c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),true) = true,
inference(orient,[status(thm)],[t79517]) ).
cnf(f674,negated_conjecture,
~ c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s,v_n____)),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(v_r,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f674_nnf,plain,
~ c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s,v_n____)),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(v_r,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(nnf_transformation,[status(thm)],[f674]) ).
fof(f674_sk,plain,
~ c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s,v_n____)),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(v_r,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(skolemisation,[status(esa)],[f674_nnf]) ).
cnf(c674,plain,
~ c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s,v_n____)),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(v_r,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(cnf_transformation,[status(esa)],[f674_sk]) ).
cnf(t144,plain,
c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s,v_n____)),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(v_r,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = false,
inference(equality_encoding,[status(esa)],[c674]) ).
cnf(t1509,plain,
c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s,v_n____)),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(v_r,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = false,
inference(orient,[status(thm)],[t144]) ).
cnf(t77369,plain,
true = ifeq(c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s,v_n____)),tc_RealDef_Oreal),v_r,tc_RealDef_Oreal),true,false,true),
inference(cp,[status(thm)],[t76522,t1509]) ).
cnf(hi603,axiom,
ifeq(c_lessequals(X0,X1,tc_RealDef_Oreal),true,ifeq(c_lessequals(X2,X0,tc_RealDef_Oreal),true,c_lessequals(X2,X1,tc_RealDef_Oreal),true),true) = true,
inference(equality_encoding,[status(esa)],[c631]) ).
cnf(f672,axiom,
c_lessequals(c_RealVector_Onorm__class_Onorm(hAPP(v_s,v_n____),tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0) ).
fof(f672_nnf,plain,
c_lessequals(c_RealVector_Onorm__class_Onorm(hAPP(v_s,v_n____),tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal),
inference(nnf_transformation,[status(thm)],[f672]) ).
cnf(c672,plain,
c_lessequals(c_RealVector_Onorm__class_Onorm(hAPP(v_s,v_n____),tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal),
inference(cnf_transformation,[status(esa)],[f672_nnf]) ).
cnf(hi644,axiom,
c_lessequals(c_RealVector_Onorm__class_Onorm(hAPP(v_s,v_n____),tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal) = true,
inference(equality_encoding,[status(esa)],[c672]) ).
cnf(f623,axiom,
c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(V_x),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(V_x,tc_Complex_Ocomplex),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__Re__le__cmod_0) ).
fof(f623_nnf,plain,
! [V_x] : c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(V_x),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(V_x,tc_Complex_Ocomplex),tc_RealDef_Oreal),
inference(nnf_transformation,[status(thm)],[f623]) ).
fof(f623_sk,plain,
! [V_x] : c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(V_x),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(V_x,tc_Complex_Ocomplex),tc_RealDef_Oreal),
inference(skolemisation,[status(esa)],[f623_nnf]) ).
cnf(c623,plain,
c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(X0),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X0,tc_Complex_Ocomplex),tc_RealDef_Oreal),
inference(cnf_transformation,[status(esa)],[f623_sk]) ).
cnf(hi595,axiom,
c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(X0),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X0,tc_Complex_Ocomplex),tc_RealDef_Oreal) = true,
inference(equality_encoding,[status(esa)],[c623]) ).
cnf(t91,plain,
c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s,v_n____)),tc_RealDef_Oreal),v_r,tc_RealDef_Oreal) = true,
inference(hyper_resolution,[status(thm)],[hi603,hi644,hi595]) ).
cnf(t540,plain,
c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s,v_n____)),tc_RealDef_Oreal),v_r,tc_RealDef_Oreal) = true,
inference(orient,[status(thm)],[t91]) ).
cnf(t79518,plain,
true = ifeq(true,true,false,true),
inference(step,[status(thm)],[t77369,t540]) ).
cnf(t79519,plain,
true = false,
inference(step,[status(thm)],[t79518,t241]) ).
cnf(t77371,plain,
false = true,
inference(orient,[status(thm)],[t79519]) ).
cnf(f12,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Odist__class_Odist(V_x,V_x,T_a),tc_RealDef_Oreal)
| ~ class_RealVector_Ometric__space(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__dist__iff_0) ).
fof(f12_nnf,plain,
! [T_a,V_x] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Odist__class_Odist(V_x,V_x,T_a),tc_RealDef_Oreal)
| ~ class_RealVector_Ometric__space(T_a) ),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [T_a,V_x] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Odist__class_Odist(V_x,V_x,T_a),tc_RealDef_Oreal)
| ~ class_RealVector_Ometric__space(T_a) ),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c12,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Odist__class_Odist(X1,X1,X0),tc_RealDef_Oreal)
| ~ class_RealVector_Ometric__space(X0) ),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(f24,axiom,
( ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(V_x,T_a),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__not__less__zero_0) ).
fof(f24_nnf,plain,
! [T_a,V_x] :
( ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(V_x,T_a),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(T_a) ),
inference(nnf_transformation,[status(thm)],[f24]) ).
fof(f24_sk,plain,
! [T_a,V_x] :
( ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(V_x,T_a),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(T_a) ),
inference(skolemisation,[status(esa)],[f24_nnf]) ).
cnf(c24,plain,
( ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(X1,X0),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X0) ),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
cnf(f88,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,T_a),c_HOL_Otimes__class_Otimes(V_y,V_y,T_a),T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__sum__squares__lt__zero_0) ).
fof(f88_nnf,plain,
! [T_a,V_x,V_y] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,T_a),c_HOL_Otimes__class_Otimes(V_y,V_y,T_a),T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
inference(nnf_transformation,[status(thm)],[f88]) ).
fof(f88_sk,plain,
! [T_a,V_x,V_y] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,T_a),c_HOL_Otimes__class_Otimes(V_y,V_y,T_a),T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
inference(skolemisation,[status(esa)],[f88_nnf]) ).
cnf(c88,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,X0),c_HOL_Otimes__class_Otimes(X2,X2,X0),X0),c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Ring__and__Field_Oordered__ring__strict(X0) ),
inference(cnf_transformation,[status(esa)],[f88_sk]) ).
cnf(f99,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(T_a),T_a),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__norm__iff_0) ).
fof(f99_nnf,plain,
! [T_a] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(T_a),T_a),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(T_a) ),
inference(nnf_transformation,[status(thm)],[f99]) ).
fof(f99_sk,plain,
! [T_a] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(T_a),T_a),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(T_a) ),
inference(skolemisation,[status(esa)],[f99_nnf]) ).
cnf(c99,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(X0),X0),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X0) ),
inference(cnf_transformation,[status(esa)],[f99_sk]) ).
cnf(f101,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal)
| c_NthRoot_Osqrt(V_x) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__not__eq__zero_0) ).
fof(f101_nnf,plain,
! [V_x] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal)
| c_NthRoot_Osqrt(V_x) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(nnf_transformation,[status(thm)],[f101]) ).
fof(f101_sk,plain,
! [V_x] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal)
| c_NthRoot_Osqrt(V_x) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(skolemisation,[status(esa)],[f101_nnf]) ).
cnf(c101,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| c_NthRoot_Osqrt(X0) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(cnf_transformation,[status(esa)],[f101_sk]) ).
cnf(f115,axiom,
( ~ c_HOL_Oord__class_Oless(c_RealVector_Odist__class_Odist(V_x,V_y,T_a),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_RealVector_Ometric__space(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dist__not__less__zero_0) ).
fof(f115_nnf,plain,
! [T_a,V_x,V_y] :
( ~ c_HOL_Oord__class_Oless(c_RealVector_Odist__class_Odist(V_x,V_y,T_a),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_RealVector_Ometric__space(T_a) ),
inference(nnf_transformation,[status(thm)],[f115]) ).
fof(f115_sk,plain,
! [T_a,V_x,V_y] :
( ~ c_HOL_Oord__class_Oless(c_RealVector_Odist__class_Odist(V_x,V_y,T_a),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_RealVector_Ometric__space(T_a) ),
inference(skolemisation,[status(esa)],[f115_nnf]) ).
cnf(c115,plain,
( ~ c_HOL_Oord__class_Oless(c_RealVector_Odist__class_Odist(X1,X2,X0),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_RealVector_Ometric__space(X0) ),
inference(cnf_transformation,[status(esa)],[f115_sk]) ).
cnf(f232,axiom,
( ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| ~ c_lessequals(V_y,V_x,T_a)
| ~ class_Orderings_Opreorder(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__le__not__le_1) ).
fof(f232_nnf,plain,
! [T_a,V_y,V_x] :
( ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| ~ c_lessequals(V_y,V_x,T_a)
| ~ class_Orderings_Opreorder(T_a) ),
inference(nnf_transformation,[status(thm)],[f232]) ).
fof(f232_sk,plain,
! [T_a,V_y,V_x] :
( ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| ~ c_lessequals(V_y,V_x,T_a)
| ~ class_Orderings_Opreorder(T_a) ),
inference(skolemisation,[status(esa)],[f232_nnf]) ).
cnf(c232,plain,
( ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_lessequals(X1,X2,X0)
| ~ class_Orderings_Opreorder(X0) ),
inference(cnf_transformation,[status(esa)],[f232_sk]) ).
cnf(f234,axiom,
( ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a)
| ~ c_lessequals(V_x,V_x,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_1) ).
fof(f234_nnf,plain,
! [T_a,V_x] :
( ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a)
| ~ c_lessequals(V_x,V_x,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
inference(nnf_transformation,[status(thm)],[f234]) ).
fof(f234_sk,plain,
! [T_a,V_x] :
( ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a)
| ~ c_lessequals(V_x,V_x,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
inference(skolemisation,[status(esa)],[f234_nnf]) ).
cnf(c234,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X0)
| ~ c_lessequals(X1,X1,X0)
| ~ class_Orderings_Olinorder(X0) ),
inference(cnf_transformation,[status(esa)],[f234_sk]) ).
cnf(f236,axiom,
( ~ c_lessequals(V_y,V_x,T_a)
| ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__less_1) ).
fof(f236_nnf,plain,
! [T_a,V_x,V_y] :
( ~ c_lessequals(V_y,V_x,T_a)
| ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
inference(nnf_transformation,[status(thm)],[f236]) ).
fof(f236_sk,plain,
! [T_a,V_x,V_y] :
( ~ c_lessequals(V_y,V_x,T_a)
| ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
inference(skolemisation,[status(esa)],[f236_nnf]) ).
cnf(c236,plain,
( ~ c_lessequals(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ class_Orderings_Olinorder(X0) ),
inference(cnf_transformation,[status(esa)],[f236_sk]) ).
cnf(f239,axiom,
( ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__le_1) ).
fof(f239_nnf,plain,
! [T_a,V_x,V_y] :
( ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
inference(nnf_transformation,[status(thm)],[f239]) ).
fof(f239_sk,plain,
! [T_a,V_x,V_y] :
( ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
inference(skolemisation,[status(esa)],[f239_nnf]) ).
cnf(c239,plain,
( ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_lessequals(X1,X2,X0)
| ~ class_Orderings_Olinorder(X0) ),
inference(cnf_transformation,[status(esa)],[f239_sk]) ).
cnf(f289,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a),T_a),T_a)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__gt__zero__iff_0) ).
fof(f289_nnf,plain,
! [T_a] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a),T_a),T_a)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
inference(nnf_transformation,[status(thm)],[f289]) ).
fof(f289_sk,plain,
! [T_a] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a),T_a),T_a)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
inference(skolemisation,[status(esa)],[f289_nnf]) ).
cnf(c289,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0),X0),X0)
| ~ class_Ring__and__Field_Oordered__ring__strict(X0) ),
inference(cnf_transformation,[status(esa)],[f289_sk]) ).
cnf(f324,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__square__less__zero_0) ).
fof(f324_nnf,plain,
! [T_a,V_a] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
inference(nnf_transformation,[status(thm)],[f324]) ).
fof(f324_sk,plain,
! [T_a,V_a] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
inference(skolemisation,[status(esa)],[f324_nnf]) ).
cnf(c324,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X1,X0),c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Ring__and__Field_Oordered__ring__strict(X0) ),
inference(cnf_transformation,[status(esa)],[f324_sk]) ).
cnf(f410,axiom,
( c_HOL_Ozero__class_Ozero(T_a) != c_HOL_Oone__class_Oone(T_a)
| ~ class_Ring__and__Field_Ozero__neq__one(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__neq__one_0) ).
fof(f410_nnf,plain,
! [T_a] :
( c_HOL_Ozero__class_Ozero(T_a) != c_HOL_Oone__class_Oone(T_a)
| ~ class_Ring__and__Field_Ozero__neq__one(T_a) ),
inference(nnf_transformation,[status(thm)],[f410]) ).
fof(f410_sk,plain,
! [T_a] :
( c_HOL_Ozero__class_Ozero(T_a) != c_HOL_Oone__class_Oone(T_a)
| ~ class_Ring__and__Field_Ozero__neq__one(T_a) ),
inference(skolemisation,[status(esa)],[f410_nnf]) ).
cnf(c410,plain,
( c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oone__class_Oone(X0)
| ~ class_Ring__and__Field_Ozero__neq__one(X0) ),
inference(cnf_transformation,[status(esa)],[f410_sk]) ).
cnf(f411,axiom,
( c_HOL_Oone__class_Oone(T_a) != c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Ring__and__Field_Ozero__neq__one(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__neq__zero_0) ).
fof(f411_nnf,plain,
! [T_a] :
( c_HOL_Oone__class_Oone(T_a) != c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Ring__and__Field_Ozero__neq__one(T_a) ),
inference(nnf_transformation,[status(thm)],[f411]) ).
fof(f411_sk,plain,
! [T_a] :
( c_HOL_Oone__class_Oone(T_a) != c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Ring__and__Field_Ozero__neq__one(T_a) ),
inference(skolemisation,[status(esa)],[f411_nnf]) ).
cnf(c411,plain,
( c_HOL_Oone__class_Oone(X0) != c_HOL_Ozero__class_Ozero(X0)
| ~ class_Ring__and__Field_Ozero__neq__one(X0) ),
inference(cnf_transformation,[status(esa)],[f411_sk]) ).
cnf(f451,axiom,
c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_HOL_Oone__class_Oone(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__zero__not__eq__one_0) ).
fof(f451_nnf,plain,
c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_HOL_Oone__class_Oone(tc_RealDef_Oreal),
inference(nnf_transformation,[status(thm)],[f451]) ).
fof(f451_sk,plain,
c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_HOL_Oone__class_Oone(tc_RealDef_Oreal),
inference(skolemisation,[status(esa)],[f451_nnf]) ).
cnf(c451,plain,
c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_HOL_Oone__class_Oone(tc_RealDef_Oreal),
inference(cnf_transformation,[status(esa)],[f451_sk]) ).
cnf(f471,axiom,
( ~ c_lessequals(c_HOL_Oone__class_Oone(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__one__le__zero_0) ).
fof(f471_nnf,plain,
! [T_a] :
( ~ c_lessequals(c_HOL_Oone__class_Oone(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
inference(nnf_transformation,[status(thm)],[f471]) ).
fof(f471_sk,plain,
! [T_a] :
( ~ c_lessequals(c_HOL_Oone__class_Oone(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
inference(skolemisation,[status(esa)],[f471_nnf]) ).
cnf(c471,plain,
( ~ c_lessequals(c_HOL_Oone__class_Oone(X0),c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) ),
inference(cnf_transformation,[status(esa)],[f471_sk]) ).
cnf(f503,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__one__less__zero_0) ).
fof(f503_nnf,plain,
! [T_a] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
inference(nnf_transformation,[status(thm)],[f503]) ).
fof(f503_sk,plain,
! [T_a] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
inference(skolemisation,[status(esa)],[f503_nnf]) ).
cnf(c503,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) ),
inference(cnf_transformation,[status(esa)],[f503_sk]) ).
cnf(f520,axiom,
( ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).
fof(f520_nnf,plain,
! [T_a,V_x] :
( ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
inference(nnf_transformation,[status(thm)],[f520]) ).
fof(f520_sk,plain,
! [T_a,V_x] :
( ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
inference(skolemisation,[status(esa)],[f520_nnf]) ).
cnf(c520,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X0)
| ~ class_Orderings_Olinorder(X0) ),
inference(cnf_transformation,[status(esa)],[f520_sk]) ).
cnf(f521,axiom,
( ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a)
| ~ class_Orderings_Oorder(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__le_1) ).
fof(f521_nnf,plain,
! [T_a,V_x] :
( ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a)
| ~ class_Orderings_Oorder(T_a) ),
inference(nnf_transformation,[status(thm)],[f521]) ).
fof(f521_sk,plain,
! [T_a,V_x] :
( ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a)
| ~ class_Orderings_Oorder(T_a) ),
inference(skolemisation,[status(esa)],[f521_nnf]) ).
cnf(c521,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X0)
| ~ class_Orderings_Oorder(X0) ),
inference(cnf_transformation,[status(esa)],[f521_sk]) ).
cnf(f522,axiom,
~ c_HOL_Oord__class_Oless(V_x,V_x,tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__less__def_1) ).
fof(f522_nnf,plain,
! [V_x] : ~ c_HOL_Oord__class_Oless(V_x,V_x,tc_RealDef_Oreal),
inference(nnf_transformation,[status(thm)],[f522]) ).
fof(f522_sk,plain,
! [V_x] : ~ c_HOL_Oord__class_Oless(V_x,V_x,tc_RealDef_Oreal),
inference(skolemisation,[status(esa)],[f522_nnf]) ).
cnf(c522,plain,
~ c_HOL_Oord__class_Oless(X0,X0,tc_RealDef_Oreal),
inference(cnf_transformation,[status(esa)],[f522_sk]) ).
cnf(f523,axiom,
( ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a)
| ~ class_Orderings_Opreorder(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__irrefl_0) ).
fof(f523_nnf,plain,
! [T_a,V_x] :
( ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a)
| ~ class_Orderings_Opreorder(T_a) ),
inference(nnf_transformation,[status(thm)],[f523]) ).
fof(f523_sk,plain,
! [T_a,V_x] :
( ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a)
| ~ class_Orderings_Opreorder(T_a) ),
inference(skolemisation,[status(esa)],[f523_nnf]) ).
cnf(c523,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X0)
| ~ class_Orderings_Opreorder(X0) ),
inference(cnf_transformation,[status(esa)],[f523_sk]) ).
cnf(f536,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__not__less__zero_0) ).
fof(f536_nnf,plain,
! [T_a,V_a] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) ),
inference(nnf_transformation,[status(thm)],[f536]) ).
fof(f536_sk,plain,
! [T_a,V_a] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) ),
inference(skolemisation,[status(esa)],[f536_nnf]) ).
cnf(c536,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0) ),
inference(cnf_transformation,[status(esa)],[f536_sk]) ).
cnf(f551,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(T_a),T_a),T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__abs__iff_0) ).
fof(f551_nnf,plain,
! [T_a] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(T_a),T_a),T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) ),
inference(nnf_transformation,[status(thm)],[f551]) ).
fof(f551_sk,plain,
! [T_a] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(T_a),T_a),T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) ),
inference(skolemisation,[status(esa)],[f551_nnf]) ).
cnf(c551,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X0),X0),X0)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0) ),
inference(cnf_transformation,[status(esa)],[f551_sk]) ).
cnf(f568,axiom,
( ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a)
| ~ class_Orderings_Opreorder(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__asym_H_0) ).
fof(f568_nnf,plain,
! [T_a,V_b,V_a] :
( ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a)
| ~ class_Orderings_Opreorder(T_a) ),
inference(nnf_transformation,[status(thm)],[f568]) ).
fof(f568_sk,plain,
! [T_a,V_b,V_a] :
( ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a)
| ~ class_Orderings_Opreorder(T_a) ),
inference(skolemisation,[status(esa)],[f568_nnf]) ).
cnf(c568,plain,
( ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ class_Orderings_Opreorder(X0) ),
inference(cnf_transformation,[status(esa)],[f568_sk]) ).
cnf(f569,axiom,
( ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| ~ class_Orderings_Opreorder(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__asym_0) ).
fof(f569_nnf,plain,
! [T_a,V_y,V_x] :
( ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| ~ class_Orderings_Opreorder(T_a) ),
inference(nnf_transformation,[status(thm)],[f569]) ).
fof(f569_sk,plain,
! [T_a,V_y,V_x] :
( ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| ~ class_Orderings_Opreorder(T_a) ),
inference(skolemisation,[status(esa)],[f569_nnf]) ).
cnf(c569,plain,
( ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ class_Orderings_Opreorder(X0) ),
inference(cnf_transformation,[status(esa)],[f569_sk]) ).
cnf(f570,axiom,
( ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_1) ).
fof(f570_nnf,plain,
! [T_a,V_x,V_y] :
( ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
inference(nnf_transformation,[status(thm)],[f570]) ).
fof(f570_sk,plain,
! [T_a,V_x,V_y] :
( ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
inference(skolemisation,[status(esa)],[f570_nnf]) ).
cnf(c570,plain,
( ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ class_Orderings_Olinorder(X0) ),
inference(cnf_transformation,[status(esa)],[f570_sk]) ).
cnf(f571,axiom,
( ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a)
| ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| ~ class_Orderings_Oorder(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).
fof(f571_nnf,plain,
! [T_a,V_a,V_b] :
( ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a)
| ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| ~ class_Orderings_Oorder(T_a) ),
inference(nnf_transformation,[status(thm)],[f571]) ).
fof(f571_sk,plain,
! [T_a,V_a,V_b] :
( ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a)
| ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| ~ class_Orderings_Oorder(T_a) ),
inference(skolemisation,[status(esa)],[f571_nnf]) ).
cnf(c571,plain,
( ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ class_Orderings_Oorder(X0) ),
inference(cnf_transformation,[status(esa)],[f571_sk]) ).
cnf(f622,axiom,
~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(V_x,tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),V_x,tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__add__one__not__less__self_0) ).
fof(f622_nnf,plain,
! [V_x] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(V_x,tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),V_x,tc_RealDef_Oreal),
inference(nnf_transformation,[status(thm)],[f622]) ).
fof(f622_sk,plain,
! [V_x] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(V_x,tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),V_x,tc_RealDef_Oreal),
inference(skolemisation,[status(esa)],[f622_nnf]) ).
cnf(c622,plain,
~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),X0,tc_RealDef_Oreal),
inference(cnf_transformation,[status(esa)],[f622_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c12,c24,c88,c99,c101,c115,c232,c234,c236,c239,c289,c324,c410,c411,c451,c471,c503,c520,c521,c522,c523,c536,c551,c568,c569,c570,c571,c622,c674]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t77371]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG362-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n007.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 : Fri Sep 25 05:26:07 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 204.59/27.22 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 204.59/27.22 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------