%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SWV594-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n020.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 03:13:46 PM UTC 2026
% Result : Unsatisfiable 54.44s 7.34s
% Output : Proof 54.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 40
% Syntax : Number of formulae : 182 ( 74 unt; 0 def)
% Number of atoms : 330 ( 71 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 430 ( 282 ~; 148 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 15 ( 13 usr; 1 prp; 0-3 aty)
% Number of functors : 20 ( 20 usr; 6 con; 0-4 aty)
% Number of variables : 244 ( 18 sgn 116 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f1073,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(V_x,c_Transcendental_Opi,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Osin(V_x),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sin__gt__zero__pi_0) ).
fof(f1073_nnf,plain,
! [V_x] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(V_x,c_Transcendental_Opi,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Osin(V_x),tc_RealDef_Oreal) ),
inference(nnf_transformation,[status(thm)],[f1073]) ).
fof(f1073_sk,plain,
! [V_x] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(V_x,c_Transcendental_Opi,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Osin(V_x),tc_RealDef_Oreal) ),
inference(skolemisation,[status(esa)],[f1073_nnf]) ).
cnf(c1073,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X0,c_Transcendental_Opi,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Osin(X0),tc_RealDef_Oreal) ),
inference(cnf_transformation,[status(esa)],[f1073_sk]) ).
cnf(t42,plain,
ifeq(c_HOL_Oord__class_Oless(X1,c_Transcendental_Opi,tc_RealDef_Oreal),true,ifeq(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1,tc_RealDef_Oreal),true,c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Osin(X1),tc_RealDef_Oreal),true),true) = true,
inference(equality_encoding,[status(esa)],[c1073]) ).
cnf(f1086,axiom,
c_Transcendental_Osin(c_Transcendental_Opi) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sin__pi_0) ).
fof(f1086_nnf,plain,
c_Transcendental_Osin(c_Transcendental_Opi) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(nnf_transformation,[status(thm)],[f1086]) ).
cnf(c1086,plain,
c_Transcendental_Osin(c_Transcendental_Opi) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(cnf_transformation,[status(esa)],[f1086_nnf]) ).
cnf(t3,plain,
c_Transcendental_Osin(c_Transcendental_Opi) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(equality_encoding,[status(esa)],[c1086]) ).
cnf(t98,plain,
c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Osin(c_Transcendental_Opi),
inference(orient,[status(thm)],[t3]) ).
cnf(f1091,negated_conjecture,
c_Transcendental_Osin(v_x) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f1091_nnf,plain,
c_Transcendental_Osin(v_x) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(nnf_transformation,[status(thm)],[f1091]) ).
cnf(c1091,plain,
c_Transcendental_Osin(v_x) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(cnf_transformation,[status(esa)],[f1091_nnf]) ).
cnf(t4,plain,
c_Transcendental_Osin(v_x) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(equality_encoding,[status(esa)],[c1091]) ).
cnf(t405,plain,
c_Transcendental_Osin(v_x) = c_Transcendental_Osin(c_Transcendental_Opi),
inference(step,[status(thm)],[t4,t98]) ).
cnf(t99,plain,
c_Transcendental_Osin(c_Transcendental_Opi) = c_Transcendental_Osin(v_x),
inference(orient,[status(thm)],[t405]) ).
cnf(t406,plain,
c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Osin(v_x),
inference(step,[status(thm)],[t98,t99]) ).
cnf(t100,plain,
c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Osin(v_x),
inference(orient,[status(thm)],[t406]) ).
cnf(t94,axiom,
sF0 = c_Transcendental_Osin(v_x),
introduced(definition) ).
cnf(t102,plain,
c_Transcendental_Osin(v_x) = sF0,
inference(orient,[status(thm)],[t94]) ).
cnf(t408,plain,
c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = sF0,
inference(step,[status(thm)],[t100,t102]) ).
cnf(t103,plain,
c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = sF0,
inference(orient,[status(thm)],[t408]) ).
cnf(t455,plain,
ifeq(c_HOL_Oord__class_Oless(X1,c_Transcendental_Opi,tc_RealDef_Oreal),true,ifeq(c_HOL_Oord__class_Oless(sF0,X1,tc_RealDef_Oreal),true,c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Osin(X1),tc_RealDef_Oreal),true),true) = true,
inference(step,[status(thm)],[t42,t103]) ).
cnf(t456,plain,
ifeq(c_HOL_Oord__class_Oless(X1,c_Transcendental_Opi,tc_RealDef_Oreal),true,ifeq(c_HOL_Oord__class_Oless(sF0,X1,tc_RealDef_Oreal),true,c_HOL_Oord__class_Oless(sF0,c_Transcendental_Osin(X1),tc_RealDef_Oreal),true),true) = true,
inference(step,[status(thm)],[t455,t103]) ).
cnf(t370,plain,
ifeq(c_HOL_Oord__class_Oless(X1,c_Transcendental_Opi,tc_RealDef_Oreal),true,ifeq(c_HOL_Oord__class_Oless(sF0,X1,tc_RealDef_Oreal),true,c_HOL_Oord__class_Oless(sF0,c_Transcendental_Osin(X1),tc_RealDef_Oreal),true),true) = true,
inference(orient,[status(thm)],[t456]) ).
cnf(t372,plain,
true = ifeq(c_HOL_Oord__class_Oless(v_x,c_Transcendental_Opi,tc_RealDef_Oreal),true,ifeq(c_HOL_Oord__class_Oless(sF0,v_x,tc_RealDef_Oreal),true,c_HOL_Oord__class_Oless(sF0,sF0,tc_RealDef_Oreal),true),true),
inference(cp,[status(thm)],[t370,t102]) ).
cnf(f1089,axiom,
c_HOL_Oord__class_Oless(v_x,c_Transcendental_Opi,tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0) ).
fof(f1089_nnf,plain,
c_HOL_Oord__class_Oless(v_x,c_Transcendental_Opi,tc_RealDef_Oreal),
inference(nnf_transformation,[status(thm)],[f1089]) ).
cnf(c1089,plain,
c_HOL_Oord__class_Oless(v_x,c_Transcendental_Opi,tc_RealDef_Oreal),
inference(cnf_transformation,[status(esa)],[f1089_nnf]) ).
cnf(t11,plain,
c_HOL_Oord__class_Oless(v_x,c_Transcendental_Opi,tc_RealDef_Oreal) = true,
inference(equality_encoding,[status(esa)],[c1089]) ).
cnf(t115,plain,
c_HOL_Oord__class_Oless(v_x,c_Transcendental_Opi,tc_RealDef_Oreal) = true,
inference(orient,[status(thm)],[t11]) ).
cnf(t457,plain,
true = ifeq(true,true,ifeq(c_HOL_Oord__class_Oless(sF0,v_x,tc_RealDef_Oreal),true,c_HOL_Oord__class_Oless(sF0,sF0,tc_RealDef_Oreal),true),true),
inference(step,[status(thm)],[t372,t115]) ).
cnf(t20,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t123,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t20]) ).
cnf(t458,plain,
true = ifeq(c_HOL_Oord__class_Oless(sF0,v_x,tc_RealDef_Oreal),true,c_HOL_Oord__class_Oless(sF0,sF0,tc_RealDef_Oreal),true),
inference(step,[status(thm)],[t457,t123]) ).
cnf(f1087,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_x,tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_0_0) ).
fof(f1087_nnf,plain,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_x,tc_RealDef_Oreal),
inference(nnf_transformation,[status(thm)],[f1087]) ).
cnf(c1087,plain,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_x,tc_RealDef_Oreal),
inference(cnf_transformation,[status(esa)],[f1087_nnf]) ).
cnf(t15,plain,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_x,tc_RealDef_Oreal) = true,
inference(equality_encoding,[status(esa)],[c1087]) ).
cnf(t416,plain,
c_HOL_Oord__class_Oless(sF0,v_x,tc_RealDef_Oreal) = true,
inference(step,[status(thm)],[t15,t103]) ).
cnf(t119,plain,
c_HOL_Oord__class_Oless(sF0,v_x,tc_RealDef_Oreal) = true,
inference(orient,[status(thm)],[t416]) ).
cnf(t459,plain,
true = ifeq(true,true,c_HOL_Oord__class_Oless(sF0,sF0,tc_RealDef_Oreal),true),
inference(step,[status(thm)],[t458,t119]) ).
cnf(t460,plain,
true = c_HOL_Oord__class_Oless(sF0,sF0,tc_RealDef_Oreal),
inference(step,[status(thm)],[t459,t123]) ).
cnf(f752,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(f752_nnf,plain,
! [V_x] : ~ c_HOL_Oord__class_Oless(V_x,V_x,tc_RealDef_Oreal),
inference(nnf_transformation,[status(thm)],[f752]) ).
fof(f752_sk,plain,
! [V_x] : ~ c_HOL_Oord__class_Oless(V_x,V_x,tc_RealDef_Oreal),
inference(skolemisation,[status(esa)],[f752_nnf]) ).
cnf(c752,plain,
~ c_HOL_Oord__class_Oless(X0,X0,tc_RealDef_Oreal),
inference(cnf_transformation,[status(esa)],[f752_sk]) ).
cnf(t10,plain,
c_HOL_Oord__class_Oless(X1,X1,tc_RealDef_Oreal) = false,
inference(equality_encoding,[status(esa)],[c752]) ).
cnf(t114,plain,
c_HOL_Oord__class_Oless(X1,X1,tc_RealDef_Oreal) = false,
inference(orient,[status(thm)],[t10]) ).
cnf(t461,plain,
true = false,
inference(step,[status(thm)],[t460,t114]) ).
cnf(t375,plain,
false = true,
inference(orient,[status(thm)],[t461]) ).
cnf(f146,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(f146_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)],[f146]) ).
fof(f146_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)],[f146_nnf]) ).
cnf(c146,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)],[f146_sk]) ).
cnf(f201,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(f201_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)],[f201]) ).
fof(f201_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)],[f201_nnf]) ).
cnf(c201,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)],[f201_sk]) ).
cnf(f238,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(f238_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)],[f238]) ).
fof(f238_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)],[f238_nnf]) ).
cnf(c238,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)],[f238_sk]) ).
cnf(f270,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(f270_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)],[f270]) ).
fof(f270_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)],[f270_nnf]) ).
cnf(c270,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)],[f270_sk]) ).
cnf(f306,axiom,
c_Transcendental_Ocos(c_Transcendental_Oarctan(V_x)) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cos__arctan__not__zero_0) ).
fof(f306_nnf,plain,
! [V_x] : c_Transcendental_Ocos(c_Transcendental_Oarctan(V_x)) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(nnf_transformation,[status(thm)],[f306]) ).
fof(f306_sk,plain,
! [V_x] : c_Transcendental_Ocos(c_Transcendental_Oarctan(V_x)) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(skolemisation,[status(esa)],[f306_nnf]) ).
cnf(c306,plain,
c_Transcendental_Ocos(c_Transcendental_Oarctan(X0)) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(cnf_transformation,[status(esa)],[f306_sk]) ).
cnf(f349,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(f349_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)],[f349]) ).
fof(f349_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)],[f349_nnf]) ).
cnf(c349,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)],[f349_sk]) ).
cnf(f420,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(f420_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)],[f420]) ).
fof(f420_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)],[f420_nnf]) ).
cnf(c420,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)],[f420_sk]) ).
cnf(f455,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(f455_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)],[f455]) ).
fof(f455_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)],[f455_nnf]) ).
cnf(c455,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)],[f455_sk]) ).
cnf(f574,axiom,
~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__real__square__gt__zero_1) ).
fof(f574_nnf,plain,
~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(nnf_transformation,[status(thm)],[f574]) ).
fof(f574_sk,plain,
~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(skolemisation,[status(esa)],[f574_nnf]) ).
cnf(c574,plain,
~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(cnf_transformation,[status(esa)],[f574_sk]) ).
cnf(f608,axiom,
~ c_HOL_Oord__class_Oless(c_Transcendental_Opi,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pi__not__less__zero_0) ).
fof(f608_nnf,plain,
~ c_HOL_Oord__class_Oless(c_Transcendental_Opi,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(nnf_transformation,[status(thm)],[f608]) ).
fof(f608_sk,plain,
~ c_HOL_Oord__class_Oless(c_Transcendental_Opi,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(skolemisation,[status(esa)],[f608_nnf]) ).
cnf(c608,plain,
~ c_HOL_Oord__class_Oless(c_Transcendental_Opi,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(cnf_transformation,[status(esa)],[f608_sk]) ).
cnf(f609,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(f609_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)],[f609]) ).
fof(f609_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)],[f609_nnf]) ).
cnf(c609,plain,
( ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_lessequals(X1,X2,X0)
| ~ class_Orderings_Opreorder(X0) ),
inference(cnf_transformation,[status(esa)],[f609_sk]) ).
cnf(f611,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(f611_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)],[f611]) ).
fof(f611_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)],[f611_nnf]) ).
cnf(c611,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X0)
| ~ c_lessequals(X1,X1,X0)
| ~ class_Orderings_Olinorder(X0) ),
inference(cnf_transformation,[status(esa)],[f611_sk]) ).
cnf(f613,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(f613_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)],[f613]) ).
fof(f613_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)],[f613_nnf]) ).
cnf(c613,plain,
( ~ c_lessequals(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ class_Orderings_Olinorder(X0) ),
inference(cnf_transformation,[status(esa)],[f613_sk]) ).
cnf(f616,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(f616_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)],[f616]) ).
fof(f616_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)],[f616_nnf]) ).
cnf(c616,plain,
( ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_lessequals(X1,X2,X0)
| ~ class_Orderings_Olinorder(X0) ),
inference(cnf_transformation,[status(esa)],[f616_sk]) ).
cnf(f721,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(f721_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)],[f721]) ).
fof(f721_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)],[f721_nnf]) ).
cnf(c721,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)],[f721_sk]) ).
cnf(f750,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(f750_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)],[f750]) ).
fof(f750_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)],[f750_nnf]) ).
cnf(c750,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X0)
| ~ class_Orderings_Olinorder(X0) ),
inference(cnf_transformation,[status(esa)],[f750_sk]) ).
cnf(f751,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(f751_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)],[f751]) ).
fof(f751_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)],[f751_nnf]) ).
cnf(c751,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X0)
| ~ class_Orderings_Oorder(X0) ),
inference(cnf_transformation,[status(esa)],[f751_sk]) ).
cnf(f753,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(f753_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)],[f753]) ).
fof(f753_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)],[f753_nnf]) ).
cnf(c753,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X0)
| ~ class_Orderings_Opreorder(X0) ),
inference(cnf_transformation,[status(esa)],[f753_sk]) ).
cnf(f757,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(f757_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)],[f757]) ).
fof(f757_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)],[f757_nnf]) ).
cnf(c757,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)],[f757_sk]) ).
cnf(f784,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(f784_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)],[f784]) ).
fof(f784_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)],[f784_nnf]) ).
cnf(c784,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)],[f784_sk]) ).
cnf(f921,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(f921_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)],[f921]) ).
fof(f921_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)],[f921_nnf]) ).
cnf(c921,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)],[f921_sk]) ).
cnf(f983,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(f983_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)],[f983]) ).
fof(f983_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)],[f983_nnf]) ).
cnf(c983,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)],[f983_sk]) ).
cnf(f984,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(f984_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)],[f984]) ).
fof(f984_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)],[f984_nnf]) ).
cnf(c984,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)],[f984_sk]) ).
cnf(f987,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(f987_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)],[f987]) ).
fof(f987_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)],[f987_nnf]) ).
cnf(c987,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)],[f987_sk]) ).
cnf(f988,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(f988_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)],[f988]) ).
fof(f988_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)],[f988_nnf]) ).
cnf(c988,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)],[f988_sk]) ).
cnf(f1000,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(f1000_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)],[f1000]) ).
fof(f1000_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)],[f1000_nnf]) ).
cnf(c1000,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)],[f1000_sk]) ).
cnf(f1012,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(f1012_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)],[f1012]) ).
fof(f1012_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)],[f1012_nnf]) ).
cnf(c1012,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)],[f1012_sk]) ).
cnf(f1041,axiom,
( c_Transcendental_Oexp(V_x,T_a) != c_HOL_Ozero__class_Ozero(T_a)
| ~ class_RealVector_Oreal__normed__field(T_a)
| ~ class_SEQ_Obanach(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp__not__eq__zero_0) ).
fof(f1041_nnf,plain,
! [T_a,V_x] :
( c_Transcendental_Oexp(V_x,T_a) != c_HOL_Ozero__class_Ozero(T_a)
| ~ class_RealVector_Oreal__normed__field(T_a)
| ~ class_SEQ_Obanach(T_a) ),
inference(nnf_transformation,[status(thm)],[f1041]) ).
fof(f1041_sk,plain,
! [T_a,V_x] :
( c_Transcendental_Oexp(V_x,T_a) != c_HOL_Ozero__class_Ozero(T_a)
| ~ class_RealVector_Oreal__normed__field(T_a)
| ~ class_SEQ_Obanach(T_a) ),
inference(skolemisation,[status(esa)],[f1041_nnf]) ).
cnf(c1041,plain,
( c_Transcendental_Oexp(X1,X0) != c_HOL_Ozero__class_Ozero(X0)
| ~ class_RealVector_Oreal__normed__field(X0)
| ~ class_SEQ_Obanach(X0) ),
inference(cnf_transformation,[status(esa)],[f1041_sk]) ).
cnf(f1052,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(f1052_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)],[f1052]) ).
fof(f1052_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)],[f1052_nnf]) ).
cnf(c1052,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)],[f1052_sk]) ).
cnf(f1058,axiom,
c_Log_Opowr(V_x,V_a) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_powr__not__zero_0) ).
fof(f1058_nnf,plain,
! [V_x,V_a] : c_Log_Opowr(V_x,V_a) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(nnf_transformation,[status(thm)],[f1058]) ).
fof(f1058_sk,plain,
! [V_x,V_a] : c_Log_Opowr(V_x,V_a) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(skolemisation,[status(esa)],[f1058_nnf]) ).
cnf(c1058,plain,
c_Log_Opowr(X0,X1) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(cnf_transformation,[status(esa)],[f1058_sk]) ).
cnf(f1063,axiom,
c_Transcendental_Opi != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pi__neq__zero_0) ).
fof(f1063_nnf,plain,
c_Transcendental_Opi != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(nnf_transformation,[status(thm)],[f1063]) ).
fof(f1063_sk,plain,
c_Transcendental_Opi != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(skolemisation,[status(esa)],[f1063_nnf]) ).
cnf(c1063,plain,
c_Transcendental_Opi != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(cnf_transformation,[status(esa)],[f1063_sk]) ).
cnf(f1064,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(f1064_nnf,plain,
c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_HOL_Oone__class_Oone(tc_RealDef_Oreal),
inference(nnf_transformation,[status(thm)],[f1064]) ).
fof(f1064_sk,plain,
c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_HOL_Oone__class_Oone(tc_RealDef_Oreal),
inference(skolemisation,[status(esa)],[f1064_nnf]) ).
cnf(c1064,plain,
c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_HOL_Oone__class_Oone(tc_RealDef_Oreal),
inference(cnf_transformation,[status(esa)],[f1064_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c146,c201,c238,c270,c306,c349,c420,c455,c574,c608,c609,c611,c613,c616,c721,c750,c751,c752,c753,c757,c784,c921,c983,c984,c987,c988,c1000,c1012,c1041,c1052,c1058,c1063,c1064]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t375]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWV594-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.41 % Computer : n020.cluster.edu
% 0.15/0.41 % Model : x86_64 x86_64
% 0.15/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.41 % Memory : 8046.5625MB
% 0.15/0.41 % OS : Linux 6.8.0-71-generic
% 0.15/0.41 % CPULimit : 300
% 0.15/0.41 % WCLimit : 300
% 0.15/0.41 % DateTime : Thu Sep 24 20:41:03 UTC 2026
% 0.15/0.41 % CPUTime :
% 0.15/0.41 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 54.44/7.34 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 54.44/7.34 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------