%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SWV596-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n002.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 54.28s 7.24s
% Output : Proof 54.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 45
% Syntax : Number of formulae : 211 ( 99 unt; 0 def)
% Number of atoms : 363 ( 100 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 446 ( 294 ~; 152 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 1 prp; 0-3 aty)
% Number of functors : 25 ( 25 usr; 9 con; 0-4 aty)
% Number of variables : 246 ( 18 sgn 116 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f1127,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(f1127_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)],[f1127]) ).
fof(f1127_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)],[f1127_nnf]) ).
cnf(c1127,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)],[f1127_sk]) ).
cnf(t108,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)],[c1127]) ).
cnf(f1138,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(f1138_nnf,plain,
c_Transcendental_Osin(c_Transcendental_Opi) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(nnf_transformation,[status(thm)],[f1138]) ).
cnf(c1138,plain,
c_Transcendental_Osin(c_Transcendental_Opi) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(cnf_transformation,[status(esa)],[f1138_nnf]) ).
cnf(t6,plain,
c_Transcendental_Osin(c_Transcendental_Opi) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(equality_encoding,[status(esa)],[c1138]) ).
cnf(t201,plain,
c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Osin(c_Transcendental_Opi),
inference(orient,[status(thm)],[t6]) ).
cnf(t195,axiom,
sF2 = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
introduced(definition) ).
cnf(t6771,plain,
sF2 = c_Transcendental_Osin(c_Transcendental_Opi),
inference(step,[status(thm)],[t195,t201]) ).
cnf(t202,plain,
c_Transcendental_Osin(c_Transcendental_Opi) = sF2,
inference(orient,[status(thm)],[t6771]) ).
cnf(t6772,plain,
c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = sF2,
inference(step,[status(thm)],[t201,t202]) ).
cnf(t203,plain,
c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = sF2,
inference(orient,[status(thm)],[t6772]) ).
cnf(t194,axiom,
sF1 = c_Transcendental_Osin(c_HOL_Ominus__class_Ominus(v_x,c_Transcendental_Opi,tc_RealDef_Oreal)),
introduced(definition) ).
cnf(f1129,axiom,
c_Transcendental_Osin(c_HOL_Ominus__class_Ominus(V_x,c_Transcendental_Opi,tc_RealDef_Oreal)) = c_HOL_Ouminus__class_Ouminus(c_Transcendental_Osin(V_x),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sin__periodic__pi__diff_0) ).
fof(f1129_nnf,plain,
! [V_x] : c_Transcendental_Osin(c_HOL_Ominus__class_Ominus(V_x,c_Transcendental_Opi,tc_RealDef_Oreal)) = c_HOL_Ouminus__class_Ouminus(c_Transcendental_Osin(V_x),tc_RealDef_Oreal),
inference(nnf_transformation,[status(thm)],[f1129]) ).
fof(f1129_sk,plain,
! [V_x] : c_Transcendental_Osin(c_HOL_Ominus__class_Ominus(V_x,c_Transcendental_Opi,tc_RealDef_Oreal)) = c_HOL_Ouminus__class_Ouminus(c_Transcendental_Osin(V_x),tc_RealDef_Oreal),
inference(skolemisation,[status(esa)],[f1129_nnf]) ).
cnf(c1129,plain,
c_Transcendental_Osin(c_HOL_Ominus__class_Ominus(X0,c_Transcendental_Opi,tc_RealDef_Oreal)) = c_HOL_Ouminus__class_Ouminus(c_Transcendental_Osin(X0),tc_RealDef_Oreal),
inference(cnf_transformation,[status(esa)],[f1129_sk]) ).
cnf(t42,plain,
c_Transcendental_Osin(c_HOL_Ominus__class_Ominus(X1,c_Transcendental_Opi,tc_RealDef_Oreal)) = c_HOL_Ouminus__class_Ouminus(c_Transcendental_Osin(X1),tc_RealDef_Oreal),
inference(equality_encoding,[status(esa)],[c1129]) ).
cnf(t232,plain,
c_Transcendental_Osin(c_HOL_Ominus__class_Ominus(X1,c_Transcendental_Opi,tc_RealDef_Oreal)) = c_HOL_Ouminus__class_Ouminus(c_Transcendental_Osin(X1),tc_RealDef_Oreal),
inference(orient,[status(thm)],[t42]) ).
cnf(t6788,plain,
sF1 = c_HOL_Ouminus__class_Ouminus(c_Transcendental_Osin(v_x),tc_RealDef_Oreal),
inference(step,[status(thm)],[t194,t232]) ).
cnf(t193,axiom,
sF0 = c_HOL_Ominus__class_Ominus(v_x,c_Transcendental_Opi,tc_RealDef_Oreal),
introduced(definition) ).
cnf(t222,plain,
c_HOL_Ominus__class_Ominus(v_x,c_Transcendental_Opi,tc_RealDef_Oreal) = sF0,
inference(orient,[status(thm)],[t193]) ).
cnf(t233,plain,
c_HOL_Ouminus__class_Ouminus(c_Transcendental_Osin(v_x),tc_RealDef_Oreal) = c_Transcendental_Osin(sF0),
inference(cp,[status(thm)],[t232,t222]) ).
cnf(f1146,negated_conjecture,
c_Transcendental_Osin(c_HOL_Ominus__class_Ominus(v_x,c_Transcendental_Opi,tc_RealDef_Oreal)) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f1146_nnf,plain,
c_Transcendental_Osin(c_HOL_Ominus__class_Ominus(v_x,c_Transcendental_Opi,tc_RealDef_Oreal)) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(nnf_transformation,[status(thm)],[f1146]) ).
cnf(c1146,plain,
c_Transcendental_Osin(c_HOL_Ominus__class_Ominus(v_x,c_Transcendental_Opi,tc_RealDef_Oreal)) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(cnf_transformation,[status(esa)],[f1146_nnf]) ).
cnf(t26,plain,
c_Transcendental_Osin(c_HOL_Ominus__class_Ominus(v_x,c_Transcendental_Opi,tc_RealDef_Oreal)) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(equality_encoding,[status(esa)],[c1146]) ).
cnf(t6785,plain,
c_Transcendental_Osin(sF0) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(step,[status(thm)],[t26,t222]) ).
cnf(t6786,plain,
c_Transcendental_Osin(sF0) = sF2,
inference(step,[status(thm)],[t6785,t203]) ).
cnf(t228,plain,
c_Transcendental_Osin(sF0) = sF2,
inference(orient,[status(thm)],[t6786]) ).
cnf(t6787,plain,
c_HOL_Ouminus__class_Ouminus(c_Transcendental_Osin(v_x),tc_RealDef_Oreal) = sF2,
inference(step,[status(thm)],[t233,t228]) ).
cnf(t234,plain,
c_HOL_Ouminus__class_Ouminus(c_Transcendental_Osin(v_x),tc_RealDef_Oreal) = sF2,
inference(orient,[status(thm)],[t6787]) ).
cnf(t6789,plain,
sF1 = sF2,
inference(step,[status(thm)],[t6788,t234]) ).
cnf(t239,plain,
sF2 = sF1,
inference(orient,[status(thm)],[t6789]) ).
cnf(t6790,plain,
c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = sF1,
inference(step,[status(thm)],[t203,t239]) ).
cnf(t240,plain,
c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = sF1,
inference(orient,[status(thm)],[t6790]) ).
cnf(t7319,plain,
ifeq(c_HOL_Oord__class_Oless(X1,c_Transcendental_Opi,tc_RealDef_Oreal),true,ifeq(c_HOL_Oord__class_Oless(sF1,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)],[t108,t240]) ).
cnf(t7320,plain,
ifeq(c_HOL_Oord__class_Oless(X1,c_Transcendental_Opi,tc_RealDef_Oreal),true,ifeq(c_HOL_Oord__class_Oless(sF1,X1,tc_RealDef_Oreal),true,c_HOL_Oord__class_Oless(sF1,c_Transcendental_Osin(X1),tc_RealDef_Oreal),true),true) = true,
inference(step,[status(thm)],[t7319,t240]) ).
cnf(t6672,plain,
ifeq(c_HOL_Oord__class_Oless(X1,c_Transcendental_Opi,tc_RealDef_Oreal),true,ifeq(c_HOL_Oord__class_Oless(sF1,X1,tc_RealDef_Oreal),true,c_HOL_Oord__class_Oless(sF1,c_Transcendental_Osin(X1),tc_RealDef_Oreal),true),true) = true,
inference(orient,[status(thm)],[t7320]) ).
cnf(t6799,plain,
c_Transcendental_Osin(sF0) = sF1,
inference(step,[status(thm)],[t228,t239]) ).
cnf(t252,plain,
c_Transcendental_Osin(sF0) = sF1,
inference(orient,[status(thm)],[t6799]) ).
cnf(t6674,plain,
true = ifeq(c_HOL_Oord__class_Oless(sF0,c_Transcendental_Opi,tc_RealDef_Oreal),true,ifeq(c_HOL_Oord__class_Oless(sF1,sF0,tc_RealDef_Oreal),true,c_HOL_Oord__class_Oless(sF1,sF1,tc_RealDef_Oreal),true),true),
inference(cp,[status(thm)],[t6672,t252]) ).
cnf(f1144,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(v_x,c_Transcendental_Opi,tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0) ).
fof(f1144_nnf,plain,
c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(v_x,c_Transcendental_Opi,tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),
inference(nnf_transformation,[status(thm)],[f1144]) ).
cnf(c1144,plain,
c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(v_x,c_Transcendental_Opi,tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),
inference(cnf_transformation,[status(esa)],[f1144_nnf]) ).
cnf(t31,plain,
c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(v_x,c_Transcendental_Opi,tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal) = true,
inference(equality_encoding,[status(esa)],[c1144]) ).
cnf(t6824,plain,
c_HOL_Oord__class_Oless(sF0,c_Transcendental_Opi,tc_RealDef_Oreal) = true,
inference(step,[status(thm)],[t31,t222]) ).
cnf(t308,plain,
c_HOL_Oord__class_Oless(sF0,c_Transcendental_Opi,tc_RealDef_Oreal) = true,
inference(orient,[status(thm)],[t6824]) ).
cnf(t7321,plain,
true = ifeq(true,true,ifeq(c_HOL_Oord__class_Oless(sF1,sF0,tc_RealDef_Oreal),true,c_HOL_Oord__class_Oless(sF1,sF1,tc_RealDef_Oreal),true),true),
inference(step,[status(thm)],[t6674,t308]) ).
cnf(t25,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t227,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t25]) ).
cnf(t7322,plain,
true = ifeq(c_HOL_Oord__class_Oless(sF1,sF0,tc_RealDef_Oreal),true,c_HOL_Oord__class_Oless(sF1,sF1,tc_RealDef_Oreal),true),
inference(step,[status(thm)],[t7321,t227]) ).
cnf(f1145,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(v_x,c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0_01) ).
fof(f1145_nnf,plain,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(v_x,c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(nnf_transformation,[status(thm)],[f1145]) ).
cnf(c1145,plain,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(v_x,c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(cnf_transformation,[status(esa)],[f1145_nnf]) ).
cnf(t41,plain,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(v_x,c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal) = true,
inference(equality_encoding,[status(esa)],[c1145]) ).
cnf(t6833,plain,
c_HOL_Oord__class_Oless(sF1,c_HOL_Ominus__class_Ominus(v_x,c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal) = true,
inference(step,[status(thm)],[t41,t240]) ).
cnf(t6834,plain,
c_HOL_Oord__class_Oless(sF1,sF0,tc_RealDef_Oreal) = true,
inference(step,[status(thm)],[t6833,t222]) ).
cnf(t367,plain,
c_HOL_Oord__class_Oless(sF1,sF0,tc_RealDef_Oreal) = true,
inference(orient,[status(thm)],[t6834]) ).
cnf(t7323,plain,
true = ifeq(true,true,c_HOL_Oord__class_Oless(sF1,sF1,tc_RealDef_Oreal),true),
inference(step,[status(thm)],[t7322,t367]) ).
cnf(t7324,plain,
true = c_HOL_Oord__class_Oless(sF1,sF1,tc_RealDef_Oreal),
inference(step,[status(thm)],[t7323,t227]) ).
cnf(f819,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(f819_nnf,plain,
! [V_x] : ~ c_HOL_Oord__class_Oless(V_x,V_x,tc_RealDef_Oreal),
inference(nnf_transformation,[status(thm)],[f819]) ).
fof(f819_sk,plain,
! [V_x] : ~ c_HOL_Oord__class_Oless(V_x,V_x,tc_RealDef_Oreal),
inference(skolemisation,[status(esa)],[f819_nnf]) ).
cnf(c819,plain,
~ c_HOL_Oord__class_Oless(X0,X0,tc_RealDef_Oreal),
inference(cnf_transformation,[status(esa)],[f819_sk]) ).
cnf(t12,plain,
c_HOL_Oord__class_Oless(X1,X1,tc_RealDef_Oreal) = false,
inference(equality_encoding,[status(esa)],[c819]) ).
cnf(t213,plain,
c_HOL_Oord__class_Oless(X1,X1,tc_RealDef_Oreal) = false,
inference(orient,[status(thm)],[t12]) ).
cnf(t7325,plain,
true = false,
inference(step,[status(thm)],[t7324,t213]) ).
cnf(t6720,plain,
false = true,
inference(orient,[status(thm)],[t7325]) ).
cnf(f92,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(f92_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)],[f92]) ).
fof(f92_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)],[f92_nnf]) ).
cnf(c92,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)],[f92_sk]) ).
cnf(f128,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(f128_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)],[f128]) ).
fof(f128_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)],[f128_nnf]) ).
cnf(c128,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)],[f128_sk]) ).
cnf(f204,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(f204_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)],[f204]) ).
fof(f204_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)],[f204_nnf]) ).
cnf(c204,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)],[f204_sk]) ).
cnf(f259,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(f259_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)],[f259]) ).
fof(f259_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)],[f259_nnf]) ).
cnf(c259,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)],[f259_sk]) ).
cnf(f303,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(f303_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)],[f303]) ).
fof(f303_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)],[f303_nnf]) ).
cnf(c303,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)],[f303_sk]) ).
cnf(f362,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(f362_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)],[f362]) ).
fof(f362_sk,plain,
! [V_x] : c_Transcendental_Ocos(c_Transcendental_Oarctan(V_x)) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(skolemisation,[status(esa)],[f362_nnf]) ).
cnf(c362,plain,
c_Transcendental_Ocos(c_Transcendental_Oarctan(X0)) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(cnf_transformation,[status(esa)],[f362_sk]) ).
cnf(f407,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(f407_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)],[f407]) ).
fof(f407_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)],[f407_nnf]) ).
cnf(c407,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)],[f407_sk]) ).
cnf(f451,axiom,
~ c_HOL_Oord__class_Oless(c_RealDef_Oreal(V_n,tc_nat),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__real__of__nat__less__zero_0) ).
fof(f451_nnf,plain,
! [V_n] : ~ c_HOL_Oord__class_Oless(c_RealDef_Oreal(V_n,tc_nat),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(nnf_transformation,[status(thm)],[f451]) ).
fof(f451_sk,plain,
! [V_n] : ~ c_HOL_Oord__class_Oless(c_RealDef_Oreal(V_n,tc_nat),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(skolemisation,[status(esa)],[f451_nnf]) ).
cnf(c451,plain,
~ c_HOL_Oord__class_Oless(c_RealDef_Oreal(X0,tc_nat),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(cnf_transformation,[status(esa)],[f451_sk]) ).
cnf(f452,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(f452_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)],[f452]) ).
fof(f452_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)],[f452_nnf]) ).
cnf(c452,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)],[f452_sk]) ).
cnf(f507,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(f507_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)],[f507]) ).
fof(f507_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)],[f507_nnf]) ).
cnf(c507,plain,
( ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_lessequals(X1,X2,X0)
| ~ class_Orderings_Opreorder(X0) ),
inference(cnf_transformation,[status(esa)],[f507_sk]) ).
cnf(f509,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(f509_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)],[f509]) ).
fof(f509_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)],[f509_nnf]) ).
cnf(c509,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X0)
| ~ c_lessequals(X1,X1,X0)
| ~ class_Orderings_Olinorder(X0) ),
inference(cnf_transformation,[status(esa)],[f509_sk]) ).
cnf(f511,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(f511_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)],[f511]) ).
fof(f511_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)],[f511_nnf]) ).
cnf(c511,plain,
( ~ c_lessequals(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ class_Orderings_Olinorder(X0) ),
inference(cnf_transformation,[status(esa)],[f511_sk]) ).
cnf(f514,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(f514_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)],[f514]) ).
fof(f514_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)],[f514_nnf]) ).
cnf(c514,plain,
( ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_lessequals(X1,X2,X0)
| ~ class_Orderings_Olinorder(X0) ),
inference(cnf_transformation,[status(esa)],[f514_sk]) ).
cnf(f628,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(f628_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)],[f628]) ).
fof(f628_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)],[f628_nnf]) ).
cnf(c628,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)],[f628_sk]) ).
cnf(f788,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(f788_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)],[f788]) ).
fof(f788_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)],[f788_nnf]) ).
cnf(c788,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)],[f788_sk]) ).
cnf(f817,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(f817_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)],[f817]) ).
fof(f817_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)],[f817_nnf]) ).
cnf(c817,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X0)
| ~ class_Orderings_Olinorder(X0) ),
inference(cnf_transformation,[status(esa)],[f817_sk]) ).
cnf(f818,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(f818_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)],[f818]) ).
fof(f818_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)],[f818_nnf]) ).
cnf(c818,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X0)
| ~ class_Orderings_Oorder(X0) ),
inference(cnf_transformation,[status(esa)],[f818_sk]) ).
cnf(f820,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(f820_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)],[f820]) ).
fof(f820_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)],[f820_nnf]) ).
cnf(c820,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X0)
| ~ class_Orderings_Opreorder(X0) ),
inference(cnf_transformation,[status(esa)],[f820_sk]) ).
cnf(f825,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(f825_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)],[f825]) ).
fof(f825_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)],[f825_nnf]) ).
cnf(c825,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)],[f825_sk]) ).
cnf(f901,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(f901_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)],[f901]) ).
fof(f901_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)],[f901_nnf]) ).
cnf(c901,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)],[f901_sk]) ).
cnf(f911,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(f911_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)],[f911]) ).
fof(f911_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)],[f911_nnf]) ).
cnf(c911,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)],[f911_sk]) ).
cnf(f937,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(f937_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)],[f937]) ).
fof(f937_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)],[f937_nnf]) ).
cnf(c937,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)],[f937_sk]) ).
cnf(f951,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(f951_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)],[f951]) ).
fof(f951_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)],[f951_nnf]) ).
cnf(c951,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)],[f951_sk]) ).
cnf(f984,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(f984_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)],[f984]) ).
fof(f984_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)],[f984_nnf]) ).
cnf(c984,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)],[f984_sk]) ).
cnf(f1038,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(f1038_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)],[f1038]) ).
fof(f1038_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)],[f1038_nnf]) ).
cnf(c1038,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)],[f1038_sk]) ).
cnf(f1039,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(f1039_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)],[f1039]) ).
fof(f1039_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)],[f1039_nnf]) ).
cnf(c1039,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)],[f1039_sk]) ).
cnf(f1042,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(f1042_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)],[f1042]) ).
fof(f1042_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)],[f1042_nnf]) ).
cnf(c1042,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)],[f1042_sk]) ).
cnf(f1043,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(f1043_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)],[f1043]) ).
fof(f1043_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)],[f1043_nnf]) ).
cnf(c1043,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)],[f1043_sk]) ).
cnf(f1044,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(f1044_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)],[f1044]) ).
fof(f1044_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)],[f1044_nnf]) ).
cnf(c1044,plain,
c_Log_Opowr(X0,X1) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(cnf_transformation,[status(esa)],[f1044_sk]) ).
cnf(f1049,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(f1049_nnf,plain,
c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_HOL_Oone__class_Oone(tc_RealDef_Oreal),
inference(nnf_transformation,[status(thm)],[f1049]) ).
fof(f1049_sk,plain,
c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_HOL_Oone__class_Oone(tc_RealDef_Oreal),
inference(skolemisation,[status(esa)],[f1049_nnf]) ).
cnf(c1049,plain,
c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_HOL_Oone__class_Oone(tc_RealDef_Oreal),
inference(cnf_transformation,[status(esa)],[f1049_sk]) ).
cnf(f1090,axiom,
( v_x != c_Transcendental_Opi
| c_Transcendental_Ocos(v_x) != c_HOL_Oone__class_Oone(tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_calculation_I2_J_0) ).
fof(f1090_nnf,plain,
( v_x != c_Transcendental_Opi
| c_Transcendental_Ocos(v_x) != c_HOL_Oone__class_Oone(tc_RealDef_Oreal) ),
inference(nnf_transformation,[status(thm)],[f1090]) ).
fof(f1090_sk,plain,
( v_x != c_Transcendental_Opi
| c_Transcendental_Ocos(v_x) != c_HOL_Oone__class_Oone(tc_RealDef_Oreal) ),
inference(skolemisation,[status(esa)],[f1090_nnf]) ).
cnf(c1090,plain,
( v_x != c_Transcendental_Opi
| c_Transcendental_Ocos(v_x) != c_HOL_Oone__class_Oone(tc_RealDef_Oreal) ),
inference(cnf_transformation,[status(esa)],[f1090_sk]) ).
cnf(f1115,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(f1115_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)],[f1115]) ).
fof(f1115_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)],[f1115_nnf]) ).
cnf(c1115,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)],[f1115_sk]) ).
cnf(f1130,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_Transcendental_Osin(v_x) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_calculation_I1_J_0) ).
fof(f1130_nnf,plain,
( ~ 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_Transcendental_Osin(v_x) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(nnf_transformation,[status(thm)],[f1130]) ).
fof(f1130_sk,plain,
( ~ 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_Transcendental_Osin(v_x) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(skolemisation,[status(esa)],[f1130_nnf]) ).
cnf(c1130,plain,
( ~ 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_Transcendental_Osin(v_x) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(cnf_transformation,[status(esa)],[f1130_sk]) ).
cnf(f1131,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(f1131_nnf,plain,
c_Transcendental_Opi != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(nnf_transformation,[status(thm)],[f1131]) ).
fof(f1131_sk,plain,
c_Transcendental_Opi != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(skolemisation,[status(esa)],[f1131_nnf]) ).
cnf(c1131,plain,
c_Transcendental_Opi != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(cnf_transformation,[status(esa)],[f1131_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c92,c128,c204,c259,c303,c362,c407,c451,c452,c507,c509,c511,c514,c628,c788,c817,c818,c819,c820,c825,c901,c911,c937,c951,c984,c1038,c1039,c1042,c1043,c1044,c1049,c1090,c1115,c1130,c1131]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t6720]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV596-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.35 % Computer : n002.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Thu Sep 24 20:42:49 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 54.28/7.24 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 54.28/7.24 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------