%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : ALG421-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n004.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 12:52:31 PM UTC 2026
% Result : Unsatisfiable 70.00s 9.44s
% Output : Proof 70.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 44
% Syntax : Number of formulae : 186 ( 114 unt; 0 def)
% Number of atoms : 286 ( 98 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 338 ( 238 ~; 100 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 1 prp; 0-3 aty)
% Number of functors : 27 ( 27 usr; 15 con; 0-4 aty)
% Number of variables : 224 ( 22 sgn 102 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f731,negated_conjecture,
c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(v_s____,v_x,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_u____,v_x,tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_Power_Opower__class_Opower(c_Polynomial_Opoly(v_r____,v_x,tc_Complex_Ocomplex),c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f731_nnf,plain,
c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(v_s____,v_x,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_u____,v_x,tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_Power_Opower__class_Opower(c_Polynomial_Opoly(v_r____,v_x,tc_Complex_Ocomplex),c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(nnf_transformation,[status(thm)],[f731]) ).
fof(f731_sk,plain,
c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(v_s____,v_x,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_u____,v_x,tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_Power_Opower__class_Opower(c_Polynomial_Opoly(v_r____,v_x,tc_Complex_Ocomplex),c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(skolemisation,[status(esa)],[f731_nnf]) ).
cnf(c731,plain,
c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(v_s____,v_x,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_u____,v_x,tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_Power_Opower__class_Opower(c_Polynomial_Opoly(v_r____,v_x,tc_Complex_Ocomplex),c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(cnf_transformation,[status(esa)],[f731_sk]) ).
cnf(t151,plain,
eq(c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(v_s____,v_x,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_u____,v_x,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Power_Opower__class_Opower(c_Polynomial_Opoly(v_r____,v_x,tc_Complex_Ocomplex),c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),tc_Complex_Ocomplex)) = false,
inference(equality_encoding,[status(esa)],[c731]) ).
cnf(f728,axiom,
( c_HOL_Otimes__class_Otimes(V_x,V_y,T_a) = c_HOL_Otimes__class_Otimes(V_y,V_x,T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__c_0) ).
fof(f728_nnf,plain,
! [T_a,V_x,V_y] :
( c_HOL_Otimes__class_Otimes(V_x,V_y,T_a) = c_HOL_Otimes__class_Otimes(V_y,V_x,T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
inference(nnf_transformation,[status(thm)],[f728]) ).
fof(f728_sk,plain,
! [T_a,V_x,V_y] :
( c_HOL_Otimes__class_Otimes(V_x,V_y,T_a) = c_HOL_Otimes__class_Otimes(V_y,V_x,T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
inference(skolemisation,[status(esa)],[f728_nnf]) ).
cnf(c728,plain,
( c_HOL_Otimes__class_Otimes(X1,X2,X0) = c_HOL_Otimes__class_Otimes(X2,X1,X0)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[status(esa)],[f728_sk]) ).
cnf(t120,plain,
ifeq(class_Ring__and__Field_Ocomm__semiring__1(X1),true,c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X3,X2,X1)) = c_HOL_Otimes__class_Otimes(X3,X2,X1),
inference(equality_encoding,[status(esa)],[c728]) ).
cnf(t1170,plain,
ifeq(class_Ring__and__Field_Ocomm__semiring__1(X1),true,c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X3,X2,X1)) = c_HOL_Otimes__class_Otimes(X3,X2,X1),
inference(orient,[status(thm)],[t120]) ).
cnf(f770,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1) ).
fof(f770_nnf,plain,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
inference(nnf_transformation,[status(thm)],[f770]) ).
cnf(c770,plain,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
inference(cnf_transformation,[status(esa)],[f770_nnf]) ).
cnf(t6,plain,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex) = true,
inference(equality_encoding,[status(esa)],[c770]) ).
cnf(t245,plain,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex) = true,
inference(orient,[status(thm)],[t6]) ).
cnf(t1171,plain,
c_HOL_Otimes__class_Otimes(X1,X2,tc_Complex_Ocomplex) = ifeq(true,true,c_HOL_Otimes__class_Otimes(X2,X1,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(X1,X2,tc_Complex_Ocomplex)),
inference(cp,[status(thm)],[t1170,t245]) ).
cnf(t26,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t266,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t26]) ).
cnf(t21776,plain,
c_HOL_Otimes__class_Otimes(X1,X2,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(X2,X1,tc_Complex_Ocomplex),
inference(step,[status(thm)],[t1171,t266]) ).
cnf(t1195,plain,
c_HOL_Otimes__class_Otimes(X1,X2,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(X2,X1,tc_Complex_Ocomplex),
inference(orient,[status(thm)],[t21776]) ).
cnf(t21966,plain,
eq(c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(v_u____,v_x,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_s____,v_x,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Power_Opower__class_Opower(c_Polynomial_Opoly(v_r____,v_x,tc_Complex_Ocomplex),c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),tc_Complex_Ocomplex)) = false,
inference(step,[status(thm)],[t151,t1195]) ).
cnf(t233,axiom,
sF1 = c_Polynomial_Opoly(v_u____,v_x,tc_Complex_Ocomplex),
introduced(definition) ).
cnf(t258,plain,
c_Polynomial_Opoly(v_u____,v_x,tc_Complex_Ocomplex) = sF1,
inference(orient,[status(thm)],[t233]) ).
cnf(t21967,plain,
eq(c_HOL_Otimes__class_Otimes(sF1,c_Polynomial_Opoly(v_s____,v_x,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Power_Opower__class_Opower(c_Polynomial_Opoly(v_r____,v_x,tc_Complex_Ocomplex),c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),tc_Complex_Ocomplex)) = false,
inference(step,[status(thm)],[t21966,t258]) ).
cnf(t232,axiom,
sF0 = c_Polynomial_Opoly(v_s____,v_x,tc_Complex_Ocomplex),
introduced(definition) ).
cnf(t257,plain,
c_Polynomial_Opoly(v_s____,v_x,tc_Complex_Ocomplex) = sF0,
inference(orient,[status(thm)],[t232]) ).
cnf(t21968,plain,
eq(c_HOL_Otimes__class_Otimes(sF1,sF0,tc_Complex_Ocomplex),c_Power_Opower__class_Opower(c_Polynomial_Opoly(v_r____,v_x,tc_Complex_Ocomplex),c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),tc_Complex_Ocomplex)) = false,
inference(step,[status(thm)],[t21967,t257]) ).
cnf(t21969,plain,
eq(c_HOL_Otimes__class_Otimes(sF0,sF1,tc_Complex_Ocomplex),c_Power_Opower__class_Opower(c_Polynomial_Opoly(v_r____,v_x,tc_Complex_Ocomplex),c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),tc_Complex_Ocomplex)) = false,
inference(step,[status(thm)],[t21968,t1195]) ).
cnf(t234,axiom,
sF2 = c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(v_s____,v_x,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_u____,v_x,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
introduced(definition) ).
cnf(t21682,plain,
sF2 = c_HOL_Otimes__class_Otimes(sF0,c_Polynomial_Opoly(v_u____,v_x,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(step,[status(thm)],[t234,t257]) ).
cnf(t21683,plain,
sF2 = c_HOL_Otimes__class_Otimes(sF0,sF1,tc_Complex_Ocomplex),
inference(step,[status(thm)],[t21682,t258]) ).
cnf(t671,plain,
c_HOL_Otimes__class_Otimes(sF0,sF1,tc_Complex_Ocomplex) = sF2,
inference(orient,[status(thm)],[t21683]) ).
cnf(t21970,plain,
eq(sF2,c_Power_Opower__class_Opower(c_Polynomial_Opoly(v_r____,v_x,tc_Complex_Ocomplex),c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),tc_Complex_Ocomplex)) = false,
inference(step,[status(thm)],[t21969,t671]) ).
cnf(t235,axiom,
sF3 = c_Polynomial_Opoly(v_r____,v_x,tc_Complex_Ocomplex),
introduced(definition) ).
cnf(t260,plain,
c_Polynomial_Opoly(v_r____,v_x,tc_Complex_Ocomplex) = sF3,
inference(orient,[status(thm)],[t235]) ).
cnf(t21971,plain,
eq(sF2,c_Power_Opower__class_Opower(sF3,c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),tc_Complex_Ocomplex)) = false,
inference(step,[status(thm)],[t21970,t260]) ).
cnf(t236,axiom,
sF4 = c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),
introduced(definition) ).
cnf(t255,plain,
c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex) = sF4,
inference(orient,[status(thm)],[t236]) ).
cnf(t21972,plain,
eq(sF2,c_Power_Opower__class_Opower(sF3,sF4,tc_Complex_Ocomplex)) = false,
inference(step,[status(thm)],[t21971,t255]) ).
cnf(t237,axiom,
sF5 = c_Power_Opower__class_Opower(c_Polynomial_Opoly(v_r____,v_x,tc_Complex_Ocomplex),c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
introduced(definition) ).
cnf(t21642,plain,
sF5 = c_Power_Opower__class_Opower(sF3,c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(step,[status(thm)],[t237,t260]) ).
cnf(t21643,plain,
sF5 = c_Power_Opower__class_Opower(sF3,sF4,tc_Complex_Ocomplex),
inference(step,[status(thm)],[t21642,t255]) ).
cnf(t454,plain,
c_Power_Opower__class_Opower(sF3,sF4,tc_Complex_Ocomplex) = sF5,
inference(orient,[status(thm)],[t21643]) ).
cnf(t21973,plain,
eq(sF2,sF5) = false,
inference(step,[status(thm)],[t21972,t454]) ).
cnf(t8684,plain,
eq(sF2,sF5) = false,
inference(orient,[status(thm)],[t21973]) ).
cnf(t21355,plain,
eq(sF2,sF2) = false,
inference(rw,[status(thm)],[t8684]) ).
cnf(t11,plain,
eq(X1,X1) = true,
introduced(definition) ).
cnf(t250,plain,
eq(X1,X1) = true,
inference(orient,[status(thm)],[t11]) ).
cnf(t22792,plain,
true = false,
inference(step,[status(thm)],[t21355,t250]) ).
cnf(t21416,plain,
false = true,
inference(orient,[status(thm)],[t22792]) ).
cnf(f32,axiom,
c_Suc(V_n) != V_n,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__n__not__n_0) ).
fof(f32_nnf,plain,
! [V_n] : c_Suc(V_n) != V_n,
inference(nnf_transformation,[status(thm)],[f32]) ).
fof(f32_sk,plain,
! [V_n] : c_Suc(V_n) != V_n,
inference(skolemisation,[status(esa)],[f32_nnf]) ).
cnf(c32,plain,
c_Suc(X0) != X0,
inference(cnf_transformation,[status(esa)],[f32_sk]) ).
cnf(f33,axiom,
V_n != c_Suc(V_n),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_n__not__Suc__n_0) ).
fof(f33_nnf,plain,
! [V_n] : V_n != c_Suc(V_n),
inference(nnf_transformation,[status(thm)],[f33]) ).
fof(f33_sk,plain,
! [V_n] : V_n != c_Suc(V_n),
inference(skolemisation,[status(esa)],[f33_nnf]) ).
cnf(c33,plain,
X0 != c_Suc(X0),
inference(cnf_transformation,[status(esa)],[f33_sk]) ).
cnf(f86,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/sandbox/benchmark/theBenchmark.p',cls_not__sum__squares__lt__zero_0) ).
fof(f86_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)],[f86]) ).
fof(f86_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)],[f86_nnf]) ).
cnf(c86,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)],[f86_sk]) ).
cnf(f87,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/sandbox/benchmark/theBenchmark.p',cls_one__neq__zero_0) ).
fof(f87_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)],[f87]) ).
fof(f87_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)],[f87_nnf]) ).
cnf(c87,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)],[f87_sk]) ).
cnf(f144,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/sandbox/benchmark/theBenchmark.p',cls_sum__squares__gt__zero__iff_0) ).
fof(f144_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)],[f144]) ).
fof(f144_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)],[f144_nnf]) ).
cnf(c144,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)],[f144_sk]) ).
cnf(f161,axiom,
( ~ c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat)
| ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq_1) ).
fof(f161_nnf,plain,
! [V_m,V_n] :
( ~ c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat)
| ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ),
inference(nnf_transformation,[status(thm)],[f161]) ).
fof(f161_sk,plain,
! [V_m,V_n] :
( ~ c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat)
| ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ),
inference(skolemisation,[status(esa)],[f161_nnf]) ).
cnf(c161,plain,
( ~ c_HOL_Oord__class_Oless(X1,c_Suc(X0),tc_nat)
| ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat) ),
inference(cnf_transformation,[status(esa)],[f161_sk]) ).
cnf(f210,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/sandbox/benchmark/theBenchmark.p',cls_not__square__less__zero_0) ).
fof(f210_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)],[f210]) ).
fof(f210_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)],[f210_nnf]) ).
cnf(c210,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)],[f210_sk]) ).
cnf(f218,axiom,
v_na____ != c_HOL_Ozero__class_Ozero(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_n0_0) ).
fof(f218_nnf,plain,
v_na____ != c_HOL_Ozero__class_Ozero(tc_nat),
inference(nnf_transformation,[status(thm)],[f218]) ).
fof(f218_sk,plain,
v_na____ != c_HOL_Ozero__class_Ozero(tc_nat),
inference(skolemisation,[status(esa)],[f218_nnf]) ).
cnf(c218,plain,
v_na____ != c_HOL_Ozero__class_Ozero(tc_nat),
inference(cnf_transformation,[status(esa)],[f218_sk]) ).
cnf(f223,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/sandbox/benchmark/theBenchmark.p',cls_zero__neq__one_0) ).
fof(f223_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)],[f223]) ).
fof(f223_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)],[f223_nnf]) ).
cnf(c223,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)],[f223_sk]) ).
cnf(f237,axiom,
c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(V_nat_H),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Osimps_I2_J_0) ).
fof(f237_nnf,plain,
! [V_nat_H] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(V_nat_H),
inference(nnf_transformation,[status(thm)],[f237]) ).
fof(f237_sk,plain,
! [V_nat_H] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(V_nat_H),
inference(skolemisation,[status(esa)],[f237_nnf]) ).
cnf(c237,plain,
c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X0),
inference(cnf_transformation,[status(esa)],[f237_sk]) ).
cnf(f238,axiom,
c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(V_m),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zero__neq__Suc_0) ).
fof(f238_nnf,plain,
! [V_m] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(V_m),
inference(nnf_transformation,[status(thm)],[f238]) ).
fof(f238_sk,plain,
! [V_m] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(V_m),
inference(skolemisation,[status(esa)],[f238_nnf]) ).
cnf(c238,plain,
c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X0),
inference(cnf_transformation,[status(esa)],[f238_sk]) ).
cnf(f285,axiom,
( c_Power_Opower__class_Opower(V_a,c_HOL_Ozero__class_Ozero(tc_nat),T_a) != c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Power_Opower(T_a)
| ~ class_Ring__and__Field_Omult__zero(T_a)
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| ~ class_Ring__and__Field_Ozero__neq__one(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__eq__0__iff_1) ).
fof(f285_nnf,plain,
! [T_a,V_a] :
( c_Power_Opower__class_Opower(V_a,c_HOL_Ozero__class_Ozero(tc_nat),T_a) != c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Power_Opower(T_a)
| ~ class_Ring__and__Field_Omult__zero(T_a)
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| ~ class_Ring__and__Field_Ozero__neq__one(T_a) ),
inference(nnf_transformation,[status(thm)],[f285]) ).
fof(f285_sk,plain,
! [T_a,V_a] :
( c_Power_Opower__class_Opower(V_a,c_HOL_Ozero__class_Ozero(tc_nat),T_a) != c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Power_Opower(T_a)
| ~ class_Ring__and__Field_Omult__zero(T_a)
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| ~ class_Ring__and__Field_Ozero__neq__one(T_a) ),
inference(skolemisation,[status(esa)],[f285_nnf]) ).
cnf(c285,plain,
( c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X0) != c_HOL_Ozero__class_Ozero(X0)
| ~ class_Power_Opower(X0)
| ~ class_Ring__and__Field_Omult__zero(X0)
| ~ class_Ring__and__Field_Ono__zero__divisors(X0)
| ~ class_Ring__and__Field_Ozero__neq__one(X0) ),
inference(cnf_transformation,[status(esa)],[f285_sk]) ).
cnf(f334,axiom,
~ c_HOL_Oord__class_Oless(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gr__implies__not0_0) ).
fof(f334_nnf,plain,
! [V_m] : ~ c_HOL_Oord__class_Oless(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(nnf_transformation,[status(thm)],[f334]) ).
fof(f334_sk,plain,
! [V_m] : ~ c_HOL_Oord__class_Oless(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(skolemisation,[status(esa)],[f334_nnf]) ).
cnf(c334,plain,
~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(cnf_transformation,[status(esa)],[f334_sk]) ).
cnf(f335,axiom,
~ c_HOL_Oord__class_Oless(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less0_0) ).
fof(f335_nnf,plain,
! [V_n] : ~ c_HOL_Oord__class_Oless(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(nnf_transformation,[status(thm)],[f335]) ).
fof(f335_sk,plain,
! [V_n] : ~ c_HOL_Oord__class_Oless(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(skolemisation,[status(esa)],[f335_nnf]) ).
cnf(c335,plain,
~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(cnf_transformation,[status(esa)],[f335_sk]) ).
cnf(f396,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/sandbox/benchmark/theBenchmark.p',cls_not__one__less__zero_0) ).
fof(f396_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)],[f396]) ).
fof(f396_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)],[f396_nnf]) ).
cnf(c396,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)],[f396_sk]) ).
cnf(f425,axiom,
( ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).
fof(f425_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)],[f425]) ).
fof(f425_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)],[f425_nnf]) ).
cnf(c425,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X0)
| ~ class_Orderings_Olinorder(X0) ),
inference(cnf_transformation,[status(esa)],[f425_sk]) ).
cnf(f426,axiom,
( ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a)
| ~ class_Orderings_Oorder(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le_1) ).
fof(f426_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)],[f426]) ).
fof(f426_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)],[f426_nnf]) ).
cnf(c426,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X0)
| ~ class_Orderings_Oorder(X0) ),
inference(cnf_transformation,[status(esa)],[f426_sk]) ).
cnf(f427,axiom,
~ c_HOL_Oord__class_Oless(V_n,V_n,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__not__refl_0) ).
fof(f427_nnf,plain,
! [V_n] : ~ c_HOL_Oord__class_Oless(V_n,V_n,tc_nat),
inference(nnf_transformation,[status(thm)],[f427]) ).
fof(f427_sk,plain,
! [V_n] : ~ c_HOL_Oord__class_Oless(V_n,V_n,tc_nat),
inference(skolemisation,[status(esa)],[f427_nnf]) ).
cnf(c427,plain,
~ c_HOL_Oord__class_Oless(X0,X0,tc_nat),
inference(cnf_transformation,[status(esa)],[f427_sk]) ).
cnf(f428,axiom,
~ c_HOL_Oord__class_Oless(V_x,V_x,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__le_1) ).
fof(f428_nnf,plain,
! [V_x] : ~ c_HOL_Oord__class_Oless(V_x,V_x,tc_nat),
inference(nnf_transformation,[status(thm)],[f428]) ).
fof(f428_sk,plain,
! [V_x] : ~ c_HOL_Oord__class_Oless(V_x,V_x,tc_nat),
inference(skolemisation,[status(esa)],[f428_nnf]) ).
cnf(c428,plain,
~ c_HOL_Oord__class_Oless(X0,X0,tc_nat),
inference(cnf_transformation,[status(esa)],[f428_sk]) ).
cnf(f429,axiom,
( ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a)
| ~ class_Orderings_Opreorder(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__irrefl_0) ).
fof(f429_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)],[f429]) ).
fof(f429_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)],[f429_nnf]) ).
cnf(c429,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X0)
| ~ class_Orderings_Opreorder(X0) ),
inference(cnf_transformation,[status(esa)],[f429_sk]) ).
cnf(f542,axiom,
c_Suc(V_m) != c_HOL_Ozero__class_Ozero(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__neq__Zero_0) ).
fof(f542_nnf,plain,
! [V_m] : c_Suc(V_m) != c_HOL_Ozero__class_Ozero(tc_nat),
inference(nnf_transformation,[status(thm)],[f542]) ).
fof(f542_sk,plain,
! [V_m] : c_Suc(V_m) != c_HOL_Ozero__class_Ozero(tc_nat),
inference(skolemisation,[status(esa)],[f542_nnf]) ).
cnf(c542,plain,
c_Suc(X0) != c_HOL_Ozero__class_Ozero(tc_nat),
inference(cnf_transformation,[status(esa)],[f542_sk]) ).
cnf(f543,axiom,
c_Suc(V_nat_H) != c_HOL_Ozero__class_Ozero(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Osimps_I3_J_0) ).
fof(f543_nnf,plain,
! [V_nat_H] : c_Suc(V_nat_H) != c_HOL_Ozero__class_Ozero(tc_nat),
inference(nnf_transformation,[status(thm)],[f543]) ).
fof(f543_sk,plain,
! [V_nat_H] : c_Suc(V_nat_H) != c_HOL_Ozero__class_Ozero(tc_nat),
inference(skolemisation,[status(esa)],[f543_nnf]) ).
cnf(c543,plain,
c_Suc(X0) != c_HOL_Ozero__class_Ozero(tc_nat),
inference(cnf_transformation,[status(esa)],[f543_sk]) ).
cnf(f547,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/sandbox/benchmark/theBenchmark.p',cls_abs__not__less__zero_0) ).
fof(f547_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)],[f547]) ).
fof(f547_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)],[f547_nnf]) ).
cnf(c547,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)],[f547_sk]) ).
cnf(f558,axiom,
~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neq0__conv_1) ).
fof(f558_nnf,plain,
~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(nnf_transformation,[status(thm)],[f558]) ).
fof(f558_sk,plain,
~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(skolemisation,[status(esa)],[f558_nnf]) ).
cnf(c558,plain,
~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(cnf_transformation,[status(esa)],[f558_sk]) ).
cnf(f579,axiom,
~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_j,V_i,tc_nat),V_i,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__add__less2_0) ).
fof(f579_nnf,plain,
! [V_j,V_i] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_j,V_i,tc_nat),V_i,tc_nat),
inference(nnf_transformation,[status(thm)],[f579]) ).
fof(f579_sk,plain,
! [V_j,V_i] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_j,V_i,tc_nat),V_i,tc_nat),
inference(skolemisation,[status(esa)],[f579_nnf]) ).
cnf(c579,plain,
~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X1,tc_nat),
inference(cnf_transformation,[status(esa)],[f579_sk]) ).
cnf(f580,axiom,
~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_i,V_j,tc_nat),V_i,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__add__less1_0) ).
fof(f580_nnf,plain,
! [V_i,V_j] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_i,V_j,tc_nat),V_i,tc_nat),
inference(nnf_transformation,[status(thm)],[f580]) ).
fof(f580_sk,plain,
! [V_i,V_j] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_i,V_j,tc_nat),V_i,tc_nat),
inference(skolemisation,[status(esa)],[f580_nnf]) ).
cnf(c580,plain,
~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X0,tc_nat),
inference(cnf_transformation,[status(esa)],[f580_sk]) ).
cnf(f585,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/sandbox/benchmark/theBenchmark.p',cls_zero__less__abs__iff_0) ).
fof(f585_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)],[f585]) ).
fof(f585_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)],[f585_nnf]) ).
cnf(c585,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)],[f585_sk]) ).
cnf(f626,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/sandbox/benchmark/theBenchmark.p',cls_order__less__asym_H_0) ).
fof(f626_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)],[f626]) ).
fof(f626_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)],[f626_nnf]) ).
cnf(c626,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)],[f626_sk]) ).
cnf(f627,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/sandbox/benchmark/theBenchmark.p',cls_order__less__asym_0) ).
fof(f627_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)],[f627]) ).
fof(f627_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)],[f627_nnf]) ).
cnf(c627,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)],[f627_sk]) ).
cnf(f628,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/sandbox/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_1) ).
fof(f628_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)],[f628]) ).
fof(f628_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)],[f628_nnf]) ).
cnf(c628,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)],[f628_sk]) ).
cnf(f629,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/sandbox/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).
fof(f629_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)],[f629]) ).
fof(f629_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)],[f629_nnf]) ).
cnf(c629,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)],[f629_sk]) ).
cnf(f698,axiom,
v_s____ != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sne_0) ).
fof(f698_nnf,plain,
v_s____ != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(nnf_transformation,[status(thm)],[f698]) ).
fof(f698_sk,plain,
v_s____ != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(skolemisation,[status(esa)],[f698_nnf]) ).
cnf(c698,plain,
v_s____ != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(cnf_transformation,[status(esa)],[f698_sk]) ).
cnf(f710,axiom,
c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ds0_0) ).
fof(f710_nnf,plain,
c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_nat),
inference(nnf_transformation,[status(thm)],[f710]) ).
fof(f710_sk,plain,
c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_nat),
inference(skolemisation,[status(esa)],[f710_nnf]) ).
cnf(c710,plain,
c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_nat),
inference(cnf_transformation,[status(esa)],[f710_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c32,c33,c86,c87,c144,c161,c210,c218,c223,c237,c238,c285,c334,c335,c396,c425,c426,c427,c428,c429,c542,c543,c547,c558,c579,c580,c585,c626,c627,c628,c629,c698,c710,c731]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t21416]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG421-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.57 % Computer : n004.cluster.edu
% 0.10/0.57 % Model : x86_64 x86_64
% 0.10/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.57 % Memory : 8046.5625MB
% 0.10/0.57 % OS : Linux 6.8.0-71-generic
% 0.10/0.57 % CPULimit : 300
% 0.10/0.57 % WCLimit : 300
% 0.10/0.57 % DateTime : Fri Sep 25 05:36:36 UTC 2026
% 0.10/0.58 % CPUTime :
% 0.10/0.58 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 70.00/9.44 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 70.00/9.44 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------