%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWW194+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n005.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 03:29:14 PM UTC 2026
% Result : Theorem 35.80s 6.24s
% Output : CNFRefutation 35.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of formulae : 35 ( 23 unt; 0 def)
% Number of atoms : 59 ( 5 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 49 ( 25 ~; 20 |; 0 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 5 con; 0-3 aty)
% Number of variables : 37 ( 0 sgn 37 !; 0 ?; 11 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),v_x____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096abs_A_I2_A_K_Ax_J_A_060_061_A1_096) ).
fof(f235,axiom,
! [X0] : c_Int_OBit1(X0) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Bit1__def) ).
fof(f239,axiom,
! [X0] : c_Int_OBit0(X0) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Bit0__def) ).
fof(f266,axiom,
! [X0,X1] :
( class_Groups_Oordered__ab__group__add__abs(X1)
=> c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oabs__class_Oabs(X1,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__ge__zero) ).
fof(f306,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Olinordered__semidom(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
=> c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X1),X0)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__mono) ).
fof(f1103,axiom,
class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__ab__group__add__abs) ).
fof(f1120,axiom,
class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semidom) ).
fof(f1199,conjecture,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),v_x____))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(f1200,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),v_x____))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
inference(negated_conjecture,[status(cth)],[f1199]) ).
fof(f1201,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),v_x____))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
inference(flattening,[],[f1200]) ).
fof(f1378,plain,
! [X0,X1] :
( ~ class_Groups_Oordered__ab__group__add__abs(X1)
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oabs__class_Oabs(X1,X0)) ),
inference(ennf_transformation,[],[f266]) ).
fof(f1400,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Olinordered__semidom(X3)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X1),X0)) ),
inference(ennf_transformation,[],[f306]) ).
fof(f1401,plain,
! [X0,X1,X2,X3] :
( ~ class_Rings_Olinordered__semidom(X3)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X1),X0)) ),
inference(flattening,[],[f1400]) ).
fof(f2572,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),v_x____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(cnf_transformation,[],[f2]) ).
fof(f2865,plain,
! [X0] : c_Int_OBit1(X0) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0),X0),
inference(cnf_transformation,[],[f235]) ).
fof(f2869,plain,
! [X0] : c_Int_OBit0(X0) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X0),
inference(cnf_transformation,[],[f239]) ).
fof(f2905,plain,
! [X0,X1] :
( ~ class_Groups_Oordered__ab__group__add__abs(X1)
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oabs__class_Oabs(X1,X0)) ),
inference(cnf_transformation,[],[f1378]) ).
fof(f2953,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Olinordered__semidom(X3)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
| c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X0),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X1),X0)) ),
inference(cnf_transformation,[],[f1401]) ).
fof(f4177,plain,
class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1103]) ).
fof(f4194,plain,
class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1120]) ).
fof(f4273,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),v_x____))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
inference(cnf_transformation,[],[f1201]) ).
fof(f4274,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),v_x____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(definition_unfolding,[],[f2572,f2869,f2865]) ).
fof(f4605,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),v_x____))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))),
inference(definition_unfolding,[],[f4273,f2869,f2865,f2869,f2865,f2869,f2865]) ).
tcf(c_50,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),v_x____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(cnf_transformation,[],[f4274]) ).
tcf(c_368,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),c_Groups_Oabs__class_Oabs(X0,X1))
| ~ class_Groups_Oordered__ab__group__add__abs(X0) ),
inference(cnf_transformation,[],[f2905]) ).
tcf(c_416,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X3),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X2),X3))
| ~ class_Rings_Olinordered__semidom(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X1) ),
inference(cnf_transformation,[],[f2953]) ).
tcf(c_1595,plain,
class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f4177]) ).
tcf(c_1612,plain,
class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f4194]) ).
tcf(c_1691,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),v_x____))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))),
inference(cnf_transformation,[],[f4605]) ).
tcf(c_2926,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),c_Groups_Oabs__class_Oabs(X0,X1))
| ~ class_Groups_Oordered__ab__group__add__abs(X0) ),
inference(prop_impl_just,[status(thm)],[c_368]) ).
tcf(c_9510,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),c_Groups_Oabs__class_Oabs(X0,X1))
| ( X0 != tc_RealDef_Oreal ) ),
inference(resolution_lifted,[status(thm)],[c_2926,c_1595]) ).
tcf(c_9511,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0)),
inference(unflattening,[status(thm)],[c_9510]) ).
tcf(c_24231,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),v_x____))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))))
| ~ class_Rings_Olinordered__semidom(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),v_x____)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),v_x____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
inference(instantiation,[status(thm)],[c_416]) ).
tcf(c_24956,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),v_x____))),
inference(instantiation,[status(thm)],[c_9511]) ).
tcf(c_24957,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_24956,c_24231,c_1691,c_50,c_1612]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW194+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.05 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.36 % Computer : n005.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Thu Sep 24 21:42:32 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.42
% 0.11/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.42
% 0.11/0.42 % Detected problem language: tptp
% 0.11/0.43 % Proving...
% 35.80/6.24 % SZS status Started for theBenchmark.p
% 35.80/6.24 ERROR - "ProverProcess:heur/409474:1.0" ran with exit code 2 and error: iprover.ml: Unexpected exception: Failure("Clausification error: res/vclausify_rel exits with an error status: 1")
% 35.80/6.24 Fatal error: exception Failure("Clausification error: res/vclausify_rel exits with an error status: 1")
% 35.80/6.24 ERROR - cmd was: ulimit -v 4023281; ./res/iproveropt --abstr_ref "[]" --abstr_ref_under "[]" --comb_inst_mult 3 --comb_mode clause_based --comb_res_mult 4 --comb_sup_deep_mult 2 --comb_sup_mult 0 --conj_cone_tolerance 3. --demod_completeness_check fast --demod_use_ground true --eq_ax_congr_red true --extra_neg_conj none --inst_activity_threshold 500 --inst_dismatching true --inst_eager_unprocessed_to_passive true --inst_eq_res_simp false --inst_learning_factor 2 --inst_learning_loop_flag true --inst_learning_start 3000 --inst_lit_activity_flag true --inst_lit_sel "[+prop;+sign;+ground;-num_var;-num_symb]" --inst_lit_sel_side num_symb --inst_orphan_elimination true --inst_passive_queue_type priority_queues --inst_passive_queues "[[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]" --inst_passive_queues_freq "[25;2]" --inst_prop_sim_given true --inst_prop_sim_new false --inst_restr_to_given false --inst_sel_renew solver --inst_solver_calls_frac 1. --inst_solver_per_active 1400 --inst_sos_flag false --inst_start_prop_sim_after_learn 3 --inst_subs_given false --inst_subs_new false --instantiation_flag true --out_options none --pred_elim true --prep_def_merge true --prep_def_merge_mbd true --prep_def_merge_prop_impl false --prep_def_merge_tr_cl false --prep_def_merge_tr_red false --prep_gs_sim true --prep_res_sim true --prep_sem_filter exhaustive --prep_sup_sim_all true --prep_sup_sim_sup false --prep_unflatten true --prep_upred true --preprocessing_flag true --prolific_symb_bound 256 --prop_solver_per_cl 1024 --pure_diseq_elim true --res_backward_subs full --res_backward_subs_resolution false --res_forward_subs subset_subsumption --res_forward_subs_resolution true --res_lit_sel pos_max --res_lit_sel_side num_var --res_ordering kbo_pred --res_passive_queue_type priority_queues --res_passive_queues "[[-num_lits];[-conj_symb;-num_symb;+num_symb]]" --res_passive_queues_freq "[15;3]" --res_prop_simpl_given false --res_prop_simpl_new true --res_sim_input true --res_time_limit 202.80 --res_to_prop_solver passive --resolution_flag true --schedule none --share_sel_clauses true --smt_ac_axioms fast --smt_preprocessing true --splitting_cvd false --splitting_cvd_svl false --splitting_grd true --splitting_mode input --splitting_nvd 32 --stats_out none --sub_typing true --subs_bck_mult 8 --sup_full_bw "[]" --sup_full_fw "[]" --sup_full_triv "[PropSubs]" --sup_fun_splitting false --sup_immed_bw_immed "[]" --sup_immed_bw_main "[]" --sup_immed_fw_immed "[ACNormalisation]" --sup_immed_fw_main "[]" --sup_immed_triv "[]" --sup_indices_passive "[]" --sup_input_bw "[]" --sup_input_fw "[ACNormalisation]" --sup_input_triv "[Unflattening]" --sup_iter_deepening 2 --sup_passive_queue_type priority_queues --sup_passive_queues "[[-conj_dist;-num_symb];[+age;-num_symb];[+score;-num_symb]]" --sup_passive_queues_freq "[8;4;4]" --sup_prop_simpl_given true --sup_prop_simpl_new true --sup_restarts_mult 2 --sup_score sim_d_gen --sup_share_max_num_cl 500 --sup_share_score_frac 0.2 --sup_smt_interval 10000 --sup_symb_ordering invfreq --sup_to_prop_solver passive --superposition_flag true --time_out_prep_mult 0.1 --suppress_sat_res true --tptp_safe_out true --proof_out true --sat_out_model pos --clausifier res/vclausify_rel --clausifier_options "--mode clausify -t 0.33" --time_out_real 1.00 /export/starexec/sandbox/benchmark/theBenchmark.p 1>> /export/starexec/sandbox/tmp/iprover_out_bvqci_e8/fztv2szq 2>> /export/starexec/sandbox/tmp/iprover_out_bvqci_e8/fztv2szq_error
% 35.80/6.24 ERROR - "ProverProcess:heur/381325:1.0" ran with exit code 2 and error: iprover.ml: Unexpected exception: Failure("Clausification error: res/vclausify_rel exits with an error status: 1")
% 35.80/6.24 Fatal error: exception Failure("Clausification error: res/vclausify_rel exits with an error status: 1")
% 35.80/6.24 ERROR - cmd was: ulimit -v 4023281; ./res/iproveropt --abstr_ref "[]" --abstr_ref_under "[]" --comb_inst_mult 3 --comb_mode clause_based --comb_res_mult 1 --comb_sup_deep_mult 1 --comb_sup_mult 3 --conj_cone_tolerance 3. --demod_completeness_check full --demod_use_ground true --eq_ax_congr_red true --extra_neg_conj none --inst_activity_threshold 500 --inst_dismatching true --inst_eager_unprocessed_to_passive true --inst_eq_res_simp false --inst_learning_factor 2 --inst_learning_loop_flag true --inst_learning_start 3000 --inst_lit_activity_flag true --inst_lit_sel "[+prop;+sign;+ground;-num_var;-num_symb]" --inst_lit_sel_side num_symb --inst_orphan_elimination true --inst_passive_queue_type priority_queues --inst_passive_queues "[[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]" --inst_passive_queues_freq "[25;2]" --inst_prop_sim_given true --inst_prop_sim_new false --inst_restr_to_given false --inst_sel_renew solver --inst_solver_calls_frac 1. --inst_solver_per_active 1400 --inst_sos_flag false --inst_start_prop_sim_after_learn 3 --inst_subs_given false --inst_subs_new false --instantiation_flag true --out_options none --pred_elim true --prep_def_merge true --prep_def_merge_mbd true --prep_def_merge_prop_impl false --prep_def_merge_tr_cl false --prep_def_merge_tr_red false --prep_gs_sim true --prep_res_sim true --prep_sem_filter exhaustive --prep_sup_sim_all true --prep_sup_sim_sup false --prep_unflatten true --prep_upred true --preprocessing_flag true --prolific_symb_bound 256 --prop_solver_per_cl 1024 --pure_diseq_elim true --res_backward_subs full --res_backward_subs_resolution true --res_forward_subs full --res_forward_subs_resolution true --res_lit_sel adaptive --res_lit_sel_side none --res_ordering kbo --res_passive_queue_type priority_queues --res_passive_queues "[[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]" --res_passive_queues_freq "[15;5]" --res_prop_simpl_given true --res_prop_simpl_new false --res_sim_input true --res_time_limit 300.00 --res_to_prop_solver active --resolution_flag true --schedule none --share_sel_clauses true --smt_ac_axioms fast --smt_preprocessing true --splitting_cvd false --splitting_cvd_svl false --splitting_grd true --splitting_mode input --splitting_nvd 32 --stats_out none --sub_typing true --subs_bck_mult 8 --sup_full_bw "[]" --sup_full_fw "[Demod;DemodLoopTriv;LightNorm;ACNormalisation]" --sup_full_triv "[]" --sup_fun_splitting true --sup_immed_bw_immed "[]" --sup_immed_bw_main "[SubsumptionRes;UnitSubsAndRes]" --sup_immed_fw_immed "[Subsumption;UnitSubsAndRes;Demod;DemodLoopTriv;LightNorm;DemodLightNormLoopTriv]" --sup_immed_fw_main "[Subsumption;SubsumptionRes;LightNorm;DemodLightNormLoopTriv]" --sup_immed_triv "[PropSubs]" --sup_indices_passive "[UnitSubsumption;NonunitSubsumption;FwDemod]" --sup_input_bw "[UnitSubsAndRes]" --sup_input_fw "[]" --sup_input_triv "[PropSubs]" --sup_iter_deepening 0 --sup_passive_queue_type priority_queues --sup_passive_queues "[[-conj_symb;-max_atom_input_occur];[+horn];[+bc_imp_inh;+ground;-conj_dist]]" --sup_passive_queues_freq "[3;1;25]" --sup_prop_simpl_given true --sup_prop_simpl_new false --sup_restarts_mult 8 --sup_score sim_d_gen --sup_share_max_num_cl 40 --sup_share_score_frac 0.1 --sup_smt_interval 10000 --sup_symb_ordering arity_random --sup_to_prop_solver active --superposition_flag true --time_out_prep_mult 0.1 --suppress_sat_res true --tptp_safe_out true --proof_out true --sat_out_model pos --clausifier res/vclausify_rel --clausifier_options "--mode clausify -t 0.33" --time_out_real 1.00 /export/starexec/sandbox/benchmark/theBenchmark.p 1>> /export/starexec/sandbox/tmp/iprover_out_bvqci_e8/2txg8y3l 2>> /export/starexec/sandbox/tmp/iprover_out_bvqci_e8/2txg8y3l_error
% 35.80/6.24 % SZS status Theorem for theBenchmark.p
% 35.80/6.24
% 35.80/6.24 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 35.80/6.24
% 35.80/6.24 % ------ iProver source info
% 35.80/6.24
% 35.80/6.24 % git: date: 2026-07-19 20:42:38 +0200
% 35.80/6.24 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 35.80/6.24 % git: non_committed_changes: false
% 35.80/6.24
% 35.80/6.24 % ------ Parsing...
% 35.80/6.24 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 35.80/6.24
% 35.80/6.24 % ------ Preprocessing... sf_s rm: 13 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe:8:0s pe:16:0s pe:32:0s pe_e %
% 35.80/6.24
% 35.80/6.24 % ------ Preprocessing... gs_s sp: 0 0s gs_e scvd_s sp: 1 0s scvd_e snvd_s sp: 0 0s snvd_e %
% 35.80/6.24
% 35.80/6.24 % ------ Preprocessing... sf_s rm: 1 0s sf_e
% 35.80/6.24 % ------ Proving...
% 35.80/6.24 % ------ Problem Properties
% 35.80/6.24
% 35.80/6.24 %
% 35.80/6.24 % clauses 1571
% 35.80/6.24 % conjectures 1
% 35.80/6.24 % EPR 90
% 35.80/6.24 % Horn 1327
% 35.80/6.24 % unary 633
% 35.80/6.24 % binary 466
% 35.80/6.24 % lits 3207
% 35.80/6.24 % lits eq 935
% 35.80/6.24 % fd_pure 0
% 35.80/6.24 % fd_pseudo 0
% 35.80/6.24 % fd_cond 133
% 35.80/6.24 % fd_pseudo_cond 60
% 35.80/6.24 % AC symbols 0
% 35.80/6.24
% 35.80/6.24 % ------ Input Options Time Limit: Unbounded
% 35.80/6.24
% 35.80/6.24
% 35.80/6.24 % ------
% 35.80/6.24 % Current options:
% 35.80/6.24 % ------
% 35.80/6.24
% 35.80/6.24
% 35.80/6.24 %
% 35.80/6.24
% 35.80/6.24 % ------ Proving...
% 35.80/6.24 %
% 35.80/6.24
% 35.80/6.24 % SZS status Theorem for theBenchmark.p
% 35.80/6.24
% 35.80/6.24 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 35.80/6.24
% 35.80/6.24
%------------------------------------------------------------------------------