%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWW232+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n017.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 03:29:18 PM UTC 2026
% Result : Theorem 10.88s 2.28s
% Output : CNFRefutation 10.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 25 ( 12 unt; 0 def)
% Number of atoms : 46 ( 8 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 40 ( 19 ~; 15 |; 2 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 2 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 6 con; 0-3 aty)
% Number of variables : 32 ( 0 sgn 28 !; 4 ?; 11 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
v_cs____ != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_H) ).
fof(f4,axiom,
! [X0,X1] :
( v_cs____ != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
=> ? [X2] :
! [X3] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X3))
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,X0,v_cs____)),X3))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pCons_Ohyps) ).
fof(f1253,axiom,
( ? [X0] :
! [X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1))
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_da____,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_c____,v_cs____)),X1))) )
=> v_thesis____ ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(f1254,conjecture,
v_thesis____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
fof(f1255,negated_conjecture,
~ v_thesis____,
inference(negated_conjecture,[status(cth)],[f1254]) ).
fof(f1260,plain,
~ v_thesis____,
inference(flattening,[],[f1255]) ).
fof(f1262,plain,
! [X0,X1] :
( v_cs____ = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ? [X2] :
! [X3] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X3))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,X0,v_cs____)),X3))) ) ),
inference(ennf_transformation,[],[f4]) ).
fof(f2399,plain,
( ! [X0] :
? [X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1))
& ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_da____,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_c____,v_cs____)),X1))) )
| v_thesis____ ),
inference(ennf_transformation,[],[f1253]) ).
fof(f2401,plain,
! [X0,X1] :
( v_cs____ = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ! [X3] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,sK1(X0,X1),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X3))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,X0,v_cs____)),X3))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X2,sK1(X0,X1))],[f1262]) ).
fof(f2763,plain,
( ! [X0] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,sK37(X0)))
& ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_da____,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_c____,v_cs____)),sK37(X0)))) )
| v_thesis____ ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK37]),skolemize(X1,sK37(X0))],[f2399]) ).
fof(f2765,plain,
v_cs____ != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(cnf_transformation,[],[f2]) ).
fof(f2767,plain,
! [X3,X0,X1] :
( v_cs____ = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,sK1(X0,X1),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X3))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,X0,v_cs____)),X3))) ),
inference(cnf_transformation,[],[f2401]) ).
fof(f4416,plain,
! [X0] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,sK37(X0)))
| v_thesis____ ),
inference(cnf_transformation,[],[f2763]) ).
fof(f4417,plain,
! [X0] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_da____,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_c____,v_cs____)),sK37(X0))))
| v_thesis____ ),
inference(cnf_transformation,[],[f2763]) ).
fof(f4418,plain,
~ v_thesis____,
inference(cnf_transformation,[],[f1260]) ).
tcf(c_50,plain,
c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != v_cs____,
inference(cnf_transformation,[],[f2765]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,X0,v_cs____)),X2)))
| ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_cs____ )
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,sK1(X0,X1),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X2)) ),
inference(cnf_transformation,[],[f2767]) ).
tcf(c_1636,plain,
! [X0: $i] :
( v_thesis____
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_da____,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_c____,v_cs____)),sK37(X0)))) ),
inference(cnf_transformation,[],[f4417]) ).
tcf(c_1637,plain,
! [X0: $i] :
( v_thesis____
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,sK37(X0))) ),
inference(cnf_transformation,[],[f4416]) ).
tcf(c_1638,negated_conjecture,
~ v_thesis____,
inference(cnf_transformation,[],[f4418]) ).
tcf(c_1793,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,sK37(X0))),
inference(global_subsumption_just,[status(thm)],[c_1637,c_1638,c_1637]) ).
tcf(c_2411,plain,
! [X0: $i] : ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_da____,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_c____,v_cs____)),sK37(X0)))),
inference(global_subsumption_just,[status(thm)],[c_1636,c_1638,c_1636]) ).
tcf(c_2441,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,X0,v_cs____)),X2)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,sK1(X0,X1),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X2)) ),
inference(global_subsumption_just,[status(thm)],[c_52,c_50,c_52]) ).
tcf(c_2448,plain,
! [X0: $i] : ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,sK1(v_c____,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_da____,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,sK37(X0))),
inference(superposition,[status(thm)],[c_2441,c_2411]) ).
tcf(c_10911,plain,
$false,
inference(superposition,[status(thm)],[c_1793,c_2448]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW232+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.35 % Computer : n017.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 21:44:16 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/0.40 Running first-order theorem proving
% 0.14/0.40 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.41
% 0.14/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.41
% 0.14/0.41 % Detected problem language: tptp
% 0.14/0.42 % Proving...
% 10.88/2.28 % SZS status Started for theBenchmark.p
% 10.88/2.28 % SZS status Theorem for theBenchmark.p
% 10.88/2.28
% 10.88/2.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 10.88/2.28
% 10.88/2.28 % ------ iProver source info
% 10.88/2.28
% 10.88/2.28 % git: date: 2026-07-19 20:42:38 +0200
% 10.88/2.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 10.88/2.28 % git: non_committed_changes: false
% 10.88/2.28
% 10.88/2.28 % ------ Parsing...
% 10.88/2.28 % ------ Clausification by vclausify_rel & Parsing by iProver...
% 10.88/2.28 % ------ Proving...
% 10.88/2.28 % ------ Problem Properties
% 10.88/2.28
% 10.88/2.28 %
% 10.88/2.28 % clauses 1590
% 10.88/2.28 % conjectures 1
% 10.88/2.28 % EPR 326
% 10.88/2.28 % Horn 1420
% 10.88/2.28 % unary 398
% 10.88/2.28 % binary 571
% 10.88/2.28 % lits 3704
% 10.88/2.28 % lits eq 802
% 10.88/2.28 % fd_pure 0
% 10.88/2.28 % fd_pseudo 0
% 10.88/2.28 % fd_cond 60
% 10.88/2.28 % fd_pseudo_cond 160
% 10.88/2.28 % AC symbols 0
% 10.88/2.28
% 10.88/2.28 % ------ Input Options Time Limit: Unbounded
% 10.88/2.28
% 10.88/2.28
% 10.88/2.28 % ------
% 10.88/2.28 % Current options:
% 10.88/2.28 % ------
% 10.88/2.28
% 10.88/2.28
% 10.88/2.28 %
% 10.88/2.28
% 10.88/2.28 % ------ Proving...
% 10.88/2.28 %
% 10.88/2.28
% 10.88/2.28 % ------ Proving...
% 10.88/2.28 %
% 10.88/2.28
% 10.88/2.28 % SZS status Theorem for theBenchmark.p
% 10.88/2.28
% 10.88/2.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 10.88/2.28
% 10.88/2.28
%------------------------------------------------------------------------------