%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWW238+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 : n010.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 03:29:19 PM UTC 2026
% Result : Theorem 21.75s 4.25s
% Output : CNFRefutation 21.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 24 ( 20 unt; 0 def)
% Number of atoms : 28 ( 6 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 12 ( 8 ~; 3 |; 0 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-3 aty)
% Number of variables : 26 ( 0 sgn 26 !; 0 ?; 13 :)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,X0)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X0))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complex__mod__triangle__sub) ).
fof(f66,axiom,
! [X0,X1,X2] :
( class_Rings_Ocomm__semiring__1(X2)
=> c_Groups_Oplus__class_Oplus(X2,X1,X0) = c_Groups_Oplus__class_Oplus(X2,X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
fof(f1142,axiom,
class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__semiring__1) ).
fof(f1188,axiom,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__1) ).
fof(f1272,conjecture,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_aa____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(f1273,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_aa____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____))),
inference(negated_conjecture,[status(cth)],[f1272]) ).
fof(f1274,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_aa____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____))),
inference(flattening,[],[f1273]) ).
fof(f1405,plain,
! [X0,X1,X2] :
( ~ class_Rings_Ocomm__semiring__1(X2)
| c_Groups_Oplus__class_Oplus(X2,X1,X0) = c_Groups_Oplus__class_Oplus(X2,X0,X1) ),
inference(ennf_transformation,[],[f66]) ).
fof(f1953,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_aa____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____))),
inference(cnf_transformation,[],[f1274]) ).
fof(f2068,plain,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1188]) ).
fof(f2070,plain,
! [X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,X0)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X0))),
inference(cnf_transformation,[],[f3]) ).
fof(f2142,plain,
class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1142]) ).
fof(f2176,plain,
! [X2,X0,X1] :
( ~ class_Rings_Ocomm__semiring__1(X2)
| c_Groups_Oplus__class_Oplus(X2,X1,X0) = c_Groups_Oplus__class_Oplus(X2,X0,X1) ),
inference(cnf_transformation,[],[f1405]) ).
tcf(c_49,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_aa____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____))),
inference(cnf_transformation,[],[f1953]) ).
tcf(c_158,plain,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f2068]) ).
tcf(c_160,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X0),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,X1)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1))),
inference(cnf_transformation,[],[f2070]) ).
tcf(c_230,plain,
class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f2142]) ).
tcf(c_264,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Oplus__class_Oplus(X0,X1,X2) = c_Groups_Oplus__class_Oplus(X0,X2,X1) )
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[],[f2176]) ).
tcf(c_36070,plain,
! [X0: $i,X1: $i] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,X1) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,X0),
inference(superposition,[status(thm)],[c_158,c_264]) ).
tcf(c_36072,plain,
! [X0: $i,X1: $i] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,X1) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0),
inference(superposition,[status(thm)],[c_230,c_264]) ).
tcf(c_36079,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_aa____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____))))),
inference(demodulation,[status(thm)],[c_49,c_36072]) ).
tcf(c_46846,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X0),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,X1)))),
inference(demodulation,[status(thm)],[c_160,c_36072]) ).
tcf(c_46847,plain,
! [X0: $i,X1: $i] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X0),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,X0)))),
inference(superposition,[status(thm)],[c_36070,c_46846]) ).
tcf(c_46919,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_36079,c_46847]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW238+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n010.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Thu Sep 24 21:49:58 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/0.40 Running first-order theorem proving
% 0.13/0.40 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
% 0.13/0.41
% 0.13/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.41
% 0.13/0.42 % Detected problem language: tptp
% 0.13/0.43 % Proving...
% 21.75/4.25 % SZS status Started for theBenchmark.p
% 21.75/4.25 % SZS status Theorem for theBenchmark.p
% 21.75/4.25
% 21.75/4.25 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 21.75/4.25
% 21.75/4.25 % ------ iProver source info
% 21.75/4.25
% 21.75/4.25 % git: date: 2026-07-19 20:42:38 +0200
% 21.75/4.25 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 21.75/4.25 % git: non_committed_changes: false
% 21.75/4.25
% 21.75/4.25 % ------ Parsing...
% 21.75/4.25 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 21.75/4.25
% 21.75/4.25 % ------ Preprocessing... sup_sim: 27 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 26 sf_s rm: 2 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 21.75/4.25
% 21.75/4.25 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 21.75/4.25
% 21.75/4.25 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 21.75/4.25 % ------ Proving...
% 21.75/4.25 % ------ Problem Properties
% 21.75/4.25
% 21.75/4.25 %
% 21.75/4.25 % clauses 583
% 21.75/4.25 % conjectures 1
% 21.75/4.25 % EPR 50
% 21.75/4.25 % Horn 517
% 21.75/4.25 % unary 166
% 21.75/4.25 % binary 208
% 21.75/4.25 % lits 1298
% 21.75/4.25 % lits eq 389
% 21.75/4.25 % fd_pure 0
% 21.75/4.25 % fd_pseudo 0
% 21.75/4.25 % fd_cond 56
% 21.75/4.25 % fd_pseudo_cond 27
% 21.75/4.25 % AC symbols 0
% 21.75/4.25
% 21.75/4.25 % ------ Schedule dynamic 5 is on
% 21.75/4.25
% 21.75/4.25 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 21.75/4.25
% 21.75/4.25
% 21.75/4.25 % ------
% 21.75/4.25 % Current options:
% 21.75/4.25 % ------
% 21.75/4.25
% 21.75/4.25
% 21.75/4.25 %
% 21.75/4.25
% 21.75/4.25 % ------ Proving...
% 21.75/4.25 %
% 21.75/4.25
% 21.75/4.25 % SZS status Theorem for theBenchmark.p
% 21.75/4.25
% 21.75/4.25 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 21.75/4.25
% 21.75/4.25
%------------------------------------------------------------------------------