%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : ALG400-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n019.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 12:54:11 PM UTC 2026
% Result : Unsatisfiable 5.80s 2.48s
% Output : CNFRefutation 5.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 7
% Syntax : Number of formulae : 22 ( 12 unt; 0 def)
% Number of atoms : 32 ( 9 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 21 ( 11 ~; 10 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 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 : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 4 con; 0-3 aty)
% Number of variables : 25 ( 0 sgn 25 !; 0 ?; 16 :)
% Comments :
%------------------------------------------------------------------------------
fof(f246,axiom,
! [X2,X3,X0,X1] :
( c_Polynomial_Opoly(c_Polynomial_Osmult(X1,X2,X0),X3,X0) = c_HOL_Otimes__class_Otimes(X1,c_Polynomial_Opoly(X2,X3,X0),X0)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_poly__smult_0) ).
fof(f247,axiom,
! [X0,X1] : c_HOL_Oinverse__class_Odivide(X0,X1,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Oinverse__class_Oinverse(X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complex__divide__def_0) ).
fof(f355,axiom,
! [X2,X0,X1] :
( c_HOL_Otimes__class_Otimes(X1,X2,X0) = c_HOL_Otimes__class_Otimes(X2,X1,X0)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I7_J_0) ).
fof(f554,negated_conjecture,
( ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Oinverse__class_Odivide(c_Polynomial_Opoly(v_q____,v_w____,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f555,negated_conjecture,
( c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Oinverse__class_Odivide(c_Polynomial_Opoly(v_q____,v_w____,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f651,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1) ).
fof(f652,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0) ).
tcf(c_653,negated_conjecture,
( ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Oinverse__class_Odivide(c_Polynomial_Opoly(v_q____,v_w____,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(cnf_transformation,[],[f554]) ).
tcf(c_654,negated_conjecture,
( c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Oinverse__class_Odivide(c_Polynomial_Opoly(v_q____,v_w____,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(cnf_transformation,[],[f555]) ).
tcf(c_799,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_HOL_Otimes__class_Otimes(X1,c_Polynomial_Opoly(X2,X3,X0),X0) = c_Polynomial_Opoly(c_Polynomial_Osmult(X1,X2,X0),X3,X0) )
| ~ class_Ring__and__Field_Ocomm__semiring__0(X0) ),
inference(cnf_transformation,[],[f246]) ).
tcf(c_816,plain,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f651]) ).
tcf(c_818,plain,
! [X0: $i,X1: $i] : c_HOL_Otimes__class_Otimes(X0,c_HOL_Oinverse__class_Oinverse(X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(X0,X1,tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f247]) ).
tcf(c_950,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( 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,[],[f355]) ).
tcf(c_969,plain,
class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f652]) ).
tcf(c_46850,plain,
! [X0: $i,X1: $i] : c_HOL_Otimes__class_Otimes(X0,X1,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(X1,X0,tc_Complex_Ocomplex),
inference(superposition,[status(thm)],[c_816,c_950]) ).
tcf(c_46970,plain,
! [X0: $i,X1: $i] : c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X0,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(X1,X0,tc_Complex_Ocomplex),
inference(superposition,[status(thm)],[c_46850,c_818]) ).
tcf(c_51958,plain,
! [X0: $i,X1: $i,X2: $i] : c_HOL_Otimes__class_Otimes(X0,c_Polynomial_Opoly(X1,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Polynomial_Opoly(c_Polynomial_Osmult(X0,X1,tc_Complex_Ocomplex),X2,tc_Complex_Ocomplex),
inference(superposition,[status(thm)],[c_969,c_799]) ).
tcf(c_51988,plain,
( ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Oinverse__class_Odivide(c_Polynomial_Opoly(v_q____,v_w____,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(demodulation,[status(thm)],[c_653,c_51958]) ).
tcf(c_51989,plain,
( c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Oinverse__class_Odivide(c_Polynomial_Opoly(v_q____,v_w____,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(demodulation,[status(thm)],[c_654,c_51958]) ).
tcf(c_52161,plain,
c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Oinverse__class_Odivide(c_Polynomial_Opoly(v_q____,v_w____,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(demodulation,[status(thm)],[c_51989,c_46970]) ).
tcf(c_52177,plain,
~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Oinverse__class_Odivide(c_Polynomial_Opoly(v_q____,v_w____,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(demodulation,[status(thm)],[c_51988,c_46970]) ).
tcf(c_52178,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_52177,c_52161]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG400-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.58 % Computer : n019.cluster.edu
% 0.11/0.58 % Model : x86_64 x86_64
% 0.11/0.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.58 % Memory : 8046.5625MB
% 0.11/0.58 % OS : Linux 6.8.0-71-generic
% 0.11/0.58 % CPULimit : 300
% 0.11/0.58 % WCLimit : 300
% 0.11/0.58 % DateTime : Fri Sep 25 05:33:51 UTC 2026
% 0.11/0.58 % CPUTime :
% 0.11/0.58 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.62 Running first-order theorem proving
% 0.11/0.62 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
% 0.15/0.63
% 0.15/0.63 % ======== iProver multi-core TPTP/SMT =========
% 0.15/0.63
% 0.15/0.63 % Detected problem language: tptp
% 0.15/0.65 % Proving...
% 5.80/2.48 % SZS status Started for theBenchmark.p
% 5.80/2.48 % SZS status Unsatisfiable for theBenchmark.p
% 5.80/2.48
% 5.80/2.48 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 5.80/2.48
% 5.80/2.48 % ------ iProver source info
% 5.80/2.48
% 5.80/2.48 % git: date: 2026-07-19 20:42:38 +0200
% 5.80/2.48 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 5.80/2.48 % git: non_committed_changes: false
% 5.80/2.48
% 5.80/2.48 % ------ Parsing...% successful
% 5.80/2.48
% 5.80/2.48
% 5.80/2.48 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 5.80/2.48
% 5.80/2.48 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe_e sup_sim: 36 sf_s rm: 7 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 7 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 7 0s sf_e pe_s pe_e %
% 5.80/2.48
% 5.80/2.48 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 5.80/2.48
% 5.80/2.48 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 5.80/2.48 % ------ Proving...
% 5.80/2.48 % ------ Problem Properties
% 5.80/2.48
% 5.80/2.48 %
% 5.80/2.48 % clauses 361
% 5.80/2.48 % conjectures 2
% 5.80/2.48 % EPR 64
% 5.80/2.48 % Horn 252
% 5.80/2.48 % unary 80
% 5.80/2.48 % binary 93
% 5.80/2.48 % lits 938
% 5.80/2.48 % lits eq 263
% 5.80/2.48 % fd_pure 0
% 5.80/2.48 % fd_pseudo 0
% 5.80/2.48 % fd_cond 28
% 5.80/2.48 % fd_pseudo_cond 13
% 5.80/2.48 % AC symbols 0
% 5.80/2.48
% 5.80/2.48 % ------ Schedule dynamic 5 is on
% 5.80/2.48
% 5.80/2.48 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 5.80/2.48
% 5.80/2.48
% 5.80/2.48 % ------
% 5.80/2.48 % Current options:
% 5.80/2.48 % ------
% 5.80/2.48
% 5.80/2.48
% 5.80/2.48 %
% 5.80/2.48
% 5.80/2.48 % ------ Proving...
% 5.80/2.48 %
% 5.80/2.48
% 5.80/2.48 % SZS status Unsatisfiable for theBenchmark.p
% 5.80/2.48
% 5.80/2.48 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 5.80/2.48
% 5.80/2.48
%------------------------------------------------------------------------------