%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : ALG370-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.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 : Sun Sep 27 06:50:05 AM UTC 2026
% Result : Unsatisfiable 31.15s 4.92s
% Output : CNFRefutation 31.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of formulae : 14 ( 10 unt; 0 def)
% Number of atoms : 23 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 20 ( 11 ~; 9 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 8 con; 0-3 aty)
% Number of variables : 12 ( 0 sgn 4 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(clsarity_RealDef__Oreal__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_RealDef_Oreal),
file('theBenchmark.p',clsarity_RealDef__Oreal__Orderings_Oorder) ).
cnf(c_40,plain,
class_Orderings_Oorder(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[clsarity_RealDef__Oreal__Orderings_Oorder]) ).
fof(cls_xt1_I7_J_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ c_HOL_Oord__class_Oless(VAR_3,VAR_2,VAR_0)
| ~ c_lessequals(VAR_1,VAR_3,VAR_0)
| c_HOL_Oord__class_Oless(VAR_1,VAR_2,VAR_0)
| ~ class_Orderings_Oorder(VAR_0) ),
file('theBenchmark.p',cls_xt1_I7_J_0) ).
cnf(c_49,plain,
( ~ c_HOL_Oord__class_Oless(D,C,A)
| ~ c_lessequals(B,D,A)
| c_HOL_Oord__class_Oless(B,C,A)
| ~ class_Orderings_Oorder(A) ),
inference(clausify,[status(thm)],[cls_xt1_I7_J_0]) ).
cnf(c_884,plain,
( ~ c_HOL_Oord__class_Oless(C,B,tc_RealDef_Oreal)
| ~ c_lessequals(A,C,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal) ),
inference(resolve,[status(thm)],[c_49,c_40]) ).
fof(cls_CHAINED_0,axiom,
c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(v_da____,v_m____,tc_RealDef_Oreal),v_e,tc_RealDef_Oreal),
file('theBenchmark.p',cls_CHAINED_0) ).
cnf(c_1024,plain,
c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(v_da____,v_m____,tc_RealDef_Oreal),v_e,tc_RealDef_Oreal),
inference(clausify,[status(thm)],[cls_CHAINED_0]) ).
fof(cls_CHAINED_0_01,axiom,
c_lessequals(c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_w____,v_z,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_cs____,c_HOL_Ominus__class_Ominus(v_w____,v_z,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_da____,v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal),
file('theBenchmark.p',cls_CHAINED_0_01) ).
cnf(c_1025,plain,
c_lessequals(c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_w____,v_z,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_cs____,c_HOL_Ominus__class_Ominus(v_w____,v_z,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_da____,v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(clausify,[status(thm)],[cls_CHAINED_0_01]) ).
fof(cls_conjecture_0,axiom,
~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_w____,v_z,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_cs____,c_HOL_Ominus__class_Ominus(v_w____,v_z,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),v_e,tc_RealDef_Oreal),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_1026,plain,
~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_w____,v_z,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_cs____,c_HOL_Ominus__class_Ominus(v_w____,v_z,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),v_e,tc_RealDef_Oreal),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
cnf(c_3700,plain,
( ~ c_lessequals(A,c_HOL_Otimes__class_Otimes(v_da____,v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(A,v_e,tc_RealDef_Oreal) ),
inference(resolve,[status(thm)],[c_1024,c_884]) ).
cnf(c_18716,plain,
c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_w____,v_z,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_cs____,c_HOL_Ominus__class_Ominus(v_w____,v_z,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),v_e,tc_RealDef_Oreal),
inference(resolve,[status(thm)],[c_3700,c_1025]) ).
cnf(c_18715,plain,
$false,
inference(resolve,[status(thm)],[c_1026,c_18716]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG370-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.37 % Computer : n020.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sat Sep 26 21:56:34 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/0.37 % Process 2593893 was started by sandbox2 on n020,
% 0.12/0.37 % Sat Sep 26 21:56:34 2026
% 0.12/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.12/0.39
% 0.12/0.39 % From the command line: assign(max_seconds, 300).
% 31.15/4.92
% 31.15/4.92 % given #500 (I,wt=7): 1060 class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex) # tptp_name(clsarity_Complex__Ocomplex__OrderedGroup_Oab__group__add) # clausal_fof(1). [assumption].
% 31.15/4.92
% 31.15/4.92 % given #1000 (A,wt=44): 1574 c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(A,B,tc_Complex_Ocomplex),C,tc_Complex_Ocomplex),D,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,C,tc_Complex_Ocomplex),D,tc_Complex_Ocomplex),tc_Complex_Ocomplex). [para(513(a,1),470(a,1,2,1,1)),flip(a)].
% 31.15/4.92
% 31.15/4.92 % given #1500 (F,wt=28): 5578 c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),A,tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(1218,c,607,a),unit_del(c,973)].
% 31.15/4.92
% 31.15/4.92 % SZS status Unsatisfiable for theBenchmark
% 31.15/4.92
% 31.15/4.92 % Proof 1 at 3.56 (+ 0.91) seconds.
% 31.15/4.92 % Length of proof is 8.
% 31.15/4.92 % Level of proof is 3.
% 31.15/4.92 % Maximum clause weight is 48.000.
% 31.15/4.92 % Given clauses 1842.
% 31.15/4.92
% 31.15/4.92 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------