%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWW217+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.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 09:13:57 AM UTC 2026
% Result : Theorem 33.27s 10.80s
% Output : CNFRefutation 33.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of formulae : 15 ( 11 unt; 0 def)
% Number of atoms : 24 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 17 ( 8 ~; 6 |; 0 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 8 con; 0-3 aty)
% Number of variables : 12 ( 0 sgn 4 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_order__le__less__trans,axiom,
! [V_z,V_y,V_x,T_a] :
( class_Orderings_Opreorder(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
=> ( c_Orderings_Oord__class_Oless(T_a,V_y,V_z)
=> c_Orderings_Oord__class_Oless(T_a,V_x,V_z) ) ) ),
file('theBenchmark.p',fact_order__le__less__trans) ).
fof(conj_0,conjecture,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z)))),v_e),
file('theBenchmark.p',conj_0) ).
fof(conj_0_neg,negated_conjecture,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z)))),v_e),
inference(assume_negation,[status(cth)],[conj_0]) ).
cnf(c_1494,plain,
( c_Orderings_Oord__class_Oless(A,B,D)
| ~ c_Orderings_Oord__class_Oless(A,C,D)
| ~ c_Orderings_Oord__class_Oless__eq(A,B,C)
| ~ class_Orderings_Opreorder(A) ),
inference(clausify,[status(thm)],[fact_order__le__less__trans]) ).
fof(arity_RealDef__Oreal__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Orderings_Opreorder) ).
cnf(c_1857,plain,
class_Orderings_Opreorder(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[arity_RealDef__Oreal__Orderings_Opreorder]) ).
fof(fact_dme,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_da____),v_m____),v_e),
file('theBenchmark.p',fact_dme) ).
cnf(c_1945,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_da____),v_m____),v_e),
inference(clausify,[status(thm)],[fact_dme]) ).
fof(fact__096cmod_A_Iw_A_N_Az_J_A_K_Acmod_A_Ipoly_Acs_A_Iw_A_N_Az_J_J_A_060_061_Ad_A_K_Am_096,axiom,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z)))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_da____),v_m____)),
file('theBenchmark.p',fact__096cmod_A_Iw_A_N_Az_J_A_K_Acmod_A_Ipoly_Acs_A_Iw_A_N_Az_J_J_A_060_061_Ad_A_K_Am_096) ).
cnf(c_1949,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z)))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_da____),v_m____)),
inference(clausify,[status(thm)],[fact__096cmod_A_Iw_A_N_Az_J_A_K_Acmod_A_Ipoly_Acs_A_Iw_A_N_Az_J_J_A_060_061_Ad_A_K_Am_096]) ).
cnf(c_2818,negated_conjecture,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z)))),v_e),
inference(clausify,[status(thm)],[conj_0_neg]) ).
cnf(c_4042,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,C)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,C)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B) ),
inference(resolve,[status(thm)],[c_1494,c_1857]) ).
cnf(c_4043,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z)))),A)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_da____),v_m____),A) ),
inference(resolve,[status(thm)],[c_4042,c_1949]) ).
cnf(c_4044,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z)))),v_e),
inference(resolve,[status(thm)],[c_4043,c_1945]) ).
cnf(c_4041,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_2818,c_4044]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWW217+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.46 % Computer : n009.cluster.edu
% 0.11/0.46 % Model : x86_64 x86_64
% 0.11/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.46 % Memory : 8046.5625MB
% 0.11/0.46 % OS : Linux 6.8.0-71-generic
% 0.11/0.46 % CPULimit : 300
% 0.11/0.46 % WCLimit : 300
% 0.11/0.46 % DateTime : Sat Sep 26 15:29:01 UTC 2026
% 0.11/0.46 % CPUTime :
% 0.11/0.47 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.47 % Process 510159 was started by sandbox on n009,
% 0.11/0.47 % Sat Sep 26 15:29:01 2026
% 0.11/0.47 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.34/0.71
% 0.34/0.71 % From the command line: assign(max_seconds, 300).
% 0.34/0.71
% 0.34/0.71 % SInE: 643 to sos, 616 to usable, of 1259 axioms (tolerance 2.00, depth 0 fixpoint).
% 33.27/10.80
% 33.27/10.80 % SZS status Theorem for theBenchmark
% 33.27/10.80
% 33.27/10.80 % Proof 1 at 0.74 (+ 0.11) seconds.
% 33.27/10.80 % Length of proof is 8.
% 33.27/10.80 % Level of proof is 2.
% 33.27/10.80 % Maximum clause weight is 42.000.
% 33.27/10.80 % Given clauses 27.
% 33.27/10.80
% 33.27/10.80 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------