%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : ALG407-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n008.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 06:50:09 AM UTC 2026
% Result : Unsatisfiable 52.85s 18.03s
% Output : CNFRefutation 52.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 29 ( 24 unt; 0 def)
% Number of atoms : 36 ( 8 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 20 ( 13 ~; 7 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 7 con; 0-3 aty)
% Number of variables : 24 ( 0 sgn 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_norm__power_0,axiom,
! [VAR_0,VAR_1,VAR_2] :
( c_RealVector_Onorm__class_Onorm(c_Power_Opower__class_Opower(VAR_1,VAR_2,VAR_0),VAR_0) = c_Power_Opower__class_Opower(c_RealVector_Onorm__class_Onorm(VAR_1,VAR_0),VAR_2,tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__div__algebra(VAR_0) ),
file('theBenchmark.p',cls_norm__power_0) ).
cnf(c_592,plain,
( c_RealVector_Onorm__class_Onorm(c_Power_Opower__class_Opower(B,C,A),A) = c_Power_Opower__class_Opower(c_RealVector_Onorm__class_Onorm(B,A),C,tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__div__algebra(A) ),
inference(clausify,[status(thm)],[cls_norm__power_0]) ).
fof(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra,axiom,
class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex),
file('theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra) ).
cnf(c_598,plain,
class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[clsarity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra]) ).
fof(cls_conjecture_2,axiom,
~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_t____,c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_RealDef_Oreal),v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('theBenchmark.p',cls_conjecture_2) ).
cnf(c_1167,plain,
~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_t____,c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_RealDef_Oreal),v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(clausify,[status(thm)],[cls_conjecture_2]) ).
fof(cls_conjecture_1,axiom,
c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(v_t____,c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_RealDef_Oreal),v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(c_1168,plain,
c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(v_t____,c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_RealDef_Oreal),v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(clausify,[status(thm)],[cls_conjecture_1]) ).
fof(cls_conjecture_0,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal),tc_RealDef_Oreal),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_1169,plain,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
fof(cls_real__mult__less__iff1_1,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),VAR_1,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(VAR_0,VAR_2,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(VAR_0,VAR_1,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(VAR_2,VAR_1,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('theBenchmark.p',cls_real__mult__less__iff1_1) ).
cnf(c_1178,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(A,C,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(C,B,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[cls_real__mult__less__iff1_1]) ).
fof(cls_real__mult__commute_0,axiom,
! [VAR_0,VAR_1] : c_HOL_Otimes__class_Otimes(VAR_0,VAR_1,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(VAR_1,VAR_0,tc_RealDef_Oreal),
file('theBenchmark.p',cls_real__mult__commute_0) ).
cnf(c_1210,plain,
c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(B,A,tc_RealDef_Oreal),
inference(clausify,[status(thm)],[cls_real__mult__commute_0]) ).
fof(cls_real__mult__1_0,axiom,
! [VAR_0] : c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),VAR_0,tc_RealDef_Oreal) = VAR_0,
file('theBenchmark.p',cls_real__mult__1_0) ).
cnf(c_1213,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),A,tc_RealDef_Oreal) = A,
inference(clausify,[status(thm)],[cls_real__mult__1_0]) ).
cnf(c_2470,plain,
c_RealVector_Onorm__class_Onorm(c_Power_Opower__class_Opower(A,B,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_RealVector_Onorm__class_Onorm(A,tc_Complex_Ocomplex),B,tc_RealDef_Oreal),
inference(resolve,[status(thm)],[c_598,c_592]) ).
cnf(c_2471,plain,
c_Power_Opower__class_Opower(c_RealVector_Onorm__class_Onorm(A,tc_Complex_Ocomplex),B,tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(c_Power_Opower__class_Opower(A,B,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(copy,[status(thm)],[c_2470]) ).
cnf(c_15145,plain,
c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(v_t____,c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(c_Power_Opower__class_Opower(v_w____,c_HOL_Oplus__class_Oplus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(paramod,[status(thm)],[c_2471,c_1168]) ).
cnf(c_2648,plain,
c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(v_t____,c_HOL_Otimes__class_Otimes(v_m____,c_RealVector_Onorm__class_Onorm(c_Power_Opower__class_Opower(v_w____,c_HOL_Oplus__class_Oplus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(paramod,[status(thm)],[c_1210,c_15145]) ).
cnf(c_15146,plain,
~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_t____,c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(c_Power_Opower__class_Opower(v_w____,c_HOL_Oplus__class_Oplus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(paramod,[status(thm)],[c_2471,c_1167]) ).
cnf(c_15147,plain,
~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_t____,c_HOL_Otimes__class_Otimes(v_m____,c_RealVector_Onorm__class_Onorm(c_Power_Opower__class_Opower(v_w____,c_HOL_Oplus__class_Oplus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(paramod,[status(thm)],[c_1210,c_15146]) ).
cnf(c_15148,plain,
~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_t____,c_HOL_Otimes__class_Otimes(v_m____,c_RealVector_Onorm__class_Onorm(c_Power_Opower__class_Opower(v_w____,c_HOL_Oplus__class_Oplus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(paramod,[status(thm)],[c_1210,c_15147]) ).
cnf(c_2649,plain,
~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_t____,c_HOL_Otimes__class_Otimes(v_m____,c_RealVector_Onorm__class_Onorm(c_Power_Opower__class_Opower(v_w____,c_HOL_Oplus__class_Oplus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(paramod,[status(thm)],[c_1213,c_15148]) ).
cnf(c_2827,plain,
( ~ c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(B,c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(resolve,[status(thm)],[c_1178,c_1169]) ).
cnf(c_15149,plain,
c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(v_t____,c_HOL_Otimes__class_Otimes(v_m____,c_RealVector_Onorm__class_Onorm(c_Power_Opower__class_Opower(v_w____,c_HOL_Oplus__class_Oplus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(resolve,[status(thm)],[c_2827,c_2648]) ).
cnf(c_15150,plain,
c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_t____,c_HOL_Otimes__class_Otimes(v_m____,c_RealVector_Onorm__class_Onorm(c_Power_Opower__class_Opower(v_w____,c_HOL_Oplus__class_Oplus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(paramod,[status(thm)],[c_1210,c_15149]) ).
cnf(c_15151,plain,
c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_t____,c_HOL_Otimes__class_Otimes(v_m____,c_RealVector_Onorm__class_Onorm(c_Power_Opower__class_Opower(v_w____,c_HOL_Oplus__class_Oplus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(paramod,[status(thm)],[c_1213,c_15150]) ).
cnf(c_15144,plain,
$false,
inference(resolve,[status(thm)],[c_2649,c_15151]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG407-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/10.38 % Computer : n008.cluster.edu
% 0.11/10.38 % Model : x86_64 x86_64
% 0.11/10.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/10.38 % Memory : 8046.5625MB
% 0.11/10.38 % OS : Linux 6.8.0-71-generic
% 0.11/10.39 % CPULimit : 300
% 0.11/10.39 % WCLimit : 300
% 0.11/10.39 % DateTime : Sat Sep 26 21:58:51 UTC 2026
% 0.11/10.39 % CPUTime :
% 0.11/10.39 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/10.39 % Process 446947 was started by sandbox on n008,
% 0.11/10.39 % Sat Sep 26 21:58:51 2026
% 0.11/10.39 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.15/10.43
% 0.15/10.43 % From the command line: assign(max_seconds, 300).
% 52.85/18.03
% 52.85/18.03 % given #500 (I,wt=9): 1527 -c_HOL_Oord__class_Oless(A,A,tc_nat) # tptp_name(cls_nat__less__le_1) # clausal_fof(1). [assumption].
% 52.85/18.03
% 52.85/18.03 % given #1000 (I,wt=31): 2434 c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(A,c_Power_Opower__class_Opower(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(586,a,557,a)].
% 52.85/18.03
% 52.85/18.03 % given #1500 (T,wt=17): 13572 c_lessequals(A,B,tc_Int_Oint) | c_lessequals(C,A,tc_Int_Oint) | -c_HOL_Oord__class_Oless(C,B,tc_Int_Oint). [resolve(10593,a,2318,a)].
% 52.85/18.03
% 52.85/18.03 % SZS status Unsatisfiable for theBenchmark
% 52.85/18.03
% 52.85/18.03 % Proof 1 at 6.83 (+ 0.68) seconds.
% 52.85/18.03 % Length of proof is 14.
% 52.85/18.03 % Level of proof is 4.
% 52.85/18.03 % Maximum clause weight is 68.000.
% 52.85/18.03 % Given clauses 1527.
% 52.85/18.03
% 52.85/18.03 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------