TSTP Solution File: ALG359-1 by Drodi---3.6.0
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%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : ALG359-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 20:11:25 EDT 2024
% Result : Unsatisfiable 46.39s 6.27s
% Output : CNFRefutation 47.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 16
% Syntax : Number of formulae : 54 ( 23 unt; 0 def)
% Number of atoms : 95 ( 44 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 74 ( 33 ~; 37 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 10 ( 8 usr; 5 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-3 aty)
% Number of variables : 43 ( 43 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f35,axiom,
! [T_a,V_x] :
( ~ class_RealVector_Oreal__algebra__1(T_a)
| c_RealVector_Oof__real(V_x,T_a) != c_HOL_Ozero__class_Ozero(T_a)
| V_x = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f321,axiom,
! [T_a,V_x] :
( ~ class_RealVector_Oreal__normed__vector(T_a)
| c_RealVector_Onorm__class_Onorm(V_x,T_a) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| V_x = c_HOL_Ozero__class_Ozero(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f710,axiom,
! [V_n,V_x] :
( c_Power_Opower__class_Opower(c_NthRoot_Oroot(V_n,V_x),V_n,tc_RealDef_Oreal) = V_x
| c_Parity_Oeven__odd__class_Oeven(V_n,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f823,axiom,
v_b != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f825,axiom,
! [V_x,V_n] : c_Power_Opower__class_Opower(c_RealVector_Oof__real(V_x,tc_Complex_Ocomplex),V_n,tc_Complex_Ocomplex) = c_RealVector_Oof__real(c_Power_Opower__class_Opower(V_x,V_n,tc_RealDef_Oreal),tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f827,axiom,
! [T_a,V_a,V_b,V_n] :
( ~ class_Ring__and__Field_Ofield(T_a)
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),V_n,T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_b,V_n,T_a),T_a)
| V_b = c_HOL_Ozero__class_Ozero(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f838,axiom,
~ c_Parity_Oeven__odd__class_Oeven(v_na____,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f856,axiom,
! [V_n] : c_NthRoot_Oroot(V_n,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f885,negated_conjecture,
c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(v_v____,c_RealVector_Oof__real(c_NthRoot_Oroot(v_na____,c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_na____,tc_Complex_Ocomplex) != c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f996,axiom,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1006,axiom,
class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1018,axiom,
class_Ring__and__Field_Ofield(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1082,plain,
! [V_x] :
( ! [T_a] :
( ~ class_RealVector_Oreal__algebra__1(T_a)
| c_RealVector_Oof__real(V_x,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
| V_x = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(miniscoping,[status(esa)],[f35]) ).
fof(f1083,plain,
! [X0,X1] :
( ~ class_RealVector_Oreal__algebra__1(X0)
| c_RealVector_Oof__real(X1,X0) != c_HOL_Ozero__class_Ozero(X0)
| X1 = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(cnf_transformation,[status(esa)],[f1082]) ).
fof(f1544,plain,
! [X0,X1] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_RealVector_Onorm__class_Onorm(X1,X0) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| X1 = c_HOL_Ozero__class_Ozero(X0) ),
inference(cnf_transformation,[status(esa)],[f321]) ).
fof(f2169,plain,
! [V_n] :
( ! [V_x] : c_Power_Opower__class_Opower(c_NthRoot_Oroot(V_n,V_x),V_n,tc_RealDef_Oreal) = V_x
| c_Parity_Oeven__odd__class_Oeven(V_n,tc_nat) ),
inference(miniscoping,[status(esa)],[f710]) ).
fof(f2170,plain,
! [X0,X1] :
( c_Power_Opower__class_Opower(c_NthRoot_Oroot(X0,X1),X0,tc_RealDef_Oreal) = X1
| c_Parity_Oeven__odd__class_Oeven(X0,tc_nat) ),
inference(cnf_transformation,[status(esa)],[f2169]) ).
fof(f2340,plain,
v_b != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(cnf_transformation,[status(esa)],[f823]) ).
fof(f2343,plain,
! [X0,X1] : c_Power_Opower__class_Opower(c_RealVector_Oof__real(X0,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex) = c_RealVector_Oof__real(c_Power_Opower__class_Opower(X0,X1,tc_RealDef_Oreal),tc_Complex_Ocomplex),
inference(cnf_transformation,[status(esa)],[f825]) ).
fof(f2346,plain,
! [T_a,V_b] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ! [V_a,V_n] : c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),V_n,T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_b,V_n,T_a),T_a)
| V_b = c_HOL_Ozero__class_Ozero(T_a) ),
inference(miniscoping,[status(esa)],[f827]) ).
fof(f2347,plain,
! [X0,X1,X2,X3] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(X1,X2,X0),X3,X0) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X1,X3,X0),c_Power_Opower__class_Opower(X2,X3,X0),X0)
| X2 = c_HOL_Ozero__class_Ozero(X0) ),
inference(cnf_transformation,[status(esa)],[f2346]) ).
fof(f2366,plain,
~ c_Parity_Oeven__odd__class_Oeven(v_na____,tc_nat),
inference(cnf_transformation,[status(esa)],[f838]) ).
fof(f2398,plain,
! [X0] : c_NthRoot_Oroot(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(cnf_transformation,[status(esa)],[f856]) ).
fof(f2449,plain,
c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(v_v____,c_RealVector_Oof__real(c_NthRoot_Oroot(v_na____,c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_na____,tc_Complex_Ocomplex) != c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(cnf_transformation,[status(esa)],[f885]) ).
fof(f2560,plain,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
inference(cnf_transformation,[status(esa)],[f996]) ).
fof(f2570,plain,
class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex),
inference(cnf_transformation,[status(esa)],[f1006]) ).
fof(f2582,plain,
class_Ring__and__Field_Ofield(tc_Complex_Ocomplex),
inference(cnf_transformation,[status(esa)],[f1018]) ).
fof(f2590,plain,
! [X0] : c_Power_Opower__class_Opower(c_NthRoot_Oroot(v_na____,X0),v_na____,tc_RealDef_Oreal) = X0,
inference(resolution,[status(thm)],[f2170,f2366]) ).
fof(f2591,plain,
c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_na____,tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(paramodulation,[status(thm)],[f2398,f2590]) ).
fof(f2698,plain,
( spl0_13
<=> class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) ),
introduced(split_symbol_definition) ).
fof(f2700,plain,
( ~ class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)
| spl0_13 ),
inference(component_clause,[status(thm)],[f2698]) ).
fof(f11389,plain,
( $false
| spl0_13 ),
inference(forward_subsumption_resolution,[status(thm)],[f2560,f2700]) ).
fof(f11390,plain,
spl0_13,
inference(contradiction_clause,[status(thm)],[f11389]) ).
fof(f24699,plain,
! [X0,X1,X2] :
( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(X0,X1,tc_Complex_Ocomplex),X2,tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X0,X2,tc_Complex_Ocomplex),c_Power_Opower__class_Opower(X1,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| X1 = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(resolution,[status(thm)],[f2582,f2347]) ).
fof(f24896,plain,
! [X0,X1,X2] :
( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(X0,c_RealVector_Oof__real(X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex),X2,tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X0,X2,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_Power_Opower__class_Opower(X1,X2,tc_RealDef_Oreal),tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| c_RealVector_Oof__real(X1,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(paramodulation,[status(thm)],[f2343,f24699]) ).
fof(f25121,plain,
! [X0,X1] :
( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(X0,c_RealVector_Oof__real(c_NthRoot_Oroot(v_na____,X1),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_na____,tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X0,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| c_RealVector_Oof__real(c_NthRoot_Oroot(v_na____,X1),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(paramodulation,[status(thm)],[f2590,f24896]) ).
fof(f30771,plain,
c_RealVector_Oof__real(c_NthRoot_Oroot(v_na____,c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex)),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(resolution,[status(thm)],[f25121,f2449]) ).
fof(f30833,plain,
( spl0_3877
<=> class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex) ),
introduced(split_symbol_definition) ).
fof(f30835,plain,
( ~ class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex)
| spl0_3877 ),
inference(component_clause,[status(thm)],[f30833]) ).
fof(f30836,plain,
( spl0_3878
<=> c_NthRoot_Oroot(v_na____,c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex)) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ),
introduced(split_symbol_definition) ).
fof(f30837,plain,
( c_NthRoot_Oroot(v_na____,c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex)) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ spl0_3878 ),
inference(component_clause,[status(thm)],[f30836]) ).
fof(f30839,plain,
( ~ class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex)
| c_NthRoot_Oroot(v_na____,c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex)) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f30771,f1083]) ).
fof(f30840,plain,
( ~ spl0_3877
| spl0_3878 ),
inference(split_clause,[status(thm)],[f30839,f30833,f30836]) ).
fof(f30860,plain,
( $false
| spl0_3877 ),
inference(forward_subsumption_resolution,[status(thm)],[f30835,f2570]) ).
fof(f30861,plain,
spl0_3877,
inference(contradiction_clause,[status(thm)],[f30860]) ).
fof(f33362,plain,
( c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_na____,tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex)
| ~ spl0_3878 ),
inference(paramodulation,[status(thm)],[f30837,f2590]) ).
fof(f33363,plain,
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex)
| ~ spl0_3878 ),
inference(forward_demodulation,[status(thm)],[f2591,f33362]) ).
fof(f33378,plain,
( spl0_4193
<=> v_b = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
introduced(split_symbol_definition) ).
fof(f33379,plain,
( v_b = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| ~ spl0_4193 ),
inference(component_clause,[status(thm)],[f33378]) ).
fof(f33381,plain,
( ~ class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)
| v_b = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| ~ spl0_3878 ),
inference(resolution,[status(thm)],[f33363,f1544]) ).
fof(f33382,plain,
( ~ spl0_13
| spl0_4193
| ~ spl0_3878 ),
inference(split_clause,[status(thm)],[f33381,f2698,f33378,f30836]) ).
fof(f33388,plain,
( $false
| ~ spl0_4193 ),
inference(forward_subsumption_resolution,[status(thm)],[f33379,f2340]) ).
fof(f33389,plain,
~ spl0_4193,
inference(contradiction_clause,[status(thm)],[f33388]) ).
fof(f33390,plain,
$false,
inference(sat_refutation,[status(thm)],[f11390,f30840,f30861,f33382,f33389]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ALG359-1 : TPTP v8.1.2. Released v4.1.0.
% 0.07/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34 % Computer : n026.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Apr 29 23:50:34 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.19/0.40 % Drodi V3.6.0
% 46.39/6.27 % Refutation found
% 46.39/6.27 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 46.39/6.27 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 47.45/6.41 % Elapsed time: 6.043851 seconds
% 47.45/6.41 % CPU time: 47.270570 seconds
% 47.45/6.41 % Total memory used: 791.735 MB
% 47.45/6.41 % Net memory used: 782.215 MB
%------------------------------------------------------------------------------