%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : HWV020-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /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 : Thu Sep 24 12:45:59 PM UTC 2026
% Result : Unsatisfiable 0.12s 0.41s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 23
% Syntax : Number of formulae : 84 ( 21 unt; 6 def)
% Number of atoms : 211 ( 38 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 185 ( 58 ~; 121 |; 0 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 7 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 44 ( 44 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X_0] : plus(X_0,n1) != n0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [Y_12,X_11] :
( gt(plus(Y_12,n1),plus(X_11,n1))
| ~ gt(Y_12,X_11) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [X_26] :
( X_26 = plus(y_27(X_26),n1)
| X_26 = n0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [X_28] : ~ gt(X_28,X_28),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [X_31] : plus(n0,X_31) = X_31,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [X_t_32] : level(X_t_32) = int_level(X_t_32),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,axiom,
! [X_t_35] :
( p_Empty(X_t_35)
| int_level(X_t_35) != n0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,axiom,
! [X_t_36] :
( ~ p_Empty(X_t_36)
| int_level(X_t_36) = n0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f58,axiom,
! [X_t_42] :
( p_Rd_error(plus(X_t_42,n1))
| gt(int_level(X_t_42),n0)
| ~ p_Rd(X_t_42)
| ~ p_Wr(X_t_42)
| p_Reset(X_t_42) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f76,axiom,
! [X_t_42] :
( p_Rd_error(plus(X_t_42,n1))
| gt(int_level(X_t_42),n0)
| ~ p_Rd(X_t_42)
| p_Wr(X_t_42)
| p_Reset(X_t_42) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f78,axiom,
! [X_t_42] :
( int_level(plus(X_t_42,n1)) = int_level(X_t_42)
| gt(int_level(X_t_42),n0)
| ~ p_Rd(X_t_42)
| p_Wr(X_t_42)
| p_Reset(X_t_42) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f82,axiom,
! [X_t_42] :
( int_level(plus(X_t_42,n1)) = int_level(X_t_42)
| p_Rd(X_t_42)
| p_Wr(X_t_42)
| p_Reset(X_t_42) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f91,negated_conjecture,
p_Rd(t_139),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f92,negated_conjecture,
p_Empty(t_139),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f93,negated_conjecture,
~ p_Wr(t_139),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f94,negated_conjecture,
~ p_Reset(t_139),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f95,negated_conjecture,
( ~ p_Rd_error(plus(t_139,n1))
| ~ p_Empty(plus(t_139,n1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f96,plain,
! [X0] : plus(X0,n1) != n0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f105,plain,
! [X0,X1] :
( gt(plus(X0,n1),plus(X1,n1))
| ~ gt(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f114,plain,
! [X0] :
( X0 = plus(y_27(X0),n1)
| X0 = n0 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f115,plain,
! [X0] : ~ gt(X0,X0),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f117,plain,
! [X0] : plus(n0,X0) = X0,
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f119,plain,
! [X0] : level(X0) = int_level(X0),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f122,plain,
! [X0] :
( p_Empty(X0)
| int_level(X0) != n0 ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f123,plain,
! [X0] :
( ~ p_Empty(X0)
| int_level(X0) = n0 ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f158,plain,
! [X0] :
( p_Rd_error(plus(X0,n1))
| gt(int_level(X0),n0)
| ~ p_Rd(X0)
| ~ p_Wr(X0)
| p_Reset(X0) ),
inference(cnf_transformation,[status(thm)],[f58]) ).
fof(f176,plain,
! [X0] :
( p_Rd_error(plus(X0,n1))
| gt(int_level(X0),n0)
| ~ p_Rd(X0)
| p_Wr(X0)
| p_Reset(X0) ),
inference(cnf_transformation,[status(thm)],[f76]) ).
fof(f178,plain,
! [X0] :
( int_level(plus(X0,n1)) = int_level(X0)
| gt(int_level(X0),n0)
| ~ p_Rd(X0)
| p_Wr(X0)
| p_Reset(X0) ),
inference(cnf_transformation,[status(thm)],[f78]) ).
fof(f182,plain,
! [X0] :
( int_level(plus(X0,n1)) = int_level(X0)
| p_Rd(X0)
| p_Wr(X0)
| p_Reset(X0) ),
inference(cnf_transformation,[status(thm)],[f82]) ).
fof(f191,plain,
p_Rd(t_139),
inference(cnf_transformation,[status(thm)],[f91]) ).
fof(f192,plain,
p_Empty(t_139),
inference(cnf_transformation,[status(thm)],[f92]) ).
fof(f193,plain,
~ p_Wr(t_139),
inference(cnf_transformation,[status(thm)],[f93]) ).
fof(f194,plain,
~ p_Reset(t_139),
inference(cnf_transformation,[status(thm)],[f94]) ).
fof(f195,plain,
( ~ p_Rd_error(plus(t_139,n1))
| ~ p_Empty(plus(t_139,n1)) ),
inference(cnf_transformation,[status(thm)],[f95]) ).
fof(f196,definition,
( sQ0_spl
<=> p_Empty(plus(t_139,n1)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f198,plain,
( sQ0_spl
| ~ p_Empty(plus(t_139,n1)) ),
inference(component_clause,[status(thm)],[f196]) ).
fof(f199,definition,
( sQ1_spl
<=> p_Rd_error(plus(t_139,n1)) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f202,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f195,f196,f199]) ).
fof(f208,plain,
! [X0] :
( p_Empty(X0)
| level(X0) != n0 ),
inference(forward_demodulation,[status(thm)],[f119,f122]) ).
fof(f209,plain,
! [X0] :
( ~ p_Empty(X0)
| level(X0) = n0 ),
inference(forward_demodulation,[status(thm)],[f119,f123]) ).
fof(f250,plain,
! [X0] :
( p_Rd_error(plus(X0,n1))
| gt(level(X0),n0)
| ~ p_Rd(X0)
| ~ p_Wr(X0)
| p_Reset(X0) ),
inference(forward_demodulation,[status(thm)],[f119,f158]) ).
fof(f284,plain,
! [X0] :
( p_Rd_error(plus(X0,n1))
| gt(level(X0),n0)
| ~ p_Rd(X0)
| p_Wr(X0)
| p_Reset(X0) ),
inference(forward_demodulation,[status(thm)],[f119,f176]) ).
fof(f285,plain,
! [X0] :
( p_Rd_error(plus(X0,n1))
| gt(level(X0),n0)
| ~ p_Rd(X0)
| p_Reset(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f284,f250]) ).
fof(f288,plain,
! [X0] :
( int_level(plus(X0,n1)) = int_level(X0)
| gt(level(X0),n0)
| ~ p_Rd(X0)
| p_Wr(X0)
| p_Reset(X0) ),
inference(forward_demodulation,[status(thm)],[f119,f178]) ).
fof(f289,plain,
! [X0] :
( level(plus(X0,n1)) = int_level(X0)
| gt(level(X0),n0)
| ~ p_Rd(X0)
| p_Wr(X0)
| p_Reset(X0) ),
inference(forward_demodulation,[status(thm)],[f119,f288]) ).
fof(f290,plain,
! [X0] :
( level(plus(X0,n1)) = level(X0)
| gt(level(X0),n0)
| ~ p_Rd(X0)
| p_Wr(X0)
| p_Reset(X0) ),
inference(forward_demodulation,[status(thm)],[f119,f289]) ).
fof(f298,plain,
! [X0] :
( level(plus(X0,n1)) = int_level(X0)
| p_Rd(X0)
| p_Wr(X0)
| p_Reset(X0) ),
inference(forward_demodulation,[status(thm)],[f119,f182]) ).
fof(f300,plain,
! [X0] :
( level(plus(X0,n1)) = level(X0)
| gt(level(X0),n0)
| p_Wr(X0)
| p_Reset(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f290,f301]) ).
fof(f301,plain,
! [X0] :
( level(plus(X0,n1)) = level(X0)
| p_Rd(X0)
| p_Wr(X0)
| p_Reset(X0) ),
inference(forward_demodulation,[status(thm)],[f119,f298]) ).
fof(f322,plain,
level(t_139) = n0,
inference(resolution,[status(thm)],[f209,f192]) ).
fof(f340,plain,
! [X0] :
( gt(plus(level(X0),n1),plus(n0,n1))
| p_Rd_error(plus(X0,n1))
| ~ p_Rd(X0)
| p_Reset(X0) ),
inference(resolution,[status(thm)],[f285,f105]) ).
fof(f341,plain,
! [X0] :
( gt(plus(level(X0),n1),n1)
| p_Rd_error(plus(X0,n1))
| ~ p_Rd(X0)
| p_Reset(X0) ),
inference(forward_demodulation,[status(thm)],[f117,f340]) ).
fof(f342,plain,
! [X0] :
( gt(plus(level(X0),n1),plus(n0,n1))
| level(plus(X0,n1)) = level(X0)
| p_Wr(X0)
| p_Reset(X0) ),
inference(resolution,[status(thm)],[f300,f105]) ).
fof(f343,plain,
! [X0] :
( gt(plus(level(X0),n1),n1)
| level(plus(X0,n1)) = level(X0)
| p_Wr(X0)
| p_Reset(X0) ),
inference(forward_demodulation,[status(thm)],[f117,f342]) ).
fof(f344,plain,
! [X0] :
( gt(plus(plus(level(X0),n1),n1),plus(n1,n1))
| p_Rd_error(plus(X0,n1))
| ~ p_Rd(X0)
| p_Reset(X0) ),
inference(resolution,[status(thm)],[f341,f105]) ).
fof(f345,plain,
! [X0] :
( gt(plus(plus(level(X0),n1),n1),plus(n1,n1))
| level(plus(X0,n1)) = level(X0)
| p_Wr(X0)
| p_Reset(X0) ),
inference(resolution,[status(thm)],[f343,f105]) ).
fof(f346,plain,
( gt(plus(plus(level(t_139),n1),n1),plus(n1,n1))
| p_Rd_error(plus(t_139,n1))
| ~ p_Rd(t_139) ),
inference(resolution,[status(thm)],[f344,f194]) ).
fof(f347,definition,
( sQ4_spl
<=> p_Rd(t_139) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f349,plain,
( sQ4_spl
| ~ p_Rd(t_139) ),
inference(component_clause,[status(thm)],[f347]) ).
fof(f350,definition,
( sQ5_spl
<=> gt(plus(plus(level(t_139),n1),n1),plus(n1,n1)) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f351,plain,
( ~ sQ5_spl
| gt(plus(plus(level(t_139),n1),n1),plus(n1,n1)) ),
inference(component_clause,[status(thm)],[f350]) ).
fof(f353,plain,
( sQ5_spl
| sQ1_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f346,f347,f199,f350]) ).
fof(f354,plain,
( ~ sQ5_spl
| gt(plus(plus(n0,n1),n1),plus(n1,n1)) ),
inference(forward_demodulation,[status(thm)],[f322,f351]) ).
fof(f355,plain,
( ~ sQ5_spl
| gt(plus(n1,n1),plus(n1,n1)) ),
inference(forward_demodulation,[status(thm)],[f117,f354]) ).
fof(f356,plain,
( ~ sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f355,f115]) ).
fof(f357,plain,
~ sQ5_spl,
inference(contradiction_clause,[status(thm)],[f356]) ).
fof(f358,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f349,f191]) ).
fof(f359,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f358]) ).
fof(f362,plain,
( gt(plus(plus(level(t_139),n1),n1),plus(n1,n1))
| level(plus(t_139,n1)) = level(t_139)
| p_Reset(t_139) ),
inference(resolution,[status(thm)],[f345,f193]) ).
fof(f363,definition,
( sQ6_spl
<=> p_Reset(t_139) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f364,plain,
( ~ sQ6_spl
| p_Reset(t_139) ),
inference(component_clause,[status(thm)],[f363]) ).
fof(f366,definition,
( sQ7_spl
<=> level(plus(t_139,n1)) = level(t_139) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f367,plain,
( ~ sQ7_spl
| level(plus(t_139,n1)) = level(t_139) ),
inference(component_clause,[status(thm)],[f366]) ).
fof(f369,plain,
( sQ5_spl
| sQ7_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f362,f363,f366,f350]) ).
fof(f370,plain,
( ~ sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f364,f194]) ).
fof(f371,plain,
~ sQ6_spl,
inference(contradiction_clause,[status(thm)],[f370]) ).
fof(f372,plain,
( ~ sQ7_spl
| level(plus(t_139,n1)) = n0 ),
inference(forward_demodulation,[status(thm)],[f322,f367]) ).
fof(f387,plain,
! [X0] :
( p_Empty(X0)
| level(X0) = plus(y_27(level(X0)),n1) ),
inference(resolution,[status(thm)],[f114,f208]) ).
fof(f395,plain,
( sQ0_spl
| level(plus(t_139,n1)) = plus(y_27(level(plus(t_139,n1))),n1) ),
inference(resolution,[status(thm)],[f387,f198]) ).
fof(f397,plain,
( sQ0_spl
| ~ sQ7_spl
| n0 = plus(y_27(level(plus(t_139,n1))),n1) ),
inference(forward_demodulation,[status(thm)],[f372,f395]) ).
fof(f398,plain,
( sQ0_spl
| ~ sQ7_spl
| n0 = plus(y_27(n0),n1) ),
inference(forward_demodulation,[status(thm)],[f372,f397]) ).
fof(f399,plain,
( sQ0_spl
| ~ sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f398,f96]) ).
fof(f400,plain,
( sQ0_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f399]) ).
fof(f401,plain,
$false,
inference(sat_refutation,[status(thm)],[f202,f353,f357,f359,f369,f371,f400]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : HWV020-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n008.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sun Sep 20 20:49:09 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.12/0.37 % Drodi V4.1.1
% 0.12/0.41 % Refutation found
% 0.12/0.41 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.12/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.44 % Elapsed time: 0.069381 seconds
% 0.12/0.44 % CPU time: 0.287416 seconds
% 0.12/0.44 % Total memory used: 105.149 MB
% 0.12/0.44 % Net memory used: 104.751 MB
%------------------------------------------------------------------------------