%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : HWV016-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n001.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 12:45:57 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.42s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 52
% Syntax : Number of formulae : 177 ( 40 unt; 26 def)
% Number of atoms : 389 ( 96 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 351 ( 139 ~; 186 |; 0 &)
% ( 26 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 34 ( 32 usr; 27 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 82 ( 82 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X_0] : plus(X_0,n1) != n0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X_1] : gt(plus(X_1,n1),n0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X_2] :
( gt(X_2,minus(X_2,n1))
| ~ gt(X_2,n0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X_3,Y_4,Z_5] :
( def_10(Y_4,X_3)
| plus(Z_5,Y_4) != X_3
| minus(X_3,Y_4) = Z_5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [Y_4,X_3] :
( X_3 != Y_4
| ~ def_10(Y_4,X_3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [Y_12,X_11] :
( ~ gt(plus(Y_12,n1),plus(X_11,n1))
| gt(Y_12,X_11) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [X_13,Y_14] :
( Y_14 = X_13
| ~ gt(plus(X_13,n1),Y_14)
| gt(X_13,Y_14) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [Y_18,X_17] :
( gt(X_17,Y_18)
| X_17 = Y_18
| gt(Y_18,X_17) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [Z_21,Y_20,X_19] :
( ~ gt(Y_20,X_19)
| gt(Z_21,X_19)
| ~ gt(Z_21,Y_20) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [Y_24,X_23] :
( gt(Y_24,plus(X_23,n1))
| plus(X_23,n1) = Y_24
| ~ gt(Y_24,X_23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [X_25] :
( gt(X_25,n0)
| X_25 = n0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [X_26] :
( X_26 = plus(y_27(X_26),n1)
| X_26 = n0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [X_28] : ~ gt(X_28,X_28),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [X_29,Y_30] :
( X_29 = Y_30
| plus(X_29,n1) != plus(Y_30,n1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [X_31] : plus(n0,X_31) = X_31,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [X_t_32] : level(X_t_32) = int_level(X_t_32),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,axiom,
! [X_t_36] :
( ~ p_Empty(X_t_36)
| int_level(X_t_36) = n0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f35,axiom,
! [X_t_42] :
( int_level(plus(X_t_42,n1)) = plus(int_level(X_t_42),n1)
| ~ gt(fifo_length,int_level(X_t_42))
| p_Rd(X_t_42)
| ~ p_Wr(X_t_42)
| p_Reset(X_t_42) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f44,axiom,
! [X_t_42] :
( int_level(plus(X_t_42,n1)) = int_level(X_t_42)
| gt(fifo_length,int_level(X_t_42))
| p_Rd(X_t_42)
| ~ p_Wr(X_t_42)
| p_Reset(X_t_42) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f53,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/sandbox2/benchmark/theBenchmark.p') ).
fof(f59,axiom,
! [X_t_42] :
( int_level(plus(X_t_42,n1)) = plus(int_level(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/sandbox2/benchmark/theBenchmark.p') ).
fof(f91,negated_conjecture,
~ gt(n0,level(t_139)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f92,negated_conjecture,
p_Wr(t_139),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f93,negated_conjecture,
~ p_Reset(t_139),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f94,negated_conjecture,
p_Empty(plus(t_139,n1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f95,negated_conjecture,
gt(fifo_length,n0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f96,plain,
! [X0] : plus(X0,n1) != n0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f97,plain,
! [X0] : gt(plus(X0,n1),n0),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f98,plain,
! [X0] :
( gt(X0,minus(X0,n1))
| ~ gt(X0,n0) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f101,plain,
! [X_3,Y_4] :
( def_10(Y_4,X_3)
| ! [Z_5] :
( plus(Z_5,Y_4) != X_3
| minus(X_3,Y_4) = Z_5 ) ),
inference(miniscoping,[status(thm)],[f5]) ).
fof(f102,plain,
! [X0,X1,X2] :
( def_10(X1,X0)
| plus(X2,X1) != X0
| minus(X0,X1) = X2 ),
inference(cnf_transformation,[status(thm)],[f101]) ).
fof(f104,plain,
! [X0,X1] :
( X1 != X0
| ~ def_10(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f106,plain,
! [X0,X1] :
( ~ gt(plus(X0,n1),plus(X1,n1))
| gt(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f107,plain,
! [X0,X1] :
( X1 = X0
| ~ gt(plus(X0,n1),X1)
| gt(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f109,plain,
! [X0,X1] :
( gt(X1,X0)
| X1 = X0
| gt(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f110,plain,
! [Y_20,X_19] :
( ~ gt(Y_20,X_19)
| ! [Z_21] :
( gt(Z_21,X_19)
| ~ gt(Z_21,Y_20) ) ),
inference(miniscoping,[status(thm)],[f13]) ).
fof(f111,plain,
! [X0,X1,X2] :
( ~ gt(X1,X2)
| gt(X0,X2)
| ~ gt(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f110]) ).
fof(f112,plain,
! [X0,X1] :
( gt(X0,plus(X1,n1))
| plus(X1,n1) = X0
| ~ gt(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f113,plain,
! [X0] :
( gt(X0,n0)
| X0 = n0 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
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(f116,plain,
! [X0,X1] :
( X0 = X1
| plus(X0,n1) != plus(X1,n1) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
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(f123,plain,
! [X0] :
( ~ p_Empty(X0)
| int_level(X0) = n0 ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f135,plain,
! [X0] :
( int_level(plus(X0,n1)) = plus(int_level(X0),n1)
| ~ gt(fifo_length,int_level(X0))
| p_Rd(X0)
| ~ p_Wr(X0)
| p_Reset(X0) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f144,plain,
! [X0] :
( int_level(plus(X0,n1)) = int_level(X0)
| gt(fifo_length,int_level(X0))
| p_Rd(X0)
| ~ p_Wr(X0)
| p_Reset(X0) ),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f153,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)],[f53]) ).
fof(f159,plain,
! [X0] :
( int_level(plus(X0,n1)) = plus(int_level(X0),n1)
| gt(int_level(X0),n0)
| ~ p_Rd(X0)
| ~ p_Wr(X0)
| p_Reset(X0) ),
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f191,plain,
~ gt(n0,level(t_139)),
inference(cnf_transformation,[status(thm)],[f91]) ).
fof(f192,plain,
p_Wr(t_139),
inference(cnf_transformation,[status(thm)],[f92]) ).
fof(f193,plain,
~ p_Reset(t_139),
inference(cnf_transformation,[status(thm)],[f93]) ).
fof(f194,plain,
p_Empty(plus(t_139,n1)),
inference(cnf_transformation,[status(thm)],[f94]) ).
fof(f195,plain,
gt(fifo_length,n0),
inference(cnf_transformation,[status(thm)],[f95]) ).
fof(f197,plain,
! [X0,X1] :
( def_10(X1,plus(X0,X1))
| minus(plus(X0,X1),X1) = X0 ),
inference(destructive_equality_resolution,[status(thm)],[f102]) ).
fof(f198,plain,
! [X0] : ~ def_10(X0,X0),
inference(destructive_equality_resolution,[status(thm)],[f104]) ).
fof(f199,plain,
gt(n1,n0),
inference(paramodulation,[status(thm)],[f117,f97]) ).
fof(f200,plain,
n1 != n0,
inference(paramodulation,[status(thm)],[f117,f96]) ).
fof(f205,plain,
~ gt(n0,int_level(t_139)),
inference(backward_demodulation,[status(thm)],[f119,f191]) ).
fof(f211,definition,
( sQ0_spl
<=> gt(n1,n0) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f220,plain,
( n0 = int_level(t_139)
| gt(int_level(t_139),n0) ),
inference(resolution,[status(thm)],[f205,f109]) ).
fof(f223,definition,
( sQ1_spl
<=> gt(int_level(t_139),n0) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f224,plain,
( ~ sQ1_spl
| gt(int_level(t_139),n0) ),
inference(component_clause,[status(thm)],[f223]) ).
fof(f226,definition,
( sQ2_spl
<=> n0 = int_level(t_139) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f227,plain,
( ~ sQ2_spl
| n0 = int_level(t_139) ),
inference(component_clause,[status(thm)],[f226]) ).
fof(f229,plain,
( sQ2_spl
| sQ1_spl ),
inference(split_clause,[status(thm)],[f220,f223,f226]) ).
fof(f252,plain,
! [X0,X1] :
( ~ gt(X1,X0)
| ~ gt(X0,X1) ),
inference(resolution,[status(thm)],[f111,f115]) ).
fof(f264,plain,
! [X0] :
( plus(X0,n1) = n0
| X0 = y_27(plus(X0,n1)) ),
inference(resolution,[status(thm)],[f116,f114]) ).
fof(f271,plain,
! [X0] : X0 = y_27(plus(X0,n1)),
inference(forward_subsumption_resolution,[status(thm)],[f264,f96]) ).
fof(f277,plain,
int_level(plus(t_139,n1)) = n0,
inference(resolution,[status(thm)],[f123,f194]) ).
fof(f280,plain,
~ gt(n0,n1),
inference(resolution,[status(thm)],[f252,f199]) ).
fof(f281,plain,
~ gt(n0,fifo_length),
inference(resolution,[status(thm)],[f252,f195]) ).
fof(f285,plain,
! [X0] :
( X0 = n0
| ~ gt(n0,X0) ),
inference(resolution,[status(thm)],[f252,f113]) ).
fof(f292,plain,
( n0 = n1
| gt(n1,n0) ),
inference(resolution,[status(thm)],[f280,f109]) ).
fof(f293,plain,
( n1 = n0
| ~ gt(plus(n0,n1),n1) ),
inference(resolution,[status(thm)],[f280,f107]) ).
fof(f295,definition,
( sQ7_spl
<=> n0 = n1 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f296,plain,
( ~ sQ7_spl
| n0 = n1 ),
inference(component_clause,[status(thm)],[f295]) ).
fof(f298,plain,
( sQ7_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f292,f211,f295]) ).
fof(f299,definition,
( sQ8_spl
<=> gt(plus(n0,n1),n1) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f302,plain,
( sQ7_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f293,f299,f295]) ).
fof(f304,plain,
( ~ sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f296,f200]) ).
fof(f305,plain,
~ sQ7_spl,
inference(contradiction_clause,[status(thm)],[f304]) ).
fof(f308,plain,
( n0 = fifo_length
| gt(fifo_length,n0) ),
inference(resolution,[status(thm)],[f281,f109]) ).
fof(f309,plain,
( fifo_length = n0
| ~ gt(plus(n0,n1),fifo_length) ),
inference(resolution,[status(thm)],[f281,f107]) ).
fof(f310,plain,
~ gt(plus(n0,n1),plus(fifo_length,n1)),
inference(resolution,[status(thm)],[f281,f106]) ).
fof(f311,definition,
( sQ9_spl
<=> gt(fifo_length,n0) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f312,plain,
( ~ sQ9_spl
| gt(fifo_length,n0) ),
inference(component_clause,[status(thm)],[f311]) ).
fof(f314,definition,
( sQ10_spl
<=> n0 = fifo_length ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f315,plain,
( ~ sQ10_spl
| n0 = fifo_length ),
inference(component_clause,[status(thm)],[f314]) ).
fof(f317,plain,
( sQ10_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f308,f311,f314]) ).
fof(f318,definition,
( sQ11_spl
<=> gt(plus(n0,n1),fifo_length) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f320,plain,
( sQ11_spl
| ~ gt(plus(n0,n1),fifo_length) ),
inference(component_clause,[status(thm)],[f318]) ).
fof(f321,plain,
( sQ10_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f309,f318,f314]) ).
fof(f322,plain,
~ gt(n1,plus(fifo_length,n1)),
inference(forward_demodulation,[status(thm)],[f117,f310]) ).
fof(f327,plain,
( ~ sQ10_spl
| gt(n0,n0) ),
inference(backward_demodulation,[status(thm)],[f315,f195]) ).
fof(f328,plain,
( ~ sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f327,f115]) ).
fof(f329,plain,
~ sQ10_spl,
inference(contradiction_clause,[status(thm)],[f328]) ).
fof(f330,plain,
( sQ11_spl
| ~ gt(n1,fifo_length) ),
inference(forward_demodulation,[status(thm)],[f117,f320]) ).
fof(f333,plain,
( sQ11_spl
| n1 = fifo_length
| gt(fifo_length,n1) ),
inference(resolution,[status(thm)],[f330,f109]) ).
fof(f334,plain,
( sQ11_spl
| fifo_length = n1
| ~ gt(plus(n1,n1),fifo_length) ),
inference(resolution,[status(thm)],[f330,f107]) ).
fof(f336,definition,
( sQ12_spl
<=> gt(fifo_length,n1) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f339,definition,
( sQ13_spl
<=> n1 = fifo_length ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f340,plain,
( ~ sQ13_spl
| n1 = fifo_length ),
inference(component_clause,[status(thm)],[f339]) ).
fof(f342,plain,
( sQ11_spl
| sQ13_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f333,f336,f339,f318]) ).
fof(f343,definition,
( sQ14_spl
<=> gt(plus(n1,n1),fifo_length) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f346,plain,
( sQ11_spl
| sQ13_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f334,f343,f339,f318]) ).
fof(f362,plain,
n0 = y_27(n1),
inference(paramodulation,[status(thm)],[f117,f271]) ).
fof(f364,plain,
( n1 = plus(n0,n1)
| n1 = n0 ),
inference(paramodulation,[status(thm)],[f362,f114]) ).
fof(f365,definition,
( sQ15_spl
<=> n1 = plus(n0,n1) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f368,plain,
( sQ15_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f364,f295,f365]) ).
fof(f370,plain,
( int_level(plus(t_139,n1)) = int_level(t_139)
| ~ gt(int_level(t_139),n0)
| ~ p_Rd(t_139)
| p_Reset(t_139) ),
inference(resolution,[status(thm)],[f153,f192]) ).
fof(f371,definition,
( sQ16_spl
<=> p_Reset(t_139) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f372,plain,
( ~ sQ16_spl
| p_Reset(t_139) ),
inference(component_clause,[status(thm)],[f371]) ).
fof(f374,definition,
( sQ17_spl
<=> p_Rd(t_139) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f375,plain,
( ~ sQ17_spl
| p_Rd(t_139) ),
inference(component_clause,[status(thm)],[f374]) ).
fof(f377,definition,
( sQ18_spl
<=> int_level(plus(t_139,n1)) = int_level(t_139) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f378,plain,
( ~ sQ18_spl
| int_level(plus(t_139,n1)) = int_level(t_139) ),
inference(component_clause,[status(thm)],[f377]) ).
fof(f380,plain,
( sQ18_spl
| ~ sQ1_spl
| ~ sQ17_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f370,f371,f374,f223,f377]) ).
fof(f381,plain,
( ~ sQ18_spl
| n0 = int_level(t_139) ),
inference(forward_demodulation,[status(thm)],[f277,f378]) ).
fof(f386,plain,
( ~ sQ13_spl
| ~ gt(n1,plus(n1,n1)) ),
inference(forward_demodulation,[status(thm)],[f340,f322]) ).
fof(f387,plain,
( ~ sQ13_spl
| plus(n1,n1) = n1
| ~ gt(n1,n1) ),
inference(resolution,[status(thm)],[f386,f112]) ).
fof(f389,plain,
( ~ sQ13_spl
| n1 = plus(n1,n1)
| gt(plus(n1,n1),n1) ),
inference(resolution,[status(thm)],[f386,f109]) ).
fof(f390,plain,
( ~ sQ13_spl
| plus(n1,n1) = n1
| ~ gt(plus(n1,n1),plus(n1,n1)) ),
inference(resolution,[status(thm)],[f386,f107]) ).
fof(f392,definition,
( sQ19_spl
<=> gt(n1,n1) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f395,definition,
( sQ20_spl
<=> plus(n1,n1) = n1 ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f396,plain,
( ~ sQ20_spl
| plus(n1,n1) = n1 ),
inference(component_clause,[status(thm)],[f395]) ).
fof(f398,plain,
( ~ sQ13_spl
| sQ20_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f387,f392,f395,f339]) ).
fof(f399,definition,
( sQ21_spl
<=> gt(plus(n1,n1),n1) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f402,plain,
( ~ sQ13_spl
| sQ20_spl
| sQ21_spl ),
inference(split_clause,[status(thm)],[f389,f399,f395,f339]) ).
fof(f403,definition,
( sQ22_spl
<=> gt(plus(n1,n1),plus(n1,n1)) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f406,plain,
( ~ sQ13_spl
| sQ20_spl
| ~ sQ22_spl ),
inference(split_clause,[status(thm)],[f390,f403,f395,f339]) ).
fof(f431,definition,
( sQ23_spl
<=> gt(fifo_length,int_level(t_139)) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f433,plain,
( sQ23_spl
| ~ gt(fifo_length,int_level(t_139)) ),
inference(component_clause,[status(thm)],[f431]) ).
fof(f438,plain,
( ~ sQ16_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f372,f193]) ).
fof(f439,plain,
~ sQ16_spl,
inference(contradiction_clause,[status(thm)],[f438]) ).
fof(f440,plain,
( sQ23_spl
| ~ sQ2_spl
| ~ gt(fifo_length,n0) ),
inference(forward_demodulation,[status(thm)],[f227,f433]) ).
fof(f442,plain,
( sQ23_spl
| ~ sQ2_spl
| ~ sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f440,f312]) ).
fof(f443,plain,
( sQ23_spl
| ~ sQ2_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f442]) ).
fof(f445,plain,
( ~ sQ18_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f381,f226,f377]) ).
fof(f447,plain,
( int_level(plus(t_139,n1)) = plus(int_level(t_139),n1)
| ~ gt(fifo_length,int_level(t_139))
| p_Rd(t_139)
| p_Reset(t_139) ),
inference(resolution,[status(thm)],[f135,f192]) ).
fof(f448,definition,
( sQ25_spl
<=> int_level(plus(t_139,n1)) = plus(int_level(t_139),n1) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f449,plain,
( ~ sQ25_spl
| int_level(plus(t_139,n1)) = plus(int_level(t_139),n1) ),
inference(component_clause,[status(thm)],[f448]) ).
fof(f451,plain,
( sQ25_spl
| ~ sQ23_spl
| sQ17_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f447,f371,f374,f431,f448]) ).
fof(f458,plain,
( ~ sQ25_spl
| n0 = plus(int_level(t_139),n1) ),
inference(forward_demodulation,[status(thm)],[f277,f449]) ).
fof(f459,plain,
( ~ sQ25_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f458,f96]) ).
fof(f460,plain,
~ sQ25_spl,
inference(contradiction_clause,[status(thm)],[f459]) ).
fof(f463,definition,
( sQ27_spl
<=> p_Wr(t_139) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f465,plain,
( sQ27_spl
| ~ p_Wr(t_139) ),
inference(component_clause,[status(thm)],[f463]) ).
fof(f470,plain,
( sQ27_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f465,f192]) ).
fof(f471,plain,
sQ27_spl,
inference(contradiction_clause,[status(thm)],[f470]) ).
fof(f495,plain,
( ~ sQ20_spl
| def_10(n1,n1)
| minus(plus(n1,n1),n1) = n1 ),
inference(paramodulation,[status(thm)],[f396,f197]) ).
fof(f496,definition,
( sQ32_spl
<=> minus(plus(n1,n1),n1) = n1 ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f499,definition,
( sQ33_spl
<=> def_10(n1,n1) ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f500,plain,
( ~ sQ33_spl
| def_10(n1,n1) ),
inference(component_clause,[status(thm)],[f499]) ).
fof(f502,plain,
( ~ sQ20_spl
| sQ33_spl
| sQ32_spl ),
inference(split_clause,[status(thm)],[f495,f496,f499,f395]) ).
fof(f503,plain,
( ~ sQ33_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f500,f198]) ).
fof(f504,plain,
~ sQ33_spl,
inference(contradiction_clause,[status(thm)],[f503]) ).
fof(f512,plain,
! [X0] :
( plus(X0,n1) = n0
| ~ gt(n0,X0)
| plus(X0,n1) = n0 ),
inference(resolution,[status(thm)],[f285,f112]) ).
fof(f513,plain,
( n0 = n0
| n0 = n0 ),
inference(resolution,[status(thm)],[f285,f113]) ).
fof(f517,plain,
! [X0] :
( X0 = n0
| ~ gt(plus(n0,n1),X0)
| X0 = n0 ),
inference(resolution,[status(thm)],[f285,f107]) ).
fof(f519,plain,
! [X0] :
( ~ gt(n0,X0)
| plus(X0,n1) = n0 ),
inference(duplicate_literals_removal,[status(thm)],[f512]) ).
fof(f520,plain,
! [X0] : ~ gt(n0,X0),
inference(forward_subsumption_resolution,[status(thm)],[f519,f96]) ).
fof(f521,definition,
( sQ34_spl
<=> n0 = n0 ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f524,plain,
sQ34_spl,
inference(split_clause,[status(thm)],[f513,f521]) ).
fof(f533,plain,
! [X0] :
( X0 = n0
| ~ gt(n1,X0)
| X0 = n0 ),
inference(forward_demodulation,[status(thm)],[f117,f517]) ).
fof(f534,plain,
! [X0] :
( ~ gt(n1,X0)
| X0 = n0 ),
inference(duplicate_literals_removal,[status(thm)],[f533]) ).
fof(f546,plain,
( int_level(plus(t_139,n1)) = int_level(t_139)
| gt(fifo_length,int_level(t_139))
| p_Rd(t_139)
| p_Reset(t_139) ),
inference(resolution,[status(thm)],[f144,f192]) ).
fof(f547,plain,
( sQ18_spl
| sQ23_spl
| sQ17_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f546,f371,f374,f431,f377]) ).
fof(f549,plain,
( ~ sQ17_spl
| int_level(plus(t_139,n1)) = plus(int_level(t_139),n1)
| gt(int_level(t_139),n0)
| ~ p_Wr(t_139)
| p_Reset(t_139) ),
inference(resolution,[status(thm)],[f375,f159]) ).
fof(f551,plain,
( ~ sQ17_spl
| sQ25_spl
| sQ1_spl
| ~ sQ27_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f549,f371,f463,f223,f448,f374]) ).
fof(f568,plain,
( ~ gt(n1,n0)
| minus(n1,n1) = n0 ),
inference(resolution,[status(thm)],[f534,f98]) ).
fof(f575,definition,
( sQ39_spl
<=> minus(n1,n1) = n0 ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f578,plain,
( ~ sQ0_spl
| sQ39_spl ),
inference(split_clause,[status(thm)],[f568,f575,f211]) ).
fof(f590,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| gt(n0,n0) ),
inference(forward_demodulation,[status(thm)],[f227,f224]) ).
fof(f591,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f590,f520]) ).
fof(f592,plain,
( ~ sQ1_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f591]) ).
fof(f593,plain,
$false,
inference(sat_refutation,[status(thm)],[f229,f298,f302,f305,f317,f321,f329,f342,f346,f368,f380,f398,f402,f406,f439,f443,f445,f451,f460,f471,f502,f504,f524,f547,f551,f578,f592]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HWV016-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n001.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sun Sep 20 20:54:12 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.13/0.42 % Refutation found
% 0.13/0.42 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.45 % Elapsed time: 0.084821 seconds
% 0.13/0.45 % CPU time: 0.352728 seconds
% 0.13/0.45 % Total memory used: 108.677 MB
% 0.13/0.45 % Net memory used: 108.163 MB
%------------------------------------------------------------------------------