%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC015-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n015.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 02:39:35 PM UTC 2026
% Result : Unsatisfiable 7.27s 6.49s
% Output : CNFRefutation 1.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 48
% Syntax : Number of formulae : 171 ( 21 unt; 26 def)
% Number of atoms : 526 ( 109 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 693 ( 338 ~; 329 |; 0 &)
% ( 26 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 32 ( 30 usr; 27 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-2 aty)
% Number of variables : 142 ( 142 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,axiom,
! [U] : ssItem(skaf64(U)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f48,axiom,
! [U,V] : ssList(skaf48(U,V)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f72,axiom,
! [U,V] :
( ssItem(V)
| duplicatefreeP(U)
| ~ ssList(U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f74,axiom,
! [U] :
( app(nil,U) = U
| ~ ssList(U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f75,axiom,
! [U] :
( nil = U
| ssList(tl(U))
| ~ ssList(U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f85,axiom,
! [U,V] :
( ssList(app(V,U))
| ~ ssList(V)
| ~ ssList(U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f86,axiom,
! [U,V] :
( ssList(cons(U,V))
| ~ ssList(V)
| ~ ssItem(U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f99,axiom,
! [U,V] :
( ~ ssList(V)
| ~ ssItem(U)
| cons(U,V) != V ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f100,axiom,
! [U,V] :
( V = U
| neq(V,U)
| ~ ssList(V)
| ~ ssList(U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f104,axiom,
! [U] :
( nil = U
| cons(hd(U),tl(U)) = U
| ~ ssList(U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f115,axiom,
! [U,V] :
( ~ ssList(U)
| ~ ssList(V)
| ~ neq(U,V)
| U != V ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f133,axiom,
! [U,V] :
( tl(app(V,U)) = app(tl(V),U)
| nil = V
| ~ ssList(V)
| ~ ssList(U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f151,axiom,
! [U,V,W] :
( U = W
| ~ ssList(W)
| ~ ssList(V)
| ~ ssList(U)
| app(U,V) != app(W,V) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f179,axiom,
! [U,V,W,X,Y] :
( ~ ssList(Y)
| ~ duplicatefreeP(Y)
| ~ ssItem(V)
| ~ ssList(U)
| ~ ssList(W)
| ~ ssList(X)
| app(app(U,cons(V,W)),cons(V,X)) != Y ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f186,negated_conjecture,
ssList(sk1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f187,negated_conjecture,
ssList(sk2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f190,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f191,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f192,negated_conjecture,
( neq(sk2,nil)
| neq(sk2,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f196,negated_conjecture,
! [A,B] :
( ~ neq(sk4,nil)
| ~ neq(nil,sk4)
| app(sk3,B) != A
| tl(sk4) != B
| ~ ssList(B)
| sk4 = A
| ~ ssList(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f197,negated_conjecture,
! [A,B] :
( ~ neq(sk4,nil)
| app(cons(A,nil),B) != sk2
| cons(A,nil) != sk1
| ~ ssList(B)
| ~ ssItem(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f205,plain,
ssList(nil),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f228,plain,
! [X0] : ssItem(skaf64(X0)),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f245,plain,
! [X0,X1] : ssList(skaf48(X0,X1)),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f269,plain,
( ! [V] : ssItem(V)
| ! [U] :
( duplicatefreeP(U)
| ~ ssList(U) ) ),
inference(miniscoping,[status(thm)],[f72]) ).
fof(f270,plain,
! [X0,X1] :
( ssItem(X1)
| duplicatefreeP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f269]) ).
fof(f272,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f74]) ).
fof(f273,plain,
! [X0] :
( nil = X0
| ssList(tl(X0))
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f75]) ).
fof(f283,plain,
! [X0,X1] :
( ssList(app(X1,X0))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f85]) ).
fof(f284,plain,
! [X0,X1] :
( ssList(cons(X0,X1))
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f86]) ).
fof(f298,plain,
! [V] :
( ~ ssList(V)
| ! [U] :
( ~ ssItem(U)
| cons(U,V) != V ) ),
inference(miniscoping,[status(thm)],[f99]) ).
fof(f299,plain,
! [X0,X1] :
( ~ ssList(X1)
| ~ ssItem(X0)
| cons(X0,X1) != X1 ),
inference(cnf_transformation,[status(thm)],[f298]) ).
fof(f300,plain,
! [X0,X1] :
( X1 = X0
| neq(X1,X0)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f100]) ).
fof(f304,plain,
! [X0] :
( nil = X0
| cons(hd(X0),tl(X0)) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f104]) ).
fof(f318,plain,
! [U] :
( ~ ssList(U)
| ! [V] :
( ~ ssList(V)
| ~ neq(U,V)
| U != V ) ),
inference(miniscoping,[status(thm)],[f115]) ).
fof(f319,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ~ neq(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[status(thm)],[f318]) ).
fof(f343,plain,
! [X0,X1] :
( tl(app(X1,X0)) = app(tl(X1),X0)
| nil = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f133]) ).
fof(f369,plain,
! [U,W] :
( U = W
| ~ ssList(W)
| ! [V] :
( ~ ssList(V)
| ~ ssList(U)
| app(U,V) != app(W,V) ) ),
inference(miniscoping,[status(thm)],[f151]) ).
fof(f370,plain,
! [X0,X1,X2] :
( X0 = X2
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| app(X0,X1) != app(X2,X1) ),
inference(cnf_transformation,[status(thm)],[f369]) ).
fof(f414,plain,
! [Y] :
( ~ ssList(Y)
| ~ duplicatefreeP(Y)
| ! [V] :
( ~ ssItem(V)
| ! [U] :
( ~ ssList(U)
| ! [W] :
( ~ ssList(W)
| ! [X] :
( ~ ssList(X)
| app(app(U,cons(V,W)),cons(V,X)) != Y ) ) ) ) ),
inference(miniscoping,[status(thm)],[f179]) ).
fof(f415,plain,
! [X0,X1,X2,X3,X4] :
( ~ ssList(X4)
| ~ duplicatefreeP(X4)
| ~ ssItem(X1)
| ~ ssList(X0)
| ~ ssList(X2)
| ~ ssList(X3)
| app(app(X0,cons(X1,X2)),cons(X1,X3)) != X4 ),
inference(cnf_transformation,[status(thm)],[f414]) ).
fof(f428,plain,
ssList(sk1),
inference(cnf_transformation,[status(thm)],[f186]) ).
fof(f429,plain,
ssList(sk2),
inference(cnf_transformation,[status(thm)],[f187]) ).
fof(f432,plain,
sk2 = sk4,
inference(cnf_transformation,[status(thm)],[f190]) ).
fof(f433,plain,
sk1 = sk3,
inference(cnf_transformation,[status(thm)],[f191]) ).
fof(f434,plain,
( neq(sk2,nil)
| neq(sk2,nil) ),
inference(cnf_transformation,[status(thm)],[f192]) ).
fof(f440,plain,
( ~ neq(sk4,nil)
| ~ neq(nil,sk4)
| ! [A,B] :
( app(sk3,B) != A
| tl(sk4) != B
| ~ ssList(B)
| sk4 = A
| ~ ssList(A) ) ),
inference(miniscoping,[status(thm)],[f196]) ).
fof(f441,plain,
! [X0,X1] :
( ~ neq(sk4,nil)
| ~ neq(nil,sk4)
| app(sk3,X1) != X0
| tl(sk4) != X1
| ~ ssList(X1)
| sk4 = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f440]) ).
fof(f442,plain,
( ~ neq(sk4,nil)
| ! [A,B] :
( app(cons(A,nil),B) != sk2
| cons(A,nil) != sk1
| ~ ssList(B)
| ~ ssItem(A) ) ),
inference(miniscoping,[status(thm)],[f197]) ).
fof(f443,plain,
! [X0,X1] :
( ~ neq(sk4,nil)
| app(cons(X0,nil),X1) != sk2
| cons(X0,nil) != sk1
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f442]) ).
fof(f444,definition,
! [X0] :
( sQ0_spl
<=> ( duplicatefreeP(X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f445,plain,
! [X0] :
( ~ sQ0_spl
| duplicatefreeP(X0)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f444]) ).
fof(f447,definition,
! [X1] :
( sQ1_spl
<=> ssItem(X1) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f448,plain,
! [X0] :
( ~ sQ1_spl
| ssItem(X0) ),
inference(component_clause,[status(thm)],[f447]) ).
fof(f450,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f270,f444,f447]) ).
fof(f451,definition,
( sQ2_spl
<=> neq(sk2,nil) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f452,plain,
( ~ sQ2_spl
| neq(sk2,nil) ),
inference(component_clause,[status(thm)],[f451]) ).
fof(f454,plain,
sQ2_spl,
inference(split_clause,[status(thm)],[f434,f451]) ).
fof(f455,definition,
( sQ3_spl
<=> neq(sk4,nil) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f457,plain,
( sQ3_spl
| ~ neq(sk4,nil) ),
inference(component_clause,[status(thm)],[f455]) ).
fof(f459,definition,
! [X0,X1] :
( sQ4_spl
<=> ( app(sk3,X1) != X0
| tl(sk4) != X1
| ~ ssList(X1)
| sk4 = X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f460,plain,
! [X0,X1] :
( ~ sQ4_spl
| app(sk3,X1) != X0
| tl(sk4) != X1
| ~ ssList(X1)
| sk4 = X0
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f459]) ).
fof(f462,definition,
( sQ5_spl
<=> neq(nil,sk4) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f464,plain,
( sQ5_spl
| ~ neq(nil,sk4) ),
inference(component_clause,[status(thm)],[f462]) ).
fof(f466,definition,
! [X0,X1] :
( sQ6_spl
<=> ( app(cons(X0,nil),X1) != sk2
| cons(X0,nil) != sk1
| ~ ssList(X1)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f467,plain,
! [X0,X1] :
( ~ sQ6_spl
| app(cons(X0,nil),X1) != sk2
| cons(X0,nil) != sk1
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f466]) ).
fof(f470,plain,
( ~ sQ3_spl
| ~ sQ5_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f441,f459,f462,f455]) ).
fof(f471,plain,
( ~ sQ3_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f443,f466,f455]) ).
fof(f479,plain,
! [X1] :
( ~ ssList(X1)
| ~ ssList(X1)
| ~ neq(X1,X1) ),
inference(destructive_equality_resolution,[status(thm)],[f319]) ).
fof(f480,plain,
! [X0] :
( ~ ssList(X0)
| ~ neq(X0,X0) ),
inference(duplicate_literals_removal,[status(thm)],[f479]) ).
fof(f496,plain,
! [X0,X1,X2,X3] :
( ~ ssList(app(app(X2,cons(X3,X1)),cons(X3,X0)))
| ~ duplicatefreeP(app(app(X2,cons(X3,X1)),cons(X3,X0)))
| ~ ssItem(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f415]) ).
fof(f505,plain,
( sQ3_spl
| ~ neq(sk2,nil) ),
inference(forward_demodulation,[status(thm)],[f432,f457]) ).
fof(f506,plain,
( sQ3_spl
| ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f505,f452]) ).
fof(f507,plain,
( sQ3_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f506]) ).
fof(f508,plain,
! [X0,X1,X2,X3] :
( ~ sQ0_spl
| ~ ssList(app(app(X2,cons(X3,X1)),cons(X3,X0)))
| ~ ssItem(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f496,f445]) ).
fof(f509,plain,
! [X0,X1] :
( ~ sQ4_spl
| app(sk3,X1) != X0
| tl(sk4) != X1
| ~ ssList(X1)
| sk2 = X0
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f432,f460]) ).
fof(f510,plain,
! [X0,X1] :
( ~ sQ4_spl
| app(sk3,X1) != X0
| tl(sk2) != X1
| ~ ssList(X1)
| sk2 = X0
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f432,f509]) ).
fof(f511,plain,
! [X0,X1] :
( ~ sQ4_spl
| app(sk1,X1) != X0
| tl(sk2) != X1
| ~ ssList(X1)
| sk2 = X0
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f433,f510]) ).
fof(f512,plain,
( ~ sQ4_spl
| ~ ssList(tl(sk2))
| sk2 = app(sk1,tl(sk2))
| ~ ssList(app(sk1,tl(sk2))) ),
inference(destructive_equality_resolution,[status(thm)],[f511]) ).
fof(f514,plain,
( ~ sQ4_spl
| ~ ssList(tl(sk2))
| sk2 = app(sk1,tl(sk2))
| ~ ssList(sk1)
| ~ ssList(tl(sk2)) ),
inference(resolution,[status(thm)],[f283,f512]) ).
fof(f515,definition,
( sQ7_spl
<=> ssList(tl(sk2)) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f517,plain,
( sQ7_spl
| ~ ssList(tl(sk2)) ),
inference(component_clause,[status(thm)],[f515]) ).
fof(f518,definition,
( sQ8_spl
<=> ssList(sk1) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f520,plain,
( sQ8_spl
| ~ ssList(sk1) ),
inference(component_clause,[status(thm)],[f518]) ).
fof(f521,definition,
( sQ9_spl
<=> sk2 = app(sk1,tl(sk2)) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f522,plain,
( ~ sQ9_spl
| sk2 = app(sk1,tl(sk2)) ),
inference(component_clause,[status(thm)],[f521]) ).
fof(f524,plain,
( ~ sQ4_spl
| sQ9_spl
| ~ sQ8_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f514,f515,f518,f521,f459]) ).
fof(f525,plain,
( sQ5_spl
| ~ neq(nil,sk2) ),
inference(forward_demodulation,[status(thm)],[f432,f464]) ).
fof(f527,definition,
( sQ10_spl
<=> ssList(sk2) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f529,plain,
( sQ10_spl
| ~ ssList(sk2) ),
inference(component_clause,[status(thm)],[f527]) ).
fof(f531,plain,
( sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f520,f428]) ).
fof(f532,plain,
sQ8_spl,
inference(contradiction_clause,[status(thm)],[f531]) ).
fof(f533,plain,
( sQ7_spl
| nil = sk2
| ~ ssList(sk2) ),
inference(resolution,[status(thm)],[f517,f273]) ).
fof(f534,definition,
( sQ11_spl
<=> nil = sk2 ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f535,plain,
( ~ sQ11_spl
| nil = sk2 ),
inference(component_clause,[status(thm)],[f534]) ).
fof(f537,plain,
( sQ7_spl
| sQ11_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f533,f527,f534,f515]) ).
fof(f541,plain,
( ~ sQ2_spl
| ~ sQ11_spl
| neq(nil,nil) ),
inference(backward_demodulation,[status(thm)],[f535,f452]) ).
fof(f614,plain,
( sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f429,f529]) ).
fof(f615,plain,
sQ10_spl,
inference(contradiction_clause,[status(thm)],[f614]) ).
fof(f618,plain,
( sQ5_spl
| nil = sk2
| ~ ssList(nil)
| ~ ssList(sk2) ),
inference(resolution,[status(thm)],[f300,f525]) ).
fof(f621,definition,
( sQ13_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f623,plain,
( sQ13_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f621]) ).
fof(f624,plain,
( sQ5_spl
| sQ11_spl
| ~ sQ13_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f618,f527,f621,f534,f462]) ).
fof(f637,plain,
( sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f623,f205]) ).
fof(f638,plain,
sQ13_spl,
inference(contradiction_clause,[status(thm)],[f637]) ).
fof(f640,plain,
( ~ sQ2_spl
| ~ sQ11_spl
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f541,f480]) ).
fof(f641,plain,
( ~ sQ2_spl
| ~ sQ11_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f640,f621,f534,f451]) ).
fof(f648,definition,
( sQ15_spl
<=> nil = sk1 ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f649,plain,
( ~ sQ15_spl
| nil = sk1 ),
inference(component_clause,[status(thm)],[f648]) ).
fof(f677,plain,
( ~ sQ9_spl
| tl(sk2) = app(tl(sk1),tl(sk2))
| nil = sk1
| ~ ssList(sk1)
| ~ ssList(tl(sk2)) ),
inference(paramodulation,[status(thm)],[f522,f343]) ).
fof(f678,definition,
( sQ20_spl
<=> tl(sk2) = app(tl(sk1),tl(sk2)) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f679,plain,
( ~ sQ20_spl
| tl(sk2) = app(tl(sk1),tl(sk2)) ),
inference(component_clause,[status(thm)],[f678]) ).
fof(f681,plain,
( ~ sQ9_spl
| sQ20_spl
| sQ15_spl
| ~ sQ8_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f677,f515,f518,f648,f678,f521]) ).
fof(f683,plain,
( ~ sQ9_spl
| ~ sQ15_spl
| sk2 = app(nil,tl(sk2)) ),
inference(backward_demodulation,[status(thm)],[f649,f522]) ).
fof(f687,plain,
( ~ sQ9_spl
| ~ sQ15_spl
| sk2 = tl(sk2)
| ~ ssList(tl(sk2)) ),
inference(paramodulation,[status(thm)],[f683,f272]) ).
fof(f693,definition,
( sQ21_spl
<=> sk2 = tl(sk2) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f694,plain,
( ~ sQ21_spl
| sk2 = tl(sk2) ),
inference(component_clause,[status(thm)],[f693]) ).
fof(f696,plain,
( ~ sQ9_spl
| ~ sQ15_spl
| sQ21_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f687,f515,f693,f648,f521]) ).
fof(f708,plain,
( ~ sQ21_spl
| nil = sk2
| cons(hd(sk2),sk2) = sk2
| ~ ssList(sk2) ),
inference(paramodulation,[status(thm)],[f694,f304]) ).
fof(f710,definition,
( sQ23_spl
<=> cons(hd(sk2),sk2) = sk2 ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f711,plain,
( ~ sQ23_spl
| cons(hd(sk2),sk2) = sk2 ),
inference(component_clause,[status(thm)],[f710]) ).
fof(f713,plain,
( ~ sQ21_spl
| sQ11_spl
| sQ23_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f708,f527,f710,f534,f693]) ).
fof(f736,plain,
( ~ sQ23_spl
| ~ ssList(sk2)
| ~ ssItem(hd(sk2)) ),
inference(resolution,[status(thm)],[f711,f299]) ).
fof(f741,definition,
( sQ27_spl
<=> ssItem(hd(sk2)) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f743,plain,
( sQ27_spl
| ~ ssItem(hd(sk2)) ),
inference(component_clause,[status(thm)],[f741]) ).
fof(f744,plain,
( ~ sQ23_spl
| ~ sQ10_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f736,f741,f527,f710]) ).
fof(f772,definition,
! [X1] :
( sQ32_spl
<=> ~ ssList(X1) ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f773,plain,
! [X0] :
( ~ sQ32_spl
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f772]) ).
fof(f838,definition,
! [X1] :
( sQ40_spl
<=> ( ~ ssList(X1)
| ~ ssList(X1) ) ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f839,plain,
! [X0] :
( ~ sQ40_spl
| ~ ssList(X0)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f838]) ).
fof(f886,plain,
( sQ27_spl
| ~ sQ1_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f743,f448]) ).
fof(f916,plain,
( sQ27_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f886]) ).
fof(f1150,plain,
! [X0] :
( ~ sQ20_spl
| X0 = tl(sk1)
| ~ ssList(tl(sk1))
| ~ ssList(tl(sk2))
| ~ ssList(X0)
| app(X0,tl(sk2)) != tl(sk2) ),
inference(paramodulation,[status(thm)],[f679,f370]) ).
fof(f1164,definition,
( sQ63_spl
<=> ssList(tl(sk1)) ),
introduced(definition,[new_symbols(definition,[sQ63_spl])],[split_symbol_definition]) ).
fof(f1166,plain,
( sQ63_spl
| ~ ssList(tl(sk1)) ),
inference(component_clause,[status(thm)],[f1164]) ).
fof(f1172,definition,
! [X0] :
( sQ65_spl
<=> ( X0 = tl(sk1)
| ~ ssList(X0)
| app(X0,tl(sk2)) != tl(sk2) ) ),
introduced(definition,[new_symbols(definition,[sQ65_spl])],[split_symbol_definition]) ).
fof(f1173,plain,
! [X0] :
( ~ sQ65_spl
| X0 = tl(sk1)
| ~ ssList(X0)
| app(X0,tl(sk2)) != tl(sk2) ),
inference(component_clause,[status(thm)],[f1172]) ).
fof(f1175,plain,
( ~ sQ20_spl
| ~ sQ63_spl
| ~ sQ7_spl
| sQ65_spl ),
inference(split_clause,[status(thm)],[f1150,f1172,f515,f1164,f678]) ).
fof(f1190,definition,
( sQ69_spl
<=> nil = tl(sk1) ),
introduced(definition,[new_symbols(definition,[sQ69_spl])],[split_symbol_definition]) ).
fof(f1191,plain,
( ~ sQ69_spl
| nil = tl(sk1) ),
inference(component_clause,[status(thm)],[f1190]) ).
fof(f1201,plain,
( sQ63_spl
| nil = sk1
| ~ ssList(sk1) ),
inference(resolution,[status(thm)],[f1166,f273]) ).
fof(f1202,plain,
( sQ63_spl
| sQ15_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f1201,f518,f648,f1164]) ).
fof(f1219,plain,
! [X0,X1] :
( ~ sQ6_spl
| ~ sQ1_spl
| app(cons(X1,nil),X0) != sk2
| cons(X1,nil) != sk1
| ~ ssList(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f467,f448]) ).
fof(f1223,plain,
( ~ sQ69_spl
| nil = sk1
| cons(hd(sk1),nil) = sk1
| ~ ssList(sk1) ),
inference(paramodulation,[status(thm)],[f1191,f304]) ).
fof(f1225,definition,
( sQ71_spl
<=> cons(hd(sk1),nil) = sk1 ),
introduced(definition,[new_symbols(definition,[sQ71_spl])],[split_symbol_definition]) ).
fof(f1226,plain,
( ~ sQ71_spl
| cons(hd(sk1),nil) = sk1 ),
inference(component_clause,[status(thm)],[f1225]) ).
fof(f1228,plain,
( ~ sQ69_spl
| sQ15_spl
| sQ71_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f1223,f518,f1225,f648,f1190]) ).
fof(f1313,plain,
! [X0] :
( ~ sQ71_spl
| ~ sQ6_spl
| ~ sQ1_spl
| app(sk1,X0) != sk2
| cons(hd(sk1),nil) != sk1
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1226,f1219]) ).
fof(f1321,definition,
! [X0] :
( sQ78_spl
<=> ( app(sk1,X0) != sk2
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ78_spl])],[split_symbol_definition]) ).
fof(f1322,plain,
! [X0] :
( ~ sQ78_spl
| app(sk1,X0) != sk2
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f1321]) ).
fof(f1324,plain,
( ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ71_spl
| sQ78_spl ),
inference(split_clause,[status(thm)],[f1313,f1321,f1225,f447,f466]) ).
fof(f1344,plain,
( ~ sQ40_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f428,f1376]) ).
fof(f1376,plain,
! [X0] :
( ~ sQ40_spl
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f839]) ).
fof(f1377,plain,
~ sQ40_spl,
inference(contradiction_clause,[status(thm)],[f1344]) ).
fof(f1470,plain,
( ~ sQ65_spl
| ~ ssList(tl(sk2))
| nil = tl(sk1)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f1173,f272]) ).
fof(f1475,plain,
( ~ sQ65_spl
| ~ sQ7_spl
| sQ69_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f1470,f621,f1190,f515,f1172]) ).
fof(f1594,plain,
( ~ sQ9_spl
| ~ sQ78_spl
| ~ ssList(tl(sk2)) ),
inference(resolution,[status(thm)],[f1322,f522]) ).
fof(f1596,plain,
( ~ sQ9_spl
| ~ sQ78_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f1594,f515,f1321,f521]) ).
fof(f1651,plain,
( ~ sQ32_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f245,f773]) ).
fof(f1726,plain,
~ sQ32_spl,
inference(contradiction_clause,[status(thm)],[f1651]) ).
fof(f1810,plain,
! [X0,X1,X2,X3] :
( ~ sQ0_spl
| ~ ssItem(X0)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssList(app(X2,cons(X0,X3)))
| ~ ssList(cons(X0,X1)) ),
inference(resolution,[status(thm)],[f283,f508]) ).
fof(f1814,plain,
! [X0,X1,X2,X3] :
( ~ sQ0_spl
| ~ ssItem(X1)
| ~ ssList(X0)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssList(app(X0,cons(X1,X2))) ),
inference(forward_subsumption_resolution,[status(thm)],[f1810,f284]) ).
fof(f1821,plain,
! [X0,X1,X2,X3] :
( ~ sQ0_spl
| ~ ssList(X2)
| ~ ssList(cons(X3,X1))
| ~ ssItem(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f1814,f283]) ).
fof(f1822,definition,
! [X1,X3] :
( sQ100_spl
<=> ( ~ ssList(cons(X3,X1))
| ~ ssItem(X3)
| ~ ssList(X1) ) ),
introduced(definition,[new_symbols(definition,[sQ100_spl])],[split_symbol_definition]) ).
fof(f1823,plain,
! [X0,X1] :
( ~ sQ100_spl
| ~ ssList(cons(X1,X0))
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f1822]) ).
fof(f1825,plain,
( ~ sQ0_spl
| sQ40_spl
| sQ100_spl
| sQ32_spl ),
inference(split_clause,[status(thm)],[f1821,f772,f1822,f838,f444]) ).
fof(f1827,plain,
! [X0,X1] :
( ~ sQ100_spl
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1823,f284]) ).
fof(f1828,plain,
! [X0] :
( ~ sQ100_spl
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f1827,f228]) ).
fof(f1845,plain,
( ~ sQ100_spl
| sQ32_spl ),
inference(split_clause,[status(thm)],[f1828,f772,f1822]) ).
fof(f1862,plain,
$false,
inference(sat_refutation,[status(thm)],[f450,f454,f470,f471,f507,f524,f532,f537,f615,f624,f638,f641,f681,f696,f713,f744,f916,f1175,f1202,f1228,f1324,f1377,f1475,f1596,f1726,f1825,f1845]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWC015-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/5.43 % Computer : n015.cluster.edu
% 0.17/5.43 % Model : x86_64 x86_64
% 0.17/5.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/5.43 % Memory : 8046.5625MB
% 0.17/5.43 % OS : Linux 6.8.0-71-generic
% 0.17/5.43 % CPULimit : 300
% 0.17/5.43 % WCLimit : 300
% 0.17/5.43 % DateTime : Mon Sep 21 07:52:41 UTC 2026
% 0.17/5.44 % CPUTime :
% 0.17/5.46 % Drodi V4.1.1
% 7.27/6.49 % Refutation found
% 7.27/6.49 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 7.27/6.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.07/6.53 % Elapsed time: 1.073826 seconds
% 1.07/6.53 % CPU time: 7.962269 seconds
% 1.07/6.53 % Total memory used: 181.818 MB
% 1.07/6.53 % Net memory used: 176.323 MB
%------------------------------------------------------------------------------