%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC314-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n004.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 02:40:45 PM UTC 2026
% Result : Unsatisfiable 0.18s 0.52s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 43
% Syntax : Number of formulae : 146 ( 8 unt; 22 def)
% Number of atoms : 429 ( 113 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 527 ( 244 ~; 261 |; 0 &)
% ( 22 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 27 ( 25 usr; 23 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 58 ( 58 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
ssList(nil),
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(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(f96,axiom,
! [U,V] :
( tl(cons(U,V)) = V
| ~ ssList(V)
| ~ ssItem(U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f97,axiom,
! [U,V] :
( hd(cons(U,V)) = U
| ~ ssList(V)
| ~ ssItem(U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f98,axiom,
! [U,V] :
( ~ ssList(V)
| ~ ssItem(U)
| cons(U,V) != nil ),
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(f118,axiom,
! [U,V] :
( nil = U
| ~ ssList(U)
| ~ ssList(V)
| app(U,V) != nil ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f120,axiom,
! [U,V] :
( app(cons(U,nil),V) = cons(U,V)
| ~ ssList(V)
| ~ ssItem(U) ),
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,
( nil != sk4
| nil = sk3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f193,negated_conjecture,
! [A,B,C,D] :
( ~ neq(sk4,nil)
| ~ neq(nil,sk4)
| ~ neq(nil,sk4)
| hd(sk4) != D
| cons(D,nil) != C
| ~ ssItem(D)
| app(B,C) != A
| tl(sk4) != B
| ~ ssList(C)
| ~ ssList(B)
| sk3 = A
| ~ ssList(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f194,negated_conjecture,
( nil = sk2
| ssItem(sk5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f195,negated_conjecture,
( nil != sk1
| ssItem(sk5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f196,negated_conjecture,
( nil = sk2
| ssList(sk6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f197,negated_conjecture,
( nil = sk2
| app(cons(sk5,nil),sk6) = sk2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f198,negated_conjecture,
( nil = sk2
| app(sk6,cons(sk5,nil)) != sk1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f199,negated_conjecture,
( nil != sk1
| ssList(sk6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f200,negated_conjecture,
( nil != sk1
| app(cons(sk5,nil),sk6) = sk2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f209,plain,
ssList(nil),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f276,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f74]) ).
fof(f287,plain,
! [X0,X1] :
( ssList(app(X1,X0))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f85]) ).
fof(f288,plain,
! [X0,X1] :
( ssList(cons(X0,X1))
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f86]) ).
fof(f298,plain,
! [X0,X1] :
( tl(cons(X0,X1)) = X1
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f96]) ).
fof(f299,plain,
! [X0,X1] :
( hd(cons(X0,X1)) = X0
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f97]) ).
fof(f300,plain,
! [V] :
( ~ ssList(V)
| ! [U] :
( ~ ssItem(U)
| cons(U,V) != nil ) ),
inference(miniscoping,[status(thm)],[f98]) ).
fof(f301,plain,
! [X0,X1] :
( ~ ssList(X1)
| ~ ssItem(X0)
| cons(X0,X1) != nil ),
inference(cnf_transformation,[status(thm)],[f300]) ).
fof(f304,plain,
! [X0,X1] :
( X1 = X0
| neq(X1,X0)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f100]) ).
fof(f328,plain,
! [U] :
( nil = U
| ~ ssList(U)
| ! [V] :
( ~ ssList(V)
| app(U,V) != nil ) ),
inference(miniscoping,[status(thm)],[f118]) ).
fof(f329,plain,
! [X0,X1] :
( nil = X0
| ~ ssList(X0)
| ~ ssList(X1)
| app(X0,X1) != nil ),
inference(cnf_transformation,[status(thm)],[f328]) ).
fof(f332,plain,
! [X0,X1] :
( app(cons(X0,nil),X1) = cons(X0,X1)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f120]) ).
fof(f436,plain,
sk2 = sk4,
inference(cnf_transformation,[status(thm)],[f190]) ).
fof(f437,plain,
sk1 = sk3,
inference(cnf_transformation,[status(thm)],[f191]) ).
fof(f438,plain,
( nil != sk4
| nil = sk3 ),
inference(cnf_transformation,[status(thm)],[f192]) ).
fof(f439,plain,
( ~ neq(sk4,nil)
| ~ neq(nil,sk4)
| ~ neq(nil,sk4)
| ! [D] :
( hd(sk4) != D
| ! [C] :
( cons(D,nil) != C
| ~ ssItem(D)
| ! [A,B] :
( app(B,C) != A
| tl(sk4) != B
| ~ ssList(C)
| ~ ssList(B)
| sk3 = A
| ~ ssList(A) ) ) ) ),
inference(miniscoping,[status(thm)],[f193]) ).
fof(f440,plain,
! [X0,X1,X2,X3] :
( ~ neq(sk4,nil)
| ~ neq(nil,sk4)
| ~ neq(nil,sk4)
| hd(sk4) != X3
| cons(X3,nil) != X2
| ~ ssItem(X3)
| app(X1,X2) != X0
| tl(sk4) != X1
| ~ ssList(X2)
| ~ ssList(X1)
| sk3 = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f439]) ).
fof(f441,plain,
( nil = sk2
| ssItem(sk5) ),
inference(cnf_transformation,[status(thm)],[f194]) ).
fof(f442,plain,
( nil != sk1
| ssItem(sk5) ),
inference(cnf_transformation,[status(thm)],[f195]) ).
fof(f443,plain,
( nil = sk2
| ssList(sk6) ),
inference(cnf_transformation,[status(thm)],[f196]) ).
fof(f444,plain,
( nil = sk2
| app(cons(sk5,nil),sk6) = sk2 ),
inference(cnf_transformation,[status(thm)],[f197]) ).
fof(f445,plain,
( nil = sk2
| app(sk6,cons(sk5,nil)) != sk1 ),
inference(cnf_transformation,[status(thm)],[f198]) ).
fof(f446,plain,
( nil != sk1
| ssList(sk6) ),
inference(cnf_transformation,[status(thm)],[f199]) ).
fof(f447,plain,
( nil != sk1
| app(cons(sk5,nil),sk6) = sk2 ),
inference(cnf_transformation,[status(thm)],[f200]) ).
fof(f456,definition,
( sQ2_spl
<=> nil = sk3 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f457,plain,
( ~ sQ2_spl
| nil = sk3 ),
inference(component_clause,[status(thm)],[f456]) ).
fof(f459,definition,
( sQ3_spl
<=> nil = sk4 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f460,plain,
( ~ sQ3_spl
| nil = sk4 ),
inference(component_clause,[status(thm)],[f459]) ).
fof(f461,plain,
( sQ3_spl
| nil != sk4 ),
inference(component_clause,[status(thm)],[f459]) ).
fof(f462,plain,
( ~ sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f438,f456,f459]) ).
fof(f463,definition,
! [X0,X1,X2,X3] :
( sQ4_spl
<=> ( hd(sk4) != X3
| cons(X3,nil) != X2
| ~ ssItem(X3)
| app(X1,X2) != X0
| tl(sk4) != X1
| ~ ssList(X2)
| ~ ssList(X1)
| sk3 = X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f464,plain,
! [X0,X1,X2,X3] :
( ~ sQ4_spl
| hd(sk4) != X3
| cons(X3,nil) != X2
| ~ ssItem(X3)
| app(X1,X2) != X0
| tl(sk4) != X1
| ~ ssList(X2)
| ~ ssList(X1)
| sk3 = X0
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f463]) ).
fof(f466,definition,
( sQ5_spl
<=> neq(nil,sk4) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f468,plain,
( sQ5_spl
| ~ neq(nil,sk4) ),
inference(component_clause,[status(thm)],[f466]) ).
fof(f469,definition,
( sQ6_spl
<=> neq(sk4,nil) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f471,plain,
( sQ6_spl
| ~ neq(sk4,nil) ),
inference(component_clause,[status(thm)],[f469]) ).
fof(f472,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f440,f463,f466,f469]) ).
fof(f473,definition,
( sQ7_spl
<=> ssItem(sk5) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f476,definition,
( sQ8_spl
<=> nil = sk2 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f477,plain,
( ~ sQ8_spl
| nil = sk2 ),
inference(component_clause,[status(thm)],[f476]) ).
fof(f479,plain,
( sQ8_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f441,f473,f476]) ).
fof(f480,definition,
( sQ9_spl
<=> nil = sk1 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f482,plain,
( sQ9_spl
| nil != sk1 ),
inference(component_clause,[status(thm)],[f480]) ).
fof(f483,plain,
( ~ sQ9_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f442,f473,f480]) ).
fof(f484,definition,
( sQ10_spl
<=> ssList(sk6) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f485,plain,
( ~ sQ10_spl
| ssList(sk6) ),
inference(component_clause,[status(thm)],[f484]) ).
fof(f487,plain,
( sQ8_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f443,f484,f476]) ).
fof(f488,definition,
( sQ11_spl
<=> app(cons(sk5,nil),sk6) = sk2 ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f489,plain,
( ~ sQ11_spl
| app(cons(sk5,nil),sk6) = sk2 ),
inference(component_clause,[status(thm)],[f488]) ).
fof(f491,plain,
( sQ8_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f444,f488,f476]) ).
fof(f492,definition,
( sQ12_spl
<=> app(sk6,cons(sk5,nil)) = sk1 ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f494,plain,
( sQ12_spl
| app(sk6,cons(sk5,nil)) != sk1 ),
inference(component_clause,[status(thm)],[f492]) ).
fof(f495,plain,
( sQ8_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f445,f492,f476]) ).
fof(f496,plain,
( ~ sQ9_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f446,f484,f480]) ).
fof(f497,plain,
( ~ sQ9_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f447,f488,f480]) ).
fof(f530,plain,
( sQ9_spl
| nil != sk3 ),
inference(forward_demodulation,[status(thm)],[f437,f482]) ).
fof(f531,plain,
( sQ9_spl
| ~ sQ8_spl
| sk4 != sk3 ),
inference(backward_demodulation,[status(thm)],[f533,f530]) ).
fof(f533,plain,
( ~ sQ8_spl
| nil = sk4 ),
inference(forward_demodulation,[status(thm)],[f436,f477]) ).
fof(f536,plain,
( ~ sQ2_spl
| ~ sQ8_spl
| sk4 = sk3 ),
inference(forward_demodulation,[status(thm)],[f533,f457]) ).
fof(f537,plain,
( sQ9_spl
| ~ sQ8_spl
| ~ sQ2_spl
| sk4 != sk4 ),
inference(forward_demodulation,[status(thm)],[f536,f531]) ).
fof(f538,plain,
( sQ9_spl
| ~ sQ8_spl
| ~ sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f537]) ).
fof(f539,plain,
( sQ9_spl
| ~ sQ8_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f538]) ).
fof(f541,plain,
( sQ12_spl
| app(sk6,cons(sk5,nil)) != sk3 ),
inference(forward_demodulation,[status(thm)],[f437,f494]) ).
fof(f542,plain,
( ~ sQ11_spl
| app(cons(sk5,nil),sk6) = sk4 ),
inference(forward_demodulation,[status(thm)],[f436,f489]) ).
fof(f543,plain,
( ~ sQ11_spl
| ssList(sk4)
| ~ ssList(cons(sk5,nil))
| ~ ssList(sk6) ),
inference(paramodulation,[status(thm)],[f542,f287]) ).
fof(f544,definition,
( sQ13_spl
<=> ssList(cons(sk5,nil)) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f545,plain,
( ~ sQ13_spl
| ssList(cons(sk5,nil)) ),
inference(component_clause,[status(thm)],[f544]) ).
fof(f546,plain,
( sQ13_spl
| ~ ssList(cons(sk5,nil)) ),
inference(component_clause,[status(thm)],[f544]) ).
fof(f547,definition,
( sQ14_spl
<=> ssList(sk4) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f550,plain,
( ~ sQ11_spl
| sQ14_spl
| ~ sQ13_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f543,f484,f544,f547,f488]) ).
fof(f551,plain,
( sQ13_spl
| ~ ssList(nil)
| ~ ssItem(sk5) ),
inference(resolution,[status(thm)],[f288,f546]) ).
fof(f552,definition,
( sQ15_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f554,plain,
( sQ15_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f552]) ).
fof(f555,plain,
( sQ13_spl
| ~ sQ15_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f551,f473,f552,f544]) ).
fof(f556,plain,
( sQ15_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f554,f209]) ).
fof(f557,plain,
sQ15_spl,
inference(contradiction_clause,[status(thm)],[f556]) ).
fof(f558,plain,
( ~ sQ8_spl
| sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f533,f461]) ).
fof(f559,plain,
( ~ sQ8_spl
| sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f558]) ).
fof(f591,plain,
( ~ sQ13_spl
| ~ sQ3_spl
| ssList(cons(sk5,sk4)) ),
inference(forward_demodulation,[status(thm)],[f460,f545]) ).
fof(f597,definition,
( sQ16_spl
<=> ssList(cons(sk5,sk4)) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f599,plain,
( sQ16_spl
| ~ ssList(cons(sk5,sk4)) ),
inference(component_clause,[status(thm)],[f597]) ).
fof(f601,plain,
( sQ16_spl
| ~ sQ13_spl
| ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f599,f591]) ).
fof(f602,plain,
( sQ16_spl
| ~ sQ13_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f601]) ).
fof(f603,plain,
( sQ6_spl
| sk4 = nil
| ~ ssList(sk4)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f304,f471]) ).
fof(f606,plain,
( sQ6_spl
| sQ3_spl
| ~ sQ14_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f603,f552,f547,f459,f469]) ).
fof(f607,plain,
( ~ sQ4_spl
| ~ ssItem(hd(sk4))
| ~ ssList(cons(hd(sk4),nil))
| ~ ssList(tl(sk4))
| sk3 = app(tl(sk4),cons(hd(sk4),nil))
| ~ ssList(app(tl(sk4),cons(hd(sk4),nil))) ),
inference(destructive_equality_resolution,[status(thm)],[f464]) ).
fof(f608,plain,
( ~ sQ4_spl
| ~ ssItem(hd(sk4))
| ~ ssList(cons(hd(sk4),nil))
| ~ ssList(tl(sk4))
| sk3 = app(tl(sk4),cons(hd(sk4),nil)) ),
inference(forward_subsumption_resolution,[status(thm)],[f607,f287]) ).
fof(f614,definition,
( sQ17_spl
<=> nil = nil ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f626,plain,
( ~ ssList(nil)
| nil = nil
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f329,f276]) ).
fof(f629,plain,
( sQ17_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f626,f552,f614]) ).
fof(f644,plain,
( ~ sQ11_spl
| sk4 = cons(sk5,sk6)
| ~ ssList(sk6)
| ~ ssItem(sk5) ),
inference(paramodulation,[status(thm)],[f542,f332]) ).
fof(f645,definition,
( sQ22_spl
<=> sk4 = cons(sk5,sk6) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f646,plain,
( ~ sQ22_spl
| sk4 = cons(sk5,sk6) ),
inference(component_clause,[status(thm)],[f645]) ).
fof(f648,plain,
( ~ sQ11_spl
| sQ22_spl
| ~ sQ10_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f644,f473,f484,f645,f488]) ).
fof(f649,plain,
( ~ sQ22_spl
| ~ ssList(sk6)
| ~ ssItem(sk5)
| sk4 != nil ),
inference(paramodulation,[status(thm)],[f646,f301]) ).
fof(f650,plain,
( ~ sQ22_spl
| hd(sk4) = sk5
| ~ ssList(sk6)
| ~ ssItem(sk5) ),
inference(paramodulation,[status(thm)],[f646,f299]) ).
fof(f651,plain,
( ~ sQ22_spl
| tl(sk4) = sk6
| ~ ssList(sk6)
| ~ ssItem(sk5) ),
inference(paramodulation,[status(thm)],[f646,f298]) ).
fof(f654,plain,
( ~ sQ22_spl
| ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f649,f459,f473,f484,f645]) ).
fof(f655,definition,
( sQ23_spl
<=> hd(sk4) = sk5 ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f656,plain,
( ~ sQ23_spl
| hd(sk4) = sk5 ),
inference(component_clause,[status(thm)],[f655]) ).
fof(f658,plain,
( ~ sQ22_spl
| sQ23_spl
| ~ sQ10_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f650,f473,f484,f655,f645]) ).
fof(f659,definition,
( sQ24_spl
<=> tl(sk4) = sk6 ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f660,plain,
( ~ sQ24_spl
| tl(sk4) = sk6 ),
inference(component_clause,[status(thm)],[f659]) ).
fof(f662,plain,
( ~ sQ22_spl
| sQ24_spl
| ~ sQ10_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f651,f473,f484,f659,f645]) ).
fof(f668,plain,
( ~ sQ4_spl
| ~ sQ23_spl
| ~ ssItem(sk5)
| ~ ssList(cons(hd(sk4),nil))
| ~ ssList(tl(sk4))
| sk3 = app(tl(sk4),cons(hd(sk4),nil)) ),
inference(backward_demodulation,[status(thm)],[f656,f608]) ).
fof(f671,definition,
( sQ26_spl
<=> sk3 = app(tl(sk4),cons(hd(sk4),nil)) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f672,plain,
( ~ sQ26_spl
| sk3 = app(tl(sk4),cons(hd(sk4),nil)) ),
inference(component_clause,[status(thm)],[f671]) ).
fof(f674,definition,
( sQ27_spl
<=> ssList(tl(sk4)) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f676,plain,
( sQ27_spl
| ~ ssList(tl(sk4)) ),
inference(component_clause,[status(thm)],[f674]) ).
fof(f677,definition,
( sQ28_spl
<=> ssList(cons(hd(sk4),nil)) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f679,plain,
( sQ28_spl
| ~ ssList(cons(hd(sk4),nil)) ),
inference(component_clause,[status(thm)],[f677]) ).
fof(f680,plain,
( ~ sQ4_spl
| ~ sQ23_spl
| ~ sQ7_spl
| ~ sQ28_spl
| ~ sQ27_spl
| sQ26_spl ),
inference(split_clause,[status(thm)],[f668,f671,f674,f677,f473,f655,f463]) ).
fof(f686,plain,
( sQ28_spl
| ~ sQ23_spl
| ~ ssList(cons(sk5,nil)) ),
inference(forward_demodulation,[status(thm)],[f656,f679]) ).
fof(f687,plain,
( sQ28_spl
| ~ sQ23_spl
| ~ sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f686,f545]) ).
fof(f688,plain,
( sQ28_spl
| ~ sQ23_spl
| ~ sQ13_spl ),
inference(contradiction_clause,[status(thm)],[f687]) ).
fof(f710,plain,
( sQ5_spl
| nil = sk4
| ~ ssList(nil)
| ~ ssList(sk4) ),
inference(resolution,[status(thm)],[f468,f304]) ).
fof(f718,plain,
( sQ5_spl
| sQ3_spl
| ~ sQ15_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f710,f547,f552,f459,f466]) ).
fof(f719,plain,
( ~ sQ26_spl
| ~ sQ24_spl
| sk3 = app(sk6,cons(hd(sk4),nil)) ),
inference(forward_demodulation,[status(thm)],[f660,f672]) ).
fof(f720,plain,
( ~ sQ26_spl
| ~ sQ24_spl
| ~ sQ23_spl
| sk3 = app(sk6,cons(sk5,nil)) ),
inference(forward_demodulation,[status(thm)],[f656,f719]) ).
fof(f721,plain,
( ~ sQ26_spl
| ~ sQ24_spl
| ~ sQ23_spl
| sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f720,f541]) ).
fof(f722,plain,
( ~ sQ26_spl
| ~ sQ24_spl
| ~ sQ23_spl
| sQ12_spl ),
inference(contradiction_clause,[status(thm)],[f721]) ).
fof(f723,plain,
( sQ27_spl
| ~ sQ24_spl
| ~ ssList(sk6) ),
inference(forward_demodulation,[status(thm)],[f660,f676]) ).
fof(f724,plain,
( sQ27_spl
| ~ sQ24_spl
| ~ sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f723,f485]) ).
fof(f725,plain,
( sQ27_spl
| ~ sQ24_spl
| ~ sQ10_spl ),
inference(contradiction_clause,[status(thm)],[f724]) ).
fof(f726,plain,
$false,
inference(sat_refutation,[status(thm)],[f462,f472,f479,f483,f487,f491,f495,f496,f497,f539,f550,f555,f557,f559,f602,f606,f629,f648,f654,f658,f662,f680,f688,f718,f722,f725]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWC314-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.46 % Computer : n004.cluster.edu
% 0.18/0.46 % Model : x86_64 x86_64
% 0.18/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.46 % Memory : 8046.5625MB
% 0.18/0.46 % OS : Linux 6.8.0-71-generic
% 0.18/0.46 % CPULimit : 300
% 0.18/0.46 % WCLimit : 300
% 0.18/0.46 % DateTime : Mon Sep 21 08:14:21 UTC 2026
% 0.18/0.46 % CPUTime :
% 0.18/0.49 % Drodi V4.1.1
% 0.18/0.52 % Refutation found
% 0.18/0.52 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.18/0.52 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.22/0.57 % Elapsed time: 0.098851 seconds
% 0.22/0.57 % CPU time: 0.253619 seconds
% 0.22/0.57 % Total memory used: 50.141 MB
% 0.22/0.57 % Net memory used: 49.994 MB
%------------------------------------------------------------------------------