%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC416-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n010.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 02:41:09 PM UTC 2026
% Result : Unsatisfiable 0.14s 10.49s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 30
% Syntax : Number of formulae : 101 ( 15 unt; 15 def)
% Number of atoms : 291 ( 67 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 368 ( 178 ~; 175 |; 0 &)
% ( 15 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 20 ( 18 usr; 16 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 50 ( 50 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f76,axiom,
! [U] :
( nil = U
| ssItem(hd(U))
| ~ ssList(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f86,axiom,
! [U,V] :
( ssList(cons(U,V))
| ~ ssList(V)
| ~ ssItem(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f97,axiom,
! [U,V] :
( hd(cons(U,V)) = U
| ~ ssList(V)
| ~ ssItem(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f100,axiom,
! [U,V] :
( V = U
| neq(V,U)
| ~ ssList(V)
| ~ ssList(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f115,axiom,
! [U,V] :
( ~ ssList(U)
| ~ ssList(V)
| ~ neq(U,V)
| U != V ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f120,axiom,
! [U,V] :
( app(cons(U,nil),V) = cons(U,V)
| ~ ssList(V)
| ~ ssItem(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f188,negated_conjecture,
ssList(sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f189,negated_conjecture,
ssList(sk4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f190,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f191,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f192,negated_conjecture,
( neq(sk2,nil)
| neq(sk2,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f197,negated_conjecture,
! [A,B,C] :
( ~ neq(sk4,nil)
| ~ neq(nil,sk2)
| hd(sk2) != C
| cons(C,nil) != B
| ~ ssItem(C)
| app(B,sk1) != A
| ~ ssList(B)
| sk2 != A
| ~ ssList(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f198,negated_conjecture,
( ~ neq(sk4,nil)
| ssItem(sk5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f199,negated_conjecture,
( ~ neq(sk4,nil)
| app(cons(sk5,nil),sk3) = sk4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f207,plain,
ssList(nil),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f276,plain,
! [X0] :
( nil = X0
| ssItem(hd(X0))
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f76]) ).
fof(f286,plain,
! [X0,X1] :
( ssList(cons(X0,X1))
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f86]) ).
fof(f297,plain,
! [X0,X1] :
( hd(cons(X0,X1)) = X0
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f97]) ).
fof(f302,plain,
! [X0,X1] :
( X1 = X0
| neq(X1,X0)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f100]) ).
fof(f320,plain,
! [U] :
( ~ ssList(U)
| ! [V] :
( ~ ssList(V)
| ~ neq(U,V)
| U != V ) ),
inference(miniscoping,[status(thm)],[f115]) ).
fof(f321,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ~ neq(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[status(thm)],[f320]) ).
fof(f330,plain,
! [X0,X1] :
( app(cons(X0,nil),X1) = cons(X0,X1)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f120]) ).
fof(f432,plain,
ssList(sk3),
inference(cnf_transformation,[status(thm)],[f188]) ).
fof(f433,plain,
ssList(sk4),
inference(cnf_transformation,[status(thm)],[f189]) ).
fof(f434,plain,
sk2 = sk4,
inference(cnf_transformation,[status(thm)],[f190]) ).
fof(f435,plain,
sk1 = sk3,
inference(cnf_transformation,[status(thm)],[f191]) ).
fof(f436,plain,
( neq(sk2,nil)
| neq(sk2,nil) ),
inference(cnf_transformation,[status(thm)],[f192]) ).
fof(f442,plain,
( ~ neq(sk4,nil)
| ~ neq(nil,sk2)
| ! [C] :
( hd(sk2) != C
| ! [B] :
( cons(C,nil) != B
| ~ ssItem(C)
| ! [A] :
( app(B,sk1) != A
| ~ ssList(B)
| sk2 != A
| ~ ssList(A) ) ) ) ),
inference(miniscoping,[status(thm)],[f197]) ).
fof(f443,plain,
! [X0,X1,X2] :
( ~ neq(sk4,nil)
| ~ neq(nil,sk2)
| hd(sk2) != X2
| cons(X2,nil) != X1
| ~ ssItem(X2)
| app(X1,sk1) != X0
| ~ ssList(X1)
| sk2 != X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f442]) ).
fof(f444,plain,
( ~ neq(sk4,nil)
| ssItem(sk5) ),
inference(cnf_transformation,[status(thm)],[f198]) ).
fof(f445,plain,
( ~ neq(sk4,nil)
| app(cons(sk5,nil),sk3) = sk4 ),
inference(cnf_transformation,[status(thm)],[f199]) ).
fof(f453,definition,
( sQ2_spl
<=> neq(sk2,nil) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f454,plain,
( ~ sQ2_spl
| neq(sk2,nil) ),
inference(component_clause,[status(thm)],[f453]) ).
fof(f456,plain,
sQ2_spl,
inference(split_clause,[status(thm)],[f436,f453]) ).
fof(f457,definition,
( sQ3_spl
<=> neq(sk4,nil) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f459,plain,
( sQ3_spl
| ~ neq(sk4,nil) ),
inference(component_clause,[status(thm)],[f457]) ).
fof(f461,definition,
! [X0,X1,X2] :
( sQ4_spl
<=> ( hd(sk2) != X2
| cons(X2,nil) != X1
| ~ ssItem(X2)
| app(X1,sk1) != X0
| ~ ssList(X1)
| sk2 != X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f462,plain,
! [X0,X1,X2] :
( ~ sQ4_spl
| hd(sk2) != X2
| cons(X2,nil) != X1
| ~ ssItem(X2)
| app(X1,sk1) != X0
| ~ ssList(X1)
| sk2 != X0
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f461]) ).
fof(f464,definition,
( sQ5_spl
<=> neq(nil,sk2) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f466,plain,
( sQ5_spl
| ~ neq(nil,sk2) ),
inference(component_clause,[status(thm)],[f464]) ).
fof(f468,definition,
( sQ6_spl
<=> ssItem(sk5) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f472,definition,
( sQ7_spl
<=> app(cons(sk5,nil),sk3) = sk4 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f473,plain,
( ~ sQ7_spl
| app(cons(sk5,nil),sk3) = sk4 ),
inference(component_clause,[status(thm)],[f472]) ).
fof(f476,plain,
( ~ sQ3_spl
| ~ sQ5_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f443,f461,f464,f457]) ).
fof(f477,plain,
( ~ sQ3_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f444,f468,f457]) ).
fof(f478,plain,
( ~ sQ3_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f445,f472,f457]) ).
fof(f486,plain,
! [X1] :
( ~ ssList(X1)
| ~ ssList(X1)
| ~ neq(X1,X1) ),
inference(destructive_equality_resolution,[status(thm)],[f321]) ).
fof(f487,plain,
! [X0] :
( ~ ssList(X0)
| ~ neq(X0,X0) ),
inference(duplicate_literals_removal,[status(thm)],[f486]) ).
fof(f510,plain,
( ~ sQ2_spl
| neq(sk4,nil) ),
inference(forward_demodulation,[status(thm)],[f434,f454]) ).
fof(f511,plain,
( sQ3_spl
| ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f459,f510]) ).
fof(f512,plain,
( sQ3_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f511]) ).
fof(f513,plain,
! [X0,X1,X2] :
( ~ sQ4_spl
| hd(sk2) != X2
| cons(X2,nil) != X1
| ~ ssItem(X2)
| app(X1,sk1) != X0
| ~ ssList(X1)
| sk4 != X0
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f434,f462]) ).
fof(f514,plain,
! [X0,X1,X2] :
( ~ sQ4_spl
| hd(sk2) != X2
| cons(X2,nil) != X1
| ~ ssItem(X2)
| app(X1,sk3) != X0
| ~ ssList(X1)
| sk4 != X0
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f435,f513]) ).
fof(f515,plain,
! [X0,X1,X2] :
( ~ sQ4_spl
| hd(sk4) != X2
| cons(X2,nil) != X1
| ~ ssItem(X2)
| app(X1,sk3) != X0
| ~ ssList(X1)
| sk4 != X0
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f434,f514]) ).
fof(f516,plain,
( ~ sQ4_spl
| ~ ssItem(hd(sk4))
| app(cons(hd(sk4),nil),sk3) != sk4
| ~ ssList(cons(hd(sk4),nil))
| ~ ssList(sk4) ),
inference(destructive_equality_resolution,[status(thm)],[f515]) ).
fof(f517,plain,
( ~ sQ4_spl
| ~ ssItem(hd(sk4))
| app(cons(hd(sk4),nil),sk3) != sk4
| ~ ssList(cons(hd(sk4),nil)) ),
inference(forward_subsumption_resolution,[status(thm)],[f516,f433]) ).
fof(f519,definition,
( sQ8_spl
<=> ssList(sk3) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f521,plain,
( sQ8_spl
| ~ ssList(sk3) ),
inference(component_clause,[status(thm)],[f519]) ).
fof(f525,definition,
( sQ10_spl
<=> ssList(sk4) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f527,plain,
( sQ10_spl
| ~ ssList(sk4) ),
inference(component_clause,[status(thm)],[f525]) ).
fof(f529,plain,
( sQ5_spl
| ~ neq(nil,sk4) ),
inference(forward_demodulation,[status(thm)],[f434,f466]) ).
fof(f530,plain,
( sQ5_spl
| nil = sk4
| ~ ssList(nil)
| ~ ssList(sk4) ),
inference(resolution,[status(thm)],[f302,f529]) ).
fof(f533,definition,
( sQ11_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f535,plain,
( sQ11_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f533]) ).
fof(f536,definition,
( sQ12_spl
<=> nil = sk4 ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f537,plain,
( ~ sQ12_spl
| nil = sk4 ),
inference(component_clause,[status(thm)],[f536]) ).
fof(f539,plain,
( sQ5_spl
| sQ12_spl
| ~ sQ11_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f530,f525,f533,f536,f464]) ).
fof(f540,plain,
( sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f535,f207]) ).
fof(f541,plain,
sQ11_spl,
inference(contradiction_clause,[status(thm)],[f540]) ).
fof(f558,definition,
( sQ13_spl
<=> ssList(cons(hd(sk4),nil)) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f560,plain,
( sQ13_spl
| ~ ssList(cons(hd(sk4),nil)) ),
inference(component_clause,[status(thm)],[f558]) ).
fof(f564,definition,
( sQ15_spl
<=> ssItem(hd(sk4)) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f566,plain,
( sQ15_spl
| ~ ssItem(hd(sk4)) ),
inference(component_clause,[status(thm)],[f564]) ).
fof(f568,plain,
( sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f521,f432]) ).
fof(f569,plain,
sQ8_spl,
inference(contradiction_clause,[status(thm)],[f568]) ).
fof(f570,plain,
( sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f527,f433]) ).
fof(f571,plain,
sQ10_spl,
inference(contradiction_clause,[status(thm)],[f570]) ).
fof(f572,definition,
( sQ16_spl
<=> app(cons(hd(sk4),nil),sk3) = sk4 ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f574,plain,
( sQ16_spl
| app(cons(hd(sk4),nil),sk3) != sk4 ),
inference(component_clause,[status(thm)],[f572]) ).
fof(f575,plain,
( ~ sQ4_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f517,f558,f572,f564,f461]) ).
fof(f590,plain,
( ~ sQ2_spl
| ~ sQ12_spl
| neq(sk4,sk4) ),
inference(forward_demodulation,[status(thm)],[f537,f510]) ).
fof(f592,plain,
( ~ sQ2_spl
| ~ sQ12_spl
| ~ ssList(sk4) ),
inference(resolution,[status(thm)],[f590,f487]) ).
fof(f593,plain,
( ~ sQ2_spl
| ~ sQ12_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f592,f525,f536,f453]) ).
fof(f598,plain,
( sQ15_spl
| nil = sk4
| ~ ssList(sk4) ),
inference(resolution,[status(thm)],[f276,f566]) ).
fof(f599,plain,
( sQ15_spl
| sQ12_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f598,f525,f536,f564]) ).
fof(f600,plain,
( sQ13_spl
| ~ ssList(nil)
| ~ ssItem(hd(sk4)) ),
inference(resolution,[status(thm)],[f560,f286]) ).
fof(f601,plain,
( sQ13_spl
| ~ sQ11_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f600,f564,f533,f558]) ).
fof(f614,plain,
( ~ sQ7_spl
| sk4 = cons(sk5,sk3)
| ~ ssList(sk3)
| ~ ssItem(sk5) ),
inference(paramodulation,[status(thm)],[f473,f330]) ).
fof(f615,definition,
( sQ19_spl
<=> sk4 = cons(sk5,sk3) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f616,plain,
( ~ sQ19_spl
| sk4 = cons(sk5,sk3) ),
inference(component_clause,[status(thm)],[f615]) ).
fof(f618,plain,
( ~ sQ7_spl
| sQ19_spl
| ~ sQ8_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f614,f468,f519,f615,f472]) ).
fof(f619,plain,
( ~ sQ19_spl
| hd(sk4) = sk5
| ~ ssList(sk3)
| ~ ssItem(sk5) ),
inference(paramodulation,[status(thm)],[f616,f297]) ).
fof(f622,definition,
( sQ20_spl
<=> hd(sk4) = sk5 ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f623,plain,
( ~ sQ20_spl
| hd(sk4) = sk5 ),
inference(component_clause,[status(thm)],[f622]) ).
fof(f625,plain,
( ~ sQ19_spl
| sQ20_spl
| ~ sQ8_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f619,f468,f519,f622,f615]) ).
fof(f635,plain,
( sQ16_spl
| ~ sQ20_spl
| app(cons(sk5,nil),sk3) != sk4 ),
inference(forward_demodulation,[status(thm)],[f623,f574]) ).
fof(f636,plain,
( sQ16_spl
| ~ sQ20_spl
| ~ sQ7_spl
| sk4 != sk4 ),
inference(forward_demodulation,[status(thm)],[f473,f635]) ).
fof(f637,plain,
( sQ16_spl
| ~ sQ20_spl
| ~ sQ7_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f636]) ).
fof(f638,plain,
( sQ16_spl
| ~ sQ20_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f637]) ).
fof(f639,plain,
$false,
inference(sat_refutation,[status(thm)],[f456,f476,f477,f478,f512,f539,f541,f569,f571,f575,f593,f599,f601,f618,f625,f638]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC416-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/10.43 % Computer : n010.cluster.edu
% 0.14/10.43 % Model : x86_64 x86_64
% 0.14/10.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/10.43 % Memory : 8046.5625MB
% 0.14/10.43 % OS : Linux 6.8.0-71-generic
% 0.14/10.43 % CPULimit : 300
% 0.14/10.43 % WCLimit : 300
% 0.14/10.43 % DateTime : Mon Sep 21 08:23:20 UTC 2026
% 0.14/10.44 % CPUTime :
% 0.14/10.46 % Drodi V4.1.1
% 0.14/10.49 % Refutation found
% 0.14/10.49 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/10.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.19/10.55 % Elapsed time: 0.104503 seconds
% 0.19/10.55 % CPU time: 0.160429 seconds
% 0.19/10.55 % Total memory used: 30.911 MB
% 0.19/10.55 % Net memory used: 30.876 MB
%------------------------------------------------------------------------------