%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC379-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n016.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 02:41:00 PM UTC 2026
% Result : Unsatisfiable 0.14s 0.40s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 33
% Syntax : Number of formulae : 103 ( 8 unt; 16 def)
% Number of atoms : 318 ( 23 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 395 ( 180 ~; 199 |; 0 &)
% ( 16 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 21 ( 19 usr; 17 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-1 aty)
% Number of variables : 34 ( 34 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f130,axiom,
! [U,V] :
( V = U
| ~ ssItem(V)
| ~ ssItem(U)
| ~ leq(V,U)
| ~ leq(U,V) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f156,axiom,
! [U,V,W] :
( leq(U,W)
| ~ ssItem(U)
| ~ ssItem(V)
| ~ ssItem(W)
| ~ leq(V,W)
| ~ leq(U,V) ),
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,
! [A] :
( ~ memberP(sk4,A)
| ssItem(sk5(A))
| memberP(sk3,A)
| ~ ssItem(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f193,negated_conjecture,
! [A] :
( ~ memberP(sk4,A)
| memberP(sk4,sk5(A))
| memberP(sk3,A)
| ~ ssItem(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f194,negated_conjecture,
! [A] :
( ~ memberP(sk4,A)
| leq(sk5(A),A)
| memberP(sk3,A)
| ~ ssItem(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f195,negated_conjecture,
! [A] :
( ~ memberP(sk4,A)
| A != sk5(A)
| memberP(sk3,A)
| ~ ssItem(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f196,negated_conjecture,
! [A] :
( memberP(sk4,A)
| ~ memberP(sk3,A)
| ~ ssItem(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f197,negated_conjecture,
! [A,B] :
( ~ leq(B,A)
| ~ memberP(sk4,B)
| A = B
| ~ ssItem(B)
| ~ memberP(sk3,A)
| ~ ssItem(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f198,negated_conjecture,
ssItem(sk6),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f199,negated_conjecture,
( memberP(sk2,sk6)
| memberP(sk1,sk6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f200,negated_conjecture,
! [A] :
( ~ leq(A,sk6)
| ~ memberP(sk2,A)
| sk6 = A
| ~ ssItem(A)
| memberP(sk1,sk6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f201,negated_conjecture,
( ~ memberP(sk1,sk6)
| ~ memberP(sk2,sk6)
| ssItem(sk7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f202,negated_conjecture,
( ~ memberP(sk1,sk6)
| ~ memberP(sk2,sk6)
| memberP(sk2,sk7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f203,negated_conjecture,
( ~ memberP(sk1,sk6)
| ~ memberP(sk2,sk6)
| leq(sk7,sk6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f204,negated_conjecture,
( ~ memberP(sk1,sk6)
| ~ memberP(sk2,sk6)
| sk6 != sk7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f347,plain,
! [X0,X1] :
( X1 = X0
| ~ ssItem(X1)
| ~ ssItem(X0)
| ~ leq(X1,X0)
| ~ leq(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f130]) ).
fof(f386,plain,
! [U,W] :
( leq(U,W)
| ~ ssItem(U)
| ! [V] :
( ~ ssItem(V)
| ~ ssItem(W)
| ~ leq(V,W)
| ~ leq(U,V) ) ),
inference(miniscoping,[status(thm)],[f156]) ).
fof(f387,plain,
! [X0,X1,X2] :
( leq(X0,X2)
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssItem(X2)
| ~ leq(X1,X2)
| ~ leq(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f386]) ).
fof(f439,plain,
sk2 = sk4,
inference(cnf_transformation,[status(thm)],[f190]) ).
fof(f440,plain,
sk1 = sk3,
inference(cnf_transformation,[status(thm)],[f191]) ).
fof(f441,plain,
! [X0] :
( ~ memberP(sk4,X0)
| ssItem(sk5(X0))
| memberP(sk3,X0)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f192]) ).
fof(f442,plain,
! [X0] :
( ~ memberP(sk4,X0)
| memberP(sk4,sk5(X0))
| memberP(sk3,X0)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f193]) ).
fof(f443,plain,
! [X0] :
( ~ memberP(sk4,X0)
| leq(sk5(X0),X0)
| memberP(sk3,X0)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f194]) ).
fof(f444,plain,
! [X0] :
( ~ memberP(sk4,X0)
| X0 != sk5(X0)
| memberP(sk3,X0)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f195]) ).
fof(f445,plain,
! [X0] :
( memberP(sk4,X0)
| ~ memberP(sk3,X0)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f196]) ).
fof(f446,plain,
! [X0,X1] :
( ~ leq(X1,X0)
| ~ memberP(sk4,X1)
| X0 = X1
| ~ ssItem(X1)
| ~ memberP(sk3,X0)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f197]) ).
fof(f447,plain,
ssItem(sk6),
inference(cnf_transformation,[status(thm)],[f198]) ).
fof(f448,plain,
( memberP(sk2,sk6)
| memberP(sk1,sk6) ),
inference(cnf_transformation,[status(thm)],[f199]) ).
fof(f449,plain,
! [X0] :
( ~ leq(X0,sk6)
| ~ memberP(sk2,X0)
| sk6 = X0
| ~ ssItem(X0)
| memberP(sk1,sk6) ),
inference(cnf_transformation,[status(thm)],[f200]) ).
fof(f450,plain,
( ~ memberP(sk1,sk6)
| ~ memberP(sk2,sk6)
| ssItem(sk7) ),
inference(cnf_transformation,[status(thm)],[f201]) ).
fof(f451,plain,
( ~ memberP(sk1,sk6)
| ~ memberP(sk2,sk6)
| memberP(sk2,sk7) ),
inference(cnf_transformation,[status(thm)],[f202]) ).
fof(f452,plain,
( ~ memberP(sk1,sk6)
| ~ memberP(sk2,sk6)
| leq(sk7,sk6) ),
inference(cnf_transformation,[status(thm)],[f203]) ).
fof(f453,plain,
( ~ memberP(sk1,sk6)
| ~ memberP(sk2,sk6)
| sk6 != sk7 ),
inference(cnf_transformation,[status(thm)],[f204]) ).
fof(f461,definition,
( sQ2_spl
<=> memberP(sk1,sk6) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f462,plain,
( ~ sQ2_spl
| memberP(sk1,sk6) ),
inference(component_clause,[status(thm)],[f461]) ).
fof(f463,plain,
( sQ2_spl
| ~ memberP(sk1,sk6) ),
inference(component_clause,[status(thm)],[f461]) ).
fof(f464,definition,
( sQ3_spl
<=> memberP(sk2,sk6) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f465,plain,
( ~ sQ3_spl
| memberP(sk2,sk6) ),
inference(component_clause,[status(thm)],[f464]) ).
fof(f466,plain,
( sQ3_spl
| ~ memberP(sk2,sk6) ),
inference(component_clause,[status(thm)],[f464]) ).
fof(f467,plain,
( sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f448,f461,f464]) ).
fof(f468,definition,
! [X0] :
( sQ4_spl
<=> ( ~ leq(X0,sk6)
| ~ memberP(sk2,X0)
| sk6 = X0
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f469,plain,
! [X0] :
( ~ sQ4_spl
| ~ leq(X0,sk6)
| ~ memberP(sk2,X0)
| sk6 = X0
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f468]) ).
fof(f471,plain,
( sQ4_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f449,f461,f468]) ).
fof(f472,definition,
( sQ5_spl
<=> ssItem(sk7) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f475,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f450,f472,f464,f461]) ).
fof(f476,definition,
( sQ6_spl
<=> memberP(sk2,sk7) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f477,plain,
( ~ sQ6_spl
| memberP(sk2,sk7) ),
inference(component_clause,[status(thm)],[f476]) ).
fof(f479,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f451,f476,f464,f461]) ).
fof(f480,definition,
( sQ7_spl
<=> leq(sk7,sk6) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f481,plain,
( ~ sQ7_spl
| leq(sk7,sk6) ),
inference(component_clause,[status(thm)],[f480]) ).
fof(f483,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f452,f480,f464,f461]) ).
fof(f484,definition,
( sQ8_spl
<=> sk6 = sk7 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f487,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f453,f484,f464,f461]) ).
fof(f519,plain,
( sQ3_spl
| ~ memberP(sk4,sk6) ),
inference(forward_demodulation,[status(thm)],[f439,f466]) ).
fof(f520,plain,
( ~ sQ2_spl
| memberP(sk3,sk6) ),
inference(forward_demodulation,[status(thm)],[f440,f462]) ).
fof(f521,plain,
( ~ sQ2_spl
| memberP(sk4,sk6)
| ~ ssItem(sk6) ),
inference(resolution,[status(thm)],[f445,f520]) ).
fof(f522,definition,
( sQ9_spl
<=> ssItem(sk6) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f524,plain,
( sQ9_spl
| ~ ssItem(sk6) ),
inference(component_clause,[status(thm)],[f522]) ).
fof(f525,definition,
( sQ10_spl
<=> memberP(sk4,sk6) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f526,plain,
( ~ sQ10_spl
| memberP(sk4,sk6) ),
inference(component_clause,[status(thm)],[f525]) ).
fof(f528,plain,
( ~ sQ2_spl
| sQ10_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f521,f522,f525,f461]) ).
fof(f529,plain,
( sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f524,f447]) ).
fof(f530,plain,
sQ9_spl,
inference(contradiction_clause,[status(thm)],[f529]) ).
fof(f531,plain,
! [X0] :
( ~ sQ4_spl
| ~ leq(X0,sk6)
| ~ memberP(sk4,X0)
| sk6 = X0
| ~ ssItem(X0) ),
inference(forward_demodulation,[status(thm)],[f439,f469]) ).
fof(f532,plain,
( sQ2_spl
| ~ memberP(sk3,sk6) ),
inference(forward_demodulation,[status(thm)],[f440,f463]) ).
fof(f533,plain,
( ~ sQ3_spl
| memberP(sk4,sk6) ),
inference(forward_demodulation,[status(thm)],[f439,f465]) ).
fof(f540,plain,
( ~ sQ3_spl
| ssItem(sk5(sk6))
| memberP(sk3,sk6)
| ~ ssItem(sk6) ),
inference(resolution,[status(thm)],[f441,f533]) ).
fof(f541,definition,
( sQ12_spl
<=> memberP(sk3,sk6) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f542,plain,
( ~ sQ12_spl
| memberP(sk3,sk6) ),
inference(component_clause,[status(thm)],[f541]) ).
fof(f544,definition,
( sQ13_spl
<=> ssItem(sk5(sk6)) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f547,plain,
( ~ sQ3_spl
| sQ13_spl
| sQ12_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f540,f522,f541,f544,f464]) ).
fof(f548,plain,
( ~ sQ12_spl
| sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f542,f532]) ).
fof(f549,plain,
( ~ sQ12_spl
| sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f548]) ).
fof(f550,plain,
( ~ sQ4_spl
| ~ memberP(sk4,sk5(sk6))
| sk6 = sk5(sk6)
| ~ ssItem(sk5(sk6))
| ~ memberP(sk4,sk6)
| memberP(sk3,sk6)
| ~ ssItem(sk6) ),
inference(resolution,[status(thm)],[f443,f531]) ).
fof(f552,definition,
( sQ14_spl
<=> sk6 = sk5(sk6) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f553,plain,
( ~ sQ14_spl
| sk6 = sk5(sk6) ),
inference(component_clause,[status(thm)],[f552]) ).
fof(f555,definition,
( sQ15_spl
<=> memberP(sk4,sk5(sk6)) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f557,plain,
( sQ15_spl
| ~ memberP(sk4,sk5(sk6)) ),
inference(component_clause,[status(thm)],[f555]) ).
fof(f558,plain,
( ~ sQ4_spl
| ~ sQ15_spl
| sQ14_spl
| ~ sQ13_spl
| ~ sQ10_spl
| sQ12_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f550,f522,f541,f525,f544,f552,f555,f468]) ).
fof(f563,plain,
( sQ15_spl
| ~ memberP(sk4,sk6)
| memberP(sk3,sk6)
| ~ ssItem(sk6) ),
inference(resolution,[status(thm)],[f557,f442]) ).
fof(f564,plain,
( sQ15_spl
| ~ sQ10_spl
| sQ12_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f563,f522,f541,f525,f555]) ).
fof(f565,plain,
( ~ sQ10_spl
| sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f526,f519]) ).
fof(f566,plain,
( ~ sQ10_spl
| sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f565]) ).
fof(f567,plain,
( ~ sQ14_spl
| ~ memberP(sk4,sk6)
| memberP(sk3,sk6)
| ~ ssItem(sk6) ),
inference(resolution,[status(thm)],[f553,f444]) ).
fof(f571,plain,
( ~ sQ14_spl
| ~ sQ10_spl
| sQ12_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f567,f522,f541,f525,f552]) ).
fof(f578,plain,
( ~ sQ6_spl
| memberP(sk4,sk7) ),
inference(forward_demodulation,[status(thm)],[f439,f477]) ).
fof(f589,plain,
( ~ sQ7_spl
| sk7 = sk6
| ~ ssItem(sk7)
| ~ ssItem(sk6)
| ~ leq(sk6,sk7) ),
inference(resolution,[status(thm)],[f481,f347]) ).
fof(f590,definition,
( sQ19_spl
<=> leq(sk6,sk7) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f593,plain,
( ~ sQ7_spl
| sQ8_spl
| ~ sQ5_spl
| ~ sQ9_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f589,f590,f522,f472,f484,f480]) ).
fof(f594,plain,
! [X0] :
( ~ sQ7_spl
| leq(X0,sk6)
| ~ ssItem(X0)
| ~ ssItem(sk7)
| ~ ssItem(sk6)
| ~ leq(X0,sk7) ),
inference(resolution,[status(thm)],[f387,f481]) ).
fof(f597,definition,
! [X0] :
( sQ20_spl
<=> ( leq(X0,sk6)
| ~ ssItem(X0)
| ~ leq(X0,sk7) ) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f600,plain,
( ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ9_spl
| sQ20_spl ),
inference(split_clause,[status(thm)],[f594,f597,f522,f472,f480]) ).
fof(f606,definition,
( sQ21_spl
<=> memberP(sk4,sk7) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f608,plain,
( sQ21_spl
| ~ memberP(sk4,sk7) ),
inference(component_clause,[status(thm)],[f606]) ).
fof(f610,plain,
( ~ sQ7_spl
| ~ memberP(sk4,sk7)
| sk6 = sk7
| ~ ssItem(sk7)
| ~ memberP(sk3,sk6)
| ~ ssItem(sk6) ),
inference(resolution,[status(thm)],[f446,f481]) ).
fof(f613,plain,
( ~ sQ7_spl
| ~ sQ21_spl
| sQ8_spl
| ~ sQ5_spl
| ~ sQ12_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f610,f522,f541,f472,f484,f606,f480]) ).
fof(f614,plain,
( ~ sQ2_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f520,f541,f461]) ).
fof(f615,plain,
( sQ21_spl
| ~ sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f608,f578]) ).
fof(f616,plain,
( sQ21_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f615]) ).
fof(f617,plain,
( ~ sQ3_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f533,f525,f464]) ).
fof(f619,plain,
$false,
inference(sat_refutation,[status(thm)],[f467,f471,f475,f479,f483,f487,f528,f530,f547,f549,f558,f564,f566,f571,f593,f600,f613,f614,f616,f617]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC379-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n016.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 08:24:54 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 0.14/0.40 % Refutation found
% 0.14/0.40 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.44 % Elapsed time: 0.063242 seconds
% 0.14/0.44 % CPU time: 0.167700 seconds
% 0.14/0.44 % Total memory used: 108.987 MB
% 0.14/0.44 % Net memory used: 108.839 MB
%------------------------------------------------------------------------------