%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC153-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n005.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 02:40:11 PM UTC 2026
% Result : Unsatisfiable 0.15s 0.47s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 30
% Syntax : Number of formulae : 95 ( 23 unt; 15 def)
% Number of atoms : 327 ( 21 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 445 ( 213 ~; 217 |; 0 &)
% ( 15 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 21 ( 19 usr; 16 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 79 ( 79 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f130,axiom,
! [U,V] :
( V = U
| ~ ssItem(V)
| ~ ssItem(U)
| ~ leq(V,U)
| ~ leq(U,V) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f191,negated_conjecture,
sk3 = sk1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f192,negated_conjecture,
! [A,B,C,D,E] :
( leq(A,B)
| ~ leq(B,A)
| app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3
| ~ ssList(E)
| ~ ssList(D)
| ~ ssList(C)
| ~ ssItem(B)
| ~ ssItem(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f193,negated_conjecture,
! [A,B,C,D,E,F] :
( leq(A,F)
| ~ memberP(D,F)
| ~ ssItem(F)
| ~ leq(B,A)
| app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3
| ~ ssList(E)
| ~ ssList(D)
| ~ ssList(C)
| ~ ssItem(B)
| ~ ssItem(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f194,negated_conjecture,
! [A,B,C,D,E,F] :
( leq(F,B)
| ~ memberP(D,F)
| ~ ssItem(F)
| ~ leq(B,A)
| app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3
| ~ ssList(E)
| ~ ssList(D)
| ~ ssList(C)
| ~ ssItem(B)
| ~ ssItem(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f195,negated_conjecture,
ssItem(sk5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f196,negated_conjecture,
ssItem(sk6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f197,negated_conjecture,
ssList(sk7),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f198,negated_conjecture,
ssList(sk8),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f199,negated_conjecture,
ssList(sk9),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f200,negated_conjecture,
app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) = sk1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f201,negated_conjecture,
leq(sk6,sk5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f202,negated_conjecture,
( ~ leq(sk5,sk6)
| ssItem(sk10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f203,negated_conjecture,
( ~ leq(sk5,sk6)
| memberP(sk8,sk10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f204,negated_conjecture,
( ~ leq(sk5,sk6)
| ~ leq(sk5,sk10)
| ~ leq(sk10,sk6) ),
file('/export/starexec/sandbox/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(f440,plain,
sk3 = sk1,
inference(cnf_transformation,[status(thm)],[f191]) ).
fof(f441,plain,
! [A,B] :
( leq(A,B)
| ~ leq(B,A)
| ! [C,D,E] :
( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3
| ~ ssList(E)
| ~ ssList(D)
| ~ ssList(C)
| ~ ssItem(B)
| ~ ssItem(A) ) ),
inference(miniscoping,[status(thm)],[f192]) ).
fof(f442,plain,
! [X0,X1,X2,X3,X4] :
( leq(X0,X1)
| ~ leq(X1,X0)
| app(app(app(app(X2,cons(X0,nil)),X3),cons(X1,nil)),X4) != sk3
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f441]) ).
fof(f443,plain,
! [A,F] :
( leq(A,F)
| ! [D] :
( ~ memberP(D,F)
| ~ ssItem(F)
| ! [B] :
( ~ leq(B,A)
| ! [C,E] :
( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3
| ~ ssList(E)
| ~ ssList(D)
| ~ ssList(C)
| ~ ssItem(B)
| ~ ssItem(A) ) ) ) ),
inference(miniscoping,[status(thm)],[f193]) ).
fof(f444,plain,
! [X0,X1,X2,X3,X4,X5] :
( leq(X0,X5)
| ~ memberP(X3,X5)
| ~ ssItem(X5)
| ~ leq(X1,X0)
| app(app(app(app(X2,cons(X0,nil)),X3),cons(X1,nil)),X4) != sk3
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f443]) ).
fof(f445,plain,
! [B,F] :
( leq(F,B)
| ! [D] :
( ~ memberP(D,F)
| ~ ssItem(F)
| ! [A] :
( ~ leq(B,A)
| ! [C,E] :
( app(app(app(app(C,cons(A,nil)),D),cons(B,nil)),E) != sk3
| ~ ssList(E)
| ~ ssList(D)
| ~ ssList(C)
| ~ ssItem(B)
| ~ ssItem(A) ) ) ) ),
inference(miniscoping,[status(thm)],[f194]) ).
fof(f446,plain,
! [X0,X1,X2,X3,X4,X5] :
( leq(X5,X1)
| ~ memberP(X3,X5)
| ~ ssItem(X5)
| ~ leq(X1,X0)
| app(app(app(app(X2,cons(X0,nil)),X3),cons(X1,nil)),X4) != sk3
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f445]) ).
fof(f447,plain,
ssItem(sk5),
inference(cnf_transformation,[status(thm)],[f195]) ).
fof(f448,plain,
ssItem(sk6),
inference(cnf_transformation,[status(thm)],[f196]) ).
fof(f449,plain,
ssList(sk7),
inference(cnf_transformation,[status(thm)],[f197]) ).
fof(f450,plain,
ssList(sk8),
inference(cnf_transformation,[status(thm)],[f198]) ).
fof(f451,plain,
ssList(sk9),
inference(cnf_transformation,[status(thm)],[f199]) ).
fof(f452,plain,
app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) = sk1,
inference(cnf_transformation,[status(thm)],[f200]) ).
fof(f453,plain,
leq(sk6,sk5),
inference(cnf_transformation,[status(thm)],[f201]) ).
fof(f454,plain,
( ~ leq(sk5,sk6)
| ssItem(sk10) ),
inference(cnf_transformation,[status(thm)],[f202]) ).
fof(f455,plain,
( ~ leq(sk5,sk6)
| memberP(sk8,sk10) ),
inference(cnf_transformation,[status(thm)],[f203]) ).
fof(f456,plain,
( ~ leq(sk5,sk6)
| ~ leq(sk5,sk10)
| ~ leq(sk10,sk6) ),
inference(cnf_transformation,[status(thm)],[f204]) ).
fof(f464,definition,
( sQ2_spl
<=> ssItem(sk10) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f467,definition,
( sQ3_spl
<=> leq(sk5,sk6) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f470,plain,
( ~ sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f454,f464,f467]) ).
fof(f471,definition,
( sQ4_spl
<=> memberP(sk8,sk10) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f472,plain,
( ~ sQ4_spl
| memberP(sk8,sk10) ),
inference(component_clause,[status(thm)],[f471]) ).
fof(f474,plain,
( ~ sQ3_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f455,f471,f467]) ).
fof(f475,definition,
( sQ5_spl
<=> leq(sk10,sk6) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f477,plain,
( sQ5_spl
| ~ leq(sk10,sk6) ),
inference(component_clause,[status(thm)],[f475]) ).
fof(f478,definition,
( sQ6_spl
<=> leq(sk5,sk10) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f481,plain,
( ~ sQ3_spl
| ~ sQ6_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f456,f475,f478,f467]) ).
fof(f494,plain,
! [X0,X1,X2,X3,X4] :
( leq(X0,X1)
| ~ leq(X1,X0)
| app(app(app(app(X2,cons(X0,nil)),X3),cons(X1,nil)),X4) != sk1
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(forward_demodulation,[status(thm)],[f440,f442]) ).
fof(f495,plain,
! [X0,X1,X2,X3,X4,X5] :
( leq(X0,X5)
| ~ memberP(X3,X5)
| ~ ssItem(X5)
| ~ leq(X1,X0)
| app(app(app(app(X2,cons(X0,nil)),X3),cons(X1,nil)),X4) != sk1
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(forward_demodulation,[status(thm)],[f440,f444]) ).
fof(f508,plain,
! [X0] :
( leq(sk5,X0)
| ~ memberP(sk8,X0)
| ~ ssItem(X0)
| ~ leq(sk6,sk5)
| ~ ssList(sk9)
| ~ ssList(sk8)
| ~ ssList(sk7)
| ~ ssItem(sk6)
| ~ ssItem(sk5) ),
inference(resolution,[status(thm)],[f452,f495]) ).
fof(f509,plain,
( leq(sk5,sk6)
| ~ leq(sk6,sk5)
| ~ ssList(sk9)
| ~ ssList(sk8)
| ~ ssList(sk7)
| ~ ssItem(sk6)
| ~ ssItem(sk5) ),
inference(resolution,[status(thm)],[f452,f494]) ).
fof(f516,definition,
( sQ9_spl
<=> ssItem(sk5) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f518,plain,
( sQ9_spl
| ~ ssItem(sk5) ),
inference(component_clause,[status(thm)],[f516]) ).
fof(f519,definition,
( sQ10_spl
<=> ssItem(sk6) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f521,plain,
( sQ10_spl
| ~ ssItem(sk6) ),
inference(component_clause,[status(thm)],[f519]) ).
fof(f522,definition,
( sQ11_spl
<=> ssList(sk7) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f524,plain,
( sQ11_spl
| ~ ssList(sk7) ),
inference(component_clause,[status(thm)],[f522]) ).
fof(f525,definition,
( sQ12_spl
<=> ssList(sk8) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f527,plain,
( sQ12_spl
| ~ ssList(sk8) ),
inference(component_clause,[status(thm)],[f525]) ).
fof(f528,definition,
( sQ13_spl
<=> ssList(sk9) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f530,plain,
( sQ13_spl
| ~ ssList(sk9) ),
inference(component_clause,[status(thm)],[f528]) ).
fof(f531,definition,
( sQ14_spl
<=> leq(sk6,sk5) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f533,plain,
( sQ14_spl
| ~ leq(sk6,sk5) ),
inference(component_clause,[status(thm)],[f531]) ).
fof(f534,definition,
! [X0] :
( sQ15_spl
<=> ( leq(sk5,X0)
| ~ memberP(sk8,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f535,plain,
! [X0] :
( ~ sQ15_spl
| leq(sk5,X0)
| ~ memberP(sk8,X0)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f534]) ).
fof(f537,plain,
( sQ15_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ10_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f508,f516,f519,f522,f525,f528,f531,f534]) ).
fof(f538,plain,
( sQ3_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ10_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f509,f516,f519,f522,f525,f528,f531,f467]) ).
fof(f572,plain,
( sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f530,f451]) ).
fof(f573,plain,
sQ13_spl,
inference(contradiction_clause,[status(thm)],[f572]) ).
fof(f574,plain,
( sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f521,f448]) ).
fof(f575,plain,
sQ10_spl,
inference(contradiction_clause,[status(thm)],[f574]) ).
fof(f576,plain,
( sQ14_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f533,f453]) ).
fof(f577,plain,
sQ14_spl,
inference(contradiction_clause,[status(thm)],[f576]) ).
fof(f578,plain,
( sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f527,f450]) ).
fof(f579,plain,
sQ12_spl,
inference(contradiction_clause,[status(thm)],[f578]) ).
fof(f580,plain,
( sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f518,f447]) ).
fof(f581,plain,
sQ9_spl,
inference(contradiction_clause,[status(thm)],[f580]) ).
fof(f582,plain,
( sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f524,f449]) ).
fof(f583,plain,
sQ11_spl,
inference(contradiction_clause,[status(thm)],[f582]) ).
fof(f584,plain,
! [X0,X1,X2,X3,X4,X5] :
( leq(X5,X1)
| ~ memberP(X3,X5)
| ~ ssItem(X5)
| ~ leq(X1,X0)
| app(app(app(app(X2,cons(X0,nil)),X3),cons(X1,nil)),X4) != sk1
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(forward_demodulation,[status(thm)],[f440,f446]) ).
fof(f585,plain,
! [X0] :
( leq(X0,sk6)
| ~ memberP(sk8,X0)
| ~ ssItem(X0)
| ~ leq(sk6,sk5)
| ~ ssList(sk9)
| ~ ssList(sk8)
| ~ ssList(sk7)
| ~ ssItem(sk6)
| ~ ssItem(sk5) ),
inference(resolution,[status(thm)],[f584,f452]) ).
fof(f588,definition,
! [X0] :
( sQ25_spl
<=> ( leq(X0,sk6)
| ~ memberP(sk8,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f589,plain,
! [X0] :
( ~ sQ25_spl
| leq(X0,sk6)
| ~ memberP(sk8,X0)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f588]) ).
fof(f591,plain,
( sQ25_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ10_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f585,f516,f519,f522,f525,f528,f531,f588]) ).
fof(f606,plain,
( ~ sQ4_spl
| ~ sQ15_spl
| leq(sk5,sk10)
| ~ ssItem(sk10) ),
inference(resolution,[status(thm)],[f535,f472]) ).
fof(f607,plain,
( ~ sQ4_spl
| ~ sQ15_spl
| sQ6_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f606,f464,f478,f534,f471]) ).
fof(f609,plain,
( sk6 = sk5
| ~ ssItem(sk6)
| ~ ssItem(sk5)
| ~ leq(sk5,sk6) ),
inference(resolution,[status(thm)],[f347,f453]) ).
fof(f611,definition,
( sQ28_spl
<=> sk5 = sk6 ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f612,plain,
( ~ sQ28_spl
| sk5 = sk6 ),
inference(component_clause,[status(thm)],[f611]) ).
fof(f615,plain,
( sQ28_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f609,f467,f516,f519,f611]) ).
fof(f617,plain,
( sQ5_spl
| ~ sQ28_spl
| ~ leq(sk10,sk5) ),
inference(backward_demodulation,[status(thm)],[f612,f477]) ).
fof(f622,definition,
( sQ29_spl
<=> leq(sk10,sk5) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f623,plain,
( ~ sQ29_spl
| leq(sk10,sk5) ),
inference(component_clause,[status(thm)],[f622]) ).
fof(f694,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ28_spl
| leq(X0,sk5)
| ~ memberP(sk8,X0)
| ~ ssItem(X0) ),
inference(forward_demodulation,[status(thm)],[f612,f589]) ).
fof(f695,plain,
( ~ sQ4_spl
| ~ sQ25_spl
| ~ sQ28_spl
| leq(sk10,sk5)
| ~ ssItem(sk10) ),
inference(resolution,[status(thm)],[f694,f472]) ).
fof(f696,plain,
( ~ sQ4_spl
| ~ sQ25_spl
| ~ sQ28_spl
| sQ29_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f695,f464,f622,f611,f588,f471]) ).
fof(f697,plain,
( ~ sQ29_spl
| sQ5_spl
| ~ sQ28_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f623,f617]) ).
fof(f698,plain,
( ~ sQ29_spl
| sQ5_spl
| ~ sQ28_spl ),
inference(contradiction_clause,[status(thm)],[f697]) ).
fof(f699,plain,
$false,
inference(sat_refutation,[status(thm)],[f470,f474,f481,f537,f538,f573,f575,f577,f579,f581,f583,f591,f607,f615,f696,f698]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWC153-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.41 % Computer : n005.cluster.edu
% 0.15/0.41 % Model : x86_64 x86_64
% 0.15/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.41 % Memory : 8046.5625MB
% 0.15/0.41 % OS : Linux 6.8.0-71-generic
% 0.15/0.41 % CPULimit : 300
% 0.15/0.41 % WCLimit : 300
% 0.15/0.41 % DateTime : Mon Sep 21 08:00:18 UTC 2026
% 0.15/0.42 % CPUTime :
% 0.15/0.44 % Drodi V4.1.1
% 0.15/0.47 % Refutation found
% 0.15/0.47 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.15/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.51 % Elapsed time: 0.077533 seconds
% 0.15/0.51 % CPU time: 0.255228 seconds
% 0.15/0.51 % Total memory used: 106.713 MB
% 0.15/0.51 % Net memory used: 106.591 MB
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