%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC239-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n020.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 02:40:29 PM UTC 2026
% Result : Unsatisfiable 0.29s 1.13s
% Output : CNFRefutation 0.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 17
% Syntax : Number of formulae : 77 ( 21 unt; 0 def)
% Number of atoms : 254 ( 21 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 369 ( 192 ~; 177 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-3 aty)
% Number of variables : 128 ( 128 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f47,axiom,
! [U] : ssItem(skaf44(U)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f48,axiom,
! [U,V] : ssList(skaf48(U,V)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f49,axiom,
! [U,V] : ssList(skaf47(U,V)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f53,axiom,
! [U,V] : ssList(skaf42(U,V)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f57,axiom,
! [U] :
( segmentP(U,U)
| ~ ssList(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f72,axiom,
! [U,V] :
( ssItem(V)
| duplicatefreeP(U)
| ~ ssList(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f85,axiom,
! [U,V] :
( ssList(app(V,U))
| ~ ssList(V)
| ~ 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(f103,axiom,
! [U,V] :
( leq(U,V)
| ~ ssItem(U)
| ~ ssItem(V)
| ~ lt(U,V) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f168,axiom,
! [U,V] :
( app(app(skaf47(U,V),V),skaf48(V,U)) = U
| ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f188,negated_conjecture,
ssList(sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f191,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f192,negated_conjecture,
nil != sk1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f196,negated_conjecture,
! [A,B,C] :
( lt(A,sk5(C,B,A))
| app(app(B,cons(A,nil)),C) != sk1
| ~ ssList(C)
| ~ ssList(B)
| ~ ssItem(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f197,negated_conjecture,
! [A,B,C] :
( ~ leq(A,sk5(C,B,A))
| app(app(B,cons(A,nil)),C) != sk1
| ~ ssList(C)
| ~ ssList(B)
| ~ ssItem(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f203,negated_conjecture,
( nil = sk3
| cons(sk6,nil) = sk3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f252,plain,
! [X0] : ssItem(skaf44(X0)),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f253,plain,
! [X0,X1] : ssList(skaf48(X0,X1)),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f254,plain,
! [X0,X1] : ssList(skaf47(X0,X1)),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f258,plain,
! [X0,X1] : ssList(skaf42(X0,X1)),
inference(cnf_transformation,[status(thm)],[f53]) ).
fof(f262,plain,
! [X0] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f57]) ).
fof(f277,plain,
( ! [V] : ssItem(V)
| ! [U] :
( duplicatefreeP(U)
| ~ ssList(U) ) ),
inference(miniscoping,[status(thm)],[f72]) ).
fof(f278,plain,
! [X0,X1] :
( ssItem(X1)
| duplicatefreeP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f277]) ).
fof(f291,plain,
! [X0,X1] :
( ssList(app(X1,X0))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f85]) ).
fof(f292,plain,
! [X0,X1] :
( ssList(cons(X0,X1))
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f86]) ).
fof(f311,plain,
! [X0,X1] :
( leq(X0,X1)
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ lt(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f103]) ).
fof(f404,plain,
! [X0,X1] :
( app(app(skaf47(X0,X1),X1),skaf48(X1,X0)) = X0
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f168]) ).
fof(f422,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(f423,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)],[f422]) ).
fof(f438,plain,
ssList(sk3),
inference(cnf_transformation,[status(thm)],[f188]) ).
fof(f441,plain,
sk1 = sk3,
inference(cnf_transformation,[status(thm)],[f191]) ).
fof(f442,plain,
nil != sk1,
inference(cnf_transformation,[status(thm)],[f192]) ).
fof(f446,plain,
! [X0,X1,X2] :
( lt(X0,sk5(X2,X1,X0))
| app(app(X1,cons(X0,nil)),X2) != sk1
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f196]) ).
fof(f447,plain,
! [X0,X1,X2] :
( ~ leq(X0,sk5(X2,X1,X0))
| app(app(X1,cons(X0,nil)),X2) != sk1
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f197]) ).
fof(f454,plain,
( nil = sk3
| cons(sk6,nil) = sk3 ),
inference(cnf_transformation,[status(thm)],[f203]) ).
fof(f480,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)],[f423]) ).
fof(f489,plain,
nil != sk3,
inference(forward_demodulation,[status(thm)],[f441,f442]) ).
fof(f510,plain,
cons(sk6,nil) = sk3,
inference(forward_subsumption_resolution,[status(thm)],[f454,f489]) ).
fof(f557,plain,
! [X0,X1,X2] :
( lt(X0,sk5(X2,X1,X0))
| app(app(X1,cons(X0,nil)),X2) != sk3
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(forward_demodulation,[status(thm)],[f441,f446]) ).
fof(f560,plain,
! [X0,X1,X2] :
( ~ leq(X0,sk5(X2,X1,X0))
| app(app(X1,cons(X0,nil)),X2) != sk3
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(forward_demodulation,[status(thm)],[f441,f447]) ).
fof(f614,plain,
! [X0,X1,X2] :
( ~ ssList(X0)
| ~ ssList(X1)
| ssItem(X2)
| duplicatefreeP(app(X0,X1)) ),
inference(resolution,[status(thm)],[f278,f291]) ).
fof(f1263,plain,
! [X0] :
( ~ leq(X0,sk5(skaf48(cons(X0,nil),sk3),skaf47(sk3,cons(X0,nil)),X0))
| ~ ssList(skaf48(cons(X0,nil),sk3))
| ~ ssList(skaf47(sk3,cons(X0,nil)))
| ~ ssItem(X0)
| ~ ssList(sk3)
| ~ ssList(cons(X0,nil))
| ~ segmentP(sk3,cons(X0,nil)) ),
inference(resolution,[status(thm)],[f404,f560]) ).
fof(f1264,plain,
! [X0] :
( lt(X0,sk5(skaf48(cons(X0,nil),sk3),skaf47(sk3,cons(X0,nil)),X0))
| ~ ssList(skaf48(cons(X0,nil),sk3))
| ~ ssList(skaf47(sk3,cons(X0,nil)))
| ~ ssItem(X0)
| ~ ssList(sk3)
| ~ ssList(cons(X0,nil))
| ~ segmentP(sk3,cons(X0,nil)) ),
inference(resolution,[status(thm)],[f404,f557]) ).
fof(f1280,plain,
! [X0] :
( ~ leq(X0,sk5(skaf48(cons(X0,nil),sk3),skaf47(sk3,cons(X0,nil)),X0))
| ~ ssList(skaf48(cons(X0,nil),sk3))
| ~ ssList(skaf47(sk3,cons(X0,nil)))
| ~ ssItem(X0)
| ~ ssList(cons(X0,nil))
| ~ segmentP(sk3,cons(X0,nil)) ),
inference(forward_subsumption_resolution,[status(thm)],[f1263,f438]) ).
fof(f1281,plain,
! [X0] :
( lt(X0,sk5(skaf48(cons(X0,nil),sk3),skaf47(sk3,cons(X0,nil)),X0))
| ~ ssList(skaf48(cons(X0,nil),sk3))
| ~ ssList(skaf47(sk3,cons(X0,nil)))
| ~ ssItem(X0)
| ~ ssList(cons(X0,nil))
| ~ segmentP(sk3,cons(X0,nil)) ),
inference(forward_subsumption_resolution,[status(thm)],[f1264,f438]) ).
fof(f1563,plain,
! [X0] :
( ~ leq(X0,sk5(skaf48(cons(X0,nil),sk3),skaf47(sk3,cons(X0,nil)),X0))
| ~ ssList(skaf48(cons(X0,nil),sk3))
| ~ ssItem(X0)
| ~ ssList(cons(X0,nil))
| ~ segmentP(sk3,cons(X0,nil)) ),
inference(forward_subsumption_resolution,[status(thm)],[f1280,f254]) ).
fof(f1698,plain,
! [X0] :
( lt(X0,sk5(skaf48(cons(X0,nil),sk3),skaf47(sk3,cons(X0,nil)),X0))
| ~ ssList(skaf48(cons(X0,nil),sk3))
| ~ ssItem(X0)
| ~ ssList(cons(X0,nil))
| ~ segmentP(sk3,cons(X0,nil)) ),
inference(forward_subsumption_resolution,[status(thm)],[f1281,f254]) ).
fof(f1823,plain,
! [X0,X1,X2,X3,X4] :
( ~ ssList(app(X2,cons(X3,X1)))
| ~ ssList(cons(X3,X0))
| ssItem(X4)
| ~ ssList(app(app(X2,cons(X3,X1)),cons(X3,X0)))
| ~ ssItem(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f480,f614]) ).
fof(f1826,plain,
! [X0,X1,X2,X3,X4] :
( ~ ssList(app(X2,cons(X3,X1)))
| ~ ssList(cons(X3,X0))
| ssItem(X4)
| ~ ssItem(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1823,f291]) ).
fof(f1925,plain,
! [X0,X1,X2,X3,X4] :
( ~ ssList(app(X2,cons(X3,X1)))
| ssItem(X4)
| ~ ssItem(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1826,f292]) ).
fof(f1926,plain,
! [X0,X1,X2,X3,X4] :
( ~ ssList(X2)
| ~ ssList(cons(X3,X1))
| ssItem(X4)
| ~ ssItem(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f1925,f291]) ).
fof(f1928,plain,
! [X0,X1,X2,X3,X4] :
( ~ ssList(cons(X3,X1))
| ssItem(X4)
| ~ ssItem(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f1926]) ).
fof(f1929,plain,
! [X0,X1,X2,X3,X4] :
( ssItem(X4)
| ~ ssItem(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1928,f292]) ).
fof(f1935,plain,
! [X0,X1,X2] :
( ssItem(X2)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f1929,f258]) ).
fof(f2040,plain,
! [X0,X1] :
( ssItem(X1)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f1935,f258]) ).
fof(f2087,plain,
! [X0,X1] :
( leq(X0,X1)
| ~ ssItem(X0)
| ~ lt(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f311,f2040]) ).
fof(f2089,plain,
! [X0] : ssItem(X0),
inference(resolution,[status(thm)],[f2040,f252]) ).
fof(f2126,plain,
! [X0] :
( lt(X0,sk5(skaf48(cons(X0,nil),sk3),skaf47(sk3,cons(X0,nil)),X0))
| ~ ssList(skaf48(cons(X0,nil),sk3))
| ~ ssList(cons(X0,nil))
| ~ segmentP(sk3,cons(X0,nil)) ),
inference(backward_subsumption_resolution,[status(thm)],[f1698,f2089]) ).
fof(f2130,plain,
! [X0] :
( ~ leq(X0,sk5(skaf48(cons(X0,nil),sk3),skaf47(sk3,cons(X0,nil)),X0))
| ~ ssList(skaf48(cons(X0,nil),sk3))
| ~ ssList(cons(X0,nil))
| ~ segmentP(sk3,cons(X0,nil)) ),
inference(backward_subsumption_resolution,[status(thm)],[f1563,f2089]) ).
fof(f2199,plain,
! [X0] :
( lt(X0,sk5(skaf48(cons(X0,nil),sk3),skaf47(sk3,cons(X0,nil)),X0))
| ~ ssList(cons(X0,nil))
| ~ segmentP(sk3,cons(X0,nil)) ),
inference(forward_subsumption_resolution,[status(thm)],[f2126,f253]) ).
fof(f2200,plain,
! [X0] :
( ~ leq(X0,sk5(skaf48(cons(X0,nil),sk3),skaf47(sk3,cons(X0,nil)),X0))
| ~ ssList(cons(X0,nil))
| ~ segmentP(sk3,cons(X0,nil)) ),
inference(forward_subsumption_resolution,[status(thm)],[f2130,f253]) ).
fof(f2433,plain,
! [X0,X1] :
( leq(X0,X1)
| ~ lt(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f2087,f2089]) ).
fof(f2953,plain,
( lt(sk6,sk5(skaf48(sk3,sk3),skaf47(sk3,cons(sk6,nil)),sk6))
| ~ ssList(cons(sk6,nil))
| ~ segmentP(sk3,cons(sk6,nil)) ),
inference(paramodulation,[status(thm)],[f510,f2199]) ).
fof(f2955,plain,
( lt(sk6,sk5(skaf48(sk3,sk3),skaf47(sk3,cons(sk6,nil)),sk6))
| ~ ssList(cons(sk6,nil))
| ~ segmentP(sk3,sk3) ),
inference(forward_demodulation,[status(thm)],[f510,f2953]) ).
fof(f2956,plain,
( lt(sk6,sk5(skaf48(sk3,sk3),skaf47(sk3,cons(sk6,nil)),sk6))
| ~ ssList(sk3)
| ~ segmentP(sk3,sk3) ),
inference(forward_demodulation,[status(thm)],[f510,f2955]) ).
fof(f2957,plain,
( lt(sk6,sk5(skaf48(sk3,sk3),skaf47(sk3,sk3),sk6))
| ~ ssList(sk3)
| ~ segmentP(sk3,sk3) ),
inference(forward_demodulation,[status(thm)],[f510,f2956]) ).
fof(f2958,plain,
( lt(sk6,sk5(skaf48(sk3,sk3),skaf47(sk3,sk3),sk6))
| ~ ssList(sk3) ),
inference(forward_subsumption_resolution,[status(thm)],[f2957,f262]) ).
fof(f2963,plain,
( ~ leq(sk6,sk5(skaf48(sk3,sk3),skaf47(sk3,cons(sk6,nil)),sk6))
| ~ ssList(cons(sk6,nil))
| ~ segmentP(sk3,cons(sk6,nil)) ),
inference(paramodulation,[status(thm)],[f510,f2200]) ).
fof(f2965,plain,
( ~ leq(sk6,sk5(skaf48(sk3,sk3),skaf47(sk3,cons(sk6,nil)),sk6))
| ~ ssList(cons(sk6,nil))
| ~ segmentP(sk3,sk3) ),
inference(forward_demodulation,[status(thm)],[f510,f2963]) ).
fof(f2966,plain,
( ~ leq(sk6,sk5(skaf48(sk3,sk3),skaf47(sk3,cons(sk6,nil)),sk6))
| ~ ssList(sk3)
| ~ segmentP(sk3,sk3) ),
inference(forward_demodulation,[status(thm)],[f510,f2965]) ).
fof(f2967,plain,
( ~ leq(sk6,sk5(skaf48(sk3,sk3),skaf47(sk3,sk3),sk6))
| ~ ssList(sk3)
| ~ segmentP(sk3,sk3) ),
inference(forward_demodulation,[status(thm)],[f510,f2966]) ).
fof(f2968,plain,
( ~ leq(sk6,sk5(skaf48(sk3,sk3),skaf47(sk3,sk3),sk6))
| ~ ssList(sk3) ),
inference(forward_subsumption_resolution,[status(thm)],[f2967,f262]) ).
fof(f2988,plain,
lt(sk6,sk5(skaf48(sk3,sk3),skaf47(sk3,sk3),sk6)),
inference(forward_subsumption_resolution,[status(thm)],[f2958,f438]) ).
fof(f2989,plain,
leq(sk6,sk5(skaf48(sk3,sk3),skaf47(sk3,sk3),sk6)),
inference(resolution,[status(thm)],[f2988,f2433]) ).
fof(f3017,plain,
~ leq(sk6,sk5(skaf48(sk3,sk3),skaf47(sk3,sk3),sk6)),
inference(forward_subsumption_resolution,[status(thm)],[f2968,f438]) ).
fof(f3018,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f2989,f3017]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWC239-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.44 % Computer : n020.cluster.edu
% 0.16/0.44 % Model : x86_64 x86_64
% 0.16/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.44 % Memory : 8046.5625MB
% 0.16/0.44 % OS : Linux 6.8.0-71-generic
% 0.16/0.44 % CPULimit : 300
% 0.16/0.44 % WCLimit : 300
% 0.16/0.44 % DateTime : Mon Sep 21 08:08:32 UTC 2026
% 0.16/0.44 % CPUTime :
% 0.16/0.49 % Drodi V4.1.1
% 0.29/1.13 % Refutation found
% 0.29/1.13 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.29/1.13 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 5.16/1.18 % Elapsed time: 0.718645 seconds
% 5.16/1.18 % CPU time: 5.021531 seconds
% 5.16/1.18 % Total memory used: 151.520 MB
% 5.16/1.18 % Net memory used: 148.560 MB
%------------------------------------------------------------------------------