%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SWC312-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 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 : Fri Sep 25 03:05:58 PM UTC 2026
% Result : Unsatisfiable 27.52s 3.98s
% Output : Proof 27.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 11
% Syntax : Number of formulae : 81 ( 15 unt; 0 def)
% Number of atoms : 184 ( 104 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 195 ( 92 ~; 103 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 24 ( 0 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f190,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_6) ).
fof(f190_nnf,plain,
sk1 = sk3,
inference(nnf_transformation,[status(thm)],[f190]) ).
cnf(c190,plain,
sk1 = sk3,
inference(cnf_transformation,[status(esa)],[f190_nnf]) ).
cnf(f189,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_5) ).
fof(f189_nnf,plain,
sk2 = sk4,
inference(nnf_transformation,[status(thm)],[f189]) ).
cnf(c189,plain,
sk2 = sk4,
inference(cnf_transformation,[status(esa)],[f189_nnf]) ).
cnf(f191,negated_conjecture,
( nil != sk4
| nil = sk3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
fof(f191_nnf,plain,
( nil != sk4
| nil = sk3 ),
inference(nnf_transformation,[status(thm)],[f191]) ).
fof(f191_sk,plain,
( nil != sk4
| nil = sk3 ),
inference(skolemisation,[status(esa)],[f191_nnf]) ).
cnf(c191,plain,
( nil != sk4
| nil = sk3 ),
inference(cnf_transformation,[status(esa)],[f191_sk]) ).
cnf(p217,plain,
( nil != sk2
| nil = sk3 ),
inference(superposition,[status(thm)],[c189,c191]) ).
cnf(f192,negated_conjecture,
( ~ neq(sk4,nil)
| ssItem(sk5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_8) ).
fof(f192_nnf,plain,
( ~ neq(sk4,nil)
| ssItem(sk5) ),
inference(nnf_transformation,[status(thm)],[f192]) ).
fof(f192_sk,plain,
( ~ neq(sk4,nil)
| ssItem(sk5) ),
inference(skolemisation,[status(esa)],[f192_nnf]) ).
cnf(c192,plain,
( ~ neq(sk4,nil)
| ssItem(sk5) ),
inference(cnf_transformation,[status(esa)],[f192_sk]) ).
cnf(p221,plain,
( ~ neq(sk2,nil)
| ssItem(sk5) ),
inference(superposition,[status(thm)],[c189,c192]) ).
cnf(f196,negated_conjecture,
( neq(sk2,nil)
| nil = sk2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_12) ).
fof(f196_nnf,plain,
( neq(sk2,nil)
| nil = sk2 ),
inference(nnf_transformation,[status(thm)],[f196]) ).
fof(f196_sk,plain,
( neq(sk2,nil)
| nil = sk2 ),
inference(skolemisation,[status(esa)],[f196_nnf]) ).
cnf(c196,plain,
( neq(sk2,nil)
| nil = sk2 ),
inference(cnf_transformation,[status(esa)],[f196_sk]) ).
cnf(p225,plain,
( nil = sk2
| ssItem(sk5) ),
inference(resolution,[status(thm)],[p221,c196]) ).
cnf(p237,plain,
( ssItem(sk5)
| nil = sk3 ),
inference(resolution,[status(thm)],[p217,p225]) ).
cnf(p240,plain,
( ssItem(sk5)
| nil = sk1 ),
inference(superposition,[status(thm)],[c190,p237]) ).
cnf(f198,negated_conjecture,
( neq(sk2,nil)
| nil != sk1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_14) ).
fof(f198_nnf,plain,
( neq(sk2,nil)
| nil != sk1 ),
inference(nnf_transformation,[status(thm)],[f198]) ).
fof(f198_sk,plain,
( neq(sk2,nil)
| nil != sk1 ),
inference(skolemisation,[status(esa)],[f198_nnf]) ).
cnf(c198,plain,
( neq(sk2,nil)
| nil != sk1 ),
inference(cnf_transformation,[status(esa)],[f198_sk]) ).
cnf(p244,plain,
( neq(sk2,nil)
| ssItem(sk5) ),
inference(resolution,[status(thm)],[p240,c198]) ).
cnf(p246,plain,
( ssItem(sk5)
| ssItem(sk5) ),
inference(resolution,[status(thm)],[p244,p221]) ).
cnf(p248,plain,
ssItem(sk5),
inference(factoring,[status(thm)],[p246]) ).
cnf(f197,negated_conjecture,
( app(B,cons(A,nil)) != sk1
| app(cons(A,nil),B) != sk2
| ~ ssList(B)
| ~ ssItem(A)
| nil = sk2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_13) ).
fof(f197_nnf,plain,
! [A,B] :
( app(B,cons(A,nil)) != sk1
| app(cons(A,nil),B) != sk2
| ~ ssList(B)
| ~ ssItem(A)
| nil = sk2 ),
inference(nnf_transformation,[status(thm)],[f197]) ).
fof(f197_sk,plain,
! [A,B] :
( app(B,cons(A,nil)) != sk1
| app(cons(A,nil),B) != sk2
| ~ ssList(B)
| ~ ssItem(A)
| nil = sk2 ),
inference(skolemisation,[status(esa)],[f197_nnf]) ).
cnf(c197,plain,
( app(X1,cons(X0,nil)) != sk1
| app(cons(X0,nil),X1) != sk2
| ~ ssList(X1)
| ~ ssItem(X0)
| nil = sk2 ),
inference(cnf_transformation,[status(esa)],[f197_sk]) ).
cnf(p249,plain,
( app(X0,cons(sk5,nil)) != sk1
| app(cons(sk5,nil),X0) != sk2
| ~ ssList(X0)
| nil = sk2 ),
inference(resolution,[status(thm)],[p248,c197]) ).
cnf(f193,negated_conjecture,
( ~ neq(sk4,nil)
| ssList(sk6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_9) ).
fof(f193_nnf,plain,
( ~ neq(sk4,nil)
| ssList(sk6) ),
inference(nnf_transformation,[status(thm)],[f193]) ).
fof(f193_sk,plain,
( ~ neq(sk4,nil)
| ssList(sk6) ),
inference(skolemisation,[status(esa)],[f193_nnf]) ).
cnf(c193,plain,
( ~ neq(sk4,nil)
| ssList(sk6) ),
inference(cnf_transformation,[status(esa)],[f193_sk]) ).
cnf(p219,plain,
( ~ neq(sk2,nil)
| ssList(sk6) ),
inference(superposition,[status(thm)],[c189,c193]) ).
cnf(p224,plain,
( nil = sk2
| ssList(sk6) ),
inference(resolution,[status(thm)],[p219,c196]) ).
cnf(p226,plain,
( nil = sk4
| ssList(sk6) ),
inference(superposition,[status(thm)],[p224,c189]) ).
cnf(p233,plain,
( nil = sk3
| ssList(sk6) ),
inference(resolution,[status(thm)],[p226,c191]) ).
cnf(p267,plain,
( nil = sk1
| ssList(sk6) ),
inference(superposition,[status(thm)],[c190,p233]) ).
cnf(p269,plain,
( neq(sk2,nil)
| ssList(sk6) ),
inference(resolution,[status(thm)],[p267,c198]) ).
cnf(p270,plain,
( ssList(sk6)
| ssList(sk6) ),
inference(resolution,[status(thm)],[p269,p219]) ).
cnf(p273,plain,
ssList(sk6),
inference(factoring,[status(thm)],[p270]) ).
cnf(p329,plain,
( app(sk6,cons(sk5,nil)) != sk1
| app(cons(sk5,nil),sk6) != sk2
| nil = sk2 ),
inference(resolution,[status(thm)],[p249,p273]) ).
cnf(f194,negated_conjecture,
( ~ neq(sk4,nil)
| app(cons(sk5,nil),sk6) = sk4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_10) ).
fof(f194_nnf,plain,
( ~ neq(sk4,nil)
| app(cons(sk5,nil),sk6) = sk4 ),
inference(nnf_transformation,[status(thm)],[f194]) ).
fof(f194_sk,plain,
( ~ neq(sk4,nil)
| app(cons(sk5,nil),sk6) = sk4 ),
inference(skolemisation,[status(esa)],[f194_nnf]) ).
cnf(c194,plain,
( ~ neq(sk4,nil)
| app(cons(sk5,nil),sk6) = sk4 ),
inference(cnf_transformation,[status(esa)],[f194_sk]) ).
cnf(p218,plain,
( ~ neq(sk2,nil)
| app(cons(sk5,nil),sk6) = sk4 ),
inference(superposition,[status(thm)],[c189,c194]) ).
cnf(p253,plain,
( nil = sk2
| app(cons(sk5,nil),sk6) = sk4 ),
inference(resolution,[status(thm)],[p218,c196]) ).
cnf(p255,plain,
( nil = sk2
| app(cons(sk5,nil),sk6) = sk2 ),
inference(superposition,[status(thm)],[c189,p253]) ).
cnf(p347,plain,
( nil = sk2
| app(sk6,cons(sk5,nil)) != sk1
| nil = sk2 ),
inference(resolution,[status(thm)],[p329,p255]) ).
cnf(p348,plain,
( app(sk6,cons(sk5,nil)) != sk1
| nil = sk2 ),
inference(factoring,[status(thm)],[p347]) ).
cnf(f195,negated_conjecture,
( ~ neq(sk4,nil)
| app(sk6,cons(sk5,nil)) = sk3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_11) ).
fof(f195_nnf,plain,
( ~ neq(sk4,nil)
| app(sk6,cons(sk5,nil)) = sk3 ),
inference(nnf_transformation,[status(thm)],[f195]) ).
fof(f195_sk,plain,
( ~ neq(sk4,nil)
| app(sk6,cons(sk5,nil)) = sk3 ),
inference(skolemisation,[status(esa)],[f195_nnf]) ).
cnf(c195,plain,
( ~ neq(sk4,nil)
| app(sk6,cons(sk5,nil)) = sk3 ),
inference(cnf_transformation,[status(esa)],[f195_sk]) ).
cnf(p220,plain,
( ~ neq(sk2,nil)
| app(sk6,cons(sk5,nil)) = sk3 ),
inference(superposition,[status(thm)],[c189,c195]) ).
cnf(p254,plain,
( nil = sk2
| app(sk6,cons(sk5,nil)) = sk3 ),
inference(resolution,[status(thm)],[p220,c196]) ).
cnf(p258,plain,
( nil = sk2
| app(sk6,cons(sk5,nil)) = sk1 ),
inference(superposition,[status(thm)],[c190,p254]) ).
cnf(p350,plain,
( nil = sk2
| nil = sk2 ),
inference(resolution,[status(thm)],[p348,p258]) ).
cnf(p351,plain,
nil = sk2,
inference(factoring,[status(thm)],[p350]) ).
cnf(p353,plain,
nil = sk3,
inference(resolution,[status(thm)],[p351,p217]) ).
cnf(p359,plain,
sk1 = nil,
inference(superposition,[status(thm)],[p353,c190]) ).
cnf(p352,plain,
nil = sk4,
inference(superposition,[status(thm)],[p351,c189]) ).
cnf(p356,plain,
sk2 = nil,
inference(superposition,[status(thm)],[p352,c189]) ).
cnf(f199,negated_conjecture,
( app(B,cons(A,nil)) != sk1
| app(cons(A,nil),B) != sk2
| ~ ssList(B)
| ~ ssItem(A)
| nil != sk1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_15) ).
fof(f199_nnf,plain,
! [A,B] :
( app(B,cons(A,nil)) != sk1
| app(cons(A,nil),B) != sk2
| ~ ssList(B)
| ~ ssItem(A)
| nil != sk1 ),
inference(nnf_transformation,[status(thm)],[f199]) ).
fof(f199_sk,plain,
! [A,B] :
( app(B,cons(A,nil)) != sk1
| app(cons(A,nil),B) != sk2
| ~ ssList(B)
| ~ ssItem(A)
| nil != sk1 ),
inference(skolemisation,[status(esa)],[f199_nnf]) ).
cnf(c199,plain,
( app(X1,cons(X0,nil)) != sk1
| app(cons(X0,nil),X1) != sk2
| ~ ssList(X1)
| ~ ssItem(X0)
| nil != sk1 ),
inference(cnf_transformation,[status(esa)],[f199_sk]) ).
cnf(p358,plain,
( app(X1,cons(X0,nil)) != sk1
| app(cons(X0,nil),X1) != nil
| ~ ssList(X1)
| ~ ssItem(X0)
| nil != sk1 ),
inference(demodulation,[status(thm)],[p356,c199]) ).
cnf(p361,plain,
( app(X1,cons(X0,nil)) != nil
| app(cons(X0,nil),X1) != nil
| ~ ssList(X1)
| ~ ssItem(X0)
| nil != nil ),
inference(demodulation,[status(thm)],[p359,p358]) ).
cnf(p370,plain,
( app(X1,cons(X0,nil)) != nil
| app(cons(X0,nil),X1) != nil
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(equality_resolution,[status(thm)],[p361]) ).
cnf(p392,plain,
( app(X0,cons(sk5,nil)) != nil
| app(cons(sk5,nil),X0) != nil
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[p370,p248]) ).
cnf(p492,plain,
( nil != nil
| nil != nil ),
inference(resolution,[status(thm)],[p392,p273]) ).
cnf(p513,plain,
nil != nil,
inference(factoring,[status(thm)],[p492]) ).
cnf(p543,plain,
$false,
inference(equality_resolution,[status(thm)],[p513]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC312-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.37 % Computer : n020.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 17:34:49 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 27.52/3.98 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 27.52/3.98 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------