%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SWV411+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n015.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 03:13:11 PM UTC 2026
% Result : Theorem 103.12s 17.64s
% Output : Proof 103.12s
% Verified :
% Comments :
%------------------------------------------------------------------------------
fof(f14,axiom,
! [U,V,W,X] :
( ( contains_slb(U,W)
& V != W )
=> lookup_slb(insert_slb(U,pair(V,X)),W) = lookup_slb(U,W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax27) ).
fof(f14_nnf,plain,
! [U,V,W,X] :
( lookup_slb(insert_slb(U,pair(V,X)),W) = lookup_slb(U,W)
| ~ contains_slb(U,W)
| V = W ),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [V,W,U,X] :
( lookup_slb(insert_slb(U,pair(V,X)),W) = lookup_slb(U,W)
| ~ contains_slb(U,W)
| V = W ),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c21,plain,
( lookup_slb(insert_slb(X0,pair(X1,X3)),X2) = lookup_slb(X0,X2)
| ~ contains_slb(X0,X2)
| X1 = X2 ),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
fof(f10,axiom,
! [U,V,W,X,Y] :
( pair_in_list(insert_slb(U,pair(V,X)),W,Y)
<=> ( ( X = Y
& V = W )
| pair_in_list(U,W,Y) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax23) ).
fof(f10_nnf,plain,
! [U,V,W,X,Y] :
( ( ( ( X != Y
| V != W )
& ~ pair_in_list(U,W,Y) )
| pair_in_list(insert_slb(U,pair(V,X)),W,Y) )
& ( ( X = Y
& V = W )
| pair_in_list(U,W,Y)
| ~ pair_in_list(insert_slb(U,pair(V,X)),W,Y) ) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [U,V,X,W,Y] :
( ( ( ( X != Y
| V != W )
& ~ pair_in_list(U,W,Y) )
| pair_in_list(insert_slb(U,pair(V,X)),W,Y) )
& ( ( X = Y
& V = W )
| pair_in_list(U,W,Y)
| ~ pair_in_list(insert_slb(U,pair(V,X)),W,Y) ) ),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c16,plain,
( ~ pair_in_list(X0,X2,X4)
| pair_in_list(insert_slb(X0,pair(X1,X3)),X2,X4) ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
fof(f8,axiom,
! [U,V,W,X] :
( contains_slb(insert_slb(U,pair(V,X)),W)
<=> ( V = W
| contains_slb(U,W) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax21) ).
fof(f8_nnf,plain,
! [U,V,W,X] :
( ( ( V != W
& ~ contains_slb(U,W) )
| contains_slb(insert_slb(U,pair(V,X)),W) )
& ( V = W
| contains_slb(U,W)
| ~ contains_slb(insert_slb(U,pair(V,X)),W) ) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [U,V,X,W] :
( ( ( V != W
& ~ contains_slb(U,W) )
| contains_slb(insert_slb(U,pair(V,X)),W) )
& ( V = W
| contains_slb(U,W)
| ~ contains_slb(insert_slb(U,pair(V,X)),W) ) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c10,plain,
( X1 = X2
| contains_slb(X0,X2)
| ~ contains_slb(insert_slb(X0,pair(X1,X3)),X2) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
fof(f18,conjecture,
! [U] :
( ! [V] :
( contains_slb(U,V)
=> ? [W] : pair_in_list(U,V,W) )
=> ! [X,Y,Z] :
( contains_slb(insert_slb(U,pair(Y,Z)),X)
=> ? [X1] : pair_in_list(insert_slb(U,pair(Y,Z)),X,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l47_co) ).
fof(f18_neg,negated_conjecture,
~ ! [U] :
( ! [V] :
( contains_slb(U,V)
=> ? [W] : pair_in_list(U,V,W) )
=> ! [X,Y,Z] :
( contains_slb(insert_slb(U,pair(Y,Z)),X)
=> ? [X1] : pair_in_list(insert_slb(U,pair(Y,Z)),X,X1) ) ),
inference(negated_conjecture,[status(cth)],[f18]) ).
fof(f18_nnf,plain,
? [U] :
( ? [X,Y,Z] :
( ! [X1] : ~ pair_in_list(insert_slb(U,pair(Y,Z)),X,X1)
& contains_slb(insert_slb(U,pair(Y,Z)),X) )
& ! [V] :
( ? [W] : pair_in_list(U,V,W)
| ~ contains_slb(U,V) ) ),
inference(nnf_transformation,[status(thm)],[f18_neg]) ).
fof(f18_sk,plain,
! [V,X1] :
( ~ pair_in_list(insert_slb(sk0,pair(sk3,sk4)),sk2,X1)
& contains_slb(insert_slb(sk0,pair(sk3,sk4)),sk2)
& ( pair_in_list(sk0,V,sk1(V))
| ~ contains_slb(sk0,V) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1,sk2,sk3,sk4])],[f18_nnf]) ).
cnf(c26,plain,
contains_slb(insert_slb(sk0,pair(sk3,sk4)),sk2),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(p32,plain,
( sk3 = sk2
| contains_slb(sk0,sk2) ),
inference(resolution,[status(thm)],[c10,c26]) ).
cnf(c25,plain,
( pair_in_list(sk0,X1,sk1(X1))
| ~ contains_slb(sk0,X1) ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(p33,plain,
( pair_in_list(sk0,sk2,sk1(sk2))
| sk3 = sk2 ),
inference(resolution,[status(thm)],[p32,c25]) ).
cnf(p50,plain,
( sk3 = sk2
| pair_in_list(insert_slb(sk0,pair(X0,X1)),sk2,sk1(sk2)) ),
inference(resolution,[status(thm)],[c16,p33]) ).
cnf(c27,plain,
~ pair_in_list(insert_slb(sk0,pair(sk3,sk4)),sk2,X6),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(p51,plain,
sk3 = sk2,
inference(resolution,[status(thm)],[p50,c27]) ).
cnf(c11,plain,
( ~ contains_slb(X0,X2)
| contains_slb(insert_slb(X0,pair(X1,X3)),X2) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p31,plain,
contains_slb(insert_slb(insert_slb(sk0,pair(sk3,sk4)),pair(X0,X1)),sk2),
inference(resolution,[status(thm)],[c11,c26]) ).
cnf(p53,plain,
contains_slb(insert_slb(insert_slb(sk0,pair(sk2,sk4)),pair(X0,X1)),sk2),
inference(demodulation,[status(thm)],[p51,p31]) ).
cnf(p76,plain,
( lookup_slb(insert_slb(insert_slb(insert_slb(sk0,pair(sk2,sk4)),pair(X1,X2)),pair(X0,X3)),sk2) = lookup_slb(insert_slb(insert_slb(sk0,pair(sk2,sk4)),pair(X1,X2)),sk2)
| X0 = sk2 ),
inference(resolution,[status(thm)],[c21,p53]) ).
fof(f13,axiom,
! [U,V,W] : lookup_slb(insert_slb(U,pair(V,W)),V) = W,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax26) ).
fof(f13_nnf,plain,
! [U,V,W] : lookup_slb(insert_slb(U,pair(V,W)),V) = W,
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [U,V,W] : lookup_slb(insert_slb(U,pair(V,W)),V) = W,
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c20,plain,
lookup_slb(insert_slb(X0,pair(X1,X2)),X1) = X2,
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(p83,plain,
( lookup_slb(insert_slb(insert_slb(insert_slb(sk0,pair(sk2,sk4)),pair(sk2,X1)),pair(X0,X2)),sk2) = X1
| X0 = sk2 ),
inference(superposition,[status(thm)],[c20,p76]) ).
cnf(c12,plain,
( X1 != X2
| contains_slb(insert_slb(X0,pair(X1,X3)),X2) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p86,plain,
( contains_slb(insert_slb(X1,pair(lookup_slb(insert_slb(insert_slb(insert_slb(sk0,pair(sk2,sk4)),pair(sk2,X2)),pair(X0,X3)),sk2),X4)),X2)
| X0 = sk2 ),
inference(resolution,[status(thm)],[p83,c12]) ).
cnf(p88,plain,
( contains_slb(insert_slb(insert_slb(X1,pair(lookup_slb(insert_slb(insert_slb(insert_slb(sk0,pair(sk2,sk4)),pair(sk2,X2)),pair(X0,X3)),sk2),X4)),pair(X5,X6)),X2)
| X0 = sk2 ),
inference(resolution,[status(thm)],[p86,c11]) ).
cnf(p94,plain,
( contains_slb(insert_slb(insert_slb(X1,pair(X2,X3)),pair(X4,X5)),X2)
| X0 = sk2
| X0 = sk2 ),
inference(superposition,[status(thm)],[p76,p88]) ).
cnf(p96,plain,
( contains_slb(insert_slb(insert_slb(X1,pair(X2,X3)),pair(X4,X5)),X2)
| X0 = sk2 ),
inference(factoring,[status(thm)],[p94]) ).
cnf(p99,plain,
( sk2 = X5
| contains_slb(insert_slb(insert_slb(X0,pair(X1,X2)),pair(X3,X4)),X1) ),
inference(superposition,[status(thm)],[p96,p51]) ).
cnf(p113,plain,
( contains_slb(insert_slb(X5,pair(sk2,X6)),X7)
| contains_slb(insert_slb(insert_slb(X0,pair(X1,X2)),pair(X3,X4)),X1) ),
inference(resolution,[status(thm)],[p99,c12]) ).
cnf(p158,plain,
contains_slb(insert_slb(insert_slb(X0,pair(X1,X2)),pair(sk2,X3)),X1),
inference(factoring,[status(thm)],[p113]) ).
cnf(p165,plain,
( lookup_slb(insert_slb(insert_slb(insert_slb(X2,pair(X1,X3)),pair(sk2,X4)),pair(X0,X5)),X1) = lookup_slb(insert_slb(insert_slb(X2,pair(X1,X3)),pair(sk2,X4)),X1)
| X0 = X1 ),
inference(resolution,[status(thm)],[p158,c21]) ).
cnf(p98,plain,
( contains_slb(insert_slb(X5,pair(X6,X7)),sk2)
| contains_slb(insert_slb(insert_slb(X0,pair(X1,X2)),pair(X3,X4)),X1) ),
inference(resolution,[status(thm)],[p96,c12]) ).
cnf(p136,plain,
contains_slb(insert_slb(insert_slb(X0,pair(sk2,X1)),pair(X2,X3)),sk2),
inference(factoring,[status(thm)],[p98]) ).
cnf(p143,plain,
( lookup_slb(insert_slb(insert_slb(insert_slb(X1,pair(sk2,X2)),pair(X3,X4)),pair(X0,X5)),sk2) = lookup_slb(insert_slb(insert_slb(X1,pair(sk2,X2)),pair(X3,X4)),sk2)
| X0 = sk2 ),
inference(resolution,[status(thm)],[p136,c21]) ).
cnf(p389,plain,
( lookup_slb(insert_slb(insert_slb(insert_slb(insert_slb(X2,pair(sk2,X3)),pair(sk2,X4)),pair(X0,X5)),pair(X1,X6)),sk2) = X4
| X1 = sk2
| X0 = sk2 ),
inference(superposition,[status(thm)],[p165,p143]) ).
cnf(p392,plain,
( lookup_slb(insert_slb(insert_slb(insert_slb(insert_slb(X1,pair(sk2,X2)),pair(sk2,X3)),pair(X0,X4)),pair(X0,X5)),sk2) = X3
| X0 = sk2 ),
inference(factoring,[status(thm)],[p389]) ).
cnf(p408,plain,
( X1 = lookup_slb(insert_slb(insert_slb(insert_slb(X2,pair(sk2,X3)),pair(sk2,X1)),pair(X0,X4)),sk2)
| X0 = sk2
| X0 = sk2 ),
inference(superposition,[status(thm)],[p392,p143]) ).
cnf(p411,plain,
( X1 = lookup_slb(insert_slb(insert_slb(insert_slb(X2,pair(sk2,X3)),pair(sk2,X1)),pair(X0,X4)),sk2)
| X0 = sk2 ),
inference(factoring,[status(thm)],[p408]) ).
cnf(c17,plain,
( X3 != X4
| X1 != X2
| pair_in_list(insert_slb(X0,pair(X1,X3)),X2,X4) ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(p62,plain,
( X2 != X3
| pair_in_list(insert_slb(X0,pair(X1,X2)),X1,X3) ),
inference(equality_resolution,[status(thm)],[c17]) ).
cnf(p429,plain,
( pair_in_list(insert_slb(X1,pair(X2,X3)),X2,lookup_slb(insert_slb(insert_slb(insert_slb(X4,pair(sk2,X5)),pair(sk2,X3)),pair(X0,X6)),sk2))
| X0 = sk2 ),
inference(resolution,[status(thm)],[p411,p62]) ).
cnf(p52,plain,
~ pair_in_list(insert_slb(sk0,pair(sk2,sk4)),sk2,X0),
inference(demodulation,[status(thm)],[p51,c27]) ).
cnf(p453,plain,
X0 = sk2,
inference(resolution,[status(thm)],[p429,p52]) ).
fof(f5,axiom,
~ isnonempty_slb(create_slb),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax18) ).
fof(f5_nnf,plain,
~ isnonempty_slb(create_slb),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
~ isnonempty_slb(create_slb),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c7,plain,
~ isnonempty_slb(create_slb),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p457,plain,
~ sk2,
inference(demodulation,[status(thm)],[p453,c7]) ).
fof(f2,axiom,
! [U] : less_than(U,U),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity) ).
fof(f2_nnf,plain,
! [U] : less_than(U,U),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [U] : less_than(U,U),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
less_than(X0,X0),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p455,plain,
sk2,
inference(demodulation,[status(thm)],[p453,c2]) ).
cnf(p458,plain,
$false,
inference(resolution,[status(thm)],[p457,p455]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV411+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.38 % Computer : n015.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Thu Sep 24 19:34:11 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 103.12/17.64 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 103.12/17.64 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------