%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SWV409+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 : n010.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 120.17s 17.98s
% Output : Proof 120.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 44 ( 9 unt; 0 def)
% Number of atoms : 126 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 134 ( 52 ~; 54 |; 22 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-4 aty)
% Number of variables : 85 ( 0 sgn 50 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [U,V] :
( strictly_less_than(U,V)
<=> ( ~ less_than(V,U)
& less_than(U,V) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',stricly_smaller_definition) ).
fof(f3_nnf,plain,
! [U,V] :
( ( less_than(V,U)
| ~ less_than(U,V)
| strictly_less_than(U,V) )
& ( ( ~ less_than(V,U)
& less_than(U,V) )
| ~ strictly_less_than(U,V) ) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [U,V] :
( ( less_than(V,U)
| ~ less_than(U,V)
| strictly_less_than(U,V) )
& ( ( ~ less_than(V,U)
& less_than(U,V) )
| ~ strictly_less_than(U,V) ) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c5,plain,
( less_than(X1,X0)
| ~ less_than(X0,X1)
| strictly_less_than(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
fof(f1,axiom,
! [U,V] :
( less_than(V,U)
| less_than(U,V) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',totality) ).
fof(f1_nnf,plain,
! [U,V] :
( less_than(V,U)
| less_than(U,V) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [U,V] :
( less_than(V,U)
| less_than(U,V) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( less_than(X1,X0)
| less_than(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p41,plain,
( less_than(X1,X0)
| less_than(X1,X0)
| strictly_less_than(X0,X1) ),
inference(resolution,[status(thm)],[c5,c1]) ).
cnf(p317,plain,
( less_than(X1,X0)
| strictly_less_than(X0,X1) ),
inference(factoring,[status(thm)],[p41]) ).
fof(f19,lemma,
! [U,V,W,X] :
( ( strictly_less_than(W,X)
& strictly_less_than(V,X)
& pair_in_list(U,V,W) )
=> pair_in_list(update_slb(U,X),V,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l45_l48) ).
fof(f19_nnf,plain,
! [U,V,W,X] :
( pair_in_list(update_slb(U,X),V,X)
| ~ strictly_less_than(W,X)
| ~ strictly_less_than(V,X)
| ~ pair_in_list(U,V,W) ),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
! [U,V,W,X] :
( pair_in_list(update_slb(U,X),V,X)
| ~ strictly_less_than(W,X)
| ~ strictly_less_than(V,X)
| ~ pair_in_list(U,V,W) ),
inference(skolemisation,[status(esa)],[f19_nnf]) ).
cnf(c26,plain,
( pair_in_list(update_slb(X0,X3),X1,X3)
| ~ strictly_less_than(X2,X3)
| ~ strictly_less_than(X1,X3)
| ~ pair_in_list(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
fof(f18,lemma,
! [U,V] :
( contains_slb(U,V)
=> ? [W] : pair_in_list(U,V,W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l45_li4647) ).
fof(f18_nnf,plain,
! [U,V] :
( ? [W] : pair_in_list(U,V,W)
| ~ contains_slb(U,V) ),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
! [U,V] :
( pair_in_list(U,V,sk0(U,V))
| ~ contains_slb(U,V) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f18_nnf]) ).
cnf(c25,plain,
( pair_in_list(X0,X1,sk0(X0,X1))
| ~ contains_slb(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
fof(f21,conjecture,
! [U,V,W] :
( ( strictly_less_than(V,W)
& contains_slb(U,V) )
=> ( ? [X] :
( less_than(W,X)
& pair_in_list(update_slb(U,W),V,X) )
| pair_in_list(update_slb(U,W),V,W) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l45_co) ).
fof(f21_neg,negated_conjecture,
~ ! [U,V,W] :
( ( strictly_less_than(V,W)
& contains_slb(U,V) )
=> ( ? [X] :
( less_than(W,X)
& pair_in_list(update_slb(U,W),V,X) )
| pair_in_list(update_slb(U,W),V,W) ) ),
inference(negated_conjecture,[status(cth)],[f21]) ).
fof(f21_nnf,plain,
? [U,V,W] :
( ! [X] :
( ~ less_than(W,X)
| ~ pair_in_list(update_slb(U,W),V,X) )
& ~ pair_in_list(update_slb(U,W),V,W)
& strictly_less_than(V,W)
& contains_slb(U,V) ),
inference(nnf_transformation,[status(thm)],[f21_neg]) ).
fof(f21_sk,plain,
! [X] :
( ( ~ less_than(sk4,X)
| ~ pair_in_list(update_slb(sk2,sk4),sk3,X) )
& ~ pair_in_list(update_slb(sk2,sk4),sk3,sk4)
& strictly_less_than(sk3,sk4)
& contains_slb(sk2,sk3) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2,sk3,sk4])],[f21_nnf]) ).
cnf(c29,plain,
contains_slb(sk2,sk3),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(p215,plain,
pair_in_list(sk2,sk3,sk0(sk2,sk3)),
inference(resolution,[status(thm)],[c25,c29]) ).
cnf(p228,plain,
( pair_in_list(update_slb(sk2,X0),sk3,X0)
| ~ strictly_less_than(sk0(sk2,sk3),X0)
| ~ strictly_less_than(sk3,X0) ),
inference(resolution,[status(thm)],[c26,p215]) ).
cnf(c30,plain,
strictly_less_than(sk3,sk4),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(p234,plain,
( pair_in_list(update_slb(sk2,sk4),sk3,sk4)
| ~ strictly_less_than(sk0(sk2,sk3),sk4) ),
inference(resolution,[status(thm)],[p228,c30]) ).
cnf(p5561,plain,
( pair_in_list(update_slb(sk2,sk4),sk3,sk4)
| less_than(sk4,sk0(sk2,sk3)) ),
inference(resolution,[status(thm)],[p317,p234]) ).
cnf(c31,plain,
~ pair_in_list(update_slb(sk2,sk4),sk3,sk4),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(p5598,plain,
less_than(sk4,sk0(sk2,sk3)),
inference(resolution,[status(thm)],[p5561,c31]) ).
fof(f20,lemma,
! [U,V,W,X] :
( ( less_than(X,W)
& strictly_less_than(V,X)
& pair_in_list(U,V,W) )
=> ? [Y] :
( less_than(X,Y)
& pair_in_list(update_slb(U,X),V,Y) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l45_l49) ).
fof(f20_nnf,plain,
! [U,V,W,X] :
( ? [Y] :
( less_than(X,Y)
& pair_in_list(update_slb(U,X),V,Y) )
| ~ less_than(X,W)
| ~ strictly_less_than(V,X)
| ~ pair_in_list(U,V,W) ),
inference(nnf_transformation,[status(thm)],[f20]) ).
fof(f20_sk,plain,
! [U,V,W,X] :
( ( less_than(X,sk1(U,V,W,X))
& pair_in_list(update_slb(U,X),V,sk1(U,V,W,X)) )
| ~ less_than(X,W)
| ~ strictly_less_than(V,X)
| ~ pair_in_list(U,V,W) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1])],[f20_nnf]) ).
cnf(c27,plain,
( pair_in_list(update_slb(X0,X3),X1,sk1(X0,X1,X2,X3))
| ~ less_than(X3,X2)
| ~ strictly_less_than(X1,X3)
| ~ pair_in_list(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(p255,plain,
( pair_in_list(update_slb(sk2,X0),sk3,sk1(sk2,sk3,sk0(sk2,sk3),X0))
| ~ less_than(X0,sk0(sk2,sk3))
| ~ strictly_less_than(sk3,X0) ),
inference(resolution,[status(thm)],[c27,p215]) ).
cnf(p426,plain,
( pair_in_list(update_slb(sk2,sk4),sk3,sk1(sk2,sk3,sk0(sk2,sk3),sk4))
| ~ less_than(sk4,sk0(sk2,sk3)) ),
inference(resolution,[status(thm)],[p255,c30]) ).
cnf(p5604,plain,
pair_in_list(update_slb(sk2,sk4),sk3,sk1(sk2,sk3,sk0(sk2,sk3),sk4)),
inference(resolution,[status(thm)],[p5598,p426]) ).
cnf(c32,plain,
( ~ less_than(sk4,X3)
| ~ pair_in_list(update_slb(sk2,sk4),sk3,X3) ),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(p5692,plain,
~ less_than(sk4,sk1(sk2,sk3,sk0(sk2,sk3),sk4)),
inference(resolution,[status(thm)],[p5604,c32]) ).
cnf(c28,plain,
( less_than(X3,sk1(X0,X1,X2,X3))
| ~ less_than(X3,X2)
| ~ strictly_less_than(X1,X3)
| ~ pair_in_list(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(p271,plain,
( less_than(X0,sk1(sk2,sk3,sk0(sk2,sk3),X0))
| ~ less_than(X0,sk0(sk2,sk3))
| ~ strictly_less_than(sk3,X0) ),
inference(resolution,[status(thm)],[c28,p215]) ).
cnf(p327,plain,
( less_than(sk4,sk1(sk2,sk3,sk0(sk2,sk3),sk4))
| ~ less_than(sk4,sk0(sk2,sk3)) ),
inference(resolution,[status(thm)],[p271,c30]) ).
cnf(p5603,plain,
less_than(sk4,sk1(sk2,sk3,sk0(sk2,sk3),sk4)),
inference(resolution,[status(thm)],[p5598,p327]) ).
cnf(p5755,plain,
$false,
inference(resolution,[status(thm)],[p5692,p5603]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV409+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.35 % Computer : n010.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Thu Sep 24 19:30:58 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 120.17/17.98 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 120.17/17.98 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------