%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SWV399+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n011.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 03:13:09 PM UTC 2026
% Result : Theorem 48.01s 6.59s
% Output : Proof 48.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of formulae : 45 ( 7 unt; 0 def)
% Number of atoms : 114 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 111 ( 42 ~; 47 |; 16 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 93 ( 0 sgn 53 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [U,V] :
( strictly_less_than(U,V)
<=> ( ~ less_than(V,U)
& less_than(U,V) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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(p39,plain,
( less_than(X1,X0)
| less_than(X1,X0)
| strictly_less_than(X0,X1) ),
inference(resolution,[status(thm)],[c5,c1]) ).
cnf(p276,plain,
( less_than(X1,X0)
| strictly_less_than(X0,X1) ),
inference(factoring,[status(thm)],[p39]) ).
fof(f19,lemma,
! [U,V,W,X] :
( ( strictly_less_than(W,X)
& pair_in_list(U,V,W) )
=> pair_in_list(update_slb(U,X),V,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l35_li3839) ).
fof(f19_nnf,plain,
! [U,V,W,X] :
( pair_in_list(update_slb(U,X),V,X)
| ~ strictly_less_than(W,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)
| ~ 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)
| ~ pair_in_list(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
fof(f20,conjecture,
! [U] :
( ? [V,W] :
( strictly_less_than(V,W)
& pair_in_list(U,V,W) )
=> ! [X] :
? [Y,Z] :
( strictly_less_than(Y,Z)
& pair_in_list(update_slb(U,X),Y,Z) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l35_co) ).
fof(f20_neg,negated_conjecture,
~ ! [U] :
( ? [V,W] :
( strictly_less_than(V,W)
& pair_in_list(U,V,W) )
=> ! [X] :
? [Y,Z] :
( strictly_less_than(Y,Z)
& pair_in_list(update_slb(U,X),Y,Z) ) ),
inference(negated_conjecture,[status(cth)],[f20]) ).
fof(f20_nnf,plain,
? [U] :
( ? [X] :
! [Y,Z] :
( ~ strictly_less_than(Y,Z)
| ~ pair_in_list(update_slb(U,X),Y,Z) )
& ? [V,W] :
( strictly_less_than(V,W)
& pair_in_list(U,V,W) ) ),
inference(nnf_transformation,[status(thm)],[f20_neg]) ).
fof(f20_sk,plain,
! [Y,Z] :
( ( ~ strictly_less_than(Y,Z)
| ~ pair_in_list(update_slb(sk0,sk3),Y,Z) )
& strictly_less_than(sk1,sk2)
& pair_in_list(sk0,sk1,sk2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1,sk2,sk3])],[f20_nnf]) ).
cnf(c27,plain,
pair_in_list(sk0,sk1,sk2),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(p218,plain,
( pair_in_list(update_slb(sk0,X0),sk1,X0)
| ~ strictly_less_than(sk2,X0) ),
inference(resolution,[status(thm)],[c26,c27]) ).
cnf(p2792,plain,
( pair_in_list(update_slb(sk0,X0),sk1,X0)
| less_than(X0,sk2) ),
inference(resolution,[status(thm)],[p276,p218]) ).
cnf(c29,plain,
( ~ strictly_less_than(X4,X5)
| ~ pair_in_list(update_slb(sk0,sk3),X4,X5) ),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(p2825,plain,
( ~ strictly_less_than(sk1,sk3)
| less_than(sk3,sk2) ),
inference(resolution,[status(thm)],[p2792,c29]) ).
cnf(p2829,plain,
( less_than(sk3,sk1)
| less_than(sk3,sk2) ),
inference(resolution,[status(thm)],[p2825,p276]) ).
fof(f18,lemma,
! [U,V,W,X] :
( ( less_than(X,W)
& pair_in_list(U,V,W) )
=> pair_in_list(update_slb(U,X),V,W) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l35_li3637) ).
fof(f18_nnf,plain,
! [U,V,W,X] :
( pair_in_list(update_slb(U,X),V,W)
| ~ less_than(X,W)
| ~ pair_in_list(U,V,W) ),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
! [U,V,W,X] :
( pair_in_list(update_slb(U,X),V,W)
| ~ less_than(X,W)
| ~ pair_in_list(U,V,W) ),
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c25,plain,
( pair_in_list(update_slb(X0,X3),X1,X2)
| ~ less_than(X3,X2)
| ~ pair_in_list(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(p195,plain,
( pair_in_list(update_slb(sk0,X0),sk1,sk2)
| ~ less_than(X0,sk2) ),
inference(resolution,[status(thm)],[c25,c27]) ).
cnf(p2832,plain,
( pair_in_list(update_slb(sk0,sk3),sk1,sk2)
| less_than(sk3,sk1) ),
inference(resolution,[status(thm)],[p2829,p195]) ).
cnf(p2866,plain,
( ~ strictly_less_than(sk1,sk2)
| less_than(sk3,sk1) ),
inference(resolution,[status(thm)],[p2832,c29]) ).
cnf(c28,plain,
strictly_less_than(sk1,sk2),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(p2909,plain,
less_than(sk3,sk1),
inference(resolution,[status(thm)],[p2866,c28]) ).
cnf(p202,plain,
( less_than(sk2,X0)
| pair_in_list(update_slb(sk0,X0),sk1,sk2) ),
inference(resolution,[status(thm)],[p195,c1]) ).
cnf(p226,plain,
( ~ strictly_less_than(sk1,sk2)
| less_than(sk2,sk3) ),
inference(resolution,[status(thm)],[p202,c29]) ).
cnf(p230,plain,
less_than(sk2,sk3),
inference(resolution,[status(thm)],[p226,c28]) ).
fof(f0,axiom,
! [U,V,W] :
( ( less_than(V,W)
& less_than(U,V) )
=> less_than(U,W) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity) ).
fof(f0_nnf,plain,
! [U,V,W] :
( less_than(U,W)
| ~ less_than(V,W)
| ~ less_than(U,V) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [U,V,W] :
( less_than(U,W)
| ~ less_than(V,W)
| ~ less_than(U,V) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( less_than(X0,X2)
| ~ less_than(X1,X2)
| ~ less_than(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p231,plain,
( less_than(sk2,X0)
| ~ less_than(sk3,X0) ),
inference(resolution,[status(thm)],[p230,c0]) ).
cnf(p2913,plain,
less_than(sk2,sk1),
inference(resolution,[status(thm)],[p2909,p231]) ).
cnf(c4,plain,
( ~ less_than(X1,X0)
| ~ strictly_less_than(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p33,plain,
~ less_than(sk2,sk1),
inference(resolution,[status(thm)],[c4,c28]) ).
cnf(p2917,plain,
$false,
inference(resolution,[status(thm)],[p2913,p33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWV399+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.07 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/0.42 % Computer : n011.cluster.edu
% 0.17/0.42 % Model : x86_64 x86_64
% 0.17/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.42 % Memory : 8046.5625MB
% 0.17/0.42 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Thu Sep 24 19:28:58 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.43 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 48.01/6.59 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 48.01/6.59 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------