%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SWV408+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n005.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 03:13:10 PM UTC 2026
% Result : Theorem 65.86s 10.10s
% Output : Proof 65.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 6
% Syntax : Number of formulae : 40 ( 8 unt; 0 def)
% Number of atoms : 102 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 99 ( 37 ~; 39 |; 17 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-3 aty)
% Number of variables : 78 ( 0 sgn 52 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f43,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/sandbox/benchmark/theBenchmark.p',l49_li3637) ).
fof(f43_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)],[f43]) ).
fof(f43_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)],[f43_nnf]) ).
cnf(c54,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)],[f43_sk]) ).
fof(f41,lemma,
! [U,V] :
( contains_slb(U,V)
=> ? [W] : pair_in_list(U,V,W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l45_li4647) ).
fof(f41_nnf,plain,
! [U,V] :
( ? [W] : pair_in_list(U,V,W)
| ~ contains_slb(U,V) ),
inference(nnf_transformation,[status(thm)],[f41]) ).
fof(f41_sk,plain,
! [U,V] :
( pair_in_list(U,V,sk0(U,V))
| ~ contains_slb(U,V) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f41_nnf]) ).
cnf(c52,plain,
( pair_in_list(X0,X1,sk0(X0,X1))
| ~ contains_slb(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f41_sk]) ).
fof(f44,conjecture,
! [U,V,W,X] :
( ( strictly_less_than(X,findmin_cpq_res(triple(U,V,W)))
& contains_slb(V,X) )
=> ( ? [Y] :
( less_than(findmin_pqp_res(U),Y)
& pair_in_list(update_slb(V,findmin_pqp_res(U)),X,Y) )
| pair_in_list(update_slb(V,findmin_pqp_res(U)),X,findmin_pqp_res(U)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l44_co) ).
fof(f44_neg,negated_conjecture,
~ ! [U,V,W,X] :
( ( strictly_less_than(X,findmin_cpq_res(triple(U,V,W)))
& contains_slb(V,X) )
=> ( ? [Y] :
( less_than(findmin_pqp_res(U),Y)
& pair_in_list(update_slb(V,findmin_pqp_res(U)),X,Y) )
| pair_in_list(update_slb(V,findmin_pqp_res(U)),X,findmin_pqp_res(U)) ) ),
inference(negated_conjecture,[status(cth)],[f44]) ).
fof(f44_nnf,plain,
? [U,V,W,X] :
( ! [Y] :
( ~ less_than(findmin_pqp_res(U),Y)
| ~ pair_in_list(update_slb(V,findmin_pqp_res(U)),X,Y) )
& ~ pair_in_list(update_slb(V,findmin_pqp_res(U)),X,findmin_pqp_res(U))
& strictly_less_than(X,findmin_cpq_res(triple(U,V,W)))
& contains_slb(V,X) ),
inference(nnf_transformation,[status(thm)],[f44_neg]) ).
fof(f44_sk,plain,
! [Y] :
( ( ~ less_than(findmin_pqp_res(sk1),Y)
| ~ pair_in_list(update_slb(sk2,findmin_pqp_res(sk1)),sk4,Y) )
& ~ pair_in_list(update_slb(sk2,findmin_pqp_res(sk1)),sk4,findmin_pqp_res(sk1))
& strictly_less_than(sk4,findmin_cpq_res(triple(sk1,sk2,sk3)))
& contains_slb(sk2,sk4) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1,sk2,sk3,sk4])],[f44_nnf]) ).
cnf(c55,plain,
contains_slb(sk2,sk4),
inference(cnf_transformation,[status(esa)],[f44_sk]) ).
cnf(p789,plain,
pair_in_list(sk2,sk4,sk0(sk2,sk4)),
inference(resolution,[status(thm)],[c52,c55]) ).
cnf(p860,plain,
( pair_in_list(update_slb(sk2,X0),sk4,sk0(sk2,sk4))
| ~ less_than(X0,sk0(sk2,sk4)) ),
inference(resolution,[status(thm)],[c54,p789]) ).
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(p867,plain,
( less_than(sk0(sk2,sk4),X0)
| pair_in_list(update_slb(sk2,X0),sk4,sk0(sk2,sk4)) ),
inference(resolution,[status(thm)],[p860,c1]) ).
cnf(c58,plain,
( ~ less_than(findmin_pqp_res(sk1),X4)
| ~ pair_in_list(update_slb(sk2,findmin_pqp_res(sk1)),sk4,X4) ),
inference(cnf_transformation,[status(esa)],[f44_sk]) ).
cnf(p906,plain,
( ~ less_than(findmin_pqp_res(sk1),sk0(sk2,sk4))
| less_than(sk0(sk2,sk4),findmin_pqp_res(sk1)) ),
inference(resolution,[status(thm)],[p867,c58]) ).
cnf(p910,plain,
( less_than(sk0(sk2,sk4),findmin_pqp_res(sk1))
| less_than(sk0(sk2,sk4),findmin_pqp_res(sk1)) ),
inference(resolution,[status(thm)],[p906,c1]) ).
cnf(p927,plain,
less_than(sk0(sk2,sk4),findmin_pqp_res(sk1)),
inference(factoring,[status(thm)],[p910]) ).
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]) ).
cnf(p931,plain,
( less_than(findmin_pqp_res(sk1),sk0(sk2,sk4))
| strictly_less_than(sk0(sk2,sk4),findmin_pqp_res(sk1)) ),
inference(resolution,[status(thm)],[p927,c5]) ).
fof(f42,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/sandbox/benchmark/theBenchmark.p',l48_li3839) ).
fof(f42_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)],[f42]) ).
fof(f42_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)],[f42_nnf]) ).
cnf(c53,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)],[f42_sk]) ).
cnf(p816,plain,
( pair_in_list(update_slb(sk2,X0),sk4,X0)
| ~ strictly_less_than(sk0(sk2,sk4),X0) ),
inference(resolution,[status(thm)],[c53,p789]) ).
cnf(p985,plain,
( pair_in_list(update_slb(sk2,findmin_pqp_res(sk1)),sk4,findmin_pqp_res(sk1))
| less_than(findmin_pqp_res(sk1),sk0(sk2,sk4)) ),
inference(resolution,[status(thm)],[p931,p816]) ).
cnf(c57,plain,
~ pair_in_list(update_slb(sk2,findmin_pqp_res(sk1)),sk4,findmin_pqp_res(sk1)),
inference(cnf_transformation,[status(esa)],[f44_sk]) ).
cnf(p1040,plain,
less_than(findmin_pqp_res(sk1),sk0(sk2,sk4)),
inference(resolution,[status(thm)],[p985,c57]) ).
cnf(p1052,plain,
pair_in_list(update_slb(sk2,findmin_pqp_res(sk1)),sk4,sk0(sk2,sk4)),
inference(resolution,[status(thm)],[p1040,p860]) ).
cnf(p1059,plain,
~ less_than(findmin_pqp_res(sk1),sk0(sk2,sk4)),
inference(resolution,[status(thm)],[p1052,c58]) ).
cnf(p1066,plain,
$false,
inference(resolution,[status(thm)],[p1059,p1040]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV408+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.35 % Computer : n005.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Thu Sep 24 19:30:17 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 65.86/10.10 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 65.86/10.10 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------