%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWV408+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 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 : Thu Sep 24 02:47:36 PM UTC 2026
% Result : Theorem 0.09s 0.38s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 33 ( 5 unt; 0 def)
% Number of atoms : 94 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 105 ( 44 ~; 35 |; 20 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 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 : 81 ( 69 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [U,V] :
( less_than(V,U)
| less_than(U,V) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [U,V] :
( strictly_less_than(U,V)
<=> ( ~ less_than(V,U)
& less_than(U,V) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f42,lemma,
! [U,V] :
( contains_slb(U,V)
=> ? [W] : pair_in_list(U,V,W) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f43,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') ).
fof(f44,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') ).
fof(f45,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/sandbox2/benchmark/theBenchmark.p') ).
fof(f46,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)],[f45]) ).
fof(f50,plain,
! [X0,X1] :
( less_than(X1,X0)
| less_than(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f52,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)],[f4]) ).
fof(f53,plain,
( ! [U,V] :
( less_than(V,U)
| ~ less_than(U,V)
| strictly_less_than(U,V) )
& ! [U,V] :
( ( ~ less_than(V,U)
& less_than(U,V) )
| ~ strictly_less_than(U,V) ) ),
inference(miniscoping,[status(thm)],[f52]) ).
fof(f56,plain,
! [X0,X1] :
( less_than(X1,X0)
| ~ less_than(X0,X1)
| strictly_less_than(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f53]) ).
fof(f147,plain,
! [U,V] :
( ? [W] : pair_in_list(U,V,W)
| ~ contains_slb(U,V) ),
inference(pre_NNF_transformation,[status(thm)],[f42]) ).
fof(f148,plain,
! [U,V] :
( pair_in_list(U,V,sK0_skl(V,U))
| ~ contains_slb(U,V) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(W,sK0_skl(V,U))],[f147]) ).
fof(f149,plain,
! [X0,X1] :
( pair_in_list(X0,X1,sK0_skl(X1,X0))
| ~ contains_slb(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f148]) ).
fof(f150,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(pre_NNF_transformation,[status(thm)],[f43]) ).
fof(f151,plain,
! [U,V,X] :
( pair_in_list(update_slb(U,X),V,X)
| ! [W] :
( ~ strictly_less_than(W,X)
| ~ pair_in_list(U,V,W) ) ),
inference(miniscoping,[status(thm)],[f150]) ).
fof(f152,plain,
! [X0,X1,X2,X3] :
( pair_in_list(update_slb(X0,X3),X1,X3)
| ~ strictly_less_than(X2,X3)
| ~ pair_in_list(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f151]) ).
fof(f153,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(pre_NNF_transformation,[status(thm)],[f44]) ).
fof(f154,plain,
! [X0,X1,X2,X3] :
( pair_in_list(update_slb(X0,X3),X1,X2)
| ~ less_than(X3,X2)
| ~ pair_in_list(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f153]) ).
fof(f155,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(pre_NNF_transformation,[status(thm)],[f46]) ).
fof(f156,plain,
? [U,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))
& ? [W] : strictly_less_than(X,findmin_cpq_res(triple(U,V,W)))
& contains_slb(V,X) ),
inference(miniscoping,[status(thm)],[f155]) ).
fof(f157,plain,
( ! [Y] :
( ~ less_than(findmin_pqp_res(sK1_skl),Y)
| ~ pair_in_list(update_slb(sK2_skl,findmin_pqp_res(sK1_skl)),sK3_skl,Y) )
& ~ pair_in_list(update_slb(sK2_skl,findmin_pqp_res(sK1_skl)),sK3_skl,findmin_pqp_res(sK1_skl))
& strictly_less_than(sK3_skl,findmin_cpq_res(triple(sK1_skl,sK2_skl,sK4_skl)))
& contains_slb(sK2_skl,sK3_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl,sK2_skl,sK3_skl,sK4_skl]),skolemize(U,sK1_skl),skolemize(V,sK2_skl),skolemize(X,sK3_skl),skolemize(W,sK4_skl)],[f156]) ).
fof(f158,plain,
contains_slb(sK2_skl,sK3_skl),
inference(cnf_transformation,[status(thm)],[f157]) ).
fof(f160,plain,
~ pair_in_list(update_slb(sK2_skl,findmin_pqp_res(sK1_skl)),sK3_skl,findmin_pqp_res(sK1_skl)),
inference(cnf_transformation,[status(thm)],[f157]) ).
fof(f161,plain,
! [X0] :
( ~ less_than(findmin_pqp_res(sK1_skl),X0)
| ~ pair_in_list(update_slb(sK2_skl,findmin_pqp_res(sK1_skl)),sK3_skl,X0) ),
inference(cnf_transformation,[status(thm)],[f157]) ).
fof(f169,plain,
! [X0,X1] :
( less_than(X1,X0)
| strictly_less_than(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f56,f50]) ).
fof(f420,plain,
! [X0] :
( ~ strictly_less_than(X0,findmin_pqp_res(sK1_skl))
| ~ pair_in_list(sK2_skl,sK3_skl,X0) ),
inference(resolution,[status(thm)],[f152,f160]) ).
fof(f431,plain,
! [X0] :
( ~ less_than(findmin_pqp_res(sK1_skl),X0)
| ~ less_than(findmin_pqp_res(sK1_skl),X0)
| ~ pair_in_list(sK2_skl,sK3_skl,X0) ),
inference(resolution,[status(thm)],[f154,f161]) ).
fof(f437,plain,
! [X0] :
( ~ less_than(findmin_pqp_res(sK1_skl),X0)
| ~ pair_in_list(sK2_skl,sK3_skl,X0) ),
inference(duplicate_literals_removal,[status(thm)],[f431]) ).
fof(f919,plain,
! [X0] :
( strictly_less_than(X0,findmin_pqp_res(sK1_skl))
| ~ pair_in_list(sK2_skl,sK3_skl,X0) ),
inference(resolution,[status(thm)],[f437,f169]) ).
fof(f928,plain,
! [X0] : ~ pair_in_list(sK2_skl,sK3_skl,X0),
inference(forward_subsumption_resolution,[status(thm)],[f919,f420]) ).
fof(f929,plain,
~ contains_slb(sK2_skl,sK3_skl),
inference(resolution,[status(thm)],[f928,f149]) ).
fof(f930,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f929,f158]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV408+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.34 % Computer : n010.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.34 % CPULimit : 300
% 0.09/0.34 % WCLimit : 300
% 0.09/0.34 % DateTime : Mon Sep 21 08:45:25 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.36 % Drodi V4.1.1
% 0.09/0.38 % Refutation found
% 0.09/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.42 % Elapsed time: 0.060499 seconds
% 0.15/0.42 % CPU time: 0.158376 seconds
% 0.15/0.42 % Total memory used: 31.214 MB
% 0.15/0.42 % Net memory used: 31.037 MB
%------------------------------------------------------------------------------