%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWV390+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n019.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 02:47:33 PM UTC 2026
% Result : Theorem 0.09s 0.42s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 31 ( 11 unt; 0 def)
% Number of atoms : 76 ( 2 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 82 ( 37 ~; 27 |; 10 &)
% ( 4 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-3 aty)
% Number of variables : 111 ( 103 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [U] : less_than(bottom,U),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,axiom,
! [U,V,W,X,Y] :
( less_than(Y,X)
=> ( check_cpq(triple(U,insert_slb(V,pair(X,Y)),W))
<=> check_cpq(triple(U,V,W)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,axiom,
! [U,V,W,X] : insert_cpq(triple(U,V,W),X) = triple(insert_pqp(U,X),insert_slb(V,pair(X,bottom)),W),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f42,lemma,
! [U,V,W] :
( check_cpq(triple(U,V,W))
<=> ! [X,Y] :
( pair_in_list(V,X,Y)
=> less_than(Y,X) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f43,conjecture,
! [U,V,W] :
( ~ check_cpq(triple(U,V,W))
=> ! [X] : ~ check_cpq(insert_cpq(triple(U,V,W),X)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f44,negated_conjecture,
~ ! [U,V,W] :
( ~ check_cpq(triple(U,V,W))
=> ! [X] : ~ check_cpq(insert_cpq(triple(U,V,W),X)) ),
inference(negated_conjecture,[status(cth)],[f43]) ).
fof(f55,plain,
! [X0] : less_than(bottom,X0),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f98,plain,
! [U,V,W,X,Y] :
( ( check_cpq(triple(U,insert_slb(V,pair(X,Y)),W))
<=> check_cpq(triple(U,V,W)) )
| ~ less_than(Y,X) ),
inference(pre_NNF_transformation,[status(thm)],[f25]) ).
fof(f99,plain,
! [U,V,W,X,Y] :
( ( ( ~ check_cpq(triple(U,V,W))
| check_cpq(triple(U,insert_slb(V,pair(X,Y)),W)) )
& ( check_cpq(triple(U,V,W))
| ~ check_cpq(triple(U,insert_slb(V,pair(X,Y)),W)) ) )
| ~ less_than(Y,X) ),
inference(NNF_transformation,[status(thm)],[f98]) ).
fof(f100,plain,
! [X,Y] :
( ( ! [U,V,W] :
( ~ check_cpq(triple(U,V,W))
| check_cpq(triple(U,insert_slb(V,pair(X,Y)),W)) )
& ! [U,V,W] :
( check_cpq(triple(U,V,W))
| ~ check_cpq(triple(U,insert_slb(V,pair(X,Y)),W)) ) )
| ~ less_than(Y,X) ),
inference(miniscoping,[status(thm)],[f99]) ).
fof(f101,plain,
! [X0,X1,X2,X3,X4] :
( check_cpq(triple(X2,X3,X4))
| ~ check_cpq(triple(X2,insert_slb(X3,pair(X1,X0)),X4))
| ~ less_than(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f100]) ).
fof(f119,plain,
! [X0,X1,X2,X3] : insert_cpq(triple(X0,X1,X2),X3) = triple(insert_pqp(X0,X3),insert_slb(X1,pair(X3,bottom)),X2),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f145,plain,
! [U,V,W] :
( check_cpq(triple(U,V,W))
<=> ! [X,Y] :
( less_than(Y,X)
| ~ pair_in_list(V,X,Y) ) ),
inference(pre_NNF_transformation,[status(thm)],[f42]) ).
fof(f146,plain,
! [U,V,W] :
( ( ? [X,Y] :
( ~ less_than(Y,X)
& pair_in_list(V,X,Y) )
| check_cpq(triple(U,V,W)) )
& ( ! [X,Y] :
( less_than(Y,X)
| ~ pair_in_list(V,X,Y) )
| ~ check_cpq(triple(U,V,W)) ) ),
inference(NNF_transformation,[status(thm)],[f145]) ).
fof(f147,plain,
( ! [V] :
( ? [X,Y] :
( ~ less_than(Y,X)
& pair_in_list(V,X,Y) )
| ! [U,W] : check_cpq(triple(U,V,W)) )
& ! [V] :
( ! [X,Y] :
( less_than(Y,X)
| ~ pair_in_list(V,X,Y) )
| ! [U,W] : ~ check_cpq(triple(U,V,W)) ) ),
inference(miniscoping,[status(thm)],[f146]) ).
fof(f148,plain,
( ! [V] :
( ( ~ less_than(sK1_skl(V),sK0_skl(V))
& pair_in_list(V,sK0_skl(V),sK1_skl(V)) )
| ! [U,W] : check_cpq(triple(U,V,W)) )
& ! [V] :
( ! [X,Y] :
( less_than(Y,X)
| ~ pair_in_list(V,X,Y) )
| ! [U,W] : ~ check_cpq(triple(U,V,W)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(X,sK0_skl(V)),skolemize(Y,sK1_skl(V))],[f147]) ).
fof(f149,plain,
! [X0,X1,X2,X3,X4] :
( less_than(X4,X3)
| ~ pair_in_list(X1,X3,X4)
| ~ check_cpq(triple(X0,X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f148]) ).
fof(f150,plain,
! [X0,X1,X2] :
( pair_in_list(X1,sK0_skl(X1),sK1_skl(X1))
| check_cpq(triple(X0,X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f148]) ).
fof(f151,plain,
! [X0,X1,X2] :
( ~ less_than(sK1_skl(X1),sK0_skl(X1))
| check_cpq(triple(X0,X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f148]) ).
fof(f152,plain,
? [U,V,W] :
( ? [X] : check_cpq(insert_cpq(triple(U,V,W),X))
& ~ check_cpq(triple(U,V,W)) ),
inference(pre_NNF_transformation,[status(thm)],[f44]) ).
fof(f153,plain,
( check_cpq(insert_cpq(triple(sK2_skl,sK3_skl,sK4_skl),sK5_skl))
& ~ check_cpq(triple(sK2_skl,sK3_skl,sK4_skl)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl,sK4_skl,sK5_skl]),skolemize(U,sK2_skl),skolemize(V,sK3_skl),skolemize(W,sK4_skl),skolemize(X,sK5_skl)],[f152]) ).
fof(f154,plain,
~ check_cpq(triple(sK2_skl,sK3_skl,sK4_skl)),
inference(cnf_transformation,[status(thm)],[f153]) ).
fof(f155,plain,
check_cpq(insert_cpq(triple(sK2_skl,sK3_skl,sK4_skl),sK5_skl)),
inference(cnf_transformation,[status(thm)],[f153]) ).
fof(f263,plain,
~ less_than(sK1_skl(sK3_skl),sK0_skl(sK3_skl)),
inference(resolution,[status(thm)],[f151,f154]) ).
fof(f318,plain,
! [X0,X1,X2,X3] :
( check_cpq(triple(insert_pqp(X1,X0),X2,X3))
| ~ check_cpq(insert_cpq(triple(X1,X2,X3),X0))
| ~ less_than(bottom,X0) ),
inference(paramodulation,[status(thm)],[f119,f101]) ).
fof(f327,plain,
! [X0,X1,X2,X3] :
( check_cpq(triple(insert_pqp(X0,X3),X1,X2))
| ~ check_cpq(insert_cpq(triple(X0,X1,X2),X3)) ),
inference(forward_subsumption_resolution,[status(thm)],[f318,f55]) ).
fof(f356,plain,
pair_in_list(sK3_skl,sK0_skl(sK3_skl),sK1_skl(sK3_skl)),
inference(resolution,[status(thm)],[f150,f154]) ).
fof(f360,plain,
! [X0,X1] :
( less_than(sK1_skl(sK3_skl),sK0_skl(sK3_skl))
| ~ check_cpq(triple(X0,sK3_skl,X1)) ),
inference(resolution,[status(thm)],[f356,f149]) ).
fof(f362,plain,
! [X0,X1] : ~ check_cpq(triple(X0,sK3_skl,X1)),
inference(forward_subsumption_resolution,[status(thm)],[f360,f263]) ).
fof(f375,plain,
! [X0,X1,X2] : ~ check_cpq(insert_cpq(triple(X0,sK3_skl,X1),X2)),
inference(resolution,[status(thm)],[f362,f327]) ).
fof(f379,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f155,f375]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV390+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n019.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 08:44:34 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 0.09/0.42 % Refutation found
% 0.09/0.42 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.45 % Elapsed time: 0.073600 seconds
% 0.09/0.45 % CPU time: 0.342446 seconds
% 0.09/0.45 % Total memory used: 105.544 MB
% 0.09/0.45 % Net memory used: 105.177 MB
%------------------------------------------------------------------------------