%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWV055+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.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 02:46:32 PM UTC 2026
% Result : Theorem 1.33s 0.61s
% Output : CNFRefutation 1.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 8
% Syntax : Number of formulae : 56 ( 19 unt; 1 def)
% Number of atoms : 191 ( 30 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 209 ( 74 ~; 75 |; 49 &)
% ( 2 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 7 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 22 ( 22 usr; 13 con; 0-3 aty)
% Number of variables : 80 ( 68 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X] : ~ gt(X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X,Y,Z] :
( ( leq(Y,Z)
& leq(X,Y) )
=> leq(X,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [X,Y] :
( leq(X,Y)
<=> gt(succ(Y),X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,axiom,
succ(tptp_minus_1) = n0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f39,axiom,
! [X] : minus(X,n1) = pred(X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f40,axiom,
! [X] : pred(succ(X)) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f53,conjecture,
( ( ! [A,B] :
( ( leq(A,minus(pv10,n1))
& leq(n0,A) )
=> sum(n0,minus(n5,n1),a_select3(q,A,B)) = n1 )
& leq(pv10,minus(n135300,n1))
& leq(n0,pv10) )
=> ( ! [E,F] :
( ( leq(E,minus(pv10,n1))
& leq(n0,E) )
=> sum(n0,minus(n5,n1),a_select3(q,E,F)) = n1 )
& ! [C,D] :
( ( leq(C,minus(n0,n1))
& leq(n0,C) )
=> a_select3(q,pv10,C) = divide(sqrt(times(minus(a_select3(center,C,n0),a_select2(x,pv10)),minus(a_select3(center,C,n0),a_select2(x,pv10)))),sum(n0,minus(n5,n1),sqrt(times(minus(a_select3(center,D,n0),a_select2(x,pv10)),minus(a_select3(center,D,n0),a_select2(x,pv10)))))) )
& leq(pv10,minus(n135300,n1))
& leq(n0,pv10) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f54,negated_conjecture,
~ ( ( ! [A,B] :
( ( leq(A,minus(pv10,n1))
& leq(n0,A) )
=> sum(n0,minus(n5,n1),a_select3(q,A,B)) = n1 )
& leq(pv10,minus(n135300,n1))
& leq(n0,pv10) )
=> ( ! [E,F] :
( ( leq(E,minus(pv10,n1))
& leq(n0,E) )
=> sum(n0,minus(n5,n1),a_select3(q,E,F)) = n1 )
& ! [C,D] :
( ( leq(C,minus(n0,n1))
& leq(n0,C) )
=> a_select3(q,pv10,C) = divide(sqrt(times(minus(a_select3(center,C,n0),a_select2(x,pv10)),minus(a_select3(center,C,n0),a_select2(x,pv10)))),sum(n0,minus(n5,n1),sqrt(times(minus(a_select3(center,D,n0),a_select2(x,pv10)),minus(a_select3(center,D,n0),a_select2(x,pv10)))))) )
& leq(pv10,minus(n135300,n1))
& leq(n0,pv10) ) ),
inference(negated_conjecture,[status(cth)],[f53]) ).
fof(f98,plain,
! [X0] : ~ gt(X0,X0),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f100,plain,
! [X,Y,Z] :
( leq(X,Z)
| ~ leq(Y,Z)
| ~ leq(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f101,plain,
! [X,Z] :
( leq(X,Z)
| ! [Y] :
( ~ leq(Y,Z)
| ~ leq(X,Y) ) ),
inference(miniscoping,[status(thm)],[f100]) ).
fof(f102,plain,
! [X0,X1,X2] :
( leq(X0,X2)
| ~ leq(X1,X2)
| ~ leq(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f101]) ).
fof(f122,plain,
! [X,Y] :
( ( ~ gt(succ(Y),X)
| leq(X,Y) )
& ( gt(succ(Y),X)
| ~ leq(X,Y) ) ),
inference(NNF_transformation,[status(thm)],[f13]) ).
fof(f123,plain,
( ! [X,Y] :
( ~ gt(succ(Y),X)
| leq(X,Y) )
& ! [X,Y] :
( gt(succ(Y),X)
| ~ leq(X,Y) ) ),
inference(miniscoping,[status(thm)],[f122]) ).
fof(f124,plain,
! [X0,X1] :
( gt(succ(X1),X0)
| ~ leq(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f123]) ).
fof(f206,plain,
succ(tptp_minus_1) = n0,
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f217,plain,
! [X0] : minus(X0,n1) = pred(X0),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f218,plain,
! [X0] : pred(succ(X0)) = X0,
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f251,plain,
( ( ? [E,F] :
( sum(n0,minus(n5,n1),a_select3(q,E,F)) != n1
& leq(E,minus(pv10,n1))
& leq(n0,E) )
| ? [C,D] :
( a_select3(q,pv10,C) != divide(sqrt(times(minus(a_select3(center,C,n0),a_select2(x,pv10)),minus(a_select3(center,C,n0),a_select2(x,pv10)))),sum(n0,minus(n5,n1),sqrt(times(minus(a_select3(center,D,n0),a_select2(x,pv10)),minus(a_select3(center,D,n0),a_select2(x,pv10))))))
& leq(C,minus(n0,n1))
& leq(n0,C) )
| ~ leq(pv10,minus(n135300,n1))
| ~ leq(n0,pv10) )
& ! [A,B] :
( sum(n0,minus(n5,n1),a_select3(q,A,B)) = n1
| ~ leq(A,minus(pv10,n1))
| ~ leq(n0,A) )
& leq(pv10,minus(n135300,n1))
& leq(n0,pv10) ),
inference(pre_NNF_transformation,[status(thm)],[f54]) ).
fof(f252,definition,
! [C,D] :
( sP3_prd(D,C)
<=> ( a_select3(q,pv10,C) != divide(sqrt(times(minus(a_select3(center,C,n0),a_select2(x,pv10)),minus(a_select3(center,C,n0),a_select2(x,pv10)))),sum(n0,minus(n5,n1),sqrt(times(minus(a_select3(center,D,n0),a_select2(x,pv10)),minus(a_select3(center,D,n0),a_select2(x,pv10))))))
& leq(C,minus(n0,n1))
& leq(n0,C) ) ),
introduced(definition,[new_symbols(definition,[sP3_prd])],[]) ).
fof(f253,plain,
( ( ? [E,F] :
( sum(n0,minus(n5,n1),a_select3(q,E,F)) != n1
& leq(E,minus(pv10,n1))
& leq(n0,E) )
| ? [C,D] : sP3_prd(D,C)
| ~ leq(pv10,minus(n135300,n1))
| ~ leq(n0,pv10) )
& ! [A,B] :
( sum(n0,minus(n5,n1),a_select3(q,A,B)) = n1
| ~ leq(A,minus(pv10,n1))
| ~ leq(n0,A) )
& leq(pv10,minus(n135300,n1))
& leq(n0,pv10) ),
inference(formula_renaming,[status(thm)],[f251,f252]) ).
fof(f254,plain,
( ( ? [E] :
( ? [F] : sum(n0,minus(n5,n1),a_select3(q,E,F)) != n1
& leq(E,minus(pv10,n1))
& leq(n0,E) )
| ? [C,D] : sP3_prd(D,C)
| ~ leq(pv10,minus(n135300,n1))
| ~ leq(n0,pv10) )
& ! [A] :
( ! [B] : sum(n0,minus(n5,n1),a_select3(q,A,B)) = n1
| ~ leq(A,minus(pv10,n1))
| ~ leq(n0,A) )
& leq(pv10,minus(n135300,n1))
& leq(n0,pv10) ),
inference(miniscoping,[status(thm)],[f253]) ).
fof(f255,plain,
( ( ( sum(n0,minus(n5,n1),a_select3(q,sK25_skl,sK26_skl)) != n1
& leq(sK25_skl,minus(pv10,n1))
& leq(n0,sK25_skl) )
| sP3_prd(sK24_skl,sK23_skl)
| ~ leq(pv10,minus(n135300,n1))
| ~ leq(n0,pv10) )
& ! [A] :
( ! [B] : sum(n0,minus(n5,n1),a_select3(q,A,B)) = n1
| ~ leq(A,minus(pv10,n1))
| ~ leq(n0,A) )
& leq(pv10,minus(n135300,n1))
& leq(n0,pv10) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK23_skl,sK24_skl,sK25_skl,sK26_skl]),skolemize(C,sK23_skl),skolemize(D,sK24_skl),skolemize(E,sK25_skl),skolemize(F,sK26_skl)],[f254]) ).
fof(f256,plain,
leq(n0,pv10),
inference(cnf_transformation,[status(thm)],[f255]) ).
fof(f257,plain,
leq(pv10,minus(n135300,n1)),
inference(cnf_transformation,[status(thm)],[f255]) ).
fof(f258,plain,
! [X0,X1] :
( sum(n0,minus(n5,n1),a_select3(q,X0,X1)) = n1
| ~ leq(X0,minus(pv10,n1))
| ~ leq(n0,X0) ),
inference(cnf_transformation,[status(thm)],[f255]) ).
fof(f259,plain,
( leq(n0,sK25_skl)
| sP3_prd(sK24_skl,sK23_skl)
| ~ leq(pv10,minus(n135300,n1))
| ~ leq(n0,pv10) ),
inference(cnf_transformation,[status(thm)],[f255]) ).
fof(f260,plain,
( leq(sK25_skl,minus(pv10,n1))
| sP3_prd(sK24_skl,sK23_skl)
| ~ leq(pv10,minus(n135300,n1))
| ~ leq(n0,pv10) ),
inference(cnf_transformation,[status(thm)],[f255]) ).
fof(f261,plain,
( sum(n0,minus(n5,n1),a_select3(q,sK25_skl,sK26_skl)) != n1
| sP3_prd(sK24_skl,sK23_skl)
| ~ leq(pv10,minus(n135300,n1))
| ~ leq(n0,pv10) ),
inference(cnf_transformation,[status(thm)],[f255]) ).
fof(f335,plain,
! [C,D] :
( ( a_select3(q,pv10,C) = divide(sqrt(times(minus(a_select3(center,C,n0),a_select2(x,pv10)),minus(a_select3(center,C,n0),a_select2(x,pv10)))),sum(n0,minus(n5,n1),sqrt(times(minus(a_select3(center,D,n0),a_select2(x,pv10)),minus(a_select3(center,D,n0),a_select2(x,pv10))))))
| ~ leq(C,minus(n0,n1))
| ~ leq(n0,C)
| sP3_prd(D,C) )
& ( ( a_select3(q,pv10,C) != divide(sqrt(times(minus(a_select3(center,C,n0),a_select2(x,pv10)),minus(a_select3(center,C,n0),a_select2(x,pv10)))),sum(n0,minus(n5,n1),sqrt(times(minus(a_select3(center,D,n0),a_select2(x,pv10)),minus(a_select3(center,D,n0),a_select2(x,pv10))))))
& leq(C,minus(n0,n1))
& leq(n0,C) )
| ~ sP3_prd(D,C) ) ),
inference(NNF_transformation,[status(thm)],[f252]) ).
fof(f336,plain,
( ! [C,D] :
( a_select3(q,pv10,C) = divide(sqrt(times(minus(a_select3(center,C,n0),a_select2(x,pv10)),minus(a_select3(center,C,n0),a_select2(x,pv10)))),sum(n0,minus(n5,n1),sqrt(times(minus(a_select3(center,D,n0),a_select2(x,pv10)),minus(a_select3(center,D,n0),a_select2(x,pv10))))))
| ~ leq(C,minus(n0,n1))
| ~ leq(n0,C)
| sP3_prd(D,C) )
& ! [C,D] :
( ( a_select3(q,pv10,C) != divide(sqrt(times(minus(a_select3(center,C,n0),a_select2(x,pv10)),minus(a_select3(center,C,n0),a_select2(x,pv10)))),sum(n0,minus(n5,n1),sqrt(times(minus(a_select3(center,D,n0),a_select2(x,pv10)),minus(a_select3(center,D,n0),a_select2(x,pv10))))))
& leq(C,minus(n0,n1))
& leq(n0,C) )
| ~ sP3_prd(D,C) ) ),
inference(miniscoping,[status(thm)],[f335]) ).
fof(f337,plain,
! [X0,X1] :
( leq(n0,X1)
| ~ sP3_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f336]) ).
fof(f338,plain,
! [X0,X1] :
( leq(X1,minus(n0,n1))
| ~ sP3_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f336]) ).
fof(f357,plain,
pred(n0) = tptp_minus_1,
inference(paramodulation,[status(thm)],[f206,f218]) ).
fof(f377,plain,
( leq(n0,sK25_skl)
| sP3_prd(sK24_skl,sK23_skl)
| ~ leq(pv10,minus(n135300,n1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f259,f256]) ).
fof(f378,plain,
( leq(n0,sK25_skl)
| sP3_prd(sK24_skl,sK23_skl) ),
inference(resolution,[status(thm)],[f377,f257]) ).
fof(f393,plain,
( leq(sK25_skl,minus(pv10,n1))
| sP3_prd(sK24_skl,sK23_skl)
| ~ leq(pv10,minus(n135300,n1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f260,f256]) ).
fof(f409,plain,
( sum(n0,minus(n5,n1),a_select3(q,sK25_skl,sK26_skl)) != n1
| sP3_prd(sK24_skl,sK23_skl)
| ~ leq(pv10,minus(n135300,n1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f261,f256]) ).
fof(f410,plain,
( ~ leq(sK25_skl,minus(pv10,n1))
| ~ leq(n0,sK25_skl)
| sP3_prd(sK24_skl,sK23_skl)
| ~ leq(pv10,minus(n135300,n1)) ),
inference(resolution,[status(thm)],[f409,f258]) ).
fof(f411,plain,
( ~ leq(sK25_skl,minus(pv10,n1))
| ~ leq(n0,sK25_skl)
| sP3_prd(sK24_skl,sK23_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f410,f257]) ).
fof(f558,plain,
! [X0] : ~ leq(succ(X0),X0),
inference(resolution,[status(thm)],[f124,f98]) ).
fof(f830,plain,
~ leq(n0,tptp_minus_1),
inference(paramodulation,[status(thm)],[f206,f558]) ).
fof(f889,plain,
! [X0,X1] :
( leq(X1,pred(n0))
| ~ sP3_prd(X0,X1) ),
inference(backward_demodulation,[status(thm)],[f217,f338]) ).
fof(f893,plain,
( leq(sK25_skl,pred(pv10))
| sP3_prd(sK24_skl,sK23_skl)
| ~ leq(pv10,minus(n135300,n1)) ),
inference(backward_demodulation,[status(thm)],[f217,f393]) ).
fof(f895,plain,
leq(pv10,pred(n135300)),
inference(backward_demodulation,[status(thm)],[f217,f257]) ).
fof(f903,plain,
! [X0,X1] :
( leq(X1,tptp_minus_1)
| ~ sP3_prd(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f357,f889]) ).
fof(f906,plain,
( leq(sK25_skl,pred(pv10))
| sP3_prd(sK24_skl,sK23_skl)
| ~ leq(pv10,pred(n135300)) ),
inference(forward_demodulation,[status(thm)],[f217,f893]) ).
fof(f1093,plain,
( leq(sK25_skl,pred(pv10))
| sP3_prd(sK24_skl,sK23_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f906,f895]) ).
fof(f1236,plain,
( ~ leq(sK25_skl,pred(pv10))
| ~ leq(n0,sK25_skl)
| sP3_prd(sK24_skl,sK23_skl) ),
inference(forward_demodulation,[status(thm)],[f217,f411]) ).
fof(f1237,plain,
sP3_prd(sK24_skl,sK23_skl),
inference(backward_subsumption_resolution,[status(thm)],[f1093,f1238]) ).
fof(f1238,plain,
( ~ leq(sK25_skl,pred(pv10))
| sP3_prd(sK24_skl,sK23_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f1236,f378]) ).
fof(f1267,plain,
leq(sK23_skl,tptp_minus_1),
inference(resolution,[status(thm)],[f1237,f903]) ).
fof(f1268,plain,
leq(n0,sK23_skl),
inference(resolution,[status(thm)],[f1237,f337]) ).
fof(f1295,plain,
! [X0] :
( leq(X0,tptp_minus_1)
| ~ leq(X0,sK23_skl) ),
inference(resolution,[status(thm)],[f1267,f102]) ).
fof(f1858,plain,
leq(n0,tptp_minus_1),
inference(resolution,[status(thm)],[f1295,f1268]) ).
fof(f1863,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f1858,f830]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV055+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n018.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 : Mon Sep 21 08:31:13 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.13/0.37 % Drodi V4.1.1
% 1.33/0.61 % Refutation found
% 1.33/0.61 % SZS status Theorem for theBenchmark: Theorem is valid
% 1.33/0.61 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.33/0.64 % Elapsed time: 0.277755 seconds
% 1.33/0.64 % CPU time: 1.847577 seconds
% 1.33/0.64 % Total memory used: 131.992 MB
% 1.33/0.64 % Net memory used: 128.982 MB
%------------------------------------------------------------------------------