%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU141+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.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 02:19:21 PM UTC 2026
% Result : Theorem 3.79s 0.92s
% Output : CNFRefutation 3.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 49 ( 15 unt; 0 def)
% Number of atoms : 105 ( 55 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 95 ( 39 ~; 38 |; 11 &)
% ( 5 <=>; 1 =>; 0 <=; 1 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 70 ( 65 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [A,B] :
( A = B
<=> ( subset(B,A)
& subset(A,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [A,B] :
( disjoint(A,B)
<=> set_intersection2(A,B) = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,lemma,
! [A,B] :
( set_difference(A,B) = empty_set
<=> subset(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,axiom,
? [A] : empty(A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f39,lemma,
! [A,B] : subset(set_difference(A,B),A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f47,lemma,
! [A,B] : set_difference(A,set_difference(A,B)) = set_intersection2(A,B),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f52,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f55,conjecture,
! [A,B] :
( disjoint(A,B)
<=> set_difference(A,B) = A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f56,negated_conjecture,
~ ! [A,B] :
( disjoint(A,B)
<=> set_difference(A,B) = A ),
inference(negated_conjecture,[status(cth)],[f55]) ).
fof(f65,plain,
! [A,B] :
( ( ~ subset(B,A)
| ~ subset(A,B)
| A = B )
& ( ( subset(B,A)
& subset(A,B) )
| A != B ) ),
inference(NNF_transformation,[status(thm)],[f5]) ).
fof(f66,plain,
( ! [A,B] :
( ~ subset(B,A)
| ~ subset(A,B)
| A = B )
& ! [A,B] :
( ( subset(B,A)
& subset(A,B) )
| A != B ) ),
inference(miniscoping,[status(thm)],[f65]) ).
fof(f67,plain,
! [X0,X1] :
( subset(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f69,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f109,plain,
! [A,B] :
( ( set_intersection2(A,B) != empty_set
| disjoint(A,B) )
& ( set_intersection2(A,B) = empty_set
| ~ disjoint(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f11]) ).
fof(f110,plain,
( ! [A,B] :
( set_intersection2(A,B) != empty_set
| disjoint(A,B) )
& ! [A,B] :
( set_intersection2(A,B) = empty_set
| ~ disjoint(A,B) ) ),
inference(miniscoping,[status(thm)],[f109]) ).
fof(f111,plain,
! [X0,X1] :
( set_intersection2(X0,X1) = empty_set
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f110]) ).
fof(f112,plain,
! [X0,X1] :
( set_intersection2(X0,X1) != empty_set
| disjoint(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f110]) ).
fof(f131,plain,
! [A,B] :
( ( ~ subset(A,B)
| set_difference(A,B) = empty_set )
& ( subset(A,B)
| set_difference(A,B) != empty_set ) ),
inference(NNF_transformation,[status(thm)],[f23]) ).
fof(f132,plain,
( ! [A,B] :
( ~ subset(A,B)
| set_difference(A,B) = empty_set )
& ! [A,B] :
( subset(A,B)
| set_difference(A,B) != empty_set ) ),
inference(miniscoping,[status(thm)],[f131]) ).
fof(f133,plain,
! [X0,X1] :
( subset(X0,X1)
| set_difference(X0,X1) != empty_set ),
inference(cnf_transformation,[status(thm)],[f132]) ).
fof(f134,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| set_difference(X0,X1) = empty_set ),
inference(cnf_transformation,[status(thm)],[f132]) ).
fof(f135,plain,
empty(sK5_skl),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl]),skolemize(A,sK5_skl)],[f24]) ).
fof(f136,plain,
empty(sK5_skl),
inference(cnf_transformation,[status(thm)],[f135]) ).
fof(f167,plain,
! [X0,X1] : subset(set_difference(X0,X1),X0),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f185,plain,
! [X0,X1] : set_difference(X0,set_difference(X0,X1)) = set_intersection2(X0,X1),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f197,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f52]) ).
fof(f198,plain,
! [X0] :
( X0 = empty_set
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f197]) ).
fof(f203,plain,
? [A,B] :
( disjoint(A,B)
<~> set_difference(A,B) = A ),
inference(pre_NNF_transformation,[status(thm)],[f56]) ).
fof(f204,plain,
? [A,B] :
( ( set_difference(A,B) != A
| ~ disjoint(A,B) )
& ( set_difference(A,B) = A
| disjoint(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f203]) ).
fof(f205,plain,
( ( set_difference(sK10_skl,sK11_skl) != sK10_skl
| ~ disjoint(sK10_skl,sK11_skl) )
& ( set_difference(sK10_skl,sK11_skl) = sK10_skl
| disjoint(sK10_skl,sK11_skl) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10_skl,sK11_skl]),skolemize(A,sK10_skl),skolemize(B,sK11_skl)],[f204]) ).
fof(f206,plain,
( set_difference(sK10_skl,sK11_skl) = sK10_skl
| disjoint(sK10_skl,sK11_skl) ),
inference(cnf_transformation,[status(thm)],[f205]) ).
fof(f207,plain,
( set_difference(sK10_skl,sK11_skl) != sK10_skl
| ~ disjoint(sK10_skl,sK11_skl) ),
inference(cnf_transformation,[status(thm)],[f205]) ).
fof(f213,plain,
! [X0] : subset(X0,X0),
inference(destructive_equality_resolution,[status(thm)],[f67]) ).
fof(f230,plain,
( set_difference(sK10_skl,sK11_skl) = sK10_skl
| set_intersection2(sK10_skl,sK11_skl) = empty_set ),
inference(resolution,[status(thm)],[f111,f206]) ).
fof(f268,plain,
sK5_skl = empty_set,
inference(resolution,[status(thm)],[f198,f136]) ).
fof(f281,plain,
! [X0,X1] :
( set_intersection2(X0,X1) != sK5_skl
| disjoint(X0,X1) ),
inference(backward_demodulation,[status(thm)],[f268,f112]) ).
fof(f282,plain,
( set_difference(sK10_skl,sK11_skl) = sK10_skl
| set_intersection2(sK10_skl,sK11_skl) = sK5_skl ),
inference(backward_demodulation,[status(thm)],[f268,f230]) ).
fof(f298,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| set_difference(X0,X1) = sK5_skl ),
inference(backward_demodulation,[status(thm)],[f268,f134]) ).
fof(f299,plain,
! [X0,X1] :
( subset(X0,X1)
| set_difference(X0,X1) != sK5_skl ),
inference(backward_demodulation,[status(thm)],[f268,f133]) ).
fof(f334,plain,
( set_difference(sK10_skl,sK11_skl) != sK10_skl
| set_intersection2(sK10_skl,sK11_skl) != sK5_skl ),
inference(resolution,[status(thm)],[f281,f207]) ).
fof(f558,plain,
! [X0,X1] :
( ~ subset(X0,set_difference(X0,X1))
| X0 = set_difference(X0,X1) ),
inference(resolution,[status(thm)],[f69,f167]) ).
fof(f1011,plain,
! [X0] : set_difference(X0,X0) = sK5_skl,
inference(resolution,[status(thm)],[f298,f213]) ).
fof(f1464,plain,
! [X0,X1] :
( X0 = set_difference(X0,X1)
| set_difference(X0,set_difference(X0,X1)) != sK5_skl ),
inference(resolution,[status(thm)],[f299,f558]) ).
fof(f1474,plain,
set_difference(sK10_skl,sK11_skl) = sK10_skl,
inference(backward_subsumption_resolution,[status(thm)],[f282,f1476]) ).
fof(f1475,plain,
set_intersection2(sK10_skl,sK11_skl) != sK5_skl,
inference(backward_subsumption_resolution,[status(thm)],[f334,f1476]) ).
fof(f1476,plain,
! [X0,X1] :
( X0 = set_difference(X0,X1)
| set_intersection2(X0,X1) != sK5_skl ),
inference(forward_demodulation,[status(thm)],[f185,f1464]) ).
fof(f2420,plain,
set_difference(sK10_skl,sK10_skl) = set_intersection2(sK10_skl,sK11_skl),
inference(paramodulation,[status(thm)],[f1474,f185]) ).
fof(f2454,plain,
sK5_skl = set_intersection2(sK10_skl,sK11_skl),
inference(forward_demodulation,[status(thm)],[f1011,f2420]) ).
fof(f2455,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f2454,f1475]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU141+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n009.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 05:52:42 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 3.79/0.92 % Refutation found
% 3.79/0.92 % SZS status Theorem for theBenchmark: Theorem is valid
% 3.79/0.92 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 3.79/0.94 % Elapsed time: 0.563697 seconds
% 3.79/0.94 % CPU time: 4.154216 seconds
% 3.79/0.94 % Total memory used: 146.466 MB
% 3.79/0.94 % Net memory used: 139.458 MB
%------------------------------------------------------------------------------