%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU140+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n008.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 0.09s 0.40s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 41 ( 17 unt; 0 def)
% Number of atoms : 74 ( 24 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 57 ( 24 ~; 17 |; 10 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 55 ( 48 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A,B] :
( disjoint(A,B)
<=> set_intersection2(A,B) = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
? [A] : empty(A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [A,B,C] :
( subset(A,B)
=> subset(set_intersection2(A,C),set_intersection2(B,C)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [A] :
( subset(A,empty_set)
=> A = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,conjecture,
! [A,B,C] :
( ( disjoint(B,C)
& subset(A,B) )
=> disjoint(A,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
~ ! [A,B,C] :
( ( disjoint(B,C)
& subset(A,B) )
=> disjoint(A,C) ),
inference(negated_conjecture,[status(cth)],[f15]) ).
fof(f17,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f23,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)],[f3]) ).
fof(f24,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)],[f23]) ).
fof(f25,plain,
! [X0,X1] :
( set_intersection2(X0,X1) = empty_set
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f26,plain,
! [X0,X1] :
( set_intersection2(X0,X1) != empty_set
| disjoint(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f30,plain,
empty(sK0_skl),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(A,sK0_skl)],[f8]) ).
fof(f31,plain,
empty(sK0_skl),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f38,plain,
! [A,B,C] :
( subset(set_intersection2(A,C),set_intersection2(B,C))
| ~ subset(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f12]) ).
fof(f39,plain,
! [A,B] :
( ! [C] : subset(set_intersection2(A,C),set_intersection2(B,C))
| ~ subset(A,B) ),
inference(miniscoping,[status(thm)],[f38]) ).
fof(f40,plain,
! [X0,X1,X2] :
( subset(set_intersection2(X0,X2),set_intersection2(X1,X2))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f42,plain,
! [A] :
( A = empty_set
| ~ subset(A,empty_set) ),
inference(pre_NNF_transformation,[status(thm)],[f14]) ).
fof(f43,plain,
! [X0] :
( X0 = empty_set
| ~ subset(X0,empty_set) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f44,plain,
? [A,B,C] :
( ~ disjoint(A,C)
& disjoint(B,C)
& subset(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f16]) ).
fof(f45,plain,
? [A,C] :
( ~ disjoint(A,C)
& ? [B] :
( disjoint(B,C)
& subset(A,B) ) ),
inference(miniscoping,[status(thm)],[f44]) ).
fof(f46,plain,
( ~ disjoint(sK2_skl,sK3_skl)
& disjoint(sK4_skl,sK3_skl)
& subset(sK2_skl,sK4_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl,sK4_skl]),skolemize(A,sK2_skl),skolemize(C,sK3_skl),skolemize(B,sK4_skl)],[f45]) ).
fof(f47,plain,
subset(sK2_skl,sK4_skl),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f48,plain,
disjoint(sK4_skl,sK3_skl),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f49,plain,
~ disjoint(sK2_skl,sK3_skl),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f50,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f17]) ).
fof(f51,plain,
! [X0] :
( X0 = empty_set
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f62,plain,
set_intersection2(sK2_skl,sK3_skl) != empty_set,
inference(resolution,[status(thm)],[f26,f49]) ).
fof(f80,plain,
! [X0,X1,X2] :
( subset(set_intersection2(X0,X2),set_intersection2(X2,X1))
| ~ subset(X0,X1) ),
inference(paramodulation,[status(thm)],[f22,f40]) ).
fof(f89,plain,
sK0_skl = empty_set,
inference(resolution,[status(thm)],[f51,f31]) ).
fof(f94,plain,
set_intersection2(sK2_skl,sK3_skl) != sK0_skl,
inference(backward_demodulation,[status(thm)],[f89,f62]) ).
fof(f97,plain,
! [X0] :
( X0 = sK0_skl
| ~ subset(X0,empty_set) ),
inference(backward_demodulation,[status(thm)],[f89,f43]) ).
fof(f98,plain,
! [X0,X1] :
( set_intersection2(X0,X1) = sK0_skl
| ~ disjoint(X0,X1) ),
inference(backward_demodulation,[status(thm)],[f89,f25]) ).
fof(f101,plain,
! [X0] :
( X0 = sK0_skl
| ~ subset(X0,sK0_skl) ),
inference(forward_demodulation,[status(thm)],[f89,f97]) ).
fof(f113,plain,
set_intersection2(sK4_skl,sK3_skl) = sK0_skl,
inference(resolution,[status(thm)],[f98,f48]) ).
fof(f116,plain,
set_intersection2(sK3_skl,sK4_skl) = sK0_skl,
inference(paramodulation,[status(thm)],[f22,f113]) ).
fof(f148,plain,
! [X0] : subset(set_intersection2(sK2_skl,X0),set_intersection2(X0,sK4_skl)),
inference(resolution,[status(thm)],[f80,f47]) ).
fof(f164,plain,
subset(set_intersection2(sK2_skl,sK3_skl),sK0_skl),
inference(paramodulation,[status(thm)],[f116,f148]) ).
fof(f171,plain,
set_intersection2(sK2_skl,sK3_skl) = sK0_skl,
inference(resolution,[status(thm)],[f164,f101]) ).
fof(f174,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f171,f94]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU140+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n008.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 05:53:08 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 0.09/0.40 % Refutation found
% 0.09/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.43 % Elapsed time: 0.055205 seconds
% 0.09/0.43 % CPU time: 0.167651 seconds
% 0.09/0.43 % Total memory used: 67.129 MB
% 0.09/0.43 % Net memory used: 66.758 MB
%------------------------------------------------------------------------------