%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU102+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/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 02:19:13 PM UTC 2026
% Result : Theorem 0.13s 15.70s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 5
% Syntax : Number of formulae : 37 ( 18 unt; 0 def)
% Number of atoms : 95 ( 13 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 95 ( 37 ~; 30 |; 22 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 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; 3 con; 0-3 aty)
% Number of variables : 42 ( 36 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A,B,C] :
( ( element(C,A)
& element(B,A)
& preboolean(A)
& ~ empty(A) )
=> element(prebool_difference(A,B,C),A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,axiom,
! [A,B,C] :
( ( element(C,A)
& element(B,A)
& preboolean(A)
& ~ empty(A) )
=> prebool_difference(A,B,C) = set_difference(B,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,conjecture,
! [A,B,C] :
( ( preboolean(C)
& ~ empty(C) )
=> ( ( element(B,C)
& element(A,C) )
=> element(set_intersection2(A,B),C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
~ ! [A,B,C] :
( ( preboolean(C)
& ~ empty(C) )
=> ( ( element(B,C)
& element(A,C) )
=> element(set_intersection2(A,B),C) ) ),
inference(negated_conjecture,[status(cth)],[f26]) ).
fof(f33,axiom,
! [A,B] : set_difference(A,set_difference(A,B)) = set_intersection2(A,B),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f51,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f52,plain,
! [A,B,C] :
( element(prebool_difference(A,B,C),A)
| ~ element(C,A)
| ~ element(B,A)
| ~ preboolean(A)
| empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f53,plain,
! [X0,X1,X2] :
( element(prebool_difference(X0,X1,X2),X0)
| ~ element(X2,X0)
| ~ element(X1,X0)
| ~ preboolean(X0)
| empty(X0) ),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f110,plain,
! [A,B,C] :
( prebool_difference(A,B,C) = set_difference(B,C)
| ~ element(C,A)
| ~ element(B,A)
| ~ preboolean(A)
| empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f24]) ).
fof(f111,plain,
! [X0,X1,X2] :
( prebool_difference(X0,X1,X2) = set_difference(X1,X2)
| ~ element(X2,X0)
| ~ element(X1,X0)
| ~ preboolean(X0)
| empty(X0) ),
inference(cnf_transformation,[status(thm)],[f110]) ).
fof(f114,plain,
? [A,B,C] :
( ~ element(set_intersection2(A,B),C)
& element(B,C)
& element(A,C)
& preboolean(C)
& ~ empty(C) ),
inference(pre_NNF_transformation,[status(thm)],[f27]) ).
fof(f115,plain,
? [C] :
( ? [A,B] :
( ~ element(set_intersection2(A,B),C)
& element(B,C)
& element(A,C) )
& preboolean(C)
& ~ empty(C) ),
inference(miniscoping,[status(thm)],[f114]) ).
fof(f116,plain,
( ~ element(set_intersection2(sK11_skl,sK12_skl),sK10_skl)
& element(sK12_skl,sK10_skl)
& element(sK11_skl,sK10_skl)
& preboolean(sK10_skl)
& ~ empty(sK10_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10_skl,sK11_skl,sK12_skl]),skolemize(C,sK10_skl),skolemize(A,sK11_skl),skolemize(B,sK12_skl)],[f115]) ).
fof(f117,plain,
~ empty(sK10_skl),
inference(cnf_transformation,[status(thm)],[f116]) ).
fof(f118,plain,
preboolean(sK10_skl),
inference(cnf_transformation,[status(thm)],[f116]) ).
fof(f119,plain,
element(sK11_skl,sK10_skl),
inference(cnf_transformation,[status(thm)],[f116]) ).
fof(f120,plain,
element(sK12_skl,sK10_skl),
inference(cnf_transformation,[status(thm)],[f116]) ).
fof(f121,plain,
~ element(set_intersection2(sK11_skl,sK12_skl),sK10_skl),
inference(cnf_transformation,[status(thm)],[f116]) ).
fof(f132,plain,
! [X0,X1] : set_difference(X0,set_difference(X0,X1)) = set_intersection2(X0,X1),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f288,plain,
! [X0] :
( element(prebool_difference(sK10_skl,sK12_skl,X0),sK10_skl)
| ~ element(X0,sK10_skl)
| ~ preboolean(sK10_skl)
| empty(sK10_skl) ),
inference(resolution,[status(thm)],[f53,f120]) ).
fof(f290,plain,
! [X0] :
( element(prebool_difference(sK10_skl,sK12_skl,X0),sK10_skl)
| ~ element(X0,sK10_skl)
| ~ preboolean(sK10_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f288,f117]) ).
fof(f310,plain,
( element(prebool_difference(sK10_skl,sK12_skl,sK11_skl),sK10_skl)
| ~ preboolean(sK10_skl) ),
inference(resolution,[status(thm)],[f290,f119]) ).
fof(f313,plain,
element(prebool_difference(sK10_skl,sK12_skl,sK11_skl),sK10_skl),
inference(forward_subsumption_resolution,[status(thm)],[f310,f118]) ).
fof(f355,plain,
( element(prebool_difference(sK10_skl,sK12_skl,prebool_difference(sK10_skl,sK12_skl,sK11_skl)),sK10_skl)
| ~ preboolean(sK10_skl) ),
inference(resolution,[status(thm)],[f313,f290]) ).
fof(f358,plain,
element(prebool_difference(sK10_skl,sK12_skl,prebool_difference(sK10_skl,sK12_skl,sK11_skl)),sK10_skl),
inference(forward_subsumption_resolution,[status(thm)],[f355,f118]) ).
fof(f444,plain,
! [X0] :
( prebool_difference(sK10_skl,sK12_skl,X0) = set_difference(sK12_skl,X0)
| ~ element(X0,sK10_skl)
| ~ preboolean(sK10_skl)
| empty(sK10_skl) ),
inference(resolution,[status(thm)],[f111,f120]) ).
fof(f454,plain,
! [X0] :
( prebool_difference(sK10_skl,sK12_skl,X0) = set_difference(sK12_skl,X0)
| ~ element(X0,sK10_skl)
| ~ preboolean(sK10_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f444,f117]) ).
fof(f485,plain,
( prebool_difference(sK10_skl,sK12_skl,prebool_difference(sK10_skl,sK12_skl,sK11_skl)) = set_difference(sK12_skl,prebool_difference(sK10_skl,sK12_skl,sK11_skl))
| ~ preboolean(sK10_skl) ),
inference(resolution,[status(thm)],[f454,f313]) ).
fof(f489,plain,
( prebool_difference(sK10_skl,sK12_skl,sK11_skl) = set_difference(sK12_skl,sK11_skl)
| ~ preboolean(sK10_skl) ),
inference(resolution,[status(thm)],[f454,f119]) ).
fof(f494,plain,
element(set_difference(sK12_skl,prebool_difference(sK10_skl,sK12_skl,sK11_skl)),sK10_skl),
inference(backward_demodulation,[status(thm)],[f495,f358]) ).
fof(f495,plain,
prebool_difference(sK10_skl,sK12_skl,prebool_difference(sK10_skl,sK12_skl,sK11_skl)) = set_difference(sK12_skl,prebool_difference(sK10_skl,sK12_skl,sK11_skl)),
inference(forward_subsumption_resolution,[status(thm)],[f485,f118]) ).
fof(f518,plain,
prebool_difference(sK10_skl,sK12_skl,sK11_skl) = set_difference(sK12_skl,sK11_skl),
inference(forward_subsumption_resolution,[status(thm)],[f489,f118]) ).
fof(f521,plain,
element(set_difference(sK12_skl,set_difference(sK12_skl,sK11_skl)),sK10_skl),
inference(forward_demodulation,[status(thm)],[f518,f494]) ).
fof(f522,plain,
element(set_intersection2(sK12_skl,sK11_skl),sK10_skl),
inference(forward_demodulation,[status(thm)],[f132,f521]) ).
fof(f587,plain,
element(set_intersection2(sK11_skl,sK12_skl),sK10_skl),
inference(paramodulation,[status(thm)],[f51,f522]) ).
fof(f597,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f587,f121]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU102+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/15.53 % Computer : n010.cluster.edu
% 0.10/15.53 % Model : x86_64 x86_64
% 0.10/15.53 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/15.53 % Memory : 8046.5625MB
% 0.10/15.53 % OS : Linux 6.8.0-71-generic
% 0.10/15.53 % CPULimit : 300
% 0.10/15.53 % WCLimit : 300
% 0.10/15.53 % DateTime : Mon Sep 21 05:50:59 UTC 2026
% 0.10/15.53 % CPUTime :
% 0.10/15.54 % Drodi V4.1.1
% 0.13/15.70 % Refutation found
% 0.13/15.70 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/15.70 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/15.73 % Elapsed time: 0.180028 seconds
% 0.13/15.73 % CPU time: 1.155290 seconds
% 0.13/15.73 % Total memory used: 126.318 MB
% 0.13/15.73 % Net memory used: 124.366 MB
%------------------------------------------------------------------------------