%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET601+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.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 02:10:11 PM UTC 2026
% Result : Theorem 7.39s 1.40s
% Output : CNFRefutation 7.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 7
% Syntax : Number of formulae : 49 ( 49 unt; 0 def)
% Number of atoms : 49 ( 48 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 9 ( 9 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 115 ( 112 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [B,C,D] : union(union(B,C),D) = union(B,union(C,D)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [B,C,D] : intersection(intersection(B,C),D) = intersection(B,intersection(C,D)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [B,C] : union(B,intersection(B,C)) = B,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [B,C,D] : union(B,intersection(C,D)) = intersection(union(B,C),union(B,D)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [B,C] : union(B,C) = union(C,B),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [B,C] : intersection(B,C) = intersection(C,B),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,conjecture,
! [B,C,D] : union(union(intersection(B,C),intersection(C,D)),intersection(D,B)) = intersection(intersection(union(B,C),union(C,D)),union(D,B)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
~ ! [B,C,D] : union(union(intersection(B,C),intersection(C,D)),intersection(D,B)) = intersection(intersection(union(B,C),union(C,D)),union(D,B)),
inference(negated_conjecture,[status(cth)],[f14]) ).
fof(f16,plain,
! [X0,X1,X2] : union(union(X0,X1),X2) = union(X0,union(X1,X2)),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f18,plain,
! [X0,X1,X2] : intersection(intersection(X0,X1),X2) = intersection(X0,intersection(X1,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f19,plain,
! [X0,X1] : union(X0,intersection(X0,X1)) = X0,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f20,plain,
! [X0,X1,X2] : union(X0,intersection(X1,X2)) = intersection(union(X0,X1),union(X0,X2)),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f36,plain,
! [X0,X1] : union(X0,X1) = union(X1,X0),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f37,plain,
! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f53,plain,
? [B,C,D] : union(union(intersection(B,C),intersection(C,D)),intersection(D,B)) != intersection(intersection(union(B,C),union(C,D)),union(D,B)),
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f54,plain,
union(union(intersection(sK2_skl,sK3_skl),intersection(sK3_skl,sK4_skl)),intersection(sK4_skl,sK2_skl)) != intersection(intersection(union(sK2_skl,sK3_skl),union(sK3_skl,sK4_skl)),union(sK4_skl,sK2_skl)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl,sK4_skl]),skolemize(B,sK2_skl),skolemize(C,sK3_skl),skolemize(D,sK4_skl)],[f53]) ).
fof(f55,plain,
union(union(intersection(sK2_skl,sK3_skl),intersection(sK3_skl,sK4_skl)),intersection(sK4_skl,sK2_skl)) != intersection(intersection(union(sK2_skl,sK3_skl),union(sK3_skl,sK4_skl)),union(sK4_skl,sK2_skl)),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f58,plain,
union(intersection(sK2_skl,sK3_skl),union(intersection(sK3_skl,sK4_skl),intersection(sK4_skl,sK2_skl))) != intersection(intersection(union(sK2_skl,sK3_skl),union(sK3_skl,sK4_skl)),union(sK4_skl,sK2_skl)),
inference(forward_demodulation,[status(thm)],[f16,f55]) ).
fof(f59,plain,
union(intersection(sK2_skl,sK3_skl),union(intersection(sK3_skl,sK4_skl),intersection(sK4_skl,sK2_skl))) != intersection(union(sK2_skl,sK3_skl),intersection(union(sK3_skl,sK4_skl),union(sK4_skl,sK2_skl))),
inference(forward_demodulation,[status(thm)],[f18,f58]) ).
fof(f70,plain,
! [X0,X1,X2] : union(X0,union(X1,X2)) = union(X2,union(X0,X1)),
inference(paramodulation,[status(thm)],[f16,f36]) ).
fof(f88,plain,
! [X0,X1] : union(X0,intersection(X1,X0)) = X0,
inference(paramodulation,[status(thm)],[f37,f19]) ).
fof(f97,plain,
! [X0,X1,X2] : union(X0,X1) = union(X0,union(intersection(X2,X0),X1)),
inference(paramodulation,[status(thm)],[f88,f16]) ).
fof(f172,plain,
! [X0,X1,X2] : union(X0,intersection(X1,X2)) = intersection(union(X0,X2),union(X0,X1)),
inference(paramodulation,[status(thm)],[f37,f20]) ).
fof(f179,plain,
! [X0,X1,X2] : union(X0,intersection(intersection(X0,X1),X2)) = intersection(X0,union(X0,X2)),
inference(paramodulation,[status(thm)],[f19,f20]) ).
fof(f180,plain,
! [X0,X1,X2] : union(X0,intersection(X1,X2)) = intersection(union(X1,X0),union(X0,X2)),
inference(paramodulation,[status(thm)],[f36,f20]) ).
fof(f188,plain,
! [X0,X1,X2] : union(X0,intersection(X1,X2)) = intersection(union(X0,X1),union(X2,X0)),
inference(paramodulation,[status(thm)],[f36,f20]) ).
fof(f199,plain,
! [X0,X1,X2] : union(X0,intersection(X1,X2)) = union(X0,intersection(X2,X1)),
inference(forward_demodulation,[status(thm)],[f20,f172]) ).
fof(f208,plain,
! [X0,X1,X2] : union(X0,intersection(X0,intersection(X1,X2))) = intersection(X0,union(X0,X2)),
inference(forward_demodulation,[status(thm)],[f18,f179]) ).
fof(f210,plain,
! [X0,X1] : X0 = intersection(X0,union(X0,X1)),
inference(forward_demodulation,[status(thm)],[f19,f208]) ).
fof(f211,plain,
union(intersection(sK2_skl,sK3_skl),union(intersection(sK3_skl,sK4_skl),intersection(sK4_skl,sK2_skl))) != intersection(union(sK2_skl,sK3_skl),union(sK4_skl,intersection(sK3_skl,sK2_skl))),
inference(backward_demodulation,[status(thm)],[f180,f59]) ).
fof(f245,plain,
! [X0,X1] : X0 = intersection(X0,union(X1,X0)),
inference(paramodulation,[status(thm)],[f36,f210]) ).
fof(f278,plain,
! [X0,X1,X2] : X0 = intersection(X0,union(X1,union(X2,X0))),
inference(paramodulation,[status(thm)],[f16,f245]) ).
fof(f416,plain,
! [X0,X1,X2] : intersection(X0,X1) = intersection(intersection(X0,X1),union(X2,X0)),
inference(paramodulation,[status(thm)],[f19,f278]) ).
fof(f435,plain,
! [X0,X1,X2] : intersection(X0,X1) = intersection(X0,intersection(X1,union(X2,X0))),
inference(forward_demodulation,[status(thm)],[f18,f416]) ).
fof(f786,plain,
! [X0,X1,X2] : union(X0,X1) = union(intersection(X2,X1),union(X0,X1)),
inference(paramodulation,[status(thm)],[f88,f70]) ).
fof(f787,plain,
! [X0,X1,X2] : union(X0,X1) = union(intersection(X1,X2),union(X0,X1)),
inference(paramodulation,[status(thm)],[f19,f70]) ).
fof(f1598,plain,
! [X0,X1,X2] : union(intersection(X0,X1),X2) = union(X2,intersection(X1,X0)),
inference(paramodulation,[status(thm)],[f36,f199]) ).
fof(f3231,plain,
! [X0,X1,X2] : intersection(X0,union(X1,X2)) = intersection(X0,union(X1,intersection(X2,X0))),
inference(paramodulation,[status(thm)],[f20,f435]) ).
fof(f5085,plain,
! [X0,X1,X2] : union(intersection(X0,intersection(X1,X2)),X2) = union(intersection(X1,X2),X2),
inference(paramodulation,[status(thm)],[f97,f786]) ).
fof(f5150,plain,
! [X0,X1,X2] : union(X0,intersection(X1,X0)) = union(intersection(X2,intersection(X1,X0)),X0),
inference(paramodulation,[status(thm)],[f88,f786]) ).
fof(f5253,plain,
! [X0,X1,X2] : X0 = union(intersection(X1,intersection(X2,X0)),X0),
inference(forward_demodulation,[status(thm)],[f88,f5150]) ).
fof(f5258,plain,
! [X0,X1] : X0 = union(intersection(X1,X0),X0),
inference(forward_demodulation,[status(thm)],[f5085,f5253]) ).
fof(f5790,plain,
! [X0,X1,X2] : union(intersection(X0,X1),intersection(X1,X2)) = intersection(X1,union(X2,intersection(X0,X1))),
inference(paramodulation,[status(thm)],[f5258,f188]) ).
fof(f5917,plain,
union(intersection(sK2_skl,sK3_skl),intersection(sK4_skl,union(sK2_skl,sK3_skl))) != intersection(union(sK2_skl,sK3_skl),union(sK4_skl,intersection(sK3_skl,sK2_skl))),
inference(backward_demodulation,[status(thm)],[f5932,f211]) ).
fof(f5932,plain,
! [X0,X1,X2] : union(intersection(X0,X1),intersection(X1,X2)) = intersection(X1,union(X2,X0)),
inference(forward_demodulation,[status(thm)],[f3231,f5790]) ).
fof(f6822,plain,
! [X0,X1,X2,X3] : union(intersection(X0,X1),intersection(union(X2,X0),X3)) = intersection(union(X2,X0),union(X3,intersection(X0,X1))),
inference(paramodulation,[status(thm)],[f787,f188]) ).
fof(f6937,plain,
union(intersection(sK2_skl,sK3_skl),intersection(sK4_skl,union(sK2_skl,sK3_skl))) != union(intersection(sK3_skl,sK2_skl),intersection(union(sK2_skl,sK3_skl),sK4_skl)),
inference(backward_demodulation,[status(thm)],[f6822,f5917]) ).
fof(f8121,plain,
! [X0,X1,X2,X3] : union(intersection(X0,X1),intersection(X2,X3)) = union(intersection(X1,X0),intersection(X3,X2)),
inference(paramodulation,[status(thm)],[f1598,f1598]) ).
fof(f8355,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f6937,f8121]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET601+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.36 % Computer : n020.cluster.edu
% 0.12/0.36 % Model : x86_64 x86_64
% 0.12/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.36 % Memory : 8046.5625MB
% 0.12/0.36 % OS : Linux 6.8.0-71-generic
% 0.12/0.36 % CPULimit : 300
% 0.12/0.36 % WCLimit : 300
% 0.12/0.36 % DateTime : Mon Sep 21 05:29:02 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.15/0.38 % Drodi V4.1.1
% 7.39/1.40 % Refutation found
% 7.39/1.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 7.39/1.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 7.39/1.42 % Elapsed time: 1.043021 seconds
% 7.39/1.42 % CPU time: 7.967352 seconds
% 7.39/1.42 % Total memory used: 187.663 MB
% 7.39/1.42 % Net memory used: 182.870 MB
%------------------------------------------------------------------------------