%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU126+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/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 02:19:17 PM UTC 2026
% Result : Theorem 0.23s 0.61s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 38 ( 6 unt; 3 def)
% Number of atoms : 134 ( 26 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 147 ( 51 ~; 63 |; 23 &)
% ( 7 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 4 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-3 aty)
% Number of variables : 72 ( 66 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [A,B] : set_union2(A,B) = set_union2(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A,B,C] :
( C = set_union2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,B)
| in(D,A) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,conjecture,
! [A,B] :
( subset(A,B)
=> set_union2(A,B) = B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
~ ! [A,B] :
( subset(A,B)
=> set_union2(A,B) = B ),
inference(negated_conjecture,[status(cth)],[f15]) ).
fof(f23,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f29,plain,
! [A,B,C] :
( ( ? [D] :
( ( in(D,B)
| in(D,A)
| in(D,C) )
& ( ( ~ in(D,B)
& ~ in(D,A) )
| ~ in(D,C) ) )
| C = set_union2(A,B) )
& ( ! [D] :
( ( ( ~ in(D,B)
& ~ in(D,A) )
| in(D,C) )
& ( in(D,B)
| in(D,A)
| ~ in(D,C) ) )
| C != set_union2(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f4]) ).
fof(f30,plain,
( ! [A,B,C] :
( ? [D] :
( ( in(D,B)
| in(D,A)
| in(D,C) )
& ( ( ~ in(D,B)
& ~ in(D,A) )
| ~ in(D,C) ) )
| C = set_union2(A,B) )
& ! [A,B,C] :
( ( ! [D] :
( ( ~ in(D,B)
& ~ in(D,A) )
| in(D,C) )
& ! [D] :
( in(D,B)
| in(D,A)
| ~ in(D,C) ) )
| C != set_union2(A,B) ) ),
inference(miniscoping,[status(thm)],[f29]) ).
fof(f31,plain,
( ! [A,B,C] :
( ( ( in(sK0_skl(C,B,A),B)
| in(sK0_skl(C,B,A),A)
| in(sK0_skl(C,B,A),C) )
& ( ( ~ in(sK0_skl(C,B,A),B)
& ~ in(sK0_skl(C,B,A),A) )
| ~ in(sK0_skl(C,B,A),C) ) )
| C = set_union2(A,B) )
& ! [A,B,C] :
( ( ! [D] :
( ( ~ in(D,B)
& ~ in(D,A) )
| in(D,C) )
& ! [D] :
( in(D,B)
| in(D,A)
| ~ in(D,C) ) )
| C != set_union2(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(D,sK0_skl(C,B,A))],[f30]) ).
fof(f35,plain,
! [X0,X1,X2] :
( ~ in(sK0_skl(X0,X2,X1),X1)
| ~ in(sK0_skl(X0,X2,X1),X0)
| X0 = set_union2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f36,plain,
! [X0,X1,X2] :
( ~ in(sK0_skl(X0,X2,X1),X2)
| ~ in(sK0_skl(X0,X2,X1),X0)
| X0 = set_union2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f37,plain,
! [X0,X1,X2] :
( in(sK0_skl(X0,X2,X1),X2)
| in(sK0_skl(X0,X2,X1),X1)
| in(sK0_skl(X0,X2,X1),X0)
| X0 = set_union2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f38,plain,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,B)
| ~ in(C,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f39,plain,
! [A,B] :
( ( ? [C] :
( ~ in(C,B)
& in(C,A) )
| subset(A,B) )
& ( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f38]) ).
fof(f40,plain,
( ! [A,B] :
( ? [C] :
( ~ in(C,B)
& in(C,A) )
| subset(A,B) )
& ! [A,B] :
( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(miniscoping,[status(thm)],[f39]) ).
fof(f41,plain,
( ! [A,B] :
( ( ~ in(sK1_skl(B,A),B)
& in(sK1_skl(B,A),A) )
| subset(A,B) )
& ! [A,B] :
( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(C,sK1_skl(B,A))],[f40]) ).
fof(f42,plain,
! [X0,X1,X2] :
( in(X2,X1)
| ~ in(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f60,plain,
? [A,B] :
( set_union2(A,B) != B
& subset(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f16]) ).
fof(f61,plain,
( set_union2(sK4_skl,sK5_skl) != sK5_skl
& subset(sK4_skl,sK5_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl,sK5_skl]),skolemize(A,sK4_skl),skolemize(B,sK5_skl)],[f60]) ).
fof(f62,plain,
subset(sK4_skl,sK5_skl),
inference(cnf_transformation,[status(thm)],[f61]) ).
fof(f63,plain,
set_union2(sK4_skl,sK5_skl) != sK5_skl,
inference(cnf_transformation,[status(thm)],[f61]) ).
fof(f144,plain,
! [X0] :
( in(X0,sK5_skl)
| ~ in(X0,sK4_skl) ),
inference(resolution,[status(thm)],[f62,f42]) ).
fof(f187,plain,
! [X0,X1] :
( in(sK0_skl(X0,sK4_skl,X1),X1)
| in(sK0_skl(X0,sK4_skl,X1),X0)
| X0 = set_union2(X1,sK4_skl)
| in(sK0_skl(X0,sK4_skl,X1),sK5_skl) ),
inference(resolution,[status(thm)],[f144,f37]) ).
fof(f459,plain,
( ~ in(sK0_skl(sK5_skl,sK4_skl,sK5_skl),sK4_skl)
| sK5_skl = set_union2(sK5_skl,sK4_skl)
| sK5_skl = set_union2(sK5_skl,sK4_skl) ),
inference(resolution,[status(thm)],[f187,f36]) ).
fof(f461,plain,
( ~ in(sK0_skl(sK5_skl,sK4_skl,sK5_skl),sK5_skl)
| sK5_skl = set_union2(sK5_skl,sK4_skl)
| sK5_skl = set_union2(sK5_skl,sK4_skl) ),
inference(resolution,[status(thm)],[f187,f35]) ).
fof(f495,definition,
( sQ11_spl
<=> sK5_skl = set_union2(sK5_skl,sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f496,plain,
( ~ sQ11_spl
| sK5_skl = set_union2(sK5_skl,sK4_skl) ),
inference(component_clause,[status(thm)],[f495]) ).
fof(f498,definition,
( sQ12_spl
<=> in(sK0_skl(sK5_skl,sK4_skl,sK5_skl),sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f500,plain,
( sQ12_spl
| ~ in(sK0_skl(sK5_skl,sK4_skl,sK5_skl),sK4_skl) ),
inference(component_clause,[status(thm)],[f498]) ).
fof(f501,plain,
( ~ sQ12_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f459,f495,f498]) ).
fof(f503,definition,
( sQ13_spl
<=> in(sK0_skl(sK5_skl,sK4_skl,sK5_skl),sK5_skl) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f506,plain,
( ~ sQ13_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f461,f495,f503]) ).
fof(f532,plain,
( ~ sQ11_spl
| sK5_skl = set_union2(sK4_skl,sK5_skl) ),
inference(paramodulation,[status(thm)],[f23,f496]) ).
fof(f544,plain,
( ~ sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f532,f63]) ).
fof(f545,plain,
~ sQ11_spl,
inference(contradiction_clause,[status(thm)],[f544]) ).
fof(f1070,plain,
( sQ12_spl
| in(sK0_skl(sK5_skl,sK4_skl,sK5_skl),sK5_skl)
| in(sK0_skl(sK5_skl,sK4_skl,sK5_skl),sK5_skl)
| sK5_skl = set_union2(sK5_skl,sK4_skl) ),
inference(resolution,[status(thm)],[f500,f37]) ).
fof(f1073,plain,
( sQ12_spl
| sQ13_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f1070,f495,f503,f498]) ).
fof(f1074,plain,
$false,
inference(sat_refutation,[status(thm)],[f501,f506,f545,f1073]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU126+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.48 % Computer : n010.cluster.edu
% 0.18/0.48 % Model : x86_64 x86_64
% 0.18/0.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.48 % Memory : 8046.5625MB
% 0.18/0.48 % OS : Linux 6.8.0-71-generic
% 0.18/0.48 % CPULimit : 300
% 0.18/0.48 % WCLimit : 300
% 0.18/0.48 % DateTime : Mon Sep 21 05:52:10 UTC 2026
% 0.18/0.49 % CPUTime :
% 0.18/0.50 % Drodi V4.1.1
% 0.23/0.61 % Refutation found
% 0.23/0.61 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.23/0.61 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.23/0.66 % Elapsed time: 0.159954 seconds
% 0.23/0.66 % CPU time: 0.663090 seconds
% 0.23/0.66 % Total memory used: 79.283 MB
% 0.23/0.66 % Net memory used: 78.242 MB
%------------------------------------------------------------------------------