%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET962+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% 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 02:11:03 PM UTC 2026
% Result : Theorem 0.09s 0.39s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 11
% Syntax : Number of formulae : 66 ( 5 unt; 8 def)
% Number of atoms : 174 ( 27 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 195 ( 87 ~; 85 |; 9 &)
% ( 10 <=>; 3 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 9 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 85 ( 81 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(C,D))
<=> ( in(B,D)
& in(A,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,conjecture,
! [A,B] :
( cartesian_product2(A,A) = cartesian_product2(B,B)
=> A = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
~ ! [A,B] :
( cartesian_product2(A,A) = cartesian_product2(B,B)
=> A = B ),
inference(negated_conjecture,[status(cth)],[f8]) ).
fof(f10,axiom,
! [A,B] :
( ! [C] :
( in(C,A)
<=> in(C,B) )
=> A = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,plain,
! [A,B,C,D] :
( ( ~ in(B,D)
| ~ in(A,C)
| in(ordered_pair(A,B),cartesian_product2(C,D)) )
& ( ( in(B,D)
& in(A,C) )
| ~ in(ordered_pair(A,B),cartesian_product2(C,D)) ) ),
inference(NNF_transformation,[status(thm)],[f5]) ).
fof(f17,plain,
( ! [A,B,C,D] :
( ~ in(B,D)
| ~ in(A,C)
| in(ordered_pair(A,B),cartesian_product2(C,D)) )
& ! [A,B,C,D] :
( ( in(B,D)
& in(A,C) )
| ~ in(ordered_pair(A,B),cartesian_product2(C,D)) ) ),
inference(miniscoping,[status(thm)],[f16]) ).
fof(f19,plain,
! [X0,X1,X2,X3] :
( in(X1,X3)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f20,plain,
! [X0,X1,X2,X3] :
( ~ in(X1,X3)
| ~ in(X0,X2)
| in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f25,plain,
? [A,B] :
( A != B
& cartesian_product2(A,A) = cartesian_product2(B,B) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f26,plain,
( sK2_skl != sK3_skl
& cartesian_product2(sK2_skl,sK2_skl) = cartesian_product2(sK3_skl,sK3_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl]),skolemize(A,sK2_skl),skolemize(B,sK3_skl)],[f25]) ).
fof(f27,plain,
cartesian_product2(sK2_skl,sK2_skl) = cartesian_product2(sK3_skl,sK3_skl),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f28,plain,
sK2_skl != sK3_skl,
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f29,plain,
! [A,B] :
( A = B
| ? [C] :
( in(C,A)
<~> in(C,B) ) ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f30,plain,
! [A,B] :
( A = B
| ? [C] :
( ( ~ in(C,B)
| ~ in(C,A) )
& ( in(C,B)
| in(C,A) ) ) ),
inference(NNF_transformation,[status(thm)],[f29]) ).
fof(f31,plain,
! [A,B] :
( A = B
| ( ( ~ in(sK4_skl(B,A),B)
| ~ in(sK4_skl(B,A),A) )
& ( in(sK4_skl(B,A),B)
| in(sK4_skl(B,A),A) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl]),skolemize(C,sK4_skl(B,A))],[f30]) ).
fof(f32,plain,
! [X0,X1] :
( X1 = X0
| in(sK4_skl(X0,X1),X0)
| in(sK4_skl(X0,X1),X1) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f33,plain,
! [X0,X1] :
( X1 = X0
| ~ in(sK4_skl(X0,X1),X0)
| ~ in(sK4_skl(X0,X1),X1) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f35,plain,
! [X0,X1] :
( in(X1,sK3_skl)
| ~ in(ordered_pair(X0,X1),cartesian_product2(sK2_skl,sK2_skl)) ),
inference(paramodulation,[status(thm)],[f27,f19]) ).
fof(f36,plain,
! [X0,X1] :
( in(X1,sK3_skl)
| ~ in(X1,sK2_skl)
| ~ in(X0,sK2_skl) ),
inference(resolution,[status(thm)],[f20,f35]) ).
fof(f38,plain,
! [X0,X1,X2,X3] :
( in(X2,X3)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(resolution,[status(thm)],[f20,f19]) ).
fof(f40,plain,
! [X0,X1] :
( ~ in(X1,sK3_skl)
| ~ in(X0,sK3_skl)
| in(ordered_pair(X0,X1),cartesian_product2(sK2_skl,sK2_skl)) ),
inference(paramodulation,[status(thm)],[f27,f20]) ).
fof(f41,definition,
! [X0] :
( sQ0_spl
<=> ~ in(X0,sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f42,plain,
! [X0] :
( ~ sQ0_spl
| ~ in(X0,sK2_skl) ),
inference(component_clause,[status(thm)],[f41]) ).
fof(f44,definition,
! [X1] :
( sQ1_spl
<=> ( in(X1,sK3_skl)
| ~ in(X1,sK2_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f45,plain,
! [X0] :
( ~ sQ1_spl
| in(X0,sK3_skl)
| ~ in(X0,sK2_skl) ),
inference(component_clause,[status(thm)],[f44]) ).
fof(f47,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f36,f41,f44]) ).
fof(f49,definition,
! [X0,X1] :
( sQ2_spl
<=> ~ in(X0,X1) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f50,plain,
! [X0,X1] :
( ~ sQ2_spl
| ~ in(X0,X1) ),
inference(component_clause,[status(thm)],[f49]) ).
fof(f52,definition,
! [X2,X3] :
( sQ3_spl
<=> ( in(X2,X3)
| ~ in(X2,X3) ) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f55,plain,
( sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f38,f49,f52]) ).
fof(f59,plain,
! [X0,X1] :
( in(X1,sK2_skl)
| ~ in(X1,sK3_skl)
| ~ in(X0,sK3_skl) ),
inference(resolution,[status(thm)],[f40,f19]) ).
fof(f61,definition,
! [X0] :
( sQ4_spl
<=> ~ in(X0,sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f62,plain,
! [X0] :
( ~ sQ4_spl
| ~ in(X0,sK3_skl) ),
inference(component_clause,[status(thm)],[f61]) ).
fof(f69,definition,
! [X1] :
( sQ6_spl
<=> ( in(X1,sK2_skl)
| ~ in(X1,sK3_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f70,plain,
! [X0] :
( ~ sQ6_spl
| in(X0,sK2_skl)
| ~ in(X0,sK3_skl) ),
inference(component_clause,[status(thm)],[f69]) ).
fof(f72,plain,
( sQ6_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f59,f61,f69]) ).
fof(f85,plain,
! [X0,X1] :
( ~ sQ2_spl
| X1 = X0
| in(sK4_skl(X0,X1),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f32,f50]) ).
fof(f86,plain,
! [X0,X1] :
( ~ sQ2_spl
| X0 = X1 ),
inference(resolution,[status(thm)],[f85,f50]) ).
fof(f87,plain,
( ~ sQ2_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f28,f86]) ).
fof(f88,plain,
~ sQ2_spl,
inference(contradiction_clause,[status(thm)],[f87]) ).
fof(f89,plain,
! [X0,X1] :
( in(X1,sK3_skl)
| ~ in(ordered_pair(X0,X1),cartesian_product2(sK2_skl,sK2_skl)) ),
inference(paramodulation,[status(thm)],[f27,f19]) ).
fof(f90,plain,
! [X0,X1] :
( ~ sQ4_spl
| ~ in(ordered_pair(X0,X1),cartesian_product2(sK2_skl,sK2_skl)) ),
inference(forward_subsumption_resolution,[status(thm)],[f89,f62]) ).
fof(f91,plain,
! [X0,X1] :
( ~ sQ4_spl
| ~ in(X1,sK2_skl)
| ~ in(X0,sK2_skl) ),
inference(resolution,[status(thm)],[f20,f90]) ).
fof(f94,plain,
( ~ sQ4_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f91,f41,f61]) ).
fof(f130,plain,
! [X0] :
( ~ sQ0_spl
| sK2_skl = X0
| in(sK4_skl(X0,sK2_skl),X0) ),
inference(resolution,[status(thm)],[f32,f42]) ).
fof(f135,plain,
( ~ sQ4_spl
| ~ sQ0_spl
| sK2_skl = sK3_skl ),
inference(resolution,[status(thm)],[f130,f62]) ).
fof(f144,plain,
( ~ sQ4_spl
| ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f135,f28]) ).
fof(f145,plain,
( ~ sQ4_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f144]) ).
fof(f146,plain,
! [X0] :
( ~ sQ1_spl
| sK3_skl = X0
| ~ in(sK4_skl(X0,sK3_skl),X0)
| ~ in(sK4_skl(X0,sK3_skl),sK2_skl) ),
inference(resolution,[status(thm)],[f45,f33]) ).
fof(f154,plain,
! [X0] :
( ~ sQ6_spl
| ~ sQ0_spl
| ~ in(X0,sK3_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f70,f42]) ).
fof(f157,plain,
( ~ sQ6_spl
| ~ sQ0_spl
| sK2_skl = sK3_skl ),
inference(resolution,[status(thm)],[f130,f154]) ).
fof(f161,plain,
( ~ sQ6_spl
| ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f157,f28]) ).
fof(f162,plain,
( ~ sQ6_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f161]) ).
fof(f167,plain,
! [X0] :
( ~ sQ6_spl
| sK3_skl = X0
| in(sK4_skl(X0,sK3_skl),X0)
| in(sK4_skl(X0,sK3_skl),sK2_skl) ),
inference(resolution,[status(thm)],[f70,f32]) ).
fof(f223,definition,
( sQ10_spl
<=> sK3_skl = sK2_skl ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f224,plain,
( ~ sQ10_spl
| sK3_skl = sK2_skl ),
inference(component_clause,[status(thm)],[f223]) ).
fof(f229,definition,
( sQ12_spl
<=> in(sK4_skl(sK2_skl,sK3_skl),sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f230,plain,
( ~ sQ12_spl
| in(sK4_skl(sK2_skl,sK3_skl),sK2_skl) ),
inference(component_clause,[status(thm)],[f229]) ).
fof(f231,plain,
( sQ12_spl
| ~ in(sK4_skl(sK2_skl,sK3_skl),sK2_skl) ),
inference(component_clause,[status(thm)],[f229]) ).
fof(f256,plain,
( ~ sQ6_spl
| sQ12_spl
| sK3_skl = sK2_skl
| in(sK4_skl(sK2_skl,sK3_skl),sK2_skl) ),
inference(resolution,[status(thm)],[f231,f167]) ).
fof(f258,plain,
( ~ sQ6_spl
| sQ10_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f256,f229,f223,f69]) ).
fof(f260,plain,
( ~ sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f224,f28]) ).
fof(f261,plain,
~ sQ10_spl,
inference(contradiction_clause,[status(thm)],[f260]) ).
fof(f262,plain,
( ~ sQ1_spl
| ~ sQ12_spl
| sK3_skl = sK2_skl
| ~ in(sK4_skl(sK2_skl,sK3_skl),sK2_skl) ),
inference(resolution,[status(thm)],[f230,f146]) ).
fof(f264,plain,
( ~ sQ1_spl
| sQ10_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f262,f229,f223,f44]) ).
fof(f265,plain,
$false,
inference(sat_refutation,[status(thm)],[f47,f55,f72,f88,f94,f145,f162,f258,f261,f264]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET962+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n009.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Mon Sep 21 05:45:28 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.09/0.39 % Refutation found
% 0.09/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.51 % Elapsed time: 0.141330 seconds
% 0.15/0.51 % CPU time: 0.211348 seconds
% 0.15/0.51 % Total memory used: 36.382 MB
% 0.15/0.51 % Net memory used: 36.254 MB
%------------------------------------------------------------------------------