%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET903+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 : n011.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 02:10:56 PM UTC 2026
% Result : Theorem 0.13s 0.39s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 46 ( 11 unt; 5 def)
% Number of atoms : 126 ( 78 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 138 ( 58 ~; 40 |; 35 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 4 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 61 ( 55 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] : set_union2(A,B) = set_union2(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [A,B,C] :
~ ( ~ ( C = empty_set
& B = singleton(A) )
& ~ ( C = singleton(A)
& B = empty_set )
& ~ ( C = singleton(A)
& B = singleton(A) )
& singleton(A) = set_union2(B,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,conjecture,
! [A,B,C] :
~ ( C != empty_set
& B != empty_set
& B != C
& singleton(A) = set_union2(B,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
~ ! [A,B,C] :
~ ( C != empty_set
& B != empty_set
& B != C
& singleton(A) = set_union2(B,C) ),
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f11,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f25,plain,
! [A,B,C] :
( ( C = empty_set
& B = singleton(A) )
| ( C = singleton(A)
& B = empty_set )
| ( C = singleton(A)
& B = singleton(A) )
| singleton(A) != set_union2(B,C) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f26,definition,
! [A,B,C] :
( sP0_prd(C,B,A)
<=> ( C = singleton(A)
& B = singleton(A) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f27,definition,
! [A,B,C] :
( sP1_prd(C,B,A)
<=> ( C = singleton(A)
& B = empty_set ) ),
introduced(definition,[new_symbols(definition,[sP1_prd])],[]) ).
fof(f28,plain,
! [A,B,C] :
( ( C = empty_set
& B = singleton(A) )
| sP1_prd(C,B,A)
| sP0_prd(C,B,A)
| singleton(A) != set_union2(B,C) ),
inference(formula_renaming,[status(thm)],[f25,f27,f26]) ).
fof(f30,plain,
! [X0,X1,X2] :
( X2 = empty_set
| sP1_prd(X2,X1,X0)
| sP0_prd(X2,X1,X0)
| singleton(X0) != set_union2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f31,plain,
? [A,B,C] :
( C != empty_set
& B != empty_set
& B != C
& singleton(A) = set_union2(B,C) ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f32,plain,
? [C] :
( C != empty_set
& ? [B] :
( B != empty_set
& B != C
& ? [A] : singleton(A) = set_union2(B,C) ) ),
inference(miniscoping,[status(thm)],[f31]) ).
fof(f33,plain,
( sK2_skl != empty_set
& sK3_skl != empty_set
& sK3_skl != sK2_skl
& singleton(sK4_skl) = set_union2(sK3_skl,sK2_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl,sK4_skl]),skolemize(C,sK2_skl),skolemize(B,sK3_skl),skolemize(A,sK4_skl)],[f32]) ).
fof(f34,plain,
singleton(sK4_skl) = set_union2(sK3_skl,sK2_skl),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f35,plain,
sK3_skl != sK2_skl,
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f36,plain,
sK3_skl != empty_set,
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f37,plain,
sK2_skl != empty_set,
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f38,plain,
! [A,B,C] :
( ( C != singleton(A)
| B != singleton(A)
| sP0_prd(C,B,A) )
& ( ( C = singleton(A)
& B = singleton(A) )
| ~ sP0_prd(C,B,A) ) ),
inference(NNF_transformation,[status(thm)],[f26]) ).
fof(f39,plain,
( ! [A,B,C] :
( C != singleton(A)
| B != singleton(A)
| sP0_prd(C,B,A) )
& ! [A,B,C] :
( ( C = singleton(A)
& B = singleton(A) )
| ~ sP0_prd(C,B,A) ) ),
inference(miniscoping,[status(thm)],[f38]) ).
fof(f40,plain,
! [X0,X1,X2] :
( X1 = singleton(X2)
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f41,plain,
! [X0,X1,X2] :
( X0 = singleton(X2)
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f43,plain,
! [A,B,C] :
( ( C != singleton(A)
| B != empty_set
| sP1_prd(C,B,A) )
& ( ( C = singleton(A)
& B = empty_set )
| ~ sP1_prd(C,B,A) ) ),
inference(NNF_transformation,[status(thm)],[f27]) ).
fof(f44,plain,
( ! [A,B,C] :
( C != singleton(A)
| B != empty_set
| sP1_prd(C,B,A) )
& ! [A,B,C] :
( ( C = singleton(A)
& B = empty_set )
| ~ sP1_prd(C,B,A) ) ),
inference(miniscoping,[status(thm)],[f43]) ).
fof(f45,plain,
! [X0,X1,X2] :
( X1 = empty_set
| ~ sP1_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f48,plain,
singleton(sK4_skl) = set_union2(sK2_skl,sK3_skl),
inference(backward_demodulation,[status(thm)],[f11,f34]) ).
fof(f67,definition,
( sQ0_spl
<=> sP0_prd(sK3_skl,sK2_skl,sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f68,plain,
( ~ sQ0_spl
| sP0_prd(sK3_skl,sK2_skl,sK4_skl) ),
inference(component_clause,[status(thm)],[f67]) ).
fof(f70,definition,
( sQ1_spl
<=> sP1_prd(sK3_skl,sK2_skl,sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f71,plain,
( ~ sQ1_spl
| sP1_prd(sK3_skl,sK2_skl,sK4_skl) ),
inference(component_clause,[status(thm)],[f70]) ).
fof(f98,plain,
( sK3_skl = empty_set
| sP1_prd(sK3_skl,sK2_skl,sK4_skl)
| sP0_prd(sK3_skl,sK2_skl,sK4_skl) ),
inference(resolution,[status(thm)],[f48,f30]) ).
fof(f102,definition,
( sQ6_spl
<=> sK3_skl = empty_set ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f103,plain,
( ~ sQ6_spl
| sK3_skl = empty_set ),
inference(component_clause,[status(thm)],[f102]) ).
fof(f105,plain,
( sQ6_spl
| sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f98,f67,f70,f102]) ).
fof(f112,plain,
( ~ sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f103,f36]) ).
fof(f113,plain,
~ sQ6_spl,
inference(contradiction_clause,[status(thm)],[f112]) ).
fof(f114,plain,
( ~ sQ0_spl
| sK3_skl = singleton(sK4_skl) ),
inference(resolution,[status(thm)],[f68,f41]) ).
fof(f115,plain,
( ~ sQ0_spl
| sK2_skl = singleton(sK4_skl) ),
inference(resolution,[status(thm)],[f68,f40]) ).
fof(f116,plain,
( ~ sQ0_spl
| sK3_skl = set_union2(sK2_skl,sK3_skl) ),
inference(backward_demodulation,[status(thm)],[f114,f48]) ).
fof(f161,plain,
( ~ sQ1_spl
| sK2_skl = empty_set ),
inference(resolution,[status(thm)],[f71,f45]) ).
fof(f162,plain,
( ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f161,f37]) ).
fof(f163,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f162]) ).
fof(f164,plain,
( ~ sQ0_spl
| singleton(sK4_skl) = sK3_skl ),
inference(backward_demodulation,[status(thm)],[f116,f48]) ).
fof(f187,plain,
( ~ sQ0_spl
| sK2_skl = sK3_skl ),
inference(backward_demodulation,[status(thm)],[f115,f164]) ).
fof(f188,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f187,f35]) ).
fof(f189,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f188]) ).
fof(f190,plain,
$false,
inference(sat_refutation,[status(thm)],[f105,f113,f163,f189]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET903+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n011.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 05:43:25 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.13/0.37 % Drodi V4.1.1
% 0.13/0.39 % Refutation found
% 0.13/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.41 % Elapsed time: 0.046699 seconds
% 0.13/0.41 % CPU time: 0.141849 seconds
% 0.13/0.41 % Total memory used: 101.850 MB
% 0.13/0.41 % Net memory used: 101.461 MB
%------------------------------------------------------------------------------