%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET617+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/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 02:10:15 PM UTC 2026
% Result : Theorem 0.14s 0.39s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 32 ( 17 unt; 2 def)
% Number of atoms : 47 ( 32 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 30 ( 15 ~; 11 |; 2 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 3 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 23 ( 20 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [B,C] : symmetric_difference(B,C) = union(difference(B,C),difference(C,B)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [B] : union(B,empty_set) = B,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [B] : difference(B,empty_set) = B,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [B] : difference(empty_set,B) = empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [B,C] : symmetric_difference(B,C) = symmetric_difference(C,B),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,conjecture,
! [B] :
( symmetric_difference(empty_set,B) = B
& symmetric_difference(B,empty_set) = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
~ ! [B] :
( symmetric_difference(empty_set,B) = B
& symmetric_difference(B,empty_set) = B ),
inference(negated_conjecture,[status(cth)],[f13]) ).
fof(f15,plain,
! [X0,X1] : symmetric_difference(X0,X1) = union(difference(X0,X1),difference(X1,X0)),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f16,plain,
! [X0] : union(X0,empty_set) = X0,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f17,plain,
! [X0] : difference(X0,empty_set) = X0,
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f18,plain,
! [X0] : difference(empty_set,X0) = empty_set,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f26,plain,
! [X0,X1] : symmetric_difference(X0,X1) = symmetric_difference(X1,X0),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f47,plain,
? [B] :
( symmetric_difference(empty_set,B) != B
| symmetric_difference(B,empty_set) != B ),
inference(pre_NNF_transformation,[status(thm)],[f14]) ).
fof(f48,plain,
( ? [B] : symmetric_difference(empty_set,B) != B
| ? [B] : symmetric_difference(B,empty_set) != B ),
inference(miniscoping,[status(thm)],[f47]) ).
fof(f49,plain,
( symmetric_difference(empty_set,sK4_skl) != sK4_skl
| symmetric_difference(sK3_skl,empty_set) != sK3_skl ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl,sK4_skl]),skolemize(B,sK3_skl),skolemize(B,sK4_skl)],[f48]) ).
fof(f50,plain,
( symmetric_difference(empty_set,sK4_skl) != sK4_skl
| symmetric_difference(sK3_skl,empty_set) != sK3_skl ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f51,definition,
( sQ0_spl
<=> symmetric_difference(sK3_skl,empty_set) = sK3_skl ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f53,plain,
( sQ0_spl
| symmetric_difference(sK3_skl,empty_set) != sK3_skl ),
inference(component_clause,[status(thm)],[f51]) ).
fof(f54,definition,
( sQ1_spl
<=> symmetric_difference(empty_set,sK4_skl) = sK4_skl ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f56,plain,
( sQ1_spl
| symmetric_difference(empty_set,sK4_skl) != sK4_skl ),
inference(component_clause,[status(thm)],[f54]) ).
fof(f57,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f50,f51,f54]) ).
fof(f67,plain,
! [X0] : symmetric_difference(X0,empty_set) = union(X0,difference(empty_set,X0)),
inference(paramodulation,[status(thm)],[f17,f15]) ).
fof(f69,plain,
! [X0] : symmetric_difference(X0,empty_set) = union(X0,empty_set),
inference(forward_demodulation,[status(thm)],[f18,f67]) ).
fof(f70,plain,
( sQ0_spl
| sK3_skl != sK3_skl ),
inference(backward_demodulation,[status(thm)],[f71,f53]) ).
fof(f71,plain,
! [X0] : symmetric_difference(X0,empty_set) = X0,
inference(forward_demodulation,[status(thm)],[f16,f69]) ).
fof(f72,plain,
( sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f70]) ).
fof(f73,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f72]) ).
fof(f74,plain,
! [X0] : symmetric_difference(empty_set,X0) = X0,
inference(paramodulation,[status(thm)],[f26,f71]) ).
fof(f78,plain,
( sQ1_spl
| sK4_skl != sK4_skl ),
inference(backward_demodulation,[status(thm)],[f74,f56]) ).
fof(f80,plain,
( sQ1_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f78]) ).
fof(f81,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f80]) ).
fof(f82,plain,
$false,
inference(sat_refutation,[status(thm)],[f57,f73,f81]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET617+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n020.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Mon Sep 21 05:30:02 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.36 % Drodi V4.1.1
% 0.14/0.39 % Refutation found
% 0.14/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.42 % Elapsed time: 0.058278 seconds
% 0.14/0.42 % CPU time: 0.153733 seconds
% 0.14/0.42 % Total memory used: 101.537 MB
% 0.14/0.42 % Net memory used: 101.207 MB
%------------------------------------------------------------------------------