%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : REL003+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n026.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 02:03:10 PM UTC 2026
% Result : Theorem 0.13s 0.38s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 37 ( 6 unt; 4 def)
% Number of atoms : 87 ( 47 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 85 ( 35 ~; 30 |; 12 &)
% ( 4 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 4 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 32 ( 24 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
! [X0] : converse(converse(X0)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,conjecture,
! [X0,X1] :
( ( join(converse(X0),converse(X1)) = converse(X1)
=> join(X0,X1) = X1 )
& ( join(X0,X1) = X1
=> join(converse(X0),converse(X1)) = converse(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
~ ! [X0,X1] :
( ( join(converse(X0),converse(X1)) = converse(X1)
=> join(X0,X1) = X1 )
& ( join(X0,X1) = X1
=> join(converse(X0),converse(X1)) = converse(X1) ) ),
inference(negated_conjecture,[status(cth)],[f14]) ).
fof(f23,plain,
! [X0] : converse(converse(X0)) = X0,
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f24,plain,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f29,plain,
? [X0,X1] :
( ( join(X0,X1) != X1
& join(converse(X0),converse(X1)) = converse(X1) )
| ( join(converse(X0),converse(X1)) != converse(X1)
& join(X0,X1) = X1 ) ),
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f30,definition,
! [X0,X1] :
( sP0_prd(X1,X0)
<=> ( join(converse(X0),converse(X1)) != converse(X1)
& join(X0,X1) = X1 ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f31,plain,
? [X0,X1] :
( ( join(X0,X1) != X1
& join(converse(X0),converse(X1)) = converse(X1) )
| sP0_prd(X1,X0) ),
inference(formula_renaming,[status(thm)],[f29,f30]) ).
fof(f32,plain,
( ? [X0,X1] :
( join(X0,X1) != X1
& join(converse(X0),converse(X1)) = converse(X1) )
| ? [X0,X1] : sP0_prd(X1,X0) ),
inference(miniscoping,[status(thm)],[f31]) ).
fof(f33,plain,
( ( join(sK2_skl,sK3_skl) != sK3_skl
& join(converse(sK2_skl),converse(sK3_skl)) = converse(sK3_skl) )
| sP0_prd(sK1_skl,sK0_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl,sK3_skl]),skolemize(X0,sK0_skl),skolemize(X1,sK1_skl),skolemize(X0,sK2_skl),skolemize(X1,sK3_skl)],[f32]) ).
fof(f34,plain,
( join(converse(sK2_skl),converse(sK3_skl)) = converse(sK3_skl)
| sP0_prd(sK1_skl,sK0_skl) ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f35,plain,
( join(sK2_skl,sK3_skl) != sK3_skl
| sP0_prd(sK1_skl,sK0_skl) ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f36,plain,
! [X0,X1] :
( ( join(converse(X0),converse(X1)) = converse(X1)
| join(X0,X1) != X1
| sP0_prd(X1,X0) )
& ( ( join(converse(X0),converse(X1)) != converse(X1)
& join(X0,X1) = X1 )
| ~ sP0_prd(X1,X0) ) ),
inference(NNF_transformation,[status(thm)],[f30]) ).
fof(f37,plain,
( ! [X0,X1] :
( join(converse(X0),converse(X1)) = converse(X1)
| join(X0,X1) != X1
| sP0_prd(X1,X0) )
& ! [X0,X1] :
( ( join(converse(X0),converse(X1)) != converse(X1)
& join(X0,X1) = X1 )
| ~ sP0_prd(X1,X0) ) ),
inference(miniscoping,[status(thm)],[f36]) ).
fof(f38,plain,
! [X0,X1] :
( join(X1,X0) = X0
| ~ sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f39,plain,
! [X0,X1] :
( join(converse(X1),converse(X0)) != converse(X0)
| ~ sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f41,definition,
( sQ0_spl
<=> sP0_prd(sK1_skl,sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f42,plain,
( ~ sQ0_spl
| sP0_prd(sK1_skl,sK0_skl) ),
inference(component_clause,[status(thm)],[f41]) ).
fof(f44,definition,
( sQ1_spl
<=> join(converse(sK2_skl),converse(sK3_skl)) = converse(sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f45,plain,
( ~ sQ1_spl
| join(converse(sK2_skl),converse(sK3_skl)) = converse(sK3_skl) ),
inference(component_clause,[status(thm)],[f44]) ).
fof(f47,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f34,f41,f44]) ).
fof(f48,definition,
( sQ2_spl
<=> join(sK2_skl,sK3_skl) = sK3_skl ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f50,plain,
( sQ2_spl
| join(sK2_skl,sK3_skl) != sK3_skl ),
inference(component_clause,[status(thm)],[f48]) ).
fof(f51,plain,
( ~ sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f35,f41,f48]) ).
fof(f52,plain,
( ~ sQ0_spl
| join(sK0_skl,sK1_skl) = sK1_skl ),
inference(resolution,[status(thm)],[f38,f42]) ).
fof(f85,plain,
! [X0,X1] :
( converse(join(X1,X0)) != converse(X0)
| ~ sP0_prd(X0,X1) ),
inference(backward_demodulation,[status(thm)],[f24,f39]) ).
fof(f141,plain,
( ~ sQ0_spl
| converse(join(sK0_skl,sK1_skl)) != converse(sK1_skl) ),
inference(resolution,[status(thm)],[f85,f42]) ).
fof(f143,plain,
( ~ sQ0_spl
| converse(sK1_skl) != converse(sK1_skl) ),
inference(forward_demodulation,[status(thm)],[f52,f141]) ).
fof(f144,plain,
( ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f143]) ).
fof(f145,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f144]) ).
fof(f146,plain,
( ~ sQ1_spl
| converse(join(sK2_skl,sK3_skl)) = converse(sK3_skl) ),
inference(forward_demodulation,[status(thm)],[f24,f45]) ).
fof(f201,plain,
( ~ sQ1_spl
| converse(converse(sK3_skl)) = join(sK2_skl,sK3_skl) ),
inference(paramodulation,[status(thm)],[f146,f23]) ).
fof(f205,plain,
( ~ sQ1_spl
| sK3_skl = join(sK2_skl,sK3_skl) ),
inference(forward_demodulation,[status(thm)],[f23,f201]) ).
fof(f206,plain,
( ~ sQ1_spl
| sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f205,f50]) ).
fof(f207,plain,
( ~ sQ1_spl
| sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f206]) ).
fof(f208,plain,
$false,
inference(sat_refutation,[status(thm)],[f47,f51,f145,f207]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL003+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n026.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 04:00:07 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.13/0.37 % Drodi V4.1.1
% 0.13/0.38 % Refutation found
% 0.13/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.42 % Elapsed time: 0.054553 seconds
% 0.13/0.42 % CPU time: 0.163903 seconds
% 0.13/0.42 % Total memory used: 42.229 MB
% 0.13/0.42 % Net memory used: 42.152 MB
%------------------------------------------------------------------------------