%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU305+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 : n017.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 02:20:06 PM UTC 2026
% Result : Theorem 0.17s 5.47s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 13
% Syntax : Number of formulae : 68 ( 14 unt; 9 def)
% Number of atoms : 229 ( 35 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 263 ( 102 ~; 107 |; 30 &)
% ( 11 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 16 ( 14 usr; 10 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-3 aty)
% Number of variables : 47 ( 44 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [A,B,C] :
( ( element(C,the_carrier(A))
& element(B,the_carrier(A))
& join_semilatt_str(A)
& join_commutative(A)
& ~ empty_carrier(A) )
=> join_commut(A,B,C) = join_commut(A,C,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A] :
( ( join_semilatt_str(A)
& ~ empty_carrier(A) )
=> ! [B] :
( element(B,the_carrier(A))
=> ! [C] :
( element(C,the_carrier(A))
=> ( below(A,B,C)
<=> join(A,B,C) = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,axiom,
! [A,B,C] :
( ( element(C,the_carrier(A))
& element(B,the_carrier(A))
& join_semilatt_str(A)
& join_commutative(A)
& ~ empty_carrier(A) )
=> join_commut(A,B,C) = join(A,B,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f35,conjecture,
! [A] :
( ( join_semilatt_str(A)
& join_commutative(A)
& ~ empty_carrier(A) )
=> ! [B] :
( element(B,the_carrier(A))
=> ! [C] :
( element(C,the_carrier(A))
=> ( ( below(A,C,B)
& below(A,B,C) )
=> B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f36,negated_conjecture,
~ ! [A] :
( ( join_semilatt_str(A)
& join_commutative(A)
& ~ empty_carrier(A) )
=> ! [B] :
( element(B,the_carrier(A))
=> ! [C] :
( element(C,the_carrier(A))
=> ( ( below(A,C,B)
& below(A,B,C) )
=> B = C ) ) ) ),
inference(negated_conjecture,[status(cth)],[f35]) ).
fof(f51,plain,
! [A,B,C] :
( join_commut(A,B,C) = join_commut(A,C,B)
| ~ element(C,the_carrier(A))
| ~ element(B,the_carrier(A))
| ~ join_semilatt_str(A)
| ~ join_commutative(A)
| empty_carrier(A) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f52,plain,
! [X0,X1,X2] :
( join_commut(X0,X1,X2) = join_commut(X0,X2,X1)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ join_semilatt_str(X0)
| ~ join_commutative(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f55,plain,
! [A] :
( ! [B] :
( ! [C] :
( ( below(A,B,C)
<=> join(A,B,C) = C )
| ~ element(C,the_carrier(A)) )
| ~ element(B,the_carrier(A)) )
| ~ join_semilatt_str(A)
| empty_carrier(A) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f56,plain,
! [A] :
( ! [B] :
( ! [C] :
( ( ( join(A,B,C) != C
| below(A,B,C) )
& ( join(A,B,C) = C
| ~ below(A,B,C) ) )
| ~ element(C,the_carrier(A)) )
| ~ element(B,the_carrier(A)) )
| ~ join_semilatt_str(A)
| empty_carrier(A) ),
inference(NNF_transformation,[status(thm)],[f55]) ).
fof(f57,plain,
! [X0,X1,X2] :
( join(X0,X1,X2) = X2
| ~ below(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ join_semilatt_str(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f99,plain,
! [A,B,C] :
( join_commut(A,B,C) = join(A,B,C)
| ~ element(C,the_carrier(A))
| ~ element(B,the_carrier(A))
| ~ join_semilatt_str(A)
| ~ join_commutative(A)
| empty_carrier(A) ),
inference(pre_NNF_transformation,[status(thm)],[f31]) ).
fof(f100,plain,
! [X0,X1,X2] :
( join_commut(X0,X1,X2) = join(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ join_semilatt_str(X0)
| ~ join_commutative(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[status(thm)],[f99]) ).
fof(f109,plain,
? [A] :
( ? [B] :
( ? [C] :
( B != C
& below(A,C,B)
& below(A,B,C)
& element(C,the_carrier(A)) )
& element(B,the_carrier(A)) )
& join_semilatt_str(A)
& join_commutative(A)
& ~ empty_carrier(A) ),
inference(pre_NNF_transformation,[status(thm)],[f36]) ).
fof(f110,plain,
( sK8_skl != sK9_skl
& below(sK7_skl,sK9_skl,sK8_skl)
& below(sK7_skl,sK8_skl,sK9_skl)
& element(sK9_skl,the_carrier(sK7_skl))
& element(sK8_skl,the_carrier(sK7_skl))
& join_semilatt_str(sK7_skl)
& join_commutative(sK7_skl)
& ~ empty_carrier(sK7_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7_skl,sK8_skl,sK9_skl]),skolemize(A,sK7_skl),skolemize(B,sK8_skl),skolemize(C,sK9_skl)],[f109]) ).
fof(f111,plain,
~ empty_carrier(sK7_skl),
inference(cnf_transformation,[status(thm)],[f110]) ).
fof(f112,plain,
join_commutative(sK7_skl),
inference(cnf_transformation,[status(thm)],[f110]) ).
fof(f113,plain,
join_semilatt_str(sK7_skl),
inference(cnf_transformation,[status(thm)],[f110]) ).
fof(f114,plain,
element(sK8_skl,the_carrier(sK7_skl)),
inference(cnf_transformation,[status(thm)],[f110]) ).
fof(f115,plain,
element(sK9_skl,the_carrier(sK7_skl)),
inference(cnf_transformation,[status(thm)],[f110]) ).
fof(f116,plain,
below(sK7_skl,sK8_skl,sK9_skl),
inference(cnf_transformation,[status(thm)],[f110]) ).
fof(f117,plain,
below(sK7_skl,sK9_skl,sK8_skl),
inference(cnf_transformation,[status(thm)],[f110]) ).
fof(f118,plain,
sK8_skl != sK9_skl,
inference(cnf_transformation,[status(thm)],[f110]) ).
fof(f140,definition,
( sQ0_spl
<=> join_semilatt_str(sK7_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f142,plain,
( sQ0_spl
| ~ join_semilatt_str(sK7_skl) ),
inference(component_clause,[status(thm)],[f140]) ).
fof(f147,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f142,f113]) ).
fof(f148,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f147]) ).
fof(f150,definition,
( sQ2_spl
<=> empty_carrier(sK7_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f151,plain,
( ~ sQ2_spl
| empty_carrier(sK7_skl) ),
inference(component_clause,[status(thm)],[f150]) ).
fof(f157,plain,
( ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f151,f111]) ).
fof(f158,plain,
~ sQ2_spl,
inference(contradiction_clause,[status(thm)],[f157]) ).
fof(f159,plain,
( join(sK7_skl,sK8_skl,sK9_skl) = sK9_skl
| ~ element(sK9_skl,the_carrier(sK7_skl))
| ~ element(sK8_skl,the_carrier(sK7_skl))
| ~ join_semilatt_str(sK7_skl)
| empty_carrier(sK7_skl) ),
inference(resolution,[status(thm)],[f116,f57]) ).
fof(f160,definition,
( sQ4_spl
<=> element(sK8_skl,the_carrier(sK7_skl)) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f162,plain,
( sQ4_spl
| ~ element(sK8_skl,the_carrier(sK7_skl)) ),
inference(component_clause,[status(thm)],[f160]) ).
fof(f163,definition,
( sQ5_spl
<=> element(sK9_skl,the_carrier(sK7_skl)) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f165,plain,
( sQ5_spl
| ~ element(sK9_skl,the_carrier(sK7_skl)) ),
inference(component_clause,[status(thm)],[f163]) ).
fof(f166,definition,
( sQ6_spl
<=> join(sK7_skl,sK8_skl,sK9_skl) = sK9_skl ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f167,plain,
( ~ sQ6_spl
| join(sK7_skl,sK8_skl,sK9_skl) = sK9_skl ),
inference(component_clause,[status(thm)],[f166]) ).
fof(f169,plain,
( sQ6_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f159,f150,f140,f160,f163,f166]) ).
fof(f170,plain,
( join(sK7_skl,sK9_skl,sK8_skl) = sK8_skl
| ~ element(sK8_skl,the_carrier(sK7_skl))
| ~ element(sK9_skl,the_carrier(sK7_skl))
| ~ join_semilatt_str(sK7_skl)
| empty_carrier(sK7_skl) ),
inference(resolution,[status(thm)],[f117,f57]) ).
fof(f171,definition,
( sQ7_spl
<=> join(sK7_skl,sK9_skl,sK8_skl) = sK8_skl ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f172,plain,
( ~ sQ7_spl
| join(sK7_skl,sK9_skl,sK8_skl) = sK8_skl ),
inference(component_clause,[status(thm)],[f171]) ).
fof(f174,plain,
( sQ7_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ0_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f170,f150,f140,f163,f160,f171]) ).
fof(f175,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f162,f114]) ).
fof(f176,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f175]) ).
fof(f177,plain,
( sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f165,f115]) ).
fof(f178,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f177]) ).
fof(f183,plain,
! [X0,X1] :
( join_commut(sK7_skl,X0,X1) = join(sK7_skl,X0,X1)
| ~ element(X1,the_carrier(sK7_skl))
| ~ element(X0,the_carrier(sK7_skl))
| ~ join_semilatt_str(sK7_skl)
| empty_carrier(sK7_skl) ),
inference(resolution,[status(thm)],[f100,f112]) ).
fof(f184,definition,
! [X0,X1] :
( sQ8_spl
<=> ( join_commut(sK7_skl,X0,X1) = join(sK7_skl,X0,X1)
| ~ element(X1,the_carrier(sK7_skl))
| ~ element(X0,the_carrier(sK7_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f185,plain,
! [X0,X1] :
( ~ sQ8_spl
| join_commut(sK7_skl,X0,X1) = join(sK7_skl,X0,X1)
| ~ element(X1,the_carrier(sK7_skl))
| ~ element(X0,the_carrier(sK7_skl)) ),
inference(component_clause,[status(thm)],[f184]) ).
fof(f187,plain,
( sQ8_spl
| ~ sQ0_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f183,f150,f140,f184]) ).
fof(f194,plain,
! [X0] :
( ~ sQ8_spl
| join_commut(sK7_skl,X0,sK9_skl) = join(sK7_skl,X0,sK9_skl)
| ~ element(X0,the_carrier(sK7_skl)) ),
inference(resolution,[status(thm)],[f185,f115]) ).
fof(f196,plain,
! [X0] :
( ~ sQ8_spl
| join_commut(sK7_skl,X0,sK8_skl) = join(sK7_skl,X0,sK8_skl)
| ~ element(X0,the_carrier(sK7_skl)) ),
inference(resolution,[status(thm)],[f185,f114]) ).
fof(f213,plain,
( ~ sQ8_spl
| join_commut(sK7_skl,sK8_skl,sK9_skl) = join(sK7_skl,sK8_skl,sK9_skl) ),
inference(resolution,[status(thm)],[f194,f114]) ).
fof(f218,plain,
( ~ sQ8_spl
| ~ sQ6_spl
| join_commut(sK7_skl,sK8_skl,sK9_skl) = sK9_skl ),
inference(forward_demodulation,[status(thm)],[f167,f213]) ).
fof(f245,plain,
( ~ sQ8_spl
| join_commut(sK7_skl,sK9_skl,sK8_skl) = join(sK7_skl,sK9_skl,sK8_skl) ),
inference(resolution,[status(thm)],[f196,f115]) ).
fof(f248,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| join_commut(sK7_skl,sK9_skl,sK8_skl) = sK8_skl ),
inference(forward_demodulation,[status(thm)],[f172,f245]) ).
fof(f256,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| join_commut(sK7_skl,sK8_skl,sK9_skl) = sK8_skl
| ~ element(sK9_skl,the_carrier(sK7_skl))
| ~ element(sK8_skl,the_carrier(sK7_skl))
| ~ join_semilatt_str(sK7_skl)
| ~ join_commutative(sK7_skl)
| empty_carrier(sK7_skl) ),
inference(paramodulation,[status(thm)],[f248,f52]) ).
fof(f259,definition,
( sQ18_spl
<=> join_commutative(sK7_skl) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f261,plain,
( sQ18_spl
| ~ join_commutative(sK7_skl) ),
inference(component_clause,[status(thm)],[f259]) ).
fof(f262,definition,
( sQ19_spl
<=> join_commut(sK7_skl,sK8_skl,sK9_skl) = sK8_skl ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f263,plain,
( ~ sQ19_spl
| join_commut(sK7_skl,sK8_skl,sK9_skl) = sK8_skl ),
inference(component_clause,[status(thm)],[f262]) ).
fof(f265,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| sQ19_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| ~ sQ18_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f256,f150,f259,f140,f160,f163,f262,f171,f184]) ).
fof(f267,plain,
( sQ18_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f261,f112]) ).
fof(f268,plain,
sQ18_spl,
inference(contradiction_clause,[status(thm)],[f267]) ).
fof(f330,plain,
( ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ19_spl
| sK8_skl = sK9_skl ),
inference(backward_demodulation,[status(thm)],[f263,f218]) ).
fof(f332,plain,
( ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ19_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f330,f118]) ).
fof(f333,plain,
( ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ19_spl ),
inference(contradiction_clause,[status(thm)],[f332]) ).
fof(f334,plain,
$false,
inference(sat_refutation,[status(thm)],[f148,f158,f169,f174,f176,f178,f187,f265,f268,f333]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU305+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/5.43 % Computer : n017.cluster.edu
% 0.17/5.43 % Model : x86_64 x86_64
% 0.17/5.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/5.43 % Memory : 8046.5625MB
% 0.17/5.43 % OS : Linux 6.8.0-71-generic
% 0.17/5.43 % CPULimit : 300
% 0.17/5.43 % WCLimit : 300
% 0.17/5.43 % DateTime : Mon Sep 21 06:05:33 UTC 2026
% 0.17/5.44 % CPUTime :
% 0.17/5.45 % Drodi V4.1.1
% 0.17/5.47 % Refutation found
% 0.17/5.47 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.17/5.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.20/5.50 % Elapsed time: 0.052422 seconds
% 0.20/5.50 % CPU time: 0.153991 seconds
% 0.20/5.50 % Total memory used: 31.670 MB
% 0.20/5.50 % Net memory used: 31.637 MB
%------------------------------------------------------------------------------