%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU305+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n001.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 0.12s 0.46s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 16
% Syntax : Number of formulae : 83 ( 16 unt; 11 def)
% Number of atoms : 265 ( 43 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 302 ( 120 ~; 124 |; 32 &)
% ( 13 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 21 ( 19 usr; 12 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 62 ( 59 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f19,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/sandbox/benchmark/theBenchmark.p') ).
fof(f59,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/sandbox/benchmark/theBenchmark.p') ).
fof(f162,axiom,
( relation_empty_yielding(empty_set)
& relation(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f247,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/sandbox/benchmark/theBenchmark.p') ).
fof(f352,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/sandbox/benchmark/theBenchmark.p') ).
fof(f353,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)],[f352]) ).
fof(f505,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)],[f19]) ).
fof(f506,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)],[f505]) ).
fof(f779,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)],[f59]) ).
fof(f780,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)],[f779]) ).
fof(f781,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)],[f780]) ).
fof(f1119,plain,
empty(empty_set),
inference(cnf_transformation,[status(thm)],[f162]) ).
fof(f1416,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)],[f247]) ).
fof(f1417,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)],[f1416]) ).
fof(f1959,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)],[f353]) ).
fof(f1960,plain,
( sK257_skl != sK258_skl
& below(sK256_skl,sK258_skl,sK257_skl)
& below(sK256_skl,sK257_skl,sK258_skl)
& element(sK258_skl,the_carrier(sK256_skl))
& element(sK257_skl,the_carrier(sK256_skl))
& join_semilatt_str(sK256_skl)
& join_commutative(sK256_skl)
& ~ empty_carrier(sK256_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK256_skl,sK257_skl,sK258_skl]),skolemize(A,sK256_skl),skolemize(B,sK257_skl),skolemize(C,sK258_skl)],[f1959]) ).
fof(f1961,plain,
~ empty_carrier(sK256_skl),
inference(cnf_transformation,[status(thm)],[f1960]) ).
fof(f1962,plain,
join_commutative(sK256_skl),
inference(cnf_transformation,[status(thm)],[f1960]) ).
fof(f1963,plain,
join_semilatt_str(sK256_skl),
inference(cnf_transformation,[status(thm)],[f1960]) ).
fof(f1964,plain,
element(sK257_skl,the_carrier(sK256_skl)),
inference(cnf_transformation,[status(thm)],[f1960]) ).
fof(f1965,plain,
element(sK258_skl,the_carrier(sK256_skl)),
inference(cnf_transformation,[status(thm)],[f1960]) ).
fof(f1966,plain,
below(sK256_skl,sK257_skl,sK258_skl),
inference(cnf_transformation,[status(thm)],[f1960]) ).
fof(f1967,plain,
below(sK256_skl,sK258_skl,sK257_skl),
inference(cnf_transformation,[status(thm)],[f1960]) ).
fof(f1968,plain,
sK257_skl != sK258_skl,
inference(cnf_transformation,[status(thm)],[f1960]) ).
fof(f3090,plain,
! [X0,X1] :
( join_commut(sK256_skl,X0,X1) = join_commut(sK256_skl,X1,X0)
| ~ element(X1,the_carrier(sK256_skl))
| ~ element(X0,the_carrier(sK256_skl))
| ~ join_semilatt_str(sK256_skl)
| empty_carrier(sK256_skl) ),
inference(resolution,[status(thm)],[f506,f1962]) ).
fof(f3092,definition,
( sQ57_spl
<=> empty_carrier(sK256_skl) ),
introduced(definition,[new_symbols(definition,[sQ57_spl])],[split_symbol_definition]) ).
fof(f3093,plain,
( ~ sQ57_spl
| empty_carrier(sK256_skl) ),
inference(component_clause,[status(thm)],[f3092]) ).
fof(f3095,definition,
( sQ58_spl
<=> join_semilatt_str(sK256_skl) ),
introduced(definition,[new_symbols(definition,[sQ58_spl])],[split_symbol_definition]) ).
fof(f3097,plain,
( sQ58_spl
| ~ join_semilatt_str(sK256_skl) ),
inference(component_clause,[status(thm)],[f3095]) ).
fof(f3098,definition,
! [X0,X1] :
( sQ59_spl
<=> ( join_commut(sK256_skl,X0,X1) = join_commut(sK256_skl,X1,X0)
| ~ element(X1,the_carrier(sK256_skl))
| ~ element(X0,the_carrier(sK256_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ59_spl])],[split_symbol_definition]) ).
fof(f3099,plain,
! [X0,X1] :
( ~ sQ59_spl
| join_commut(sK256_skl,X0,X1) = join_commut(sK256_skl,X1,X0)
| ~ element(X1,the_carrier(sK256_skl))
| ~ element(X0,the_carrier(sK256_skl)) ),
inference(component_clause,[status(thm)],[f3098]) ).
fof(f3101,plain,
( sQ59_spl
| ~ sQ58_spl
| sQ57_spl ),
inference(split_clause,[status(thm)],[f3090,f3092,f3095,f3098]) ).
fof(f3102,definition,
( sQ60_spl
<=> join_commutative(sK256_skl) ),
introduced(definition,[new_symbols(definition,[sQ60_spl])],[split_symbol_definition]) ).
fof(f3104,plain,
( sQ60_spl
| ~ join_commutative(sK256_skl) ),
inference(component_clause,[status(thm)],[f3102]) ).
fof(f3106,plain,
! [X0] :
( ~ sQ59_spl
| join_commut(sK256_skl,X0,sK258_skl) = join_commut(sK256_skl,sK258_skl,X0)
| ~ element(X0,the_carrier(sK256_skl)) ),
inference(resolution,[status(thm)],[f3099,f1965]) ).
fof(f3111,plain,
! [X0,X1] :
( join(sK256_skl,X0,X1) = X1
| ~ below(sK256_skl,X0,X1)
| ~ element(X1,the_carrier(sK256_skl))
| ~ element(X0,the_carrier(sK256_skl))
| empty_carrier(sK256_skl) ),
inference(resolution,[status(thm)],[f781,f1963]) ).
fof(f3112,definition,
! [X0,X1] :
( sQ61_spl
<=> ( join(sK256_skl,X0,X1) = X1
| ~ below(sK256_skl,X0,X1)
| ~ element(X1,the_carrier(sK256_skl))
| ~ element(X0,the_carrier(sK256_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ61_spl])],[split_symbol_definition]) ).
fof(f3113,plain,
! [X0,X1] :
( ~ sQ61_spl
| join(sK256_skl,X0,X1) = X1
| ~ below(sK256_skl,X0,X1)
| ~ element(X1,the_carrier(sK256_skl))
| ~ element(X0,the_carrier(sK256_skl)) ),
inference(component_clause,[status(thm)],[f3112]) ).
fof(f3115,plain,
( sQ61_spl
| sQ57_spl ),
inference(split_clause,[status(thm)],[f3111,f3092,f3112]) ).
fof(f3116,plain,
( ~ sQ57_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3093,f1961]) ).
fof(f3117,plain,
~ sQ57_spl,
inference(contradiction_clause,[status(thm)],[f3116]) ).
fof(f3145,plain,
( ~ sQ59_spl
| join_commut(sK256_skl,sK257_skl,sK258_skl) = join_commut(sK256_skl,sK258_skl,sK257_skl) ),
inference(resolution,[status(thm)],[f3106,f1964]) ).
fof(f3169,definition,
( sQ71_spl
<=> element(sK258_skl,the_carrier(sK256_skl)) ),
introduced(definition,[new_symbols(definition,[sQ71_spl])],[split_symbol_definition]) ).
fof(f3171,plain,
( sQ71_spl
| ~ element(sK258_skl,the_carrier(sK256_skl)) ),
inference(component_clause,[status(thm)],[f3169]) ).
fof(f3172,definition,
( sQ72_spl
<=> element(sK257_skl,the_carrier(sK256_skl)) ),
introduced(definition,[new_symbols(definition,[sQ72_spl])],[split_symbol_definition]) ).
fof(f3174,plain,
( sQ72_spl
| ~ element(sK257_skl,the_carrier(sK256_skl)) ),
inference(component_clause,[status(thm)],[f3172]) ).
fof(f3179,plain,
( sQ58_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3097,f1963]) ).
fof(f3180,plain,
sQ58_spl,
inference(contradiction_clause,[status(thm)],[f3179]) ).
fof(f3181,plain,
( sQ60_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3104,f1962]) ).
fof(f3182,plain,
sQ60_spl,
inference(contradiction_clause,[status(thm)],[f3181]) ).
fof(f3185,plain,
! [X0,X1] :
( join_commut(sK256_skl,X0,X1) = join(sK256_skl,X0,X1)
| ~ element(X1,the_carrier(sK256_skl))
| ~ element(X0,the_carrier(sK256_skl))
| ~ join_commutative(sK256_skl)
| empty_carrier(sK256_skl) ),
inference(resolution,[status(thm)],[f1417,f1963]) ).
fof(f3186,definition,
! [X0,X1] :
( sQ74_spl
<=> ( join_commut(sK256_skl,X0,X1) = join(sK256_skl,X0,X1)
| ~ element(X1,the_carrier(sK256_skl))
| ~ element(X0,the_carrier(sK256_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ74_spl])],[split_symbol_definition]) ).
fof(f3187,plain,
! [X0,X1] :
( ~ sQ74_spl
| join_commut(sK256_skl,X0,X1) = join(sK256_skl,X0,X1)
| ~ element(X1,the_carrier(sK256_skl))
| ~ element(X0,the_carrier(sK256_skl)) ),
inference(component_clause,[status(thm)],[f3186]) ).
fof(f3194,plain,
( sQ74_spl
| ~ sQ60_spl
| sQ57_spl ),
inference(split_clause,[status(thm)],[f3185,f3092,f3102,f3186]) ).
fof(f3199,plain,
! [X0] :
( ~ sQ61_spl
| join(sK256_skl,X0,sK258_skl) = sK258_skl
| ~ below(sK256_skl,X0,sK258_skl)
| ~ element(X0,the_carrier(sK256_skl)) ),
inference(resolution,[status(thm)],[f3113,f1965]) ).
fof(f3200,plain,
! [X0] :
( ~ sQ61_spl
| join(sK256_skl,X0,sK257_skl) = sK257_skl
| ~ below(sK256_skl,X0,sK257_skl)
| ~ element(X0,the_carrier(sK256_skl)) ),
inference(resolution,[status(thm)],[f3113,f1964]) ).
fof(f3235,plain,
! [X0] :
( ~ sQ74_spl
| join_commut(sK256_skl,X0,sK258_skl) = join(sK256_skl,X0,sK258_skl)
| ~ element(X0,the_carrier(sK256_skl)) ),
inference(resolution,[status(thm)],[f3187,f1965]) ).
fof(f3236,plain,
! [X0] :
( ~ sQ74_spl
| join_commut(sK256_skl,X0,sK257_skl) = join(sK256_skl,X0,sK257_skl)
| ~ element(X0,the_carrier(sK256_skl)) ),
inference(resolution,[status(thm)],[f3187,f1964]) ).
fof(f3245,plain,
( ~ sQ74_spl
| join_commut(sK256_skl,sK257_skl,sK258_skl) = join(sK256_skl,sK257_skl,sK258_skl) ),
inference(resolution,[status(thm)],[f3235,f1964]) ).
fof(f3273,plain,
( ~ sQ74_spl
| join_commut(sK256_skl,sK258_skl,sK257_skl) = join(sK256_skl,sK258_skl,sK257_skl) ),
inference(resolution,[status(thm)],[f3236,f1965]) ).
fof(f3280,plain,
( ~ sQ74_spl
| ~ sQ59_spl
| join_commut(sK256_skl,sK257_skl,sK258_skl) = join(sK256_skl,sK258_skl,sK257_skl) ),
inference(forward_demodulation,[status(thm)],[f3145,f3273]) ).
fof(f3281,plain,
( ~ sQ61_spl
| join(sK256_skl,sK257_skl,sK258_skl) = sK258_skl
| ~ element(sK257_skl,the_carrier(sK256_skl)) ),
inference(resolution,[status(thm)],[f3199,f1966]) ).
fof(f3282,definition,
( sQ84_spl
<=> join(sK256_skl,sK257_skl,sK258_skl) = sK258_skl ),
introduced(definition,[new_symbols(definition,[sQ84_spl])],[split_symbol_definition]) ).
fof(f3283,plain,
( ~ sQ84_spl
| join(sK256_skl,sK257_skl,sK258_skl) = sK258_skl ),
inference(component_clause,[status(thm)],[f3282]) ).
fof(f3285,plain,
( ~ sQ61_spl
| sQ84_spl
| ~ sQ72_spl ),
inference(split_clause,[status(thm)],[f3281,f3172,f3282,f3112]) ).
fof(f3286,plain,
( sQ72_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3174,f1964]) ).
fof(f3287,plain,
sQ72_spl,
inference(contradiction_clause,[status(thm)],[f3286]) ).
fof(f3288,plain,
( ~ sQ84_spl
| ~ sQ74_spl
| join_commut(sK256_skl,sK257_skl,sK258_skl) = sK258_skl ),
inference(forward_demodulation,[status(thm)],[f3245,f3283]) ).
fof(f3289,plain,
( sQ71_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3171,f1965]) ).
fof(f3290,plain,
sQ71_spl,
inference(contradiction_clause,[status(thm)],[f3289]) ).
fof(f3315,plain,
( ~ sQ61_spl
| join(sK256_skl,sK258_skl,sK257_skl) = sK257_skl
| ~ element(sK258_skl,the_carrier(sK256_skl)) ),
inference(resolution,[status(thm)],[f3200,f1967]) ).
fof(f3316,definition,
( sQ88_spl
<=> join(sK256_skl,sK258_skl,sK257_skl) = sK257_skl ),
introduced(definition,[new_symbols(definition,[sQ88_spl])],[split_symbol_definition]) ).
fof(f3317,plain,
( ~ sQ88_spl
| join(sK256_skl,sK258_skl,sK257_skl) = sK257_skl ),
inference(component_clause,[status(thm)],[f3316]) ).
fof(f3319,plain,
( ~ sQ61_spl
| sQ88_spl
| ~ sQ71_spl ),
inference(split_clause,[status(thm)],[f3315,f3169,f3316,f3112]) ).
fof(f3320,plain,
( ~ sQ88_spl
| ~ sQ74_spl
| ~ sQ59_spl
| join_commut(sK256_skl,sK257_skl,sK258_skl) = sK257_skl ),
inference(forward_demodulation,[status(thm)],[f3280,f3317]) ).
fof(f3325,definition,
( sQ89_spl
<=> empty(empty_set) ),
introduced(definition,[new_symbols(definition,[sQ89_spl])],[split_symbol_definition]) ).
fof(f3327,plain,
( sQ89_spl
| ~ empty(empty_set) ),
inference(component_clause,[status(thm)],[f3325]) ).
fof(f3333,plain,
( sQ89_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3327,f1119]) ).
fof(f3334,plain,
sQ89_spl,
inference(contradiction_clause,[status(thm)],[f3333]) ).
fof(f3340,plain,
( ~ sQ88_spl
| ~ sQ74_spl
| ~ sQ59_spl
| ~ sQ84_spl
| sK258_skl = sK257_skl ),
inference(forward_demodulation,[status(thm)],[f3288,f3320]) ).
fof(f3341,plain,
( ~ sQ88_spl
| ~ sQ74_spl
| ~ sQ59_spl
| ~ sQ84_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3340,f1968]) ).
fof(f3342,plain,
( ~ sQ88_spl
| ~ sQ74_spl
| ~ sQ59_spl
| ~ sQ84_spl ),
inference(contradiction_clause,[status(thm)],[f3341]) ).
fof(f3343,plain,
$false,
inference(sat_refutation,[status(thm)],[f3101,f3115,f3117,f3180,f3182,f3194,f3285,f3287,f3290,f3319,f3334,f3342]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU305+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.35 % Computer : n001.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.36 % CPULimit : 300
% 0.07/0.36 % WCLimit : 300
% 0.07/0.36 % DateTime : Mon Sep 21 06:15:44 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.41 % Drodi V4.1.1
% 0.12/0.46 % Refutation found
% 0.12/0.46 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.50 % Elapsed time: 0.138845 seconds
% 0.12/0.50 % CPU time: 0.430693 seconds
% 0.12/0.50 % Total memory used: 165.019 MB
% 0.12/0.50 % Net memory used: 164.127 MB
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