%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET794+4 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n014.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 02:10:37 PM UTC 2026
% Result : Theorem 0.11s 0.40s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 14
% Syntax : Number of formulae : 76 ( 8 unt; 10 def)
% Number of atoms : 274 ( 14 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 328 ( 130 ~; 127 |; 50 &)
% ( 16 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 18 ( 16 usr; 11 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 122 ( 111 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [R,E] :
( total_order(R,E)
<=> ( ! [X,Y] :
( ( member(Y,E)
& member(X,E) )
=> ( apply(R,Y,X)
| apply(R,X,Y) ) )
& order(R,E) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [R,E,M] :
( least(M,R,E)
<=> ( ! [X] :
( member(X,E)
=> apply(R,M,X) )
& member(M,E) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [R,E,M] :
( min(M,R,E)
<=> ( ! [X] :
( ( apply(R,X,M)
& member(X,E) )
=> M = X )
& member(M,E) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,conjecture,
! [R,E,M] :
( ( min(M,R,E)
& total_order(R,E) )
=> least(M,R,E) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
~ ! [R,E,M] :
( ( min(M,R,E)
& total_order(R,E) )
=> least(M,R,E) ),
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f27,plain,
! [R,E] :
( total_order(R,E)
<=> ( ! [X,Y] :
( apply(R,Y,X)
| apply(R,X,Y)
| ~ member(Y,E)
| ~ member(X,E) )
& order(R,E) ) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f28,plain,
! [R,E] :
( ( ? [X,Y] :
( ~ apply(R,Y,X)
& ~ apply(R,X,Y)
& member(Y,E)
& member(X,E) )
| ~ order(R,E)
| total_order(R,E) )
& ( ( ! [X,Y] :
( apply(R,Y,X)
| apply(R,X,Y)
| ~ member(Y,E)
| ~ member(X,E) )
& order(R,E) )
| ~ total_order(R,E) ) ),
inference(NNF_transformation,[status(thm)],[f27]) ).
fof(f29,plain,
( ! [R,E] :
( ? [X,Y] :
( ~ apply(R,Y,X)
& ~ apply(R,X,Y)
& member(Y,E)
& member(X,E) )
| ~ order(R,E)
| total_order(R,E) )
& ! [R,E] :
( ( ! [X,Y] :
( apply(R,Y,X)
| apply(R,X,Y)
| ~ member(Y,E)
| ~ member(X,E) )
& order(R,E) )
| ~ total_order(R,E) ) ),
inference(miniscoping,[status(thm)],[f28]) ).
fof(f30,plain,
( ! [R,E] :
( ( ~ apply(R,sK4_skl(E,R),sK3_skl(E,R))
& ~ apply(R,sK3_skl(E,R),sK4_skl(E,R))
& member(sK4_skl(E,R),E)
& member(sK3_skl(E,R),E) )
| ~ order(R,E)
| total_order(R,E) )
& ! [R,E] :
( ( ! [X,Y] :
( apply(R,Y,X)
| apply(R,X,Y)
| ~ member(Y,E)
| ~ member(X,E) )
& order(R,E) )
| ~ total_order(R,E) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl,sK4_skl]),skolemize(X,sK3_skl(E,R)),skolemize(Y,sK4_skl(E,R))],[f29]) ).
fof(f32,plain,
! [X0,X1,X2,X3] :
( apply(X0,X3,X2)
| apply(X0,X2,X3)
| ~ member(X3,X1)
| ~ member(X2,X1)
| ~ total_order(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f59,plain,
! [R,E,M] :
( least(M,R,E)
<=> ( ! [X] :
( apply(R,M,X)
| ~ member(X,E) )
& member(M,E) ) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f60,plain,
! [R,E,M] :
( ( ? [X] :
( ~ apply(R,M,X)
& member(X,E) )
| ~ member(M,E)
| least(M,R,E) )
& ( ( ! [X] :
( apply(R,M,X)
| ~ member(X,E) )
& member(M,E) )
| ~ least(M,R,E) ) ),
inference(NNF_transformation,[status(thm)],[f59]) ).
fof(f61,plain,
( ! [R,E,M] :
( ? [X] :
( ~ apply(R,M,X)
& member(X,E) )
| ~ member(M,E)
| least(M,R,E) )
& ! [R,E,M] :
( ( ! [X] :
( apply(R,M,X)
| ~ member(X,E) )
& member(M,E) )
| ~ least(M,R,E) ) ),
inference(miniscoping,[status(thm)],[f60]) ).
fof(f62,plain,
( ! [R,E,M] :
( ( ~ apply(R,M,sK8_skl(M,E,R))
& member(sK8_skl(M,E,R),E) )
| ~ member(M,E)
| least(M,R,E) )
& ! [R,E,M] :
( ( ! [X] :
( apply(R,M,X)
| ~ member(X,E) )
& member(M,E) )
| ~ least(M,R,E) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8_skl]),skolemize(X,sK8_skl(M,E,R))],[f61]) ).
fof(f65,plain,
! [X0,X1,X2] :
( member(sK8_skl(X0,X2,X1),X2)
| ~ member(X0,X2)
| least(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f62]) ).
fof(f66,plain,
! [X0,X1,X2] :
( ~ apply(X1,X0,sK8_skl(X0,X2,X1))
| ~ member(X0,X2)
| least(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f62]) ).
fof(f76,plain,
! [R,E,M] :
( min(M,R,E)
<=> ( ! [X] :
( M = X
| ~ apply(R,X,M)
| ~ member(X,E) )
& member(M,E) ) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f77,plain,
! [R,E,M] :
( ( ? [X] :
( M != X
& apply(R,X,M)
& member(X,E) )
| ~ member(M,E)
| min(M,R,E) )
& ( ( ! [X] :
( M = X
| ~ apply(R,X,M)
| ~ member(X,E) )
& member(M,E) )
| ~ min(M,R,E) ) ),
inference(NNF_transformation,[status(thm)],[f76]) ).
fof(f78,plain,
( ! [R,E,M] :
( ? [X] :
( M != X
& apply(R,X,M)
& member(X,E) )
| ~ member(M,E)
| min(M,R,E) )
& ! [R,E,M] :
( ( ! [X] :
( M = X
| ~ apply(R,X,M)
| ~ member(X,E) )
& member(M,E) )
| ~ min(M,R,E) ) ),
inference(miniscoping,[status(thm)],[f77]) ).
fof(f79,plain,
( ! [R,E,M] :
( ( M != sK10_skl(M,E,R)
& apply(R,sK10_skl(M,E,R),M)
& member(sK10_skl(M,E,R),E) )
| ~ member(M,E)
| min(M,R,E) )
& ! [R,E,M] :
( ( ! [X] :
( M = X
| ~ apply(R,X,M)
| ~ member(X,E) )
& member(M,E) )
| ~ min(M,R,E) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10_skl]),skolemize(X,sK10_skl(M,E,R))],[f78]) ).
fof(f80,plain,
! [X0,X1,X2] :
( member(X0,X2)
| ~ min(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f79]) ).
fof(f81,plain,
! [X0,X1,X2,X3] :
( X0 = X3
| ~ apply(X1,X3,X0)
| ~ member(X3,X2)
| ~ min(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f79]) ).
fof(f105,plain,
? [R,E,M] :
( ~ least(M,R,E)
& min(M,R,E)
& total_order(R,E) ),
inference(pre_NNF_transformation,[status(thm)],[f12]) ).
fof(f106,plain,
( ~ least(sK15_skl,sK13_skl,sK14_skl)
& min(sK15_skl,sK13_skl,sK14_skl)
& total_order(sK13_skl,sK14_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13_skl,sK14_skl,sK15_skl]),skolemize(R,sK13_skl),skolemize(E,sK14_skl),skolemize(M,sK15_skl)],[f105]) ).
fof(f107,plain,
total_order(sK13_skl,sK14_skl),
inference(cnf_transformation,[status(thm)],[f106]) ).
fof(f108,plain,
min(sK15_skl,sK13_skl,sK14_skl),
inference(cnf_transformation,[status(thm)],[f106]) ).
fof(f109,plain,
~ least(sK15_skl,sK13_skl,sK14_skl),
inference(cnf_transformation,[status(thm)],[f106]) ).
fof(f127,plain,
! [X0] :
( sK15_skl = X0
| ~ apply(sK13_skl,X0,sK15_skl)
| ~ member(X0,sK14_skl) ),
inference(resolution,[status(thm)],[f81,f108]) ).
fof(f131,definition,
( sQ0_spl
<=> apply(sK13_skl,sK15_skl,sK15_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f133,plain,
( sQ0_spl
| ~ apply(sK13_skl,sK15_skl,sK15_skl) ),
inference(component_clause,[status(thm)],[f131]) ).
fof(f139,plain,
! [X0] :
( sQ0_spl
| apply(sK13_skl,sK15_skl,sK15_skl)
| ~ member(sK15_skl,X0)
| ~ member(sK15_skl,X0)
| ~ total_order(sK13_skl,X0) ),
inference(resolution,[status(thm)],[f133,f32]) ).
fof(f141,definition,
! [X0] :
( sQ2_spl
<=> ( ~ member(sK15_skl,X0)
| ~ member(sK15_skl,X0)
| ~ total_order(sK13_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f142,plain,
! [X0] :
( ~ sQ2_spl
| ~ member(sK15_skl,X0)
| ~ member(sK15_skl,X0)
| ~ total_order(sK13_skl,X0) ),
inference(component_clause,[status(thm)],[f141]) ).
fof(f144,plain,
( sQ0_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f139,f141,f131]) ).
fof(f145,plain,
! [X0] :
( ~ sQ2_spl
| ~ member(sK15_skl,X0)
| ~ total_order(sK13_skl,X0) ),
inference(duplicate_literals_removal,[status(thm)],[f142]) ).
fof(f146,plain,
( ~ sQ2_spl
| ~ member(sK15_skl,sK14_skl) ),
inference(resolution,[status(thm)],[f145,f107]) ).
fof(f147,plain,
! [X0] :
( ~ sQ2_spl
| ~ min(sK15_skl,X0,sK14_skl) ),
inference(resolution,[status(thm)],[f146,f80]) ).
fof(f149,plain,
( ~ sQ2_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f108,f147]) ).
fof(f150,plain,
~ sQ2_spl,
inference(contradiction_clause,[status(thm)],[f149]) ).
fof(f171,plain,
! [X0,X1] :
( sK15_skl = sK8_skl(X0,sK14_skl,X1)
| ~ apply(sK13_skl,sK8_skl(X0,sK14_skl,X1),sK15_skl)
| ~ member(X0,sK14_skl)
| least(X0,X1,sK14_skl) ),
inference(resolution,[status(thm)],[f65,f127]) ).
fof(f178,plain,
( ~ apply(sK13_skl,sK15_skl,sK8_skl(sK15_skl,sK14_skl,sK13_skl))
| ~ member(sK15_skl,sK14_skl) ),
inference(resolution,[status(thm)],[f66,f109]) ).
fof(f181,definition,
( sQ5_spl
<=> member(sK15_skl,sK14_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f182,plain,
( ~ sQ5_spl
| member(sK15_skl,sK14_skl) ),
inference(component_clause,[status(thm)],[f181]) ).
fof(f183,plain,
( sQ5_spl
| ~ member(sK15_skl,sK14_skl) ),
inference(component_clause,[status(thm)],[f181]) ).
fof(f184,definition,
( sQ6_spl
<=> apply(sK13_skl,sK15_skl,sK8_skl(sK15_skl,sK14_skl,sK13_skl)) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f186,plain,
( sQ6_spl
| ~ apply(sK13_skl,sK15_skl,sK8_skl(sK15_skl,sK14_skl,sK13_skl)) ),
inference(component_clause,[status(thm)],[f184]) ).
fof(f187,plain,
( ~ sQ6_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f178,f181,f184]) ).
fof(f188,plain,
! [X0] :
( sQ5_spl
| ~ min(sK15_skl,X0,sK14_skl) ),
inference(resolution,[status(thm)],[f183,f80]) ).
fof(f190,plain,
( sQ5_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f108,f188]) ).
fof(f191,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f190]) ).
fof(f204,plain,
! [X0] :
( sQ6_spl
| apply(sK13_skl,sK8_skl(sK15_skl,sK14_skl,sK13_skl),sK15_skl)
| ~ member(sK15_skl,X0)
| ~ member(sK8_skl(sK15_skl,sK14_skl,sK13_skl),X0)
| ~ total_order(sK13_skl,X0) ),
inference(resolution,[status(thm)],[f186,f32]) ).
fof(f205,definition,
! [X0] :
( sQ7_spl
<=> ( ~ member(sK15_skl,X0)
| ~ member(sK8_skl(sK15_skl,sK14_skl,sK13_skl),X0)
| ~ total_order(sK13_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f206,plain,
! [X0] :
( ~ sQ7_spl
| ~ member(sK15_skl,X0)
| ~ member(sK8_skl(sK15_skl,sK14_skl,sK13_skl),X0)
| ~ total_order(sK13_skl,X0) ),
inference(component_clause,[status(thm)],[f205]) ).
fof(f208,definition,
( sQ8_spl
<=> apply(sK13_skl,sK8_skl(sK15_skl,sK14_skl,sK13_skl),sK15_skl) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f211,plain,
( sQ6_spl
| sQ8_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f204,f205,f208,f184]) ).
fof(f220,definition,
( sQ10_spl
<=> least(sK15_skl,sK13_skl,sK14_skl) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f221,plain,
( ~ sQ10_spl
| least(sK15_skl,sK13_skl,sK14_skl) ),
inference(component_clause,[status(thm)],[f220]) ).
fof(f236,plain,
( ~ sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f221,f109]) ).
fof(f237,plain,
~ sQ10_spl,
inference(contradiction_clause,[status(thm)],[f236]) ).
fof(f241,plain,
( sK15_skl = sK8_skl(sK15_skl,sK14_skl,sK13_skl)
| ~ apply(sK13_skl,sK8_skl(sK15_skl,sK14_skl,sK13_skl),sK15_skl)
| ~ member(sK15_skl,sK14_skl) ),
inference(resolution,[status(thm)],[f171,f109]) ).
fof(f244,definition,
( sQ13_spl
<=> sK15_skl = sK8_skl(sK15_skl,sK14_skl,sK13_skl) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f245,plain,
( ~ sQ13_spl
| sK15_skl = sK8_skl(sK15_skl,sK14_skl,sK13_skl) ),
inference(component_clause,[status(thm)],[f244]) ).
fof(f247,plain,
( sQ13_spl
| ~ sQ8_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f241,f181,f208,f244]) ).
fof(f250,plain,
( sQ6_spl
| ~ sQ13_spl
| ~ apply(sK13_skl,sK15_skl,sK15_skl) ),
inference(backward_demodulation,[status(thm)],[f245,f186]) ).
fof(f253,plain,
( sQ6_spl
| ~ sQ13_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f250,f131,f244,f184]) ).
fof(f316,definition,
( sQ16_spl
<=> member(sK8_skl(sK15_skl,sK14_skl,sK13_skl),sK14_skl) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f318,plain,
( sQ16_spl
| ~ member(sK8_skl(sK15_skl,sK14_skl,sK13_skl),sK14_skl) ),
inference(component_clause,[status(thm)],[f316]) ).
fof(f369,plain,
( sQ16_spl
| ~ member(sK15_skl,sK14_skl)
| least(sK15_skl,sK13_skl,sK14_skl) ),
inference(resolution,[status(thm)],[f318,f65]) ).
fof(f372,plain,
( sQ16_spl
| ~ sQ5_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f369,f220,f181,f316]) ).
fof(f444,plain,
( ~ sQ5_spl
| ~ sQ7_spl
| ~ member(sK8_skl(sK15_skl,sK14_skl,sK13_skl),sK14_skl)
| ~ total_order(sK13_skl,sK14_skl) ),
inference(resolution,[status(thm)],[f206,f182]) ).
fof(f447,definition,
( sQ33_spl
<=> total_order(sK13_skl,sK14_skl) ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f449,plain,
( sQ33_spl
| ~ total_order(sK13_skl,sK14_skl) ),
inference(component_clause,[status(thm)],[f447]) ).
fof(f450,plain,
( ~ sQ5_spl
| ~ sQ7_spl
| ~ sQ16_spl
| ~ sQ33_spl ),
inference(split_clause,[status(thm)],[f444,f447,f316,f205,f181]) ).
fof(f451,plain,
( sQ33_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f449,f107]) ).
fof(f452,plain,
sQ33_spl,
inference(contradiction_clause,[status(thm)],[f451]) ).
fof(f453,plain,
$false,
inference(sat_refutation,[status(thm)],[f144,f150,f187,f191,f211,f237,f247,f253,f372,f450,f452]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET794+4 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n014.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Mon Sep 21 05:38:19 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.08/0.36 % Drodi V4.1.1
% 0.11/0.40 % Refutation found
% 0.11/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.42 % Elapsed time: 0.069062 seconds
% 0.11/0.42 % CPU time: 0.275977 seconds
% 0.11/0.42 % Total memory used: 64.930 MB
% 0.11/0.42 % Net memory used: 64.640 MB
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