%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET807+4 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n008.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 02:10:39 PM UTC 2026
% Result : Theorem 173.04s 27.28s
% Output : CNFRefutation 173.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 8
% Syntax : Number of formulae : 61 ( 10 unt; 4 def)
% Number of atoms : 213 ( 0 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 240 ( 88 ~; 99 |; 39 &)
% ( 10 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 4 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 131 ( 120 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( member(X,A)
=> member(X,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [R,E] :
( pre_order(R,E)
<=> ( ! [X,Y,Z] :
( ( member(Z,E)
& member(Y,E)
& member(X,E) )
=> ( ( apply(R,Y,Z)
& apply(R,X,Y) )
=> apply(R,X,Z) ) )
& ! [X] :
( member(X,E)
=> apply(R,X,X) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,hypothesis,
! [X,Y] :
( apply(subset_predicate,X,Y)
<=> subset(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,conjecture,
! [E] : pre_order(subset_predicate,power_set(E)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
~ ! [E] : pre_order(subset_predicate,power_set(E)),
inference(negated_conjecture,[status(cth)],[f18]) ).
fof(f20,plain,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( member(X,B)
| ~ member(X,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f21,plain,
! [A,B] :
( ( ? [X] :
( ~ member(X,B)
& member(X,A) )
| subset(A,B) )
& ( ! [X] :
( member(X,B)
| ~ member(X,A) )
| ~ subset(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f20]) ).
fof(f22,plain,
( ! [A,B] :
( ? [X] :
( ~ member(X,B)
& member(X,A) )
| subset(A,B) )
& ! [A,B] :
( ! [X] :
( member(X,B)
| ~ member(X,A) )
| ~ subset(A,B) ) ),
inference(miniscoping,[status(thm)],[f21]) ).
fof(f23,plain,
( ! [A,B] :
( ( ~ member(sK0_skl(B,A),B)
& member(sK0_skl(B,A),A) )
| subset(A,B) )
& ! [A,B] :
( ! [X] :
( member(X,B)
| ~ member(X,A) )
| ~ subset(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(X,sK0_skl(B,A))],[f22]) ).
fof(f24,plain,
! [X0,X1,X2] :
( ~ member(X2,X0)
| member(X2,X1)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f25,plain,
! [X0,X1] :
( subset(X1,X0)
| member(sK0_skl(X0,X1),X1) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f26,plain,
! [X0,X1] :
( ~ member(sK0_skl(X1,X0),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f113,plain,
! [R,E] :
( pre_order(R,E)
<=> ( ! [X,Y,Z] :
( apply(R,X,Z)
| ~ apply(R,Y,Z)
| ~ apply(R,X,Y)
| ~ member(Z,E)
| ~ member(Y,E)
| ~ member(X,E) )
& ! [X] :
( apply(R,X,X)
| ~ member(X,E) ) ) ),
inference(pre_NNF_transformation,[status(thm)],[f16]) ).
fof(f114,definition,
! [R,E,X] :
( sP2_prd(X,E,R)
<=> ( apply(R,X,X)
| ~ member(X,E) ) ),
introduced(definition,[new_symbols(definition,[sP2_prd])],[]) ).
fof(f115,plain,
! [R,E] :
( pre_order(R,E)
<=> ( ! [X,Y,Z] :
( apply(R,X,Z)
| ~ apply(R,Y,Z)
| ~ apply(R,X,Y)
| ~ member(Z,E)
| ~ member(Y,E)
| ~ member(X,E) )
& ! [X] : sP2_prd(X,E,R) ) ),
inference(formula_renaming,[status(thm)],[f113,f114]) ).
fof(f116,plain,
! [R,E] :
( ( ? [X,Y,Z] :
( ~ apply(R,X,Z)
& apply(R,Y,Z)
& apply(R,X,Y)
& member(Z,E)
& member(Y,E)
& member(X,E) )
| ? [X] : ~ sP2_prd(X,E,R)
| pre_order(R,E) )
& ( ( ! [X,Y,Z] :
( apply(R,X,Z)
| ~ apply(R,Y,Z)
| ~ apply(R,X,Y)
| ~ member(Z,E)
| ~ member(Y,E)
| ~ member(X,E) )
& ! [X] : sP2_prd(X,E,R) )
| ~ pre_order(R,E) ) ),
inference(NNF_transformation,[status(thm)],[f115]) ).
fof(f117,plain,
( ! [R,E] :
( ? [X,Y,Z] :
( ~ apply(R,X,Z)
& apply(R,Y,Z)
& apply(R,X,Y)
& member(Z,E)
& member(Y,E)
& member(X,E) )
| ? [X] : ~ sP2_prd(X,E,R)
| pre_order(R,E) )
& ! [R,E] :
( ( ! [X,Y,Z] :
( apply(R,X,Z)
| ~ apply(R,Y,Z)
| ~ apply(R,X,Y)
| ~ member(Z,E)
| ~ member(Y,E)
| ~ member(X,E) )
& ! [X] : sP2_prd(X,E,R) )
| ~ pre_order(R,E) ) ),
inference(miniscoping,[status(thm)],[f116]) ).
fof(f118,plain,
( ! [R,E] :
( ( ~ apply(R,sK11_skl(E,R),sK13_skl(E,R))
& apply(R,sK12_skl(E,R),sK13_skl(E,R))
& apply(R,sK11_skl(E,R),sK12_skl(E,R))
& member(sK13_skl(E,R),E)
& member(sK12_skl(E,R),E)
& member(sK11_skl(E,R),E) )
| ~ sP2_prd(sK10_skl(E,R),E,R)
| pre_order(R,E) )
& ! [R,E] :
( ( ! [X,Y,Z] :
( apply(R,X,Z)
| ~ apply(R,Y,Z)
| ~ apply(R,X,Y)
| ~ member(Z,E)
| ~ member(Y,E)
| ~ member(X,E) )
& ! [X] : sP2_prd(X,E,R) )
| ~ pre_order(R,E) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10_skl,sK11_skl,sK12_skl,sK13_skl]),skolemize(X,sK10_skl(E,R)),skolemize(X,sK11_skl(E,R)),skolemize(Y,sK12_skl(E,R)),skolemize(Z,sK13_skl(E,R))],[f117]) ).
fof(f124,plain,
! [X0,X1] :
( ~ sP2_prd(sK10_skl(X1,X0),X1,X0)
| apply(X0,sK11_skl(X1,X0),sK12_skl(X1,X0))
| pre_order(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f118]) ).
fof(f125,plain,
! [X0,X1] :
( ~ sP2_prd(sK10_skl(X1,X0),X1,X0)
| apply(X0,sK12_skl(X1,X0),sK13_skl(X1,X0))
| pre_order(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f118]) ).
fof(f126,plain,
! [X0,X1] :
( ~ sP2_prd(sK10_skl(X1,X0),X1,X0)
| pre_order(X0,X1)
| ~ apply(X0,sK11_skl(X1,X0),sK13_skl(X1,X0)) ),
inference(cnf_transformation,[status(thm)],[f118]) ).
fof(f127,plain,
! [X,Y] :
( ( ~ subset(X,Y)
| apply(subset_predicate,X,Y) )
& ( subset(X,Y)
| ~ apply(subset_predicate,X,Y) ) ),
inference(NNF_transformation,[status(thm)],[f17]) ).
fof(f128,plain,
( ! [X,Y] :
( ~ subset(X,Y)
| apply(subset_predicate,X,Y) )
& ! [X,Y] :
( subset(X,Y)
| ~ apply(subset_predicate,X,Y) ) ),
inference(miniscoping,[status(thm)],[f127]) ).
fof(f129,plain,
! [X0,X1] :
( ~ apply(subset_predicate,X0,X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f128]) ).
fof(f130,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| apply(subset_predicate,X0,X1) ),
inference(cnf_transformation,[status(thm)],[f128]) ).
fof(f131,plain,
? [E] : ~ pre_order(subset_predicate,power_set(E)),
inference(pre_NNF_transformation,[status(thm)],[f19]) ).
fof(f132,plain,
~ pre_order(subset_predicate,power_set(sK14_skl)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14_skl]),skolemize(E,sK14_skl)],[f131]) ).
fof(f133,plain,
~ pre_order(subset_predicate,power_set(sK14_skl)),
inference(cnf_transformation,[status(thm)],[f132]) ).
fof(f155,plain,
! [R,E,X] :
( ( ( ~ apply(R,X,X)
& member(X,E) )
| sP2_prd(X,E,R) )
& ( apply(R,X,X)
| ~ member(X,E)
| ~ sP2_prd(X,E,R) ) ),
inference(NNF_transformation,[status(thm)],[f114]) ).
fof(f156,plain,
( ! [R,E,X] :
( ( ~ apply(R,X,X)
& member(X,E) )
| sP2_prd(X,E,R) )
& ! [R,E,X] :
( apply(R,X,X)
| ~ member(X,E)
| ~ sP2_prd(X,E,R) ) ),
inference(miniscoping,[status(thm)],[f155]) ).
fof(f159,plain,
! [X0,X1,X2] :
( ~ apply(X2,X0,X0)
| sP2_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f156]) ).
fof(f178,plain,
! [X0,X1] :
( apply(subset_predicate,X1,X0)
| member(sK0_skl(X0,X1),X1) ),
inference(resolution,[status(thm)],[f25,f130]) ).
fof(f184,plain,
! [X0,X1] :
( sP2_prd(X0,X1,subset_predicate)
| member(sK0_skl(X0,X0),X0) ),
inference(resolution,[status(thm)],[f178,f159]) ).
fof(f192,plain,
! [X0] :
( pre_order(subset_predicate,X0)
| subset(sK12_skl(X0,subset_predicate),sK13_skl(X0,subset_predicate))
| ~ sP2_prd(sK10_skl(X0,subset_predicate),X0,subset_predicate) ),
inference(resolution,[status(thm)],[f125,f129]) ).
fof(f200,plain,
! [X0,X1] :
( ~ member(sK0_skl(X1,X0),X1)
| apply(subset_predicate,X0,X1) ),
inference(resolution,[status(thm)],[f26,f130]) ).
fof(f211,plain,
! [X0,X1] :
( sP2_prd(X0,X1,subset_predicate)
| ~ member(sK0_skl(X0,X0),X0) ),
inference(resolution,[status(thm)],[f200,f159]) ).
fof(f212,plain,
! [X0,X1] : sP2_prd(X0,X1,subset_predicate),
inference(forward_subsumption_resolution,[status(thm)],[f211,f184]) ).
fof(f218,plain,
! [X0] :
( subset(sK12_skl(X0,subset_predicate),sK13_skl(X0,subset_predicate))
| pre_order(subset_predicate,X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f192,f212]) ).
fof(f246,plain,
! [X0] :
( pre_order(subset_predicate,X0)
| ~ apply(subset_predicate,sK11_skl(X0,subset_predicate),sK13_skl(X0,subset_predicate)) ),
inference(resolution,[status(thm)],[f126,f212]) ).
fof(f262,plain,
! [X0,X1] :
( pre_order(subset_predicate,X1)
| member(X0,sK13_skl(X1,subset_predicate))
| ~ member(X0,sK12_skl(X1,subset_predicate)) ),
inference(resolution,[status(thm)],[f24,f218]) ).
fof(f293,plain,
! [X0] :
( subset(sK11_skl(X0,subset_predicate),sK12_skl(X0,subset_predicate))
| ~ sP2_prd(sK10_skl(X0,subset_predicate),X0,subset_predicate)
| pre_order(subset_predicate,X0) ),
inference(resolution,[status(thm)],[f124,f129]) ).
fof(f295,plain,
! [X0] :
( subset(sK11_skl(X0,subset_predicate),sK12_skl(X0,subset_predicate))
| pre_order(subset_predicate,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f293,f212]) ).
fof(f300,plain,
! [X0,X1] :
( ~ member(X0,sK11_skl(X1,subset_predicate))
| pre_order(subset_predicate,X1)
| member(X0,sK12_skl(X1,subset_predicate)) ),
inference(resolution,[status(thm)],[f295,f24]) ).
fof(f543,definition,
( sQ5_spl
<=> apply(subset_predicate,sK11_skl(power_set(sK14_skl),subset_predicate),sK13_skl(power_set(sK14_skl),subset_predicate)) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f544,plain,
( ~ sQ5_spl
| apply(subset_predicate,sK11_skl(power_set(sK14_skl),subset_predicate),sK13_skl(power_set(sK14_skl),subset_predicate)) ),
inference(component_clause,[status(thm)],[f543]) ).
fof(f545,plain,
( sQ5_spl
| ~ apply(subset_predicate,sK11_skl(power_set(sK14_skl),subset_predicate),sK13_skl(power_set(sK14_skl),subset_predicate)) ),
inference(component_clause,[status(thm)],[f543]) ).
fof(f670,plain,
( sQ5_spl
| ~ member(sK0_skl(sK13_skl(power_set(sK14_skl),subset_predicate),sK11_skl(power_set(sK14_skl),subset_predicate)),sK13_skl(power_set(sK14_skl),subset_predicate)) ),
inference(resolution,[status(thm)],[f545,f200]) ).
fof(f671,plain,
( sQ5_spl
| member(sK0_skl(sK13_skl(power_set(sK14_skl),subset_predicate),sK11_skl(power_set(sK14_skl),subset_predicate)),sK11_skl(power_set(sK14_skl),subset_predicate)) ),
inference(resolution,[status(thm)],[f545,f178]) ).
fof(f990,definition,
( sQ12_spl
<=> pre_order(subset_predicate,power_set(sK14_skl)) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f991,plain,
( ~ sQ12_spl
| pre_order(subset_predicate,power_set(sK14_skl)) ),
inference(component_clause,[status(thm)],[f990]) ).
fof(f1005,plain,
( ~ sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f991,f133]) ).
fof(f1006,plain,
~ sQ12_spl,
inference(contradiction_clause,[status(thm)],[f1005]) ).
fof(f1146,plain,
( sQ5_spl
| pre_order(subset_predicate,power_set(sK14_skl))
| member(sK0_skl(sK13_skl(power_set(sK14_skl),subset_predicate),sK11_skl(power_set(sK14_skl),subset_predicate)),sK12_skl(power_set(sK14_skl),subset_predicate)) ),
inference(resolution,[status(thm)],[f671,f300]) ).
fof(f1149,definition,
( sQ31_spl
<=> member(sK0_skl(sK13_skl(power_set(sK14_skl),subset_predicate),sK11_skl(power_set(sK14_skl),subset_predicate)),sK12_skl(power_set(sK14_skl),subset_predicate)) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f1152,plain,
( sQ5_spl
| sQ12_spl
| sQ31_spl ),
inference(split_clause,[status(thm)],[f1146,f1149,f990,f543]) ).
fof(f1337,plain,
~ apply(subset_predicate,sK11_skl(power_set(sK14_skl),subset_predicate),sK13_skl(power_set(sK14_skl),subset_predicate)),
inference(resolution,[status(thm)],[f246,f133]) ).
fof(f1533,plain,
( sQ5_spl
| pre_order(subset_predicate,power_set(sK14_skl))
| ~ member(sK0_skl(sK13_skl(power_set(sK14_skl),subset_predicate),sK11_skl(power_set(sK14_skl),subset_predicate)),sK12_skl(power_set(sK14_skl),subset_predicate)) ),
inference(resolution,[status(thm)],[f670,f262]) ).
fof(f1534,plain,
( sQ5_spl
| sQ12_spl
| ~ sQ31_spl ),
inference(split_clause,[status(thm)],[f1533,f1149,f990,f543]) ).
fof(f1900,plain,
( ~ sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1337,f544]) ).
fof(f1901,plain,
~ sQ5_spl,
inference(contradiction_clause,[status(thm)],[f1900]) ).
fof(f1902,plain,
$false,
inference(sat_refutation,[status(thm)],[f1006,f1152,f1534,f1901]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET807+4 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/5.36 % Computer : n008.cluster.edu
% 0.09/5.36 % Model : x86_64 x86_64
% 0.09/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.36 % Memory : 8046.5625MB
% 0.09/5.36 % OS : Linux 6.8.0-71-generic
% 0.09/5.36 % CPULimit : 300
% 0.09/5.36 % WCLimit : 300
% 0.09/5.36 % DateTime : Mon Sep 21 05:40:00 UTC 2026
% 0.09/5.36 % CPUTime :
% 0.09/5.38 % Drodi V4.1.1
% 173.04/27.28 % Refutation found
% 173.04/27.28 % SZS status Theorem for theBenchmark: Theorem is valid
% 173.04/27.28 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 108.70/27.37 % Elapsed time: 21.994208 seconds
% 108.70/27.37 % CPU time: 174.142582 seconds
% 108.70/27.37 % Total memory used: 646.323 MB
% 108.70/27.37 % Net memory used: 559.446 MB
%------------------------------------------------------------------------------