%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUN054+1 : TPTP v9.3.1. Bugfixed v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n019.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 01:57:08 PM UTC 2026
% Result : Theorem 5.15s 1.29s
% Output : CNFRefutation 5.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 12
% Syntax : Number of formulae : 73 ( 18 unt; 4 def)
% Number of atoms : 212 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 244 ( 105 ~; 85 |; 50 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 2 prp; 0-4 aty)
% Number of functors : 8 ( 8 usr; 1 con; 0-2 aty)
% Number of variables : 167 ( 145 !; 22 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
? [Y24] :
! [X19] :
( ( ~ id(X19,Y24)
& ~ r1(X19) )
| ( r1(X19)
& id(X19,Y24) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X13,X14] :
? [Y22] :
! [X15] :
( ( ~ id(X15,Y22)
& ~ r3(X13,X14,X15) )
| ( r3(X13,X14,X15)
& id(X15,Y22) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X20] : id(X20,X20),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X21,X22] :
( id(X22,X21)
| ~ id(X21,X22) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X26,X27] :
( ( r1(X27)
& r1(X26) )
| ( ~ r1(X27)
& ~ r1(X26) )
| ~ id(X26,X27) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [X1,X8] :
? [Y4] :
( ? [Y7] :
( r3(X1,X8,Y7)
& r2(Y7,Y4) )
& ? [Y5] :
( ? [Y15] :
( r3(X1,Y15,Y5)
& r2(X8,Y15) )
& id(Y5,Y4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [X4] :
? [Y9] :
( ? [Y16] :
( r3(X4,Y16,Y9)
& r1(Y16) )
& id(Y9,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,conjecture,
? [Y1] :
( ? [Y3] :
( ? [Y6] :
( r2(Y6,Y3)
& r1(Y6) )
& id(Y1,Y3) )
& ? [Y2] :
( ? [Y5] :
( r2(Y5,Y2)
& r1(Y5) )
& ? [Y4] :
( r3(Y4,Y2,Y1)
& r1(Y4) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
~ ? [Y1] :
( ? [Y3] :
( ? [Y6] :
( r2(Y6,Y3)
& r1(Y6) )
& id(Y1,Y3) )
& ? [Y2] :
( ? [Y5] :
( r2(Y5,Y2)
& r1(Y5) )
& ? [Y4] :
( r3(Y4,Y2,Y1)
& r1(Y4) ) ) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f21,definition,
! [Y24,X19] :
( sP0_prd(X19,Y24)
<=> ( r1(X19)
& id(X19,Y24) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f22,plain,
? [Y24] :
! [X19] :
( ( ~ id(X19,Y24)
& ~ r1(X19) )
| sP0_prd(X19,Y24) ),
inference(formula_renaming,[status(thm)],[f1,f21]) ).
fof(f23,plain,
! [X19] :
( ( ~ id(X19,sK0_skl)
& ~ r1(X19) )
| sP0_prd(X19,sK0_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(Y24,sK0_skl)],[f22]) ).
fof(f25,plain,
! [X0] :
( ~ id(X0,sK0_skl)
| sP0_prd(X0,sK0_skl) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f31,definition,
! [X13,X14,Y22,X15] :
( sP2_prd(X15,Y22,X14,X13)
<=> ( r3(X13,X14,X15)
& id(X15,Y22) ) ),
introduced(definition,[new_symbols(definition,[sP2_prd])],[]) ).
fof(f32,plain,
! [X13,X14] :
? [Y22] :
! [X15] :
( ( ~ id(X15,Y22)
& ~ r3(X13,X14,X15) )
| sP2_prd(X15,Y22,X14,X13) ),
inference(formula_renaming,[status(thm)],[f3,f31]) ).
fof(f33,plain,
! [X13,X14,X15] :
( ( ~ id(X15,sK2_skl(X14,X13))
& ~ r3(X13,X14,X15) )
| sP2_prd(X15,sK2_skl(X14,X13),X14,X13) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl]),skolemize(Y22,sK2_skl(X14,X13))],[f32]) ).
fof(f34,plain,
! [X0,X1,X2] :
( ~ r3(X2,X1,X0)
| sP2_prd(X0,sK2_skl(X1,X2),X1,X2) ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f41,plain,
! [X0] : id(X0,X0),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f42,plain,
! [X0,X1] :
( id(X1,X0)
| ~ id(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f45,definition,
! [X26,X27] :
( sP4_prd(X27,X26)
<=> ( ~ r1(X27)
& ~ r1(X26) ) ),
introduced(definition,[new_symbols(definition,[sP4_prd])],[]) ).
fof(f46,plain,
! [X26,X27] :
( ( r1(X27)
& r1(X26) )
| sP4_prd(X27,X26)
| ~ id(X26,X27) ),
inference(formula_renaming,[status(thm)],[f8,f45]) ).
fof(f47,plain,
! [X0,X1] :
( r1(X0)
| sP4_prd(X1,X0)
| ~ id(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f48,plain,
! [X0,X1] :
( r1(X1)
| sP4_prd(X1,X0)
| ~ id(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f61,plain,
! [X1,X8] :
( r3(X1,X8,sK7_skl(X8,X1))
& r2(sK7_skl(X8,X1),sK4_skl(X8,X1))
& r3(X1,sK6_skl(X8,X1),sK5_skl(X8,X1))
& r2(X8,sK6_skl(X8,X1))
& id(sK5_skl(X8,X1),sK4_skl(X8,X1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl,sK5_skl,sK6_skl,sK7_skl]),skolemize(Y4,sK4_skl(X8,X1)),skolemize(Y5,sK5_skl(X8,X1)),skolemize(Y15,sK6_skl(X8,X1)),skolemize(Y7,sK7_skl(X8,X1))],[f12]) ).
fof(f62,plain,
! [X0,X1] : id(sK5_skl(X0,X1),sK4_skl(X0,X1)),
inference(cnf_transformation,[status(thm)],[f61]) ).
fof(f63,plain,
! [X0,X1] : r2(X0,sK6_skl(X0,X1)),
inference(cnf_transformation,[status(thm)],[f61]) ).
fof(f64,plain,
! [X0,X1] : r3(X0,sK6_skl(X1,X0),sK5_skl(X1,X0)),
inference(cnf_transformation,[status(thm)],[f61]) ).
fof(f65,plain,
! [X0,X1] : r2(sK7_skl(X0,X1),sK4_skl(X0,X1)),
inference(cnf_transformation,[status(thm)],[f61]) ).
fof(f66,plain,
! [X0,X1] : r3(X0,X1,sK7_skl(X1,X0)),
inference(cnf_transformation,[status(thm)],[f61]) ).
fof(f74,plain,
! [X4] :
( r3(X4,sK13_skl(X4),sK12_skl(X4))
& r1(sK13_skl(X4))
& id(sK12_skl(X4),X4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12_skl,sK13_skl]),skolemize(Y9,sK12_skl(X4)),skolemize(Y16,sK13_skl(X4))],[f15]) ).
fof(f75,plain,
! [X0] : id(sK12_skl(X0),X0),
inference(cnf_transformation,[status(thm)],[f74]) ).
fof(f76,plain,
! [X0] : r1(sK13_skl(X0)),
inference(cnf_transformation,[status(thm)],[f74]) ).
fof(f77,plain,
! [X0] : r3(X0,sK13_skl(X0),sK12_skl(X0)),
inference(cnf_transformation,[status(thm)],[f74]) ).
fof(f91,plain,
! [Y1] :
( ! [Y3] :
( ! [Y6] :
( ~ r2(Y6,Y3)
| ~ r1(Y6) )
| ~ id(Y1,Y3) )
| ! [Y2] :
( ! [Y5] :
( ~ r2(Y5,Y2)
| ~ r1(Y5) )
| ! [Y4] :
( ~ r3(Y4,Y2,Y1)
| ~ r1(Y4) ) ) ),
inference(pre_NNF_transformation,[status(thm)],[f20]) ).
fof(f92,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ r2(X5,X4)
| ~ r1(X5)
| ~ id(X2,X4)
| ~ r2(X3,X1)
| ~ r1(X3)
| ~ r3(X0,X1,X2)
| ~ r1(X0) ),
inference(cnf_transformation,[status(thm)],[f91]) ).
fof(f93,plain,
! [Y24,X19] :
( ( ~ r1(X19)
| ~ id(X19,Y24)
| sP0_prd(X19,Y24) )
& ( ( r1(X19)
& id(X19,Y24) )
| ~ sP0_prd(X19,Y24) ) ),
inference(NNF_transformation,[status(thm)],[f21]) ).
fof(f94,plain,
( ! [Y24,X19] :
( ~ r1(X19)
| ~ id(X19,Y24)
| sP0_prd(X19,Y24) )
& ! [Y24,X19] :
( ( r1(X19)
& id(X19,Y24) )
| ~ sP0_prd(X19,Y24) ) ),
inference(miniscoping,[status(thm)],[f93]) ).
fof(f96,plain,
! [X0,X1] :
( r1(X0)
| ~ sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f94]) ).
fof(f103,plain,
! [X13,X14,Y22,X15] :
( ( ~ r3(X13,X14,X15)
| ~ id(X15,Y22)
| sP2_prd(X15,Y22,X14,X13) )
& ( ( r3(X13,X14,X15)
& id(X15,Y22) )
| ~ sP2_prd(X15,Y22,X14,X13) ) ),
inference(NNF_transformation,[status(thm)],[f31]) ).
fof(f104,plain,
( ! [X13,X14,Y22,X15] :
( ~ r3(X13,X14,X15)
| ~ id(X15,Y22)
| sP2_prd(X15,Y22,X14,X13) )
& ! [X13,X14,Y22,X15] :
( ( r3(X13,X14,X15)
& id(X15,Y22) )
| ~ sP2_prd(X15,Y22,X14,X13) ) ),
inference(miniscoping,[status(thm)],[f103]) ).
fof(f105,plain,
! [X0,X1,X2,X3] :
( id(X0,X1)
| ~ sP2_prd(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f104]) ).
fof(f113,plain,
! [X26,X27] :
( ( r1(X27)
| r1(X26)
| sP4_prd(X27,X26) )
& ( ( ~ r1(X27)
& ~ r1(X26) )
| ~ sP4_prd(X27,X26) ) ),
inference(NNF_transformation,[status(thm)],[f45]) ).
fof(f114,plain,
( ! [X26,X27] :
( r1(X27)
| r1(X26)
| sP4_prd(X27,X26) )
& ! [X26,X27] :
( ( ~ r1(X27)
& ~ r1(X26) )
| ~ sP4_prd(X27,X26) ) ),
inference(miniscoping,[status(thm)],[f113]) ).
fof(f115,plain,
! [X0,X1] :
( ~ r1(X1)
| ~ sP4_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f114]) ).
fof(f116,plain,
! [X0,X1] :
( ~ r1(X0)
| ~ sP4_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f114]) ).
fof(f142,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ r2(X5,X4)
| ~ r1(X5)
| ~ id(X2,X4)
| ~ r2(sK13_skl(X3),X1)
| ~ r3(X0,X1,X2)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[f76,f92]) ).
fof(f153,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ r2(X5,X4)
| ~ r1(X5)
| ~ id(X3,X4)
| ~ r3(X0,sK6_skl(sK13_skl(X1),X2),X3)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[f63,f142]) ).
fof(f164,plain,
! [X0] :
( r1(X0)
| ~ id(X0,sK0_skl) ),
inference(resolution,[status(thm)],[f25,f96]) ).
fof(f234,plain,
! [X0,X1] :
( ~ r1(X1)
| r1(X0)
| ~ id(X0,X1) ),
inference(resolution,[status(thm)],[f47,f116]) ).
fof(f312,plain,
! [X0,X1] :
( ~ r1(X0)
| r1(X1)
| ~ id(X0,X1) ),
inference(resolution,[status(thm)],[f48,f115]) ).
fof(f439,definition,
( sQ2_spl
<=> r1(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f440,plain,
( ~ sQ2_spl
| r1(sK0_skl) ),
inference(component_clause,[status(thm)],[f439]) ).
fof(f441,plain,
( sQ2_spl
| ~ r1(sK0_skl) ),
inference(component_clause,[status(thm)],[f439]) ).
fof(f452,plain,
( sQ2_spl
| ~ id(sK0_skl,sK0_skl) ),
inference(resolution,[status(thm)],[f441,f164]) ).
fof(f454,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f452,f41]) ).
fof(f455,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f454]) ).
fof(f467,plain,
! [X0,X1,X2,X3] :
( ~ r2(X3,X2)
| ~ r1(X3)
| ~ id(sK5_skl(sK13_skl(X1),X0),X2)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[f64,f153]) ).
fof(f624,plain,
! [X0,X1,X2] :
( ~ r3(X2,X1,X0)
| id(X0,sK2_skl(X1,X2)) ),
inference(resolution,[status(thm)],[f105,f34]) ).
fof(f1031,plain,
r1(sK12_skl(sK0_skl)),
inference(resolution,[status(thm)],[f164,f75]) ).
fof(f1150,plain,
! [X0] :
( r1(X0)
| ~ id(X0,sK12_skl(sK0_skl)) ),
inference(resolution,[status(thm)],[f234,f1031]) ).
fof(f1252,plain,
! [X0] :
( ~ id(sK12_skl(sK0_skl),X0)
| r1(X0) ),
inference(resolution,[status(thm)],[f1150,f42]) ).
fof(f1485,plain,
! [X0] : id(sK12_skl(X0),sK2_skl(sK13_skl(X0),X0)),
inference(resolution,[status(thm)],[f624,f77]) ).
fof(f1486,plain,
! [X0,X1] : id(sK7_skl(X0,X1),sK2_skl(X0,X1)),
inference(resolution,[status(thm)],[f624,f66]) ).
fof(f1498,plain,
! [X0,X1,X2] :
( ~ r2(X1,sK4_skl(sK13_skl(X2),X0))
| ~ r1(X1)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[f467,f62]) ).
fof(f1503,plain,
! [X0,X1] :
( ~ r1(sK7_skl(sK13_skl(X1),X0))
| ~ r1(X0) ),
inference(resolution,[status(thm)],[f1498,f65]) ).
fof(f1552,plain,
! [X0,X1,X2] :
( ~ r1(X1)
| ~ id(X1,sK7_skl(sK13_skl(X2),X0))
| ~ r1(X0) ),
inference(resolution,[status(thm)],[f1503,f312]) ).
fof(f1556,plain,
! [X0,X1,X2] :
( ~ id(sK7_skl(sK13_skl(X2),X0),X1)
| ~ r1(X1)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[f1552,f42]) ).
fof(f1588,plain,
r1(sK2_skl(sK13_skl(sK0_skl),sK0_skl)),
inference(resolution,[status(thm)],[f1485,f1252]) ).
fof(f1680,plain,
! [X0,X1] :
( ~ r1(sK2_skl(sK13_skl(X1),X0))
| ~ r1(X0) ),
inference(resolution,[status(thm)],[f1556,f1486]) ).
fof(f1685,plain,
~ r1(sK0_skl),
inference(resolution,[status(thm)],[f1680,f1588]) ).
fof(f1687,plain,
( ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1685,f440]) ).
fof(f1688,plain,
~ sQ2_spl,
inference(contradiction_clause,[status(thm)],[f1687]) ).
fof(f1689,plain,
$false,
inference(sat_refutation,[status(thm)],[f455,f1688]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUN054+1 : TPTP v9.3.1. Bugfixed v7.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.56 % Computer : n019.cluster.edu
% 0.08/0.56 % Model : x86_64 x86_64
% 0.08/0.56 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.56 % Memory : 8046.5625MB
% 0.08/0.56 % OS : Linux 6.8.0-71-generic
% 0.08/0.56 % CPULimit : 300
% 0.08/0.56 % WCLimit : 300
% 0.08/0.56 % DateTime : Mon Sep 21 03:22:36 UTC 2026
% 0.08/0.56 % CPUTime :
% 0.08/0.57 % Drodi V4.1.1
% 5.15/1.29 % Refutation found
% 5.15/1.29 % SZS status Theorem for theBenchmark: Theorem is valid
% 5.15/1.29 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.30/1.31 % Elapsed time: 0.732930 seconds
% 0.30/1.31 % CPU time: 5.546402 seconds
% 0.30/1.31 % Total memory used: 66.729 MB
% 0.30/1.31 % Net memory used: 54.289 MB
%------------------------------------------------------------------------------