%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWV415+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 : n005.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 02:47:37 PM UTC 2026
% Result : Theorem 13.36s 2.17s
% Output : CNFRefutation 13.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 9
% Syntax : Number of formulae : 40 ( 14 unt; 4 def)
% Number of atoms : 78 ( 44 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 68 ( 30 ~; 29 |; 3 &)
% ( 4 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 5 prp; 0-2 aty)
% Number of functors : 25 ( 25 usr; 18 con; 0-3 aty)
% Number of variables : 129 ( 114 !; 15 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f42,axiom,
! [U,V,W,X] : insert_cpq(triple(U,V,W),X) = triple(insert_pqp(U,X),insert_slb(V,pair(X,bottom)),W),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f54,axiom,
! [U,V] : i(triple(U,create_slb,V)) = create_pq,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f55,axiom,
! [U,V,W,X,Y] : i(triple(U,insert_slb(V,pair(X,Y)),W)) = insert_pq(i(triple(U,V,W)),X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f63,axiom,
( ( ! [Y] :
( ! [Z,X1,X2,X3] : i(triple(Z,Y,X2)) = i(triple(X1,Y,X3))
=> ! [X4,X5,X6,X7,X8,X9] : i(triple(X4,insert_slb(Y,pair(X8,X9)),X6)) = i(triple(X5,insert_slb(Y,pair(X8,X9)),X7)) )
& ! [U,V,W,X] : i(triple(U,create_slb,W)) = i(triple(V,create_slb,X)) )
=> ! [X10,X11,X12,X13,X14] : i(triple(X10,X12,X13)) = i(triple(X11,X12,X14)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f64,conjecture,
! [U,V,W,X] : i(insert_cpq(triple(U,V,W),X)) = insert_pq(i(triple(U,V,W)),X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f65,negated_conjecture,
~ ! [U,V,W,X] : i(insert_cpq(triple(U,V,W),X)) = insert_pq(i(triple(U,V,W)),X),
inference(negated_conjecture,[status(cth)],[f64]) ).
fof(f167,plain,
! [X0,X1,X2,X3] : insert_cpq(triple(X0,X1,X2),X3) = triple(insert_pqp(X0,X3),insert_slb(X1,pair(X3,bottom)),X2),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f193,plain,
! [X0,X1] : i(triple(X0,create_slb,X1)) = create_pq,
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f194,plain,
! [X0,X1,X2,X3,X4] : i(triple(X0,insert_slb(X1,pair(X2,X3)),X4)) = insert_pq(i(triple(X0,X1,X4)),X2),
inference(cnf_transformation,[status(thm)],[f55]) ).
fof(f230,plain,
( ! [X10,X11,X12,X13,X14] : i(triple(X10,X12,X13)) = i(triple(X11,X12,X14))
| ? [Y] :
( ? [X4,X5,X6,X7,X8,X9] : i(triple(X4,insert_slb(Y,pair(X8,X9)),X6)) != i(triple(X5,insert_slb(Y,pair(X8,X9)),X7))
& ! [Z,X1,X2,X3] : i(triple(Z,Y,X2)) = i(triple(X1,Y,X3)) )
| ? [U,V,W,X] : i(triple(U,create_slb,W)) != i(triple(V,create_slb,X)) ),
inference(pre_NNF_transformation,[status(thm)],[f63]) ).
fof(f231,plain,
( ! [X10,X11,X12,X13,X14] : i(triple(X10,X12,X13)) = i(triple(X11,X12,X14))
| ( i(triple(sK9_skl,insert_slb(sK8_skl,pair(sK13_skl,sK14_skl)),sK11_skl)) != i(triple(sK10_skl,insert_slb(sK8_skl,pair(sK13_skl,sK14_skl)),sK12_skl))
& ! [Z,X1,X2,X3] : i(triple(Z,sK8_skl,X2)) = i(triple(X1,sK8_skl,X3)) )
| i(triple(sK4_skl,create_slb,sK6_skl)) != i(triple(sK5_skl,create_slb,sK7_skl)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl,sK5_skl,sK6_skl,sK7_skl,sK8_skl,sK9_skl,sK10_skl,sK11_skl,sK12_skl,sK13_skl,sK14_skl]),skolemize(U,sK4_skl),skolemize(V,sK5_skl),skolemize(W,sK6_skl),skolemize(X,sK7_skl),skolemize(Y,sK8_skl),skolemize(X4,sK9_skl),skolemize(X5,sK10_skl),skolemize(X6,sK11_skl),skolemize(X7,sK12_skl),skolemize(X8,sK13_skl),skolemize(X9,sK14_skl)],[f230]) ).
fof(f232,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8] :
( i(triple(X4,X5,X6)) = i(triple(X7,X5,X8))
| i(triple(X0,sK8_skl,X1)) = i(triple(X2,sK8_skl,X3))
| i(triple(sK4_skl,create_slb,sK6_skl)) != i(triple(sK5_skl,create_slb,sK7_skl)) ),
inference(cnf_transformation,[status(thm)],[f231]) ).
fof(f233,plain,
! [X0,X1,X2,X3,X4] :
( i(triple(X0,X1,X2)) = i(triple(X3,X1,X4))
| i(triple(sK9_skl,insert_slb(sK8_skl,pair(sK13_skl,sK14_skl)),sK11_skl)) != i(triple(sK10_skl,insert_slb(sK8_skl,pair(sK13_skl,sK14_skl)),sK12_skl))
| i(triple(sK4_skl,create_slb,sK6_skl)) != i(triple(sK5_skl,create_slb,sK7_skl)) ),
inference(cnf_transformation,[status(thm)],[f231]) ).
fof(f234,plain,
? [U,V,W,X] : i(insert_cpq(triple(U,V,W),X)) != insert_pq(i(triple(U,V,W)),X),
inference(pre_NNF_transformation,[status(thm)],[f65]) ).
fof(f235,plain,
i(insert_cpq(triple(sK15_skl,sK16_skl,sK17_skl),sK18_skl)) != insert_pq(i(triple(sK15_skl,sK16_skl,sK17_skl)),sK18_skl),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15_skl,sK16_skl,sK17_skl,sK18_skl]),skolemize(U,sK15_skl),skolemize(V,sK16_skl),skolemize(W,sK17_skl),skolemize(X,sK18_skl)],[f234]) ).
fof(f236,plain,
i(insert_cpq(triple(sK15_skl,sK16_skl,sK17_skl),sK18_skl)) != insert_pq(i(triple(sK15_skl,sK16_skl,sK17_skl)),sK18_skl),
inference(cnf_transformation,[status(thm)],[f235]) ).
fof(f237,definition,
( sQ0_spl
<=> i(triple(sK4_skl,create_slb,sK6_skl)) = i(triple(sK5_skl,create_slb,sK7_skl)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f239,plain,
( sQ0_spl
| i(triple(sK4_skl,create_slb,sK6_skl)) != i(triple(sK5_skl,create_slb,sK7_skl)) ),
inference(component_clause,[status(thm)],[f237]) ).
fof(f240,definition,
! [X0,X1,X2,X3] :
( sQ1_spl
<=> i(triple(X0,sK8_skl,X1)) = i(triple(X2,sK8_skl,X3)) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f241,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| i(triple(X0,sK8_skl,X1)) = i(triple(X2,sK8_skl,X3)) ),
inference(component_clause,[status(thm)],[f240]) ).
fof(f243,definition,
! [X4,X5,X6,X7,X8] :
( sQ2_spl
<=> i(triple(X4,X5,X6)) = i(triple(X7,X5,X8)) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f244,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ2_spl
| i(triple(X0,X1,X2)) = i(triple(X3,X1,X4)) ),
inference(component_clause,[status(thm)],[f243]) ).
fof(f246,plain,
( sQ2_spl
| sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f232,f237,f240,f243]) ).
fof(f247,definition,
( sQ3_spl
<=> i(triple(sK9_skl,insert_slb(sK8_skl,pair(sK13_skl,sK14_skl)),sK11_skl)) = i(triple(sK10_skl,insert_slb(sK8_skl,pair(sK13_skl,sK14_skl)),sK12_skl)) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f249,plain,
( sQ3_spl
| i(triple(sK9_skl,insert_slb(sK8_skl,pair(sK13_skl,sK14_skl)),sK11_skl)) != i(triple(sK10_skl,insert_slb(sK8_skl,pair(sK13_skl,sK14_skl)),sK12_skl)) ),
inference(component_clause,[status(thm)],[f247]) ).
fof(f250,plain,
( sQ2_spl
| ~ sQ3_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f233,f237,f247,f243]) ).
fof(f5183,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ2_spl
| i(insert_cpq(triple(X0,X1,X2),X3)) = i(triple(X4,insert_slb(X1,pair(X3,bottom)),X5)) ),
inference(paramodulation,[status(thm)],[f167,f244]) ).
fof(f5208,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ2_spl
| i(insert_cpq(triple(X0,X1,X2),X3)) = insert_pq(i(triple(X4,X1,X5)),X3) ),
inference(forward_demodulation,[status(thm)],[f194,f5183]) ).
fof(f5386,plain,
( ~ sQ2_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f236,f5208]) ).
fof(f5462,plain,
~ sQ2_spl,
inference(contradiction_clause,[status(thm)],[f5386]) ).
fof(f5463,plain,
( sQ0_spl
| create_pq != i(triple(sK5_skl,create_slb,sK7_skl)) ),
inference(forward_demodulation,[status(thm)],[f193,f239]) ).
fof(f5464,plain,
( sQ0_spl
| create_pq != create_pq ),
inference(forward_demodulation,[status(thm)],[f193,f5463]) ).
fof(f5465,plain,
( sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f5464]) ).
fof(f5466,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f5465]) ).
fof(f5467,plain,
( sQ3_spl
| insert_pq(i(triple(sK9_skl,sK8_skl,sK11_skl)),sK13_skl) != i(triple(sK10_skl,insert_slb(sK8_skl,pair(sK13_skl,sK14_skl)),sK12_skl)) ),
inference(forward_demodulation,[status(thm)],[f194,f249]) ).
fof(f5468,plain,
( sQ3_spl
| insert_pq(i(triple(sK9_skl,sK8_skl,sK11_skl)),sK13_skl) != insert_pq(i(triple(sK10_skl,sK8_skl,sK12_skl)),sK13_skl) ),
inference(forward_demodulation,[status(thm)],[f194,f5467]) ).
fof(f5510,plain,
! [X0,X1] :
( ~ sQ1_spl
| sQ3_spl
| insert_pq(i(triple(sK9_skl,sK8_skl,sK11_skl)),sK13_skl) != insert_pq(i(triple(X0,sK8_skl,X1)),sK13_skl) ),
inference(paramodulation,[status(thm)],[f241,f5468]) ).
fof(f5609,plain,
( ~ sQ1_spl
| sQ3_spl
| $false ),
inference(equality_resolution,[status(thm)],[f5510]) ).
fof(f5610,plain,
( ~ sQ1_spl
| sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f5609]) ).
fof(f5611,plain,
$false,
inference(sat_refutation,[status(thm)],[f246,f250,f5462,f5466,f5610]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV415+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n005.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 08:45:17 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.15/0.38 % Drodi V4.1.1
% 13.36/2.17 % Refutation found
% 13.36/2.17 % SZS status Theorem for theBenchmark: Theorem is valid
% 13.36/2.17 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 13.36/2.20 % Elapsed time: 1.810839 seconds
% 13.36/2.20 % CPU time: 14.035308 seconds
% 13.36/2.20 % Total memory used: 169.696 MB
% 13.36/2.20 % Net memory used: 165.957 MB
%------------------------------------------------------------------------------