%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWV378+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n026.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 02:47:32 PM UTC 2026
% Result : Theorem 44.40s 6.23s
% Output : CNFRefutation 44.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 8
% Syntax : Number of formulae : 49 ( 9 unt; 0 def)
% Number of atoms : 118 ( 34 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 112 ( 43 ~; 49 |; 12 &)
% ( 2 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 4 usr; 2 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-3 aty)
% Number of variables : 155 ( 147 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [U,V] :
( less_than(V,U)
| less_than(U,V) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [U,V] :
( strictly_less_than(U,V)
<=> ( ~ less_than(V,U)
& less_than(U,V) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,axiom,
! [U,V] :
( ok(triple(U,V,bad))
<=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,axiom,
! [U,V,W] :
( ~ ok(triple(U,V,W))
=> W = bad ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,axiom,
! [U,V,W,X] :
( ~ contains_slb(V,X)
=> remove_cpq(triple(U,V,W),X) = triple(U,V,bad) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f32,axiom,
! [U,V,W,X] :
( ( less_than(lookup_slb(V,X),X)
& contains_slb(V,X) )
=> remove_cpq(triple(U,V,W),X) = triple(remove_pqp(U,X),remove_slb(V,X),W) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,axiom,
! [U,V,W,X] :
( ( strictly_less_than(X,lookup_slb(V,X))
& contains_slb(V,X) )
=> remove_cpq(triple(U,V,W),X) = triple(remove_pqp(U,X),remove_slb(V,X),bad) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f42,conjecture,
! [U,V,W,X] :
( ~ ok(triple(U,V,W))
=> ~ ok(remove_cpq(triple(U,V,W),X)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f43,negated_conjecture,
~ ! [U,V,W,X] :
( ~ ok(triple(U,V,W))
=> ~ ok(remove_cpq(triple(U,V,W),X)) ),
inference(negated_conjecture,[status(cth)],[f42]) ).
fof(f47,plain,
! [X0,X1] :
( less_than(X1,X0)
| less_than(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f49,plain,
! [U,V] :
( ( less_than(V,U)
| ~ less_than(U,V)
| strictly_less_than(U,V) )
& ( ( ~ less_than(V,U)
& less_than(U,V) )
| ~ strictly_less_than(U,V) ) ),
inference(NNF_transformation,[status(thm)],[f4]) ).
fof(f50,plain,
( ! [U,V] :
( less_than(V,U)
| ~ less_than(U,V)
| strictly_less_than(U,V) )
& ! [U,V] :
( ( ~ less_than(V,U)
& less_than(U,V) )
| ~ strictly_less_than(U,V) ) ),
inference(miniscoping,[status(thm)],[f49]) ).
fof(f53,plain,
! [X0,X1] :
( less_than(X1,X0)
| ~ less_than(X0,X1)
| strictly_less_than(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f111,plain,
! [U,V] :
( ( $true
| ok(triple(U,V,bad)) )
& ( $false
| ~ ok(triple(U,V,bad)) ) ),
inference(NNF_transformation,[status(thm)],[f28]) ).
fof(f112,plain,
( ( $true
| ! [U,V] : ok(triple(U,V,bad)) )
& ( $false
| ! [U,V] : ~ ok(triple(U,V,bad)) ) ),
inference(miniscoping,[status(thm)],[f111]) ).
fof(f113,plain,
! [U,V] : ~ ok(triple(U,V,bad)),
inference(true_and_false_simplification,[status(thm)],[f112]) ).
fof(f114,plain,
! [X0,X1] : ~ ok(triple(X0,X1,bad)),
inference(cnf_transformation,[status(thm)],[f113]) ).
fof(f115,plain,
! [U,V,W] :
( W = bad
| ok(triple(U,V,W)) ),
inference(pre_NNF_transformation,[status(thm)],[f29]) ).
fof(f116,plain,
! [W] :
( W = bad
| ! [U,V] : ok(triple(U,V,W)) ),
inference(miniscoping,[status(thm)],[f115]) ).
fof(f117,plain,
! [X0,X1,X2] :
( ok(triple(X1,X2,X0))
| X0 = bad ),
inference(cnf_transformation,[status(thm)],[f116]) ).
fof(f119,plain,
! [U,V,W,X] :
( remove_cpq(triple(U,V,W),X) = triple(U,V,bad)
| contains_slb(V,X) ),
inference(pre_NNF_transformation,[status(thm)],[f31]) ).
fof(f120,plain,
! [V,X] :
( ! [U,W] : remove_cpq(triple(U,V,W),X) = triple(U,V,bad)
| contains_slb(V,X) ),
inference(miniscoping,[status(thm)],[f119]) ).
fof(f121,plain,
! [X0,X1,X2,X3] :
( triple(X2,X0,bad) = remove_cpq(triple(X2,X0,X3),X1)
| contains_slb(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f120]) ).
fof(f122,plain,
! [U,V,W,X] :
( remove_cpq(triple(U,V,W),X) = triple(remove_pqp(U,X),remove_slb(V,X),W)
| ~ less_than(lookup_slb(V,X),X)
| ~ contains_slb(V,X) ),
inference(pre_NNF_transformation,[status(thm)],[f32]) ).
fof(f123,plain,
! [V,X] :
( ! [U,W] : remove_cpq(triple(U,V,W),X) = triple(remove_pqp(U,X),remove_slb(V,X),W)
| ~ less_than(lookup_slb(V,X),X)
| ~ contains_slb(V,X) ),
inference(miniscoping,[status(thm)],[f122]) ).
fof(f124,plain,
! [X0,X1,X2,X3] :
( remove_cpq(triple(X2,X0,X3),X1) = triple(remove_pqp(X2,X1),remove_slb(X0,X1),X3)
| ~ less_than(lookup_slb(X0,X1),X1)
| ~ contains_slb(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f123]) ).
fof(f125,plain,
! [U,V,W,X] :
( remove_cpq(triple(U,V,W),X) = triple(remove_pqp(U,X),remove_slb(V,X),bad)
| ~ strictly_less_than(X,lookup_slb(V,X))
| ~ contains_slb(V,X) ),
inference(pre_NNF_transformation,[status(thm)],[f33]) ).
fof(f126,plain,
! [V,X] :
( ! [U,W] : remove_cpq(triple(U,V,W),X) = triple(remove_pqp(U,X),remove_slb(V,X),bad)
| ~ strictly_less_than(X,lookup_slb(V,X))
| ~ contains_slb(V,X) ),
inference(miniscoping,[status(thm)],[f125]) ).
fof(f127,plain,
! [X0,X1,X2,X3] :
( ~ contains_slb(X2,X1)
| ~ strictly_less_than(X1,lookup_slb(X2,X1))
| triple(remove_pqp(X0,X1),remove_slb(X2,X1),bad) = remove_cpq(triple(X0,X2,X3),X1) ),
inference(cnf_transformation,[status(thm)],[f126]) ).
fof(f144,plain,
? [U,V,W,X] :
( ok(remove_cpq(triple(U,V,W),X))
& ~ ok(triple(U,V,W)) ),
inference(pre_NNF_transformation,[status(thm)],[f43]) ).
fof(f145,plain,
? [U,V,W] :
( ? [X] : ok(remove_cpq(triple(U,V,W),X))
& ~ ok(triple(U,V,W)) ),
inference(miniscoping,[status(thm)],[f144]) ).
fof(f146,plain,
( ok(remove_cpq(triple(sK0_skl,sK1_skl,sK2_skl),sK3_skl))
& ~ ok(triple(sK0_skl,sK1_skl,sK2_skl)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl,sK3_skl]),skolemize(U,sK0_skl),skolemize(V,sK1_skl),skolemize(W,sK2_skl),skolemize(X,sK3_skl)],[f145]) ).
fof(f147,plain,
~ ok(triple(sK0_skl,sK1_skl,sK2_skl)),
inference(cnf_transformation,[status(thm)],[f146]) ).
fof(f148,plain,
ok(remove_cpq(triple(sK0_skl,sK1_skl,sK2_skl),sK3_skl)),
inference(cnf_transformation,[status(thm)],[f146]) ).
fof(f150,plain,
! [X0,X1] :
( strictly_less_than(X1,X0)
| less_than(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f53,f47]) ).
fof(f154,plain,
bad = sK2_skl,
inference(resolution,[status(thm)],[f147,f117]) ).
fof(f156,plain,
! [X0,X1] : ~ ok(triple(X0,X1,sK2_skl)),
inference(backward_demodulation,[status(thm)],[f154,f114]) ).
fof(f157,plain,
! [X0,X1,X2,X3] :
( remove_cpq(triple(X2,X0,X3),X1) = triple(X2,X0,sK2_skl)
| contains_slb(X0,X1) ),
inference(backward_demodulation,[status(thm)],[f154,f121]) ).
fof(f161,plain,
! [X0,X1,X2,X3] :
( ~ strictly_less_than(X1,lookup_slb(X0,X1))
| triple(remove_pqp(X2,X1),remove_slb(X0,X1),sK2_skl) = remove_cpq(triple(X2,X0,X3),X1)
| ~ contains_slb(X0,X1) ),
inference(backward_demodulation,[status(thm)],[f154,f127]) ).
fof(f168,plain,
! [X0,X1,X2,X3] :
( ~ contains_slb(X2,X1)
| less_than(lookup_slb(X2,X1),X1)
| triple(remove_pqp(X0,X1),remove_slb(X2,X1),sK2_skl) = remove_cpq(triple(X0,X2,X3),X1) ),
inference(resolution,[status(thm)],[f150,f161]) ).
fof(f172,plain,
! [X0,X1,X2,X3,X4,X5] :
( remove_cpq(triple(X4,X1,X5),X3) = triple(X4,X1,sK2_skl)
| ~ less_than(lookup_slb(X1,X3),X3)
| remove_cpq(triple(X0,X1,X2),X3) = triple(remove_pqp(X0,X3),remove_slb(X1,X3),X2) ),
inference(resolution,[status(thm)],[f124,f157]) ).
fof(f178,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ contains_slb(X1,X3)
| triple(remove_pqp(X6,X3),remove_slb(X1,X3),sK2_skl) = remove_cpq(triple(X6,X1,X7),X3)
| remove_cpq(triple(X4,X1,X5),X3) = triple(X4,X1,sK2_skl)
| remove_cpq(triple(X0,X1,X2),X3) = triple(remove_pqp(X0,X3),remove_slb(X1,X3),X2) ),
inference(resolution,[status(thm)],[f172,f168]) ).
fof(f182,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( triple(remove_pqp(X6,X3),remove_slb(X1,X3),sK2_skl) = remove_cpq(triple(X6,X1,X7),X3)
| triple(remove_pqp(X4,X3),remove_slb(X1,X3),X5) = remove_cpq(triple(X4,X1,X5),X3)
| triple(X0,X1,sK2_skl) = remove_cpq(triple(X0,X1,X2),X3) ),
inference(forward_subsumption_resolution,[status(thm)],[f178,f157]) ).
fof(f250,plain,
! [X0,X1,X2,X3] :
( triple(remove_pqp(X2,sK3_skl),remove_slb(sK1_skl,sK3_skl),sK2_skl) = remove_cpq(triple(X2,sK1_skl,X3),sK3_skl)
| triple(remove_pqp(X0,sK3_skl),remove_slb(sK1_skl,sK3_skl),X1) = remove_cpq(triple(X0,sK1_skl,X1),sK3_skl)
| ok(triple(sK0_skl,sK1_skl,sK2_skl)) ),
inference(paramodulation,[status(thm)],[f182,f148]) ).
fof(f255,plain,
! [X0,X1,X2,X3] :
( triple(remove_pqp(X2,sK3_skl),remove_slb(sK1_skl,sK3_skl),X3) = remove_cpq(triple(X2,sK1_skl,X3),sK3_skl)
| remove_cpq(triple(X0,sK1_skl,X1),sK3_skl) = triple(remove_pqp(X0,sK3_skl),remove_slb(sK1_skl,sK3_skl),sK2_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f250,f156]) ).
fof(f265,plain,
! [X0,X1,X2,X3] :
( ~ ok(remove_cpq(triple(X2,sK1_skl,X3),sK3_skl))
| remove_cpq(triple(X0,sK1_skl,X1),sK3_skl) = triple(remove_pqp(X0,sK3_skl),remove_slb(sK1_skl,sK3_skl),X1) ),
inference(paramodulation,[status(thm)],[f255,f156]) ).
fof(f273,plain,
! [X0,X1] : triple(remove_pqp(X0,sK3_skl),remove_slb(sK1_skl,sK3_skl),X1) = remove_cpq(triple(X0,sK1_skl,X1),sK3_skl),
inference(resolution,[status(thm)],[f265,f148]) ).
fof(f297,plain,
! [X0] : ~ ok(remove_cpq(triple(X0,sK1_skl,sK2_skl),sK3_skl)),
inference(paramodulation,[status(thm)],[f273,f156]) ).
fof(f306,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f148,f297]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV378+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.56 % Computer : n026.cluster.edu
% 0.09/0.56 % Model : x86_64 x86_64
% 0.09/0.56 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.56 % Memory : 8046.5625MB
% 0.09/0.56 % OS : Linux 6.8.0-71-generic
% 0.09/0.56 % CPULimit : 300
% 0.09/0.56 % WCLimit : 300
% 0.09/0.56 % DateTime : Mon Sep 21 08:46:38 UTC 2026
% 0.09/0.57 % CPUTime :
% 0.09/0.58 % Drodi V4.1.1
% 44.40/6.23 % Refutation found
% 44.40/6.23 % SZS status Theorem for theBenchmark: Theorem is valid
% 44.40/6.23 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 44.40/6.29 % Elapsed time: 5.705141 seconds
% 44.40/6.29 % CPU time: 45.034681 seconds
% 44.40/6.29 % Total memory used: 395.351 MB
% 44.40/6.29 % Net memory used: 331.731 MB
%------------------------------------------------------------------------------