%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : MSC012+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/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 01:28:15 PM UTC 2026
% Result : Theorem 0.12s 0.40s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 7
% Syntax : Number of formulae : 40 ( 9 unt; 2 def)
% Number of atoms : 108 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 122 ( 54 ~; 59 |; 5 &)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 4 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 0 con; 1-1 aty)
% Number of variables : 55 ( 53 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] :
( ( p(B)
& less(A,B)
& p(A) )
=> goal ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A] :
( ? [B] :
( p(B)
& less(A,B) )
| p(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A,B,C] :
( ( less(B,C)
& less(A,B) )
=> less(A,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A] :
? [B] : less(A,B),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,conjecture,
goal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
~ goal,
inference(negated_conjecture,[status(cth)],[f5]) ).
fof(f7,plain,
! [A,B] :
( goal
| ~ p(B)
| ~ less(A,B)
| ~ p(A) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f8,plain,
( goal
| ! [B] :
( ~ p(B)
| ! [A] :
( ~ less(A,B)
| ~ p(A) ) ) ),
inference(miniscoping,[status(thm)],[f7]) ).
fof(f9,plain,
! [X0,X1] :
( goal
| ~ p(X1)
| ~ less(X0,X1)
| ~ p(X0) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f10,plain,
! [A] :
( ( p(sK0_skl(A))
& less(A,sK0_skl(A)) )
| p(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(B,sK0_skl(A))],[f2]) ).
fof(f11,plain,
! [X0] :
( less(X0,sK0_skl(X0))
| p(X0) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f12,plain,
! [X0] :
( p(sK0_skl(X0))
| p(X0) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f13,plain,
! [A,B,C] :
( less(A,C)
| ~ less(B,C)
| ~ less(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f14,plain,
! [A,C] :
( less(A,C)
| ! [B] :
( ~ less(B,C)
| ~ less(A,B) ) ),
inference(miniscoping,[status(thm)],[f13]) ).
fof(f15,plain,
! [X0,X1,X2] :
( less(X0,X2)
| ~ less(X1,X2)
| ~ less(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f16,plain,
! [A] : less(A,sK1_skl(A)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(B,sK1_skl(A))],[f4]) ).
fof(f17,plain,
! [X0] : less(X0,sK1_skl(X0)),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f18,plain,
~ goal,
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f19,definition,
! [X0,X1] :
( sQ0_spl
<=> ( ~ p(X1)
| ~ less(X0,X1)
| ~ p(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f20,plain,
! [X0,X1] :
( ~ sQ0_spl
| ~ p(X1)
| ~ less(X0,X1)
| ~ p(X0) ),
inference(component_clause,[status(thm)],[f19]) ).
fof(f22,definition,
( sQ1_spl
<=> goal ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f23,plain,
( ~ sQ1_spl
| goal ),
inference(component_clause,[status(thm)],[f22]) ).
fof(f25,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f9,f19,f22]) ).
fof(f26,plain,
! [X0,X1] :
( ~ sQ0_spl
| ~ less(X1,sK0_skl(X0))
| ~ p(X1)
| p(X0) ),
inference(resolution,[status(thm)],[f12,f20]) ).
fof(f27,plain,
! [X0,X1] :
( ~ sQ0_spl
| p(X1)
| ~ less(sK0_skl(X1),sK0_skl(X0))
| p(X0) ),
inference(resolution,[status(thm)],[f26,f12]) ).
fof(f30,plain,
! [X0,X1,X2] :
( ~ sQ0_spl
| p(X0)
| p(X2)
| ~ less(X1,sK0_skl(X2))
| ~ less(sK0_skl(X0),X1) ),
inference(resolution,[status(thm)],[f15,f27]) ).
fof(f31,plain,
! [X0,X1] :
( ~ sQ0_spl
| p(X1)
| p(X0)
| p(X1)
| ~ less(sK0_skl(X0),X1) ),
inference(resolution,[status(thm)],[f30,f11]) ).
fof(f33,plain,
! [X0,X1] :
( ~ sQ0_spl
| p(X0)
| p(X1)
| ~ less(sK0_skl(X0),X1) ),
inference(duplicate_literals_removal,[status(thm)],[f31]) ).
fof(f35,plain,
! [X0] :
( ~ sQ0_spl
| p(X0)
| p(sK1_skl(sK0_skl(X0))) ),
inference(resolution,[status(thm)],[f33,f17]) ).
fof(f41,plain,
! [X0,X1] :
( ~ sQ0_spl
| ~ less(X1,sK1_skl(sK0_skl(X0)))
| ~ p(X1)
| p(X0) ),
inference(resolution,[status(thm)],[f35,f20]) ).
fof(f43,plain,
! [X0,X1] :
( ~ sQ0_spl
| p(X1)
| ~ less(sK0_skl(X1),sK1_skl(sK0_skl(X0)))
| p(X0) ),
inference(resolution,[status(thm)],[f41,f12]) ).
fof(f56,plain,
! [X0] :
( ~ sQ0_spl
| p(X0)
| p(X0) ),
inference(resolution,[status(thm)],[f43,f17]) ).
fof(f58,plain,
! [X0] :
( ~ sQ0_spl
| p(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f56]) ).
fof(f59,plain,
! [X0,X1] :
( ~ sQ0_spl
| ~ p(X1)
| ~ less(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f20,f58]) ).
fof(f60,plain,
! [X0,X1] :
( ~ sQ0_spl
| ~ less(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f59,f58]) ).
fof(f61,plain,
( ~ sQ0_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f17,f60]) ).
fof(f62,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f61]) ).
fof(f63,plain,
( ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f23,f18]) ).
fof(f64,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f63]) ).
fof(f65,plain,
$false,
inference(sat_refutation,[status(thm)],[f25,f62,f64]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MSC012+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n019.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 01:27:35 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.36 % Drodi V4.1.1
% 0.12/0.40 % Refutation found
% 0.12/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.41 % Elapsed time: 0.046453 seconds
% 0.12/0.41 % CPU time: 0.169924 seconds
% 0.12/0.41 % Total memory used: 15.547 MB
% 0.12/0.41 % Net memory used: 15.103 MB
%------------------------------------------------------------------------------