%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LCL684+1.001 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n011.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 : Fri Sep 25 02:02:39 PM UTC 2026
% Result : Theorem 3.13s 0.85s
% Output : Proof 3.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 2
% Syntax : Number of formulae : 20 ( 15 unt; 0 def)
% Number of atoms : 43 ( 8 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 52 ( 29 ~; 15 |; 8 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-4 aty)
% Number of variables : 20 ( 0 sgn 11 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,conjecture,
~ ? [X] :
~ ( ~ ( p101(X)
& p201(X) )
| ~ ! [Y] :
( ! [X] :
( ~ ( p101(X)
& p201(X) )
| ~ r1(Y,X) )
| ~ r1(X,Y) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',main) ).
fof(f2_neg,negated_conjecture,
~ ~ ? [X] :
~ ( ~ ( p101(X)
& p201(X) )
| ~ ! [Y] :
( ! [X] :
( ~ ( p101(X)
& p201(X) )
| ~ r1(Y,X) )
| ~ r1(X,Y) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
fof(f2_nnf,plain,
? [X] :
( p101(X)
& p201(X)
& ! [Y] :
( ! [X] :
( ~ p101(X)
| ~ p201(X)
| ~ r1(Y,X) )
| ~ r1(X,Y) ) ),
inference(nnf_transformation,[status(thm)],[f2_neg]) ).
fof(f2_sk,plain,
! [Y,X] :
( p101(sk0)
& p201(sk0)
& ( ~ p101(X)
| ~ p201(X)
| ~ r1(Y,X)
| ~ r1(sk0,Y) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f2_nnf]) ).
cnf(c2,plain,
( ~ p101(X0)
| ~ p201(X0)
| ~ r1(X1,X0)
| ~ r1(sk0,X1) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi4,negated_conjecture,
ifeq(r1(sk0,X0),true,ifeq(r1(X0,X1),true,ifeq(p201(X1),true,ifeq(p101(X1),true,false,true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
fof(f0,axiom,
! [X] : r1(X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity) ).
fof(f0_nnf,plain,
! [X] : r1(X,X),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X] : r1(X,X),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
r1(X0,X0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi0,axiom,
r1(X0,X0) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(c3,plain,
p201(sk0),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi2,negated_conjecture,
p201(sk0) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(c4,plain,
p101(sk0),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi3,negated_conjecture,
p101(sk0) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t0,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi4,hi0,hi0,hi2,hi3]) ).
cnf(t16,plain,
false = true,
inference(orient,[status(thm)],[t0]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t16]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL684+1.001 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.36 % Computer : n011.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Thu Sep 24 00:18:58 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 3.13/0.85 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.13/0.85 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------