%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN721+1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n003.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 03:35:33 PM UTC 2026
% Result : Theorem 4.73s 1.18s
% Output : Proof 4.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 1
% Syntax : Number of formulae : 19 ( 12 unt; 0 def)
% Number of atoms : 46 ( 10 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 42 ( 15 ~; 9 |; 12 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-4 aty)
% Number of variables : 37 ( 7 sgn 20 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f0,conjecture,
( ( ! [U,V] :
( q(U,V)
=> ! [Z] : r(Z,V) )
& ! [X] :
( ? [Y] : r(X,Y)
=> q(X,X) )
& r(a,b) )
=> ? [W] :
( q(W,a)
& r(b,W) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lx1) ).
fof(f0_neg,negated_conjecture,
~ ( ( ! [U,V] :
( q(U,V)
=> ! [Z] : r(Z,V) )
& ! [X] :
( ? [Y] : r(X,Y)
=> q(X,X) )
& r(a,b) )
=> ? [W] :
( q(W,a)
& r(b,W) ) ),
inference(negated_conjecture,[status(cth)],[f0]) ).
fof(f0_nnf,plain,
( ! [W] :
( ~ q(W,a)
| ~ r(b,W) )
& ! [U,V] :
( ! [Z] : r(Z,V)
| ~ q(U,V) )
& ! [X] :
( q(X,X)
| ! [Y] : ~ r(X,Y) )
& r(a,b) ),
inference(nnf_transformation,[status(thm)],[f0_neg]) ).
fof(f0_sk,plain,
! [X,Y,U,V,Z,W] :
( ( ~ q(W,a)
| ~ r(b,W) )
& ( r(Z,V)
| ~ q(U,V) )
& ( q(X,X)
| ~ r(X,Y) )
& r(a,b) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c1,plain,
( q(X0,X0)
| ~ r(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi1,negated_conjecture,
ifeq(r(X0,X1),true,q(X0,X0),true) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(c0,plain,
r(a,b),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi0,negated_conjecture,
r(a,b) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(h0,plain,
q(a,a) = true,
inference(hyper_resolution,[status(thm)],[hi1,hi0]) ).
cnf(c2,plain,
( r(X4,X3)
| ~ q(X2,X3) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi2,negated_conjecture,
ifeq(q(X0,X1),true,r(X2,X1),true) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(h1,plain,
r(V0,a) = true,
inference(hyper_resolution,[status(thm)],[hi2,h0]) ).
cnf(c3,plain,
( ~ q(X5,a)
| ~ r(b,X5) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi3,negated_conjecture,
ifeq(r(b,X0),true,ifeq(q(X0,a),true,false,true),true) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t0,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi3,h1,h0]) ).
cnf(t22,plain,
false = true,
inference(orient,[status(thm)],[t0]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t22]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN721+1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/0.37 % Computer : n003.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Fri Sep 25 02:12:07 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 4.73/1.18 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.73/1.18 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------