%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN366+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n015.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 03:34:31 PM UTC 2026
% Result : Theorem 4.09s 0.98s
% Output : Proof 4.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 1
% Syntax : Number of formulae : 17 ( 11 unt; 0 def)
% Number of atoms : 47 ( 8 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 46 ( 16 ~; 10 |; 12 &)
% ( 4 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-4 aty)
% Number of variables : 33 ( 5 sgn 18 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f0,conjecture,
( ( ! [W,Z] :
( big_r(W,W)
<=> big_r(Z,W) )
& ! [U,V] :
( big_r(U,U)
<=> big_r(U,V) ) )
=> ( ? [X] : big_r(X,X)
=> ! [Y] : big_r(Y,Y) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x2117) ).
fof(f0_neg,negated_conjecture,
~ ( ( ! [W,Z] :
( big_r(W,W)
<=> big_r(Z,W) )
& ! [U,V] :
( big_r(U,U)
<=> big_r(U,V) ) )
=> ( ? [X] : big_r(X,X)
=> ! [Y] : big_r(Y,Y) ) ),
inference(negated_conjecture,[status(cth)],[f0]) ).
fof(f0_nnf,plain,
( ? [Y] : ~ big_r(Y,Y)
& ? [X] : big_r(X,X)
& ! [W,Z] :
( ( ~ big_r(Z,W)
| big_r(W,W) )
& ( big_r(Z,W)
| ~ big_r(W,W) ) )
& ! [U,V] :
( ( ~ big_r(U,V)
| big_r(U,U) )
& ( big_r(U,V)
| ~ big_r(U,U) ) ) ),
inference(nnf_transformation,[status(thm)],[f0_neg]) ).
fof(f0_sk,plain,
! [U,V,W,Z] :
( ~ big_r(sk1,sk1)
& big_r(sk0,sk0)
& ( ~ big_r(Z,W)
| big_r(W,W) )
& ( big_r(Z,W)
| ~ big_r(W,W) )
& ( ~ big_r(U,V)
| big_r(U,U) )
& ( big_r(U,V)
| ~ big_r(U,U) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1])],[f0_nnf]) ).
cnf(c2,plain,
( big_r(X3,X2)
| ~ big_r(X2,X2) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi2,negated_conjecture,
ifeq(big_r(X0,X0),true,big_r(X1,X0),true) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(c4,plain,
big_r(sk0,sk0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi4,negated_conjecture,
big_r(sk0,sk0) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(h0,plain,
big_r(V0,sk0) = true,
inference(hyper_resolution,[status(thm)],[hi2,hi4]) ).
cnf(c1,plain,
( ~ big_r(X0,X1)
| big_r(X0,X0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi1,negated_conjecture,
ifeq(big_r(X0,X1),true,big_r(X0,X0),true) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t0,plain,
big_r(X1,X1) = true,
inference(hyper_resolution,[status(thm)],[hi1,h0]) ).
cnf(t10,plain,
big_r(X1,X1) = true,
inference(orient,[status(thm)],[t0]) ).
cnf(c5,plain,
~ big_r(sk1,sk1),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(goal_0,negated_conjecture,
big_r(sk1,sk1) != true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t10]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN366+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.35 % Computer : n015.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Fri Sep 25 01:03:41 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 4.09/0.98 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.09/0.98 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------