%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN365+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 : n020.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 03:34:30 PM UTC 2026
% Result : Theorem 4.00s 0.97s
% Output : Proof 4.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 1
% Syntax : Number of formulae : 25 ( 16 unt; 0 def)
% Number of atoms : 62 ( 14 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 54 ( 17 ~; 11 |; 18 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-4 aty)
% Number of variables : 28 ( 0 sgn 12 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f0,conjecture,
( ( ! [W] :
( big_p(W)
=> ( big_p(h(W))
& big_p(g(W)) ) )
& ! [X] :
? [Y] :
( big_p(X)
=> ( big_p(Y)
& big_r(X,g(h(Y))) ) ) )
=> ! [X] :
( big_p(X)
=> ? [Y] :
( big_p(Y)
& big_r(X,Y) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x2116) ).
fof(f0_neg,negated_conjecture,
~ ( ( ! [W] :
( big_p(W)
=> ( big_p(h(W))
& big_p(g(W)) ) )
& ! [X] :
? [Y] :
( big_p(X)
=> ( big_p(Y)
& big_r(X,g(h(Y))) ) ) )
=> ! [X] :
( big_p(X)
=> ? [Y] :
( big_p(Y)
& big_r(X,Y) ) ) ),
inference(negated_conjecture,[status(cth)],[f0]) ).
fof(f0_nnf,plain,
( ? [X] :
( ! [Y] :
( ~ big_p(Y)
| ~ big_r(X,Y) )
& big_p(X) )
& ! [W] :
( ( big_p(h(W))
& big_p(g(W)) )
| ~ big_p(W) )
& ! [X] :
? [Y] :
( ( big_p(Y)
& big_r(X,g(h(Y))) )
| ~ big_p(X) ) ),
inference(nnf_transformation,[status(thm)],[f0_neg]) ).
fof(f0_sk,plain,
! [X,W,Y] :
( ( ~ big_p(Y)
| ~ big_r(sk1,Y) )
& big_p(sk1)
& ( ( big_p(h(W))
& big_p(g(W)) )
| ~ big_p(W) )
& ( ( big_p(sk0(X))
& big_r(X,g(h(sk0(X)))) )
| ~ big_p(X) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1])],[f0_nnf]) ).
cnf(c1,plain,
( big_p(sk0(X0))
| ~ big_p(X0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi1,negated_conjecture,
ifeq(big_p(X0),true,big_p(sk0(X0)),true) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(c4,plain,
big_p(sk1),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi4,negated_conjecture,
big_p(sk1) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(h2,plain,
big_p(sk0(sk1)) = true,
inference(hyper_resolution,[status(thm)],[hi1,hi4]) ).
cnf(c3,plain,
( big_p(h(X2))
| ~ big_p(X2) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi3,negated_conjecture,
ifeq(big_p(X0),true,big_p(h(X0)),true) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(h12,plain,
big_p(h(sk0(sk1))) = true,
inference(hyper_resolution,[status(thm)],[hi3,h2]) ).
cnf(c2,plain,
( big_p(g(X2))
| ~ big_p(X2) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi2,negated_conjecture,
ifeq(big_p(X0),true,big_p(g(X0)),true) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(h41,plain,
big_p(g(h(sk0(sk1)))) = true,
inference(hyper_resolution,[status(thm)],[hi2,h12]) ).
cnf(c0,plain,
( big_r(X0,g(h(sk0(X0))))
| ~ big_p(X0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi0,negated_conjecture,
ifeq(big_p(X0),true,big_r(X0,g(h(sk0(X0)))),true) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(h3,plain,
big_r(sk1,g(h(sk0(sk1)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi4]) ).
cnf(c5,plain,
( ~ big_p(X1)
| ~ big_r(sk1,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi5,negated_conjecture,
ifeq(big_r(sk1,X0),true,ifeq(big_p(X0),true,false,true),true) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t0,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi5,h3,h41]) ).
cnf(t629,plain,
false = true,
inference(orient,[status(thm)],[t0]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t629]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN365+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.37 % Computer : n020.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Fri Sep 25 01:00:49 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 4.00/0.97 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.00/0.97 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------