%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN058+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 : 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 03:33:38 PM UTC 2026
% Result : Theorem 4.03s 0.97s
% Output : Proof 4.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 31 ( 15 unt; 0 def)
% Number of atoms : 61 ( 11 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 50 ( 20 ~; 13 |; 11 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-4 aty)
% Number of variables : 28 ( 7 sgn 14 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f0,axiom,
! [X] :
( big_p(X)
=> ! [Z] : big_q(Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel28_1) ).
fof(f0_nnf,plain,
! [X] :
( ! [Z] : big_q(Z)
| ~ big_p(X) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X,Z] :
( big_q(Z)
| ~ big_p(X) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( big_q(X1)
| ~ big_p(X0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi0,axiom,
ifeq(big_p(X0),true,big_q(X1),true) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
fof(f3,conjecture,
! [X] :
( ( big_f(X)
& big_p(X) )
=> big_g(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel28) ).
fof(f3_neg,negated_conjecture,
~ ! [X] :
( ( big_f(X)
& big_p(X) )
=> big_g(X) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
fof(f3_nnf,plain,
? [X] :
( ~ big_g(X)
& big_f(X)
& big_p(X) ),
inference(nnf_transformation,[status(thm)],[f3_neg]) ).
fof(f3_sk,plain,
( ~ big_g(sk2)
& big_f(sk2)
& big_p(sk2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2])],[f3_nnf]) ).
cnf(c6,plain,
big_p(sk2),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(hi6,negated_conjecture,
big_p(sk2) = true,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(h0,plain,
big_q(V0) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi6]) ).
fof(f1,axiom,
( ! [X] :
( big_r(X)
| big_q(X) )
=> ? [X1] :
( big_s(X1)
& big_q(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel28_2) ).
fof(f1_nnf,plain,
( ? [X1] :
( big_s(X1)
& big_q(X1) )
| ? [X] :
( ~ big_r(X)
& ~ big_q(X) ) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
( ( big_s(sk1)
& big_q(sk1) )
| ( ~ big_r(sk0)
& ~ big_q(sk0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1])],[f1_nnf]) ).
cnf(c2,plain,
( big_s(sk1)
| ~ big_q(sk0) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(hi2,axiom,
ifeq(big_q(sk0),true,big_s(sk1),true) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(h1,plain,
big_s(sk1) = true,
inference(hyper_resolution,[status(thm)],[hi2,h0]) ).
fof(f2,axiom,
( ? [X] : big_s(X)
=> ! [X1] :
( big_f(X1)
=> big_g(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel28_3) ).
fof(f2_nnf,plain,
( ! [X1] :
( big_g(X1)
| ~ big_f(X1) )
| ! [X] : ~ big_s(X) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X,X1] :
( big_g(X1)
| ~ big_f(X1)
| ~ big_s(X) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c5,plain,
( big_g(X1)
| ~ big_f(X1)
| ~ big_s(X0) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi5,axiom,
ifeq(big_s(X0),true,ifeq(big_f(X1),true,big_g(X1),true),true) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(c7,plain,
big_f(sk2),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(hi7,negated_conjecture,
big_f(sk2) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t1,plain,
big_g(sk2) = true,
inference(hyper_resolution,[status(thm)],[hi5,h1,hi7]) ).
cnf(t30,plain,
big_g(sk2) = true,
inference(orient,[status(thm)],[t1]) ).
cnf(c8,plain,
~ big_g(sk2),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(goal_0,negated_conjecture,
big_g(sk2) != true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t30]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN058+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 : n011.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 : Thu Sep 24 23:58:58 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.38 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 4.03/0.97 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.03/0.97 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------