%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN068+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n026.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 03:33:41 PM UTC 2026
% Result : Theorem 6.90s 1.36s
% Output : Proof 6.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 3
% Syntax : Number of formulae : 28 ( 14 unt; 0 def)
% Number of atoms : 54 ( 12 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 45 ( 19 ~; 10 |; 14 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-4 aty)
% Number of variables : 24 ( 0 sgn 8 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,conjecture,
? [X] :
( ~ big_f(X)
& big_j(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel44) ).
fof(f2_neg,negated_conjecture,
~ ? [X] :
( ~ big_f(X)
& big_j(X) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
fof(f2_nnf,plain,
! [X] :
( big_f(X)
| ~ big_j(X) ),
inference(nnf_transformation,[status(thm)],[f2_neg]) ).
fof(f2_sk,plain,
! [X] :
( big_f(X)
| ~ big_j(X) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c6,plain,
( big_f(X0)
| ~ big_j(X0) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi5,negated_conjecture,
ifeq(big_j(X0),true,big_f(X0),true) = true,
inference(equality_encoding,[status(esa)],[c6]) ).
fof(f1,axiom,
? [X] :
( ! [Y] :
( big_g(Y)
=> big_h(X,Y) )
& big_j(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel44_2) ).
fof(f1_nnf,plain,
? [X] :
( ! [Y] :
( big_h(X,Y)
| ~ big_g(Y) )
& big_j(X) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [Y] :
( ( big_h(sk2,Y)
| ~ big_g(Y) )
& big_j(sk2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2])],[f1_nnf]) ).
cnf(c4,plain,
big_j(sk2),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(hi3,axiom,
big_j(sk2) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(h0,plain,
big_f(sk2) = true,
inference(hyper_resolution,[status(thm)],[hi5,hi3]) ).
fof(f0,axiom,
! [X] :
( big_f(X)
=> ( ? [Y1] :
( ~ big_h(X,Y1)
& big_g(Y1) )
& ? [Y] :
( big_h(X,Y)
& big_g(Y) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel44_1) ).
fof(f0_nnf,plain,
! [X] :
( ( ? [Y1] :
( ~ big_h(X,Y1)
& big_g(Y1) )
& ? [Y] :
( big_h(X,Y)
& big_g(Y) ) )
| ~ big_f(X) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X] :
( ( ~ big_h(X,sk1(X))
& big_g(sk1(X))
& big_h(X,sk0(X))
& big_g(sk0(X)) )
| ~ big_f(X) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1])],[f0_nnf]) ).
cnf(c2,plain,
( big_g(sk1(X0))
| ~ big_f(X0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi2,axiom,
ifeq(big_f(X0),true,big_g(sk1(X0)),true) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(h1,plain,
big_g(sk1(sk2)) = true,
inference(hyper_resolution,[status(thm)],[hi2,h0]) ).
cnf(c5,plain,
( big_h(sk2,X1)
| ~ big_g(X1) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(hi4,axiom,
ifeq(big_g(X0),true,big_h(sk2,X0),true) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(h4,plain,
big_h(sk2,sk1(sk2)) = true,
inference(hyper_resolution,[status(thm)],[hi4,h1]) ).
cnf(c3,plain,
( ~ big_h(X0,sk1(X0))
| ~ big_f(X0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi6,axiom,
ifeq(big_f(X0),true,ifeq(big_h(X0,sk1(X0)),true,false,true),true) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t0,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi6,h0,h4]) ).
cnf(t34,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,t34]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN068+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n026.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 00:05:56 UTC 2026
% 0.03/0.36 % CPUTime :
% 0.03/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 6.90/1.36 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.90/1.36 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------