%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN057+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 : n009.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 3.05s 0.83s
% Output : Proof 3.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 37 ( 18 unt; 0 def)
% Number of atoms : 68 ( 13 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 60 ( 29 ~; 18 |; 7 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-4 aty)
% Number of variables : 25 ( 0 sgn 13 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X] :
( ( big_i(X)
& big_j(X) )
=> big_f(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel27_3) ).
fof(f2_nnf,plain,
! [X] :
( big_f(X)
| ~ big_i(X)
| ~ big_j(X) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X] :
( big_f(X)
| ~ big_i(X)
| ~ big_j(X) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c3,plain,
( big_f(X0)
| ~ big_i(X0)
| ~ big_j(X0) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi2,axiom,
ifeq(big_j(X0),true,ifeq(big_i(X0),true,big_f(X0),true),true) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
fof(f4,conjecture,
! [X] :
( big_j(X)
=> ~ big_i(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel27) ).
fof(f4_neg,negated_conjecture,
~ ! [X] :
( big_j(X)
=> ~ big_i(X) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
fof(f4_nnf,plain,
? [X] :
( big_i(X)
& big_j(X) ),
inference(nnf_transformation,[status(thm)],[f4_neg]) ).
fof(f4_sk,plain,
( big_i(sk1)
& big_j(sk1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1])],[f4_nnf]) ).
cnf(c5,plain,
big_j(sk1),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(hi4,negated_conjecture,
big_j(sk1) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(c6,plain,
big_i(sk1),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(hi5,negated_conjecture,
big_i(sk1) = true,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(h1,plain,
big_f(sk1) = true,
inference(hyper_resolution,[status(thm)],[hi2,hi4,hi5]) ).
fof(f1,axiom,
! [X] :
( big_f(X)
=> big_h(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel27_2) ).
fof(f1_nnf,plain,
! [X] :
( big_h(X)
| ~ big_f(X) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X] :
( big_h(X)
| ~ big_f(X) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c2,plain,
( big_h(X0)
| ~ big_f(X0) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(hi1,axiom,
ifeq(big_f(X0),true,big_h(X0),true) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(h2,plain,
big_h(sk1) = true,
inference(hyper_resolution,[status(thm)],[hi1,h1]) ).
fof(f0,axiom,
? [X] :
( ~ big_g(X)
& big_f(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel27_1) ).
fof(f0_nnf,plain,
? [X] :
( ~ big_g(X)
& big_f(X) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
( ~ big_g(sk0)
& big_f(sk0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f0_nnf]) ).
cnf(c0,plain,
big_f(sk0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi0,axiom,
big_f(sk0) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(h0,plain,
big_h(sk0) = true,
inference(hyper_resolution,[status(thm)],[hi1,hi0]) ).
fof(f3,axiom,
( ? [X] :
( ~ big_g(X)
& big_h(X) )
=> ! [X1] :
( big_i(X1)
=> ~ big_h(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel27_4) ).
fof(f3_nnf,plain,
( ! [X1] :
( ~ big_h(X1)
| ~ big_i(X1) )
| ! [X] :
( big_g(X)
| ~ big_h(X) ) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [X,X1] :
( ~ big_h(X1)
| ~ big_i(X1)
| big_g(X)
| ~ big_h(X) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c4,plain,
( ~ big_h(X1)
| ~ big_i(X1)
| big_g(X0)
| ~ big_h(X0) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(hi3,axiom,
ifeq(big_h(X0),true,ifeq(big_i(X1),true,ifeq(big_h(X1),true,big_g(X0),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t2,plain,
big_g(sk0) = true,
inference(hyper_resolution,[status(thm)],[hi3,h0,hi5,h2]) ).
cnf(t33,plain,
big_g(sk0) = true,
inference(orient,[status(thm)],[t2]) ).
cnf(c1,plain,
~ big_g(sk0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(goal_0,negated_conjecture,
big_g(sk0) != true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t33]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN057+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.37 % Computer : n009.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 : Thu Sep 24 23:58:43 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 3.05/0.83 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.05/0.83 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------