%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN062+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 : n006.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 03:33:39 PM UTC 2026
% Result : Theorem 3.86s 0.91s
% Output : Proof 3.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 31 ( 15 unt; 0 def)
% Number of atoms : 62 ( 11 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 54 ( 23 ~; 16 |; 10 &)
% ( 0 <=>; 5 =>; 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 : 3 ( 3 usr; 2 con; 0-4 aty)
% Number of variables : 18 ( 0 sgn 11 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X] :
( big_k(X)
=> big_h(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel32_3) ).
fof(f2_nnf,plain,
! [X] :
( big_h(X)
| ~ big_k(X) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X] :
( big_h(X)
| ~ big_k(X) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c3,plain,
( big_h(X0)
| ~ big_k(X0) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi3,axiom,
ifeq(big_k(X0),true,big_h(X0),true) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
fof(f3,conjecture,
! [X] :
( ( big_k(X)
& big_f(X) )
=> big_j(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel32) ).
fof(f3_neg,negated_conjecture,
~ ! [X] :
( ( big_k(X)
& big_f(X) )
=> big_j(X) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
fof(f3_nnf,plain,
? [X] :
( ~ big_j(X)
& big_k(X)
& big_f(X) ),
inference(nnf_transformation,[status(thm)],[f3_neg]) ).
fof(f3_sk,plain,
( ~ big_j(sk0)
& big_k(sk0)
& big_f(sk0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f3_nnf]) ).
cnf(c5,plain,
big_k(sk0),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(hi5,negated_conjecture,
big_k(sk0) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(h0,plain,
big_h(sk0) = true,
inference(hyper_resolution,[status(thm)],[hi3,hi5]) ).
fof(f0,axiom,
! [X] :
( ( ( big_h(X)
| big_g(X) )
& big_f(X) )
=> big_i(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel32_1) ).
fof(f0_nnf,plain,
! [X] :
( big_i(X)
| ( ~ big_h(X)
& ~ big_g(X) )
| ~ big_f(X) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X] :
( big_i(X)
| ( ~ big_h(X)
& ~ big_g(X) )
| ~ big_f(X) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c1,plain,
( big_i(X0)
| ~ big_h(X0)
| ~ big_f(X0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi1,axiom,
ifeq(big_f(X0),true,ifeq(big_h(X0),true,big_i(X0),true),true) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(c4,plain,
big_f(sk0),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(hi4,negated_conjecture,
big_f(sk0) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(h1,plain,
big_i(sk0) = true,
inference(hyper_resolution,[status(thm)],[hi1,hi4,h0]) ).
fof(f1,axiom,
! [X] :
( ( big_h(X)
& big_i(X) )
=> big_j(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel32_2) ).
fof(f1_nnf,plain,
! [X] :
( big_j(X)
| ~ big_h(X)
| ~ big_i(X) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X] :
( big_j(X)
| ~ big_h(X)
| ~ big_i(X) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c2,plain,
( big_j(X0)
| ~ big_h(X0)
| ~ big_i(X0) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(hi2,axiom,
ifeq(big_i(X0),true,ifeq(big_h(X0),true,big_j(X0),true),true) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t3,plain,
big_j(sk0) = true,
inference(hyper_resolution,[status(thm)],[hi2,h1,h0]) ).
cnf(t26,plain,
big_j(sk0) = true,
inference(orient,[status(thm)],[t3]) ).
cnf(c6,plain,
~ big_j(sk0),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(goal_0,negated_conjecture,
big_j(sk0) != true,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t26]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN062+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.37 % Computer : n006.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 00:00:27 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 3.86/0.91 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.86/0.91 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------