%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN318+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 03:34:20 PM UTC 2026
% Result : Theorem 3.08s 0.87s
% Output : Proof 3.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 3
% Syntax : Number of formulae : 21 ( 16 unt; 0 def)
% Number of atoms : 43 ( 13 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 34 ( 12 ~; 6 |; 6 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 2 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-4 aty)
% Number of variables : 24 ( 9 sgn 8 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f0,conjecture,
? [Y] :
( ! [X] :
( big_f(X)
=> ( big_f(Y)
=> big_g(X) ) )
=> ( p
=> ! [X] :
( big_f(X)
=> big_g(Y) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',church_46_2_4) ).
fof(f0_neg,negated_conjecture,
~ ? [Y] :
( ! [X] :
( big_f(X)
=> ( big_f(Y)
=> big_g(X) ) )
=> ( p
=> ! [X] :
( big_f(X)
=> big_g(Y) ) ) ),
inference(negated_conjecture,[status(cth)],[f0]) ).
fof(f0_nnf,plain,
! [Y] :
( ? [X] :
( ~ big_g(Y)
& big_f(X) )
& p
& ! [X] :
( big_g(X)
| ~ big_f(Y)
| ~ big_f(X) ) ),
inference(nnf_transformation,[status(thm)],[f0_neg]) ).
fof(f0_sk,plain,
! [X,Y] :
( ~ big_g(Y)
& big_f(sk0(Y))
& p
& ( big_g(X)
| ~ big_f(Y)
| ~ big_f(X) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f0_nnf]) ).
cnf(c3,plain,
~ big_g(X0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t4,plain,
eq(big_g(X1),true) = efalse,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t16,plain,
eq(big_g(X1),true) = efalse,
inference(orient,[status(thm)],[t4]) ).
cnf(c0,plain,
( big_g(X1)
| ~ big_f(X0)
| ~ big_f(X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi0,negated_conjecture,
ifeq(big_f(X0),true,ifeq(big_f(X1),true,big_g(X0),true),true) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(c2,plain,
big_f(sk0(X0)),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi2,negated_conjecture,
big_f(sk0(X0)) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t2,plain,
big_g(sk0(X1)) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi2,hi2]) ).
cnf(t9,plain,
big_g(sk0(X1)) = true,
inference(orient,[status(thm)],[t2]) ).
cnf(t17,plain,
efalse = eq(true,true),
inference(cp,[status(thm)],[t16,t9]) ).
cnf(t3,plain,
eq(X1,X1) = etrue,
introduced(definition) ).
cnf(t15,plain,
eq(X1,X1) = etrue,
inference(orient,[status(thm)],[t3]) ).
cnf(t21,plain,
efalse = etrue,
inference(step,[status(thm)],[t17,t15]) ).
cnf(t18,plain,
efalse = etrue,
inference(orient,[status(thm)],[t21]) ).
cnf(goal_0,negated_conjecture,
etrue != efalse,
introduced(definition) ).
cnf(g0_0,plain,
etrue != etrue,
inference(rw,[status(thm)],[goal_0,t18]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN318+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.39 % Computer : n020.cluster.edu
% 0.09/0.39 % Model : x86_64 x86_64
% 0.09/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.39 % Memory : 8046.5625MB
% 0.09/0.39 % OS : Linux 6.8.0-71-generic
% 0.09/0.39 % CPULimit : 300
% 0.09/0.39 % WCLimit : 300
% 0.09/0.39 % DateTime : Fri Sep 25 00:49:48 UTC 2026
% 0.09/0.40 % CPUTime :
% 0.09/0.40 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 3.08/0.87 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.08/0.87 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------