%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SWV011+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n004.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 03:11:00 PM UTC 2026
% Result : Theorem 4.12s 0.92s
% Output : Proof 4.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 19 ( 14 unt; 0 def)
% Number of atoms : 24 ( 7 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 14 ( 9 ~; 3 |; 2 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-4 aty)
% Number of variables : 6 ( 0 sgn 2 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f16,conjecture,
? [U] :
( b_holds(key(U,a))
& a_holds(key(U,b)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(f16_neg,negated_conjecture,
~ ? [U] :
( b_holds(key(U,a))
& a_holds(key(U,b)) ),
inference(negated_conjecture,[status(cth)],[f16]) ).
fof(f16_nnf,plain,
! [U] :
( ~ b_holds(key(U,a))
| ~ a_holds(key(U,b)) ),
inference(nnf_transformation,[status(thm)],[f16_neg]) ).
fof(f16_sk,plain,
! [U] :
( ~ b_holds(key(U,a))
| ~ a_holds(key(U,b)) ),
inference(skolemisation,[status(esa)],[f16_nnf]) ).
cnf(c16,plain,
( ~ b_holds(key(X0,a))
| ~ a_holds(key(X0,b)) ),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(hi16,negated_conjecture,
ifeq(a_holds(key(X0,b)),true,ifeq(b_holds(key(X0,a)),true,false,true),true) = true,
inference(equality_encoding,[status(esa)],[c16]) ).
fof(f12,axiom,
a_holds(key(generate_key(an_a_nonce),b)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).
fof(f12_nnf,plain,
a_holds(key(generate_key(an_a_nonce),b)),
inference(nnf_transformation,[status(thm)],[f12]) ).
cnf(c12,plain,
a_holds(key(generate_key(an_a_nonce),b)),
inference(cnf_transformation,[status(esa)],[f12_nnf]) ).
cnf(hi12,axiom,
a_holds(key(generate_key(an_a_nonce),b)) = true,
inference(equality_encoding,[status(esa)],[c12]) ).
fof(f10,axiom,
b_holds(key(generate_key(an_a_nonce),a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1) ).
fof(f10_nnf,plain,
b_holds(key(generate_key(an_a_nonce),a)),
inference(nnf_transformation,[status(thm)],[f10]) ).
cnf(c10,plain,
b_holds(key(generate_key(an_a_nonce),a)),
inference(cnf_transformation,[status(esa)],[f10_nnf]) ).
cnf(hi10,axiom,
b_holds(key(generate_key(an_a_nonce),a)) = true,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(t0,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi16,hi12,hi10]) ).
cnf(t34,plain,
false = true,
inference(orient,[status(thm)],[t0]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c16]) ).
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
% 0.00/0.02 % Problem : SWV011+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n004.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 : Thu Sep 24 18:16:51 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 4.12/0.92 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.12/0.92 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------