%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : NUN073+1 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n013.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 02:29:30 PM UTC 2026
% Result : Theorem 10.71s 6.93s
% Output : Proof 10.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 30 ( 18 unt; 0 def)
% Number of atoms : 70 ( 12 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 79 ( 39 ~; 30 |; 10 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 7 con; 0-4 aty)
% Number of variables : 50 ( 2 sgn 31 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f13,axiom,
! [X3,X10] :
( id(X3,X10)
| ! [Y12] :
( ~ r2(X10,Y12)
| ! [Y13] :
( ~ r2(X3,Y13)
| ~ id(Y13,Y12) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_3a) ).
fof(f13_nnf,plain,
! [X3,X10] :
( id(X3,X10)
| ! [Y12] :
( ~ r2(X10,Y12)
| ! [Y13] :
( ~ r2(X3,Y13)
| ~ id(Y13,Y12) ) ) ),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [Y13,Y12,X3,X10] :
( id(X3,X10)
| ~ r2(X10,Y12)
| ~ r2(X3,Y13)
| ~ id(Y13,Y12) ),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c45,plain,
( id(X0,X1)
| ~ r2(X1,X2)
| ~ r2(X0,X3)
| ~ id(X3,X2) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(hi29,axiom,
ifeq(id(X0,X1),true,ifeq(r2(X2,X0),true,ifeq(r2(X3,X1),true,id(X2,X3),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c45]) ).
fof(f18,conjecture,
! [Y1] :
( ! [Y3] :
( ~ r2(Y3,Y1)
| ! [Y5] :
( ~ r2(Y5,Y3)
| ~ r1(Y5) ) )
| ! [Y2] :
( ~ id(Y2,Y1)
| ! [Y4] :
( ~ r2(Y4,Y2)
| ~ r1(Y4) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',oneunidtwo) ).
fof(f18_neg,negated_conjecture,
~ ! [Y1] :
( ! [Y3] :
( ~ r2(Y3,Y1)
| ! [Y5] :
( ~ r2(Y5,Y3)
| ~ r1(Y5) ) )
| ! [Y2] :
( ~ id(Y2,Y1)
| ! [Y4] :
( ~ r2(Y4,Y2)
| ~ r1(Y4) ) ) ),
inference(negated_conjecture,[status(cth)],[f18]) ).
fof(f18_nnf,plain,
? [Y1] :
( ? [Y3] :
( r2(Y3,Y1)
& ? [Y5] :
( r2(Y5,Y3)
& r1(Y5) ) )
& ? [Y2] :
( id(Y2,Y1)
& ? [Y4] :
( r2(Y4,Y2)
& r1(Y4) ) ) ),
inference(nnf_transformation,[status(thm)],[f18_neg]) ).
fof(f18_sk,plain,
( r2(sk23,sk20)
& r2(sk24,sk23)
& r1(sk24)
& id(sk21,sk20)
& r2(sk22,sk21)
& r1(sk22) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk20,sk21,sk22,sk23,sk24])],[f18_nnf]) ).
cnf(c60,plain,
id(sk21,sk20),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(hi43,negated_conjecture,
id(sk21,sk20) = true,
inference(equality_encoding,[status(esa)],[c60]) ).
cnf(c59,plain,
r2(sk22,sk21),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(hi42,negated_conjecture,
r2(sk22,sk21) = true,
inference(equality_encoding,[status(esa)],[c59]) ).
cnf(c63,plain,
r2(sk23,sk20),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(hi46,negated_conjecture,
r2(sk23,sk20) = true,
inference(equality_encoding,[status(esa)],[c63]) ).
cnf(h13,plain,
id(sk22,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi29,hi43,hi42,hi46]) ).
fof(f17,axiom,
! [X7,Y10] :
( ~ r2(X7,Y10)
| ! [Y20] :
( ~ r1(Y20)
| ~ id(Y20,Y10) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_7a) ).
fof(f17_nnf,plain,
! [X7,Y10] :
( ~ r2(X7,Y10)
| ! [Y20] :
( ~ r1(Y20)
| ~ id(Y20,Y10) ) ),
inference(nnf_transformation,[status(thm)],[f17]) ).
fof(f17_sk,plain,
! [Y20,Y10,X7] :
( ~ r2(X7,Y10)
| ~ r1(Y20)
| ~ id(Y20,Y10) ),
inference(skolemisation,[status(esa)],[f17_nnf]) ).
cnf(c57,plain,
( ~ r2(X0,X1)
| ~ r1(X2)
| ~ id(X2,X1) ),
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
cnf(hi47,axiom,
ifeq(id(X0,X1),true,ifeq(r1(X0),true,ifeq(r2(X2,X1),true,false,true),true),true) = true,
inference(equality_encoding,[status(esa)],[c57]) ).
cnf(c58,plain,
r1(sk22),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(hi41,negated_conjecture,
r1(sk22) = true,
inference(equality_encoding,[status(esa)],[c58]) ).
cnf(c62,plain,
r2(sk24,sk23),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(hi45,negated_conjecture,
r2(sk24,sk23) = true,
inference(equality_encoding,[status(esa)],[c62]) ).
cnf(t0,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi47,h13,hi41,hi45]) ).
cnf(t909,plain,
false = true,
inference(orient,[status(thm)],[t0]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c57]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t909]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUN073+1 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.06 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/5.44 % Computer : n013.cluster.edu
% 0.17/5.44 % Model : x86_64 x86_64
% 0.17/5.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/5.44 % Memory : 8046.5625MB
% 0.17/5.44 % OS : Linux 6.8.0-71-generic
% 0.17/5.44 % CPULimit : 300
% 0.17/5.44 % WCLimit : 300
% 0.17/5.44 % DateTime : Thu Sep 24 05:55:49 UTC 2026
% 0.17/5.45 % CPUTime :
% 0.17/5.45 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 10.71/6.93 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.71/6.93 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------