%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : NUN070+1 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n007.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 02:29:29 PM UTC 2026
% Result : Theorem 14.05s 2.18s
% Output : Proof 14.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 40 ( 21 unt; 0 def)
% Number of atoms : 106 ( 12 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 109 ( 43 ~; 30 |; 36 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 8 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-4 aty)
% Number of variables : 91 ( 5 sgn 36 !; 26 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f0,axiom,
? [Y24] :
! [X19] :
( ( ~ id(X19,Y24)
& ~ r1(X19) )
| ( r1(X19)
& id(X19,Y24) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1) ).
fof(f0_nnf,plain,
? [Y24] :
! [X19] :
( ( ~ id(X19,Y24)
& ~ r1(X19) )
| ( r1(X19)
& id(X19,Y24) ) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X19] :
( ( ~ id(X19,sk0)
& ~ r1(X19) )
| ( r1(X19)
& id(X19,sk0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f0_nnf]) ).
cnf(c3,plain,
( ~ id(X1,sk0)
| r1(X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi1,axiom,
ifeq(id(X0,sk0),true,r1(X0),true) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
fof(f4,axiom,
! [X20] : id(X20,X20),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_5) ).
fof(f4_nnf,plain,
! [X20] : id(X20,X20),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [X20] : id(X20,X20),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c16,plain,
id(X0,X0),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(hi8,axiom,
id(X0,X0) = true,
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(h3,plain,
r1(sk0) = true,
inference(hyper_resolution,[status(thm)],[hi1,hi8]) ).
fof(f18,conjecture,
? [Y1] :
( ? [Y3] :
( ? [Y6] :
( r2(Y6,Y3)
& r1(Y6) )
& id(Y1,Y3) )
& ? [Y2] :
( ? [Y5] :
( r2(Y5,Y2)
& r1(Y5) )
& ? [Y4] :
( r3(Y2,Y4,Y1)
& r1(Y4) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',onepluszeroidone) ).
fof(f18_neg,negated_conjecture,
~ ? [Y1] :
( ? [Y3] :
( ? [Y6] :
( r2(Y6,Y3)
& r1(Y6) )
& id(Y1,Y3) )
& ? [Y2] :
( ? [Y5] :
( r2(Y5,Y2)
& r1(Y5) )
& ? [Y4] :
( r3(Y2,Y4,Y1)
& r1(Y4) ) ) ),
inference(negated_conjecture,[status(cth)],[f18]) ).
fof(f18_nnf,plain,
! [Y1] :
( ! [Y3] :
( ! [Y6] :
( ~ r2(Y6,Y3)
| ~ r1(Y6) )
| ~ id(Y1,Y3) )
| ! [Y2] :
( ! [Y5] :
( ~ r2(Y5,Y2)
| ~ r1(Y5) )
| ! [Y4] :
( ~ r3(Y2,Y4,Y1)
| ~ r1(Y4) ) ) ),
inference(nnf_transformation,[status(thm)],[f18_neg]) ).
fof(f18_sk,plain,
! [Y4,Y2,Y1,Y5,Y3,Y6] :
( ~ r2(Y6,Y3)
| ~ r1(Y6)
| ~ id(Y1,Y3)
| ~ r2(Y5,Y2)
| ~ r1(Y5)
| ~ r3(Y2,Y4,Y1)
| ~ r1(Y4) ),
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c58,plain,
( ~ r2(X5,X4)
| ~ r1(X5)
| ~ id(X0,X4)
| ~ r2(X3,X1)
| ~ r1(X3)
| ~ r3(X1,X2,X0)
| ~ r1(X2) ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(hi42,negated_conjecture,
ifeq(r1(X0),true,ifeq(r3(X1,X0,X2),true,ifeq(r1(X3),true,ifeq(r2(X3,X1),true,ifeq(id(X2,X4),true,ifeq(r1(X5),true,ifeq(r2(X5,X4),true,false,true),true),true),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c58]) ).
fof(f14,axiom,
! [X4] :
? [Y9] :
( ? [Y16] :
( r3(X4,Y16,Y9)
& r1(Y16) )
& id(Y9,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4a) ).
fof(f14_nnf,plain,
! [X4] :
? [Y9] :
( ? [Y16] :
( r3(X4,Y16,Y9)
& r1(Y16) )
& id(Y9,X4) ),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [X4] :
( r3(X4,sk13(X4),sk12(X4))
& r1(sk13(X4))
& id(sk12(X4),X4) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk12,sk13])],[f14_nnf]) ).
cnf(c47,plain,
r1(sk13(X0)),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(hi31,axiom,
r1(sk13(X0)) = true,
inference(equality_encoding,[status(esa)],[c47]) ).
cnf(c48,plain,
r3(X0,sk13(X0),sk12(X0)),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(hi32,axiom,
r3(X0,sk13(X0),sk12(X0)) = true,
inference(equality_encoding,[status(esa)],[c48]) ).
fof(f12,axiom,
! [X2,X9] :
? [Y2] :
( ? [Y6] :
( r4(X2,X9,Y6)
& r3(Y6,X2,Y2) )
& ? [Y3] :
( ? [Y14] :
( r4(X2,Y14,Y3)
& r2(X9,Y14) )
& id(Y3,Y2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2a) ).
fof(f12_nnf,plain,
! [X2,X9] :
? [Y2] :
( ? [Y6] :
( r4(X2,X9,Y6)
& r3(Y6,X2,Y2) )
& ? [Y3] :
( ? [Y14] :
( r4(X2,Y14,Y3)
& r2(X9,Y14) )
& id(Y3,Y2) ) ),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [X2,X9] :
( r4(X2,X9,sk11(X2,X9))
& r3(sk11(X2,X9),X2,sk8(X2,X9))
& r4(X2,sk10(X2,X9),sk9(X2,X9))
& r2(X9,sk10(X2,X9))
& id(sk9(X2,X9),sk8(X2,X9)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk8,sk9,sk10,sk11])],[f12_nnf]) ).
cnf(c41,plain,
r2(X1,sk10(X0,X1)),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(hi25,axiom,
r2(X0,sk10(X1,X0)) = true,
inference(equality_encoding,[status(esa)],[c41]) ).
cnf(c46,plain,
id(sk12(X0),X0),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(hi30,axiom,
id(sk12(X0),X0) = true,
inference(equality_encoding,[status(esa)],[c46]) ).
cnf(t0,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi42,hi31,hi32,h3,hi25,hi30,h3,hi25]) ).
cnf(t2744,plain,
false = true,
inference(orient,[status(thm)],[t0]) ).
fof(f17,axiom,
! [X7,Y10] :
( ~ r2(X7,Y10)
| ! [Y20] :
( ~ r1(Y20)
| ~ id(Y20,Y10) ) ),
file('/export/starexec/sandbox/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(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c57,c58]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t2744]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUN070+1 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.07/0.35 % Computer : n007.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Thu Sep 24 05:51:37 UTC 2026
% 0.07/0.36 % CPUTime :
% 0.07/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 14.05/2.18 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 14.05/2.18 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------