%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : NUN060+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 : n001.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 02:29:26 PM UTC 2026
% Result : Theorem 9.63s 1.92s
% Output : Proof 9.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 35 ( 19 unt; 0 def)
% Number of atoms : 95 ( 11 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 103 ( 43 ~; 30 |; 30 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 8 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-4 aty)
% Number of variables : 98 ( 7 sgn 37 !; 26 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f0,axiom,
? [Y24] :
! [X19] :
( ( ~ id(X19,Y24)
& ~ r1(X19) )
| ( r1(X19)
& id(X19,Y24) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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,Y2,Y3] :
( ? [Y4] :
( ? [Y5] :
( ? [Y6] :
( ? [Y7] :
( ? [Y8] :
( r2(Y8,Y7)
& r1(Y8) )
& r2(Y7,Y6) )
& r2(Y6,Y5) )
& r2(Y5,Y4) )
& r3(Y2,Y4,Y3) )
& id(Y3,Y1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',greq4id) ).
fof(f18_neg,negated_conjecture,
~ ? [Y1,Y2,Y3] :
( ? [Y4] :
( ? [Y5] :
( ? [Y6] :
( ? [Y7] :
( ? [Y8] :
( r2(Y8,Y7)
& r1(Y8) )
& r2(Y7,Y6) )
& r2(Y6,Y5) )
& r2(Y5,Y4) )
& r3(Y2,Y4,Y3) )
& id(Y3,Y1) ),
inference(negated_conjecture,[status(cth)],[f18]) ).
fof(f18_nnf,plain,
! [Y1,Y2,Y3] :
( ! [Y4] :
( ! [Y5] :
( ! [Y6] :
( ! [Y7] :
( ! [Y8] :
( ~ r2(Y8,Y7)
| ~ r1(Y8) )
| ~ r2(Y7,Y6) )
| ~ r2(Y6,Y5) )
| ~ r2(Y5,Y4) )
| ~ r3(Y2,Y4,Y3) )
| ~ id(Y3,Y1) ),
inference(nnf_transformation,[status(thm)],[f18_neg]) ).
fof(f18_sk,plain,
! [Y3,Y1,Y2,Y4,Y5,Y6,Y7,Y8] :
( ~ r2(Y8,Y7)
| ~ r1(Y8)
| ~ r2(Y7,Y6)
| ~ r2(Y6,Y5)
| ~ r2(Y5,Y4)
| ~ r3(Y2,Y4,Y3)
| ~ id(Y3,Y1) ),
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c58,plain,
( ~ r2(X7,X6)
| ~ r1(X7)
| ~ r2(X6,X5)
| ~ r2(X5,X4)
| ~ r2(X4,X3)
| ~ r3(X1,X3,X2)
| ~ id(X2,X0) ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(hi42,negated_conjecture,
ifeq(id(X0,X1),true,ifeq(r3(X2,X3,X0),true,ifeq(r2(X4,X3),true,ifeq(r2(X5,X4),true,ifeq(r2(X6,X5),true,ifeq(r1(X7),true,ifeq(r2(X7,X6),true,false,true),true),true),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c58]) ).
fof(f11,axiom,
! [X1,X8] :
? [Y4] :
( ? [Y7] :
( r3(X1,X8,Y7)
& r2(Y7,Y4) )
& ? [Y5] :
( ? [Y15] :
( r3(X1,Y15,Y5)
& r2(X8,Y15) )
& id(Y5,Y4) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1a) ).
fof(f11_nnf,plain,
! [X1,X8] :
? [Y4] :
( ? [Y7] :
( r3(X1,X8,Y7)
& r2(Y7,Y4) )
& ? [Y5] :
( ? [Y15] :
( r3(X1,Y15,Y5)
& r2(X8,Y15) )
& id(Y5,Y4) ) ),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [X1,X8] :
( r3(X1,X8,sk7(X1,X8))
& r2(sk7(X1,X8),sk4(X1,X8))
& r3(X1,sk6(X1,X8),sk5(X1,X8))
& r2(X8,sk6(X1,X8))
& id(sk5(X1,X8),sk4(X1,X8)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk4,sk5,sk6,sk7])],[f11_nnf]) ).
cnf(c35,plain,
id(sk5(X0,X1),sk4(X0,X1)),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(hi19,axiom,
id(sk5(X0,X1),sk4(X0,X1)) = true,
inference(equality_encoding,[status(esa)],[c35]) ).
cnf(c37,plain,
r3(X0,sk6(X0,X1),sk5(X0,X1)),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(hi21,axiom,
r3(X0,sk6(X0,X1),sk5(X0,X1)) = true,
inference(equality_encoding,[status(esa)],[c37]) ).
cnf(c36,plain,
r2(X1,sk6(X0,X1)),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(hi20,axiom,
r2(X0,sk6(X1,X0)) = true,
inference(equality_encoding,[status(esa)],[c36]) ).
cnf(t0,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi42,hi19,hi21,hi20,hi20,hi20,h3,hi20]) ).
cnf(t751,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/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(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,t751]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUN060+1 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.37 % Computer : n001.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 05:57:07 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 9.63/1.92 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.63/1.92 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------