%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : NUN076+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 : n019.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 26.26s 3.78s
% Output : Proof 26.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of formulae : 67 ( 36 unt; 0 def)
% Number of atoms : 176 ( 24 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 189 ( 80 ~; 58 |; 51 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 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 : 161 ( 14 sgn 67 !; 30 ?)
% 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(c0,plain,
( ~ r1(X1)
| id(X1,sk0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi0,axiom,
ifeq(r1(X0),true,id(X0,sk0),true) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
fof(f14,axiom,
! [X4] :
? [Y9] :
( ? [Y16] :
( r3(X4,Y16,Y9)
& r1(Y16) )
& id(Y9,X4) ),
file('/export/starexec/sandbox2/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(h53,plain,
id(sk13(V0),sk0) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi31]) ).
fof(f9,axiom,
! [X32,X33,X34,X35,X36,X37] :
( ( r3(X35,X36,X37)
& r3(X32,X33,X34) )
| ( ~ r3(X35,X36,X37)
& ~ r3(X32,X33,X34) )
| ~ id(X34,X37)
| ~ id(X33,X36)
| ~ id(X32,X35) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_10) ).
fof(f9_nnf,plain,
! [X32,X33,X34,X35,X36,X37] :
( ( r3(X35,X36,X37)
& r3(X32,X33,X34) )
| ( ~ r3(X35,X36,X37)
& ~ r3(X32,X33,X34) )
| ~ id(X34,X37)
| ~ id(X33,X36)
| ~ id(X32,X35) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [X32,X35,X33,X36,X34,X37] :
( ( r3(X35,X36,X37)
& r3(X32,X33,X34) )
| ( ~ r3(X35,X36,X37)
& ~ r3(X32,X33,X34) )
| ~ id(X34,X37)
| ~ id(X33,X36)
| ~ id(X32,X35) ),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c28,plain,
( r3(X3,X4,X5)
| ~ r3(X0,X1,X2)
| ~ id(X2,X5)
| ~ id(X1,X4)
| ~ id(X0,X3) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(hi15,axiom,
ifeq(id(X0,X1),true,ifeq(id(X2,X3),true,ifeq(id(X4,X5),true,ifeq(r3(X0,X2,X4),true,r3(X1,X3,X5),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c28]) ).
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(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(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]) ).
cnf(h1331,plain,
r3(V0,sk0,V0) = true,
inference(hyper_resolution,[status(thm)],[hi15,hi8,h53,hi30,hi32]) ).
fof(f15,axiom,
! [X5] :
? [Y8] :
( ? [Y18] :
( r1(Y18)
& id(Y8,Y18) )
& ? [Y17] :
( r4(X5,Y17,Y8)
& r1(Y17) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_5a) ).
fof(f15_nnf,plain,
! [X5] :
? [Y8] :
( ? [Y18] :
( r1(Y18)
& id(Y8,Y18) )
& ? [Y17] :
( r4(X5,Y17,Y8)
& r1(Y17) ) ),
inference(nnf_transformation,[status(thm)],[f15]) ).
fof(f15_sk,plain,
! [X5] :
( r1(sk16(X5))
& id(sk14(X5),sk16(X5))
& r4(X5,sk15(X5),sk14(X5))
& r1(sk15(X5)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk14,sk15,sk16])],[f15_nnf]) ).
cnf(c49,plain,
r1(sk15(X0)),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(hi33,axiom,
r1(sk15(X0)) = true,
inference(equality_encoding,[status(esa)],[c49]) ).
cnf(h214,plain,
id(sk15(V0),sk0) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi33]) ).
fof(f1,axiom,
! [X11] :
? [Y21] :
! [X12] :
( ( ~ id(X12,Y21)
& ~ r2(X11,X12) )
| ( r2(X11,X12)
& id(X12,Y21) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2) ).
fof(f1_nnf,plain,
! [X11] :
? [Y21] :
! [X12] :
( ( ~ id(X12,Y21)
& ~ r2(X11,X12) )
| ( r2(X11,X12)
& id(X12,Y21) ) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X12,X11] :
( ( ~ id(X12,sk1(X11))
& ~ r2(X11,X12) )
| ( r2(X11,X12)
& id(X12,sk1(X11)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1])],[f1_nnf]) ).
cnf(c7,plain,
( ~ id(X2,sk1(X0))
| r2(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(hi3,axiom,
ifeq(id(X0,sk1(X1)),true,r2(X1,X0),true) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(h2,plain,
r2(V0,sk1(V0)) = true,
inference(hyper_resolution,[status(thm)],[hi3,hi8]) ).
fof(f7,axiom,
! [X26,X27] :
( ( r1(X27)
& r1(X26) )
| ( ~ r1(X27)
& ~ r1(X26) )
| ~ id(X26,X27) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_8) ).
fof(f7_nnf,plain,
! [X26,X27] :
( ( r1(X27)
& r1(X26) )
| ( ~ r1(X27)
& ~ r1(X26) )
| ~ id(X26,X27) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [X26,X27] :
( ( r1(X27)
& r1(X26) )
| ( ~ r1(X27)
& ~ r1(X26) )
| ~ id(X26,X27) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c21,plain,
( r1(X0)
| ~ r1(X1)
| ~ id(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(hi12,axiom,
ifeq(id(X0,X1),true,ifeq(r1(X1),true,r1(X0),true),true) = true,
inference(equality_encoding,[status(esa)],[c21]) ).
cnf(c51,plain,
id(sk14(X0),sk16(X0)),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(hi35,axiom,
id(sk14(X0),sk16(X0)) = true,
inference(equality_encoding,[status(esa)],[c51]) ).
cnf(c52,plain,
r1(sk16(X0)),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(hi36,axiom,
r1(sk16(X0)) = true,
inference(equality_encoding,[status(esa)],[c52]) ).
cnf(h354,plain,
r1(sk14(V0)) = true,
inference(hyper_resolution,[status(thm)],[hi12,hi35,hi36]) ).
cnf(h825,plain,
r1(sk12(sk14(V0))) = true,
inference(hyper_resolution,[status(thm)],[hi12,hi30,h354]) ).
cnf(h826,plain,
id(sk14(V0),sk0) = true,
inference(hyper_resolution,[status(thm)],[hi0,h354]) ).
fof(f18,conjecture,
? [Y1,Y2,Y3] :
( ? [Y5] :
( r3(Y2,Y3,Y5)
& id(Y5,Y1) )
& ? [Y4] :
( ? [Y6] :
( ? [Y7] :
( ? [Y8] :
( r2(Y8,Y7)
& r1(Y8) )
& r2(Y7,Y6) )
& r4(Y6,Y2,Y4) )
& id(Y4,Y1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thereexistsanevennumberid) ).
fof(f18_neg,negated_conjecture,
~ ? [Y1,Y2,Y3] :
( ? [Y5] :
( r3(Y2,Y3,Y5)
& id(Y5,Y1) )
& ? [Y4] :
( ? [Y6] :
( ? [Y7] :
( ? [Y8] :
( r2(Y8,Y7)
& r1(Y8) )
& r2(Y7,Y6) )
& r4(Y6,Y2,Y4) )
& id(Y4,Y1) ) ),
inference(negated_conjecture,[status(cth)],[f18]) ).
fof(f18_nnf,plain,
! [Y1,Y2,Y3] :
( ! [Y5] :
( ~ r3(Y2,Y3,Y5)
| ~ id(Y5,Y1) )
| ! [Y4] :
( ! [Y6] :
( ! [Y7] :
( ! [Y8] :
( ~ r2(Y8,Y7)
| ~ r1(Y8) )
| ~ r2(Y7,Y6) )
| ~ r4(Y6,Y2,Y4) )
| ~ id(Y4,Y1) ) ),
inference(nnf_transformation,[status(thm)],[f18_neg]) ).
fof(f18_sk,plain,
! [Y4,Y1,Y6,Y2,Y7,Y8,Y5,Y3] :
( ~ r3(Y2,Y3,Y5)
| ~ id(Y5,Y1)
| ~ r2(Y8,Y7)
| ~ r1(Y8)
| ~ r2(Y7,Y6)
| ~ r4(Y6,Y2,Y4)
| ~ id(Y4,Y1) ),
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c58,plain,
( ~ r3(X1,X2,X7)
| ~ id(X7,X0)
| ~ r2(X6,X5)
| ~ r1(X6)
| ~ r2(X5,X4)
| ~ r4(X4,X1,X3)
| ~ id(X3,X0) ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(hi42,negated_conjecture,
ifeq(id(X0,X1),true,ifeq(r4(X2,X3,X0),true,ifeq(r2(X4,X2),true,ifeq(r1(X5),true,ifeq(r2(X5,X4),true,ifeq(id(X6,X1),true,ifeq(r3(X3,X7,X6),true,false,true),true),true),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c58]) ).
cnf(c50,plain,
r4(X0,sk15(X0),sk14(X0)),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(hi34,axiom,
r4(X0,sk15(X0),sk14(X0)) = true,
inference(equality_encoding,[status(esa)],[c50]) ).
cnf(t0,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi42,h826,hi34,h2,h825,h2,h214,h1331]) ).
cnf(t2589,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,t2589]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUN076+1 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n019.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 05:57:37 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 26.26/3.78 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 26.26/3.78 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------