%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SWV151+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n018.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 03:12:22 PM UTC 2026
% Result : Theorem 40.43s 5.80s
% Output : Proof 40.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 8
% Syntax : Number of formulae : 58 ( 17 unt; 0 def)
% Number of atoms : 124 ( 20 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 107 ( 41 ~; 46 |; 13 &)
% ( 2 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-3 aty)
% Number of variables : 65 ( 0 sgn 41 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
! [X,Y] :
( leq(X,pred(Y))
<=> gt(Y,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_gt_pred) ).
fof(f9_nnf,plain,
! [X,Y] :
( ( ~ gt(Y,X)
| leq(X,pred(Y)) )
& ( gt(Y,X)
| ~ leq(X,pred(Y)) ) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [X,Y] :
( ( ~ gt(Y,X)
| leq(X,pred(Y)) )
& ( gt(Y,X)
| ~ leq(X,pred(Y)) ) ),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c12,plain,
( ~ gt(X1,X0)
| leq(X0,pred(X1)) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
fof(f8,axiom,
! [X,Y] :
( ( X != Y
& leq(X,Y) )
=> gt(Y,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_gt2) ).
fof(f8_nnf,plain,
! [X,Y] :
( gt(Y,X)
| X = Y
| ~ leq(X,Y) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [X,Y] :
( gt(Y,X)
| X = Y
| ~ leq(X,Y) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c10,plain,
( gt(X1,X0)
| X0 = X1
| ~ leq(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
fof(f52,conjecture,
! [A] :
( ( leq(A,tptp_minus_1)
& leq(n0,A) )
=> sum(n0,n4,a_select3(q,A,tptp_sum_index)) = n1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cl5_nebula_norm_0001) ).
fof(f52_neg,negated_conjecture,
~ ! [A] :
( ( leq(A,tptp_minus_1)
& leq(n0,A) )
=> sum(n0,n4,a_select3(q,A,tptp_sum_index)) = n1 ),
inference(negated_conjecture,[status(cth)],[f52]) ).
fof(f52_nnf,plain,
? [A] :
( sum(n0,n4,a_select3(q,A,tptp_sum_index)) != n1
& leq(A,tptp_minus_1)
& leq(n0,A) ),
inference(nnf_transformation,[status(thm)],[f52_neg]) ).
fof(f52_sk,plain,
( sum(n0,n4,a_select3(q,sk27,tptp_sum_index)) != n1
& leq(sk27,tptp_minus_1)
& leq(n0,sk27) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk27])],[f52_nnf]) ).
cnf(c255,plain,
leq(n0,sk27),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(p367,plain,
( gt(sk27,n0)
| n0 = sk27 ),
inference(resolution,[status(thm)],[c10,c255]) ).
fof(f1,axiom,
! [X,Y,Z] :
( ( gt(Y,Z)
& gt(X,Y) )
=> gt(X,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity_gt) ).
fof(f1_nnf,plain,
! [X,Y,Z] :
( gt(X,Z)
| ~ gt(Y,Z)
| ~ gt(X,Y) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X,Y,Z] :
( gt(X,Z)
| ~ gt(Y,Z)
| ~ gt(X,Y) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( gt(X0,X2)
| ~ gt(X1,X2)
| ~ gt(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p370,plain,
( gt(sk27,X0)
| ~ gt(n0,X0)
| n0 = sk27 ),
inference(resolution,[status(thm)],[p367,c1]) ).
fof(f56,axiom,
gt(n0,tptp_minus_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_0_tptp_minus_1) ).
fof(f56_nnf,plain,
gt(n0,tptp_minus_1),
inference(nnf_transformation,[status(thm)],[f56]) ).
cnf(c261,plain,
gt(n0,tptp_minus_1),
inference(cnf_transformation,[status(esa)],[f56_nnf]) ).
cnf(p379,plain,
( gt(sk27,tptp_minus_1)
| n0 = sk27 ),
inference(resolution,[status(thm)],[p370,c261]) ).
cnf(p409,plain,
( n0 = sk27
| leq(tptp_minus_1,pred(sk27)) ),
inference(resolution,[status(thm)],[c12,p379]) ).
fof(f4,axiom,
! [X,Y,Z] :
( ( leq(Y,Z)
& leq(X,Y) )
=> leq(X,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity_leq) ).
fof(f4_nnf,plain,
! [X,Y,Z] :
( leq(X,Z)
| ~ leq(Y,Z)
| ~ leq(X,Y) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [X,Y,Z] :
( leq(X,Z)
| ~ leq(Y,Z)
| ~ leq(X,Y) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
( leq(X0,X2)
| ~ leq(X1,X2)
| ~ leq(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(c256,plain,
leq(sk27,tptp_minus_1),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(p298,plain,
( leq(sk27,X0)
| ~ leq(tptp_minus_1,X0) ),
inference(resolution,[status(thm)],[c4,c256]) ).
cnf(p427,plain,
( leq(sk27,pred(sk27))
| n0 = sk27 ),
inference(resolution,[status(thm)],[p409,p298]) ).
cnf(c11,plain,
( gt(X1,X0)
| ~ leq(X0,pred(X1)) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(p2613,plain,
( gt(sk27,sk27)
| n0 = sk27 ),
inference(resolution,[status(thm)],[p427,c11]) ).
fof(f2,axiom,
! [X] : ~ gt(X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',irreflexivity_gt) ).
fof(f2_nnf,plain,
! [X] : ~ gt(X,X),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X] : ~ gt(X,X),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
~ gt(X0,X0),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p2618,plain,
n0 = sk27,
inference(resolution,[status(thm)],[p2613,c2]) ).
fof(f12,axiom,
! [X,Y] :
( leq(X,Y)
<=> gt(succ(Y),X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_succ_gt_equiv) ).
fof(f12_nnf,plain,
! [X,Y] :
( ( ~ gt(succ(Y),X)
| leq(X,Y) )
& ( gt(succ(Y),X)
| ~ leq(X,Y) ) ),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [X,Y] :
( ( ~ gt(succ(Y),X)
| leq(X,Y) )
& ( gt(succ(Y),X)
| ~ leq(X,Y) ) ),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c15,plain,
( gt(succ(X1),X0)
| ~ leq(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(p450,plain,
gt(succ(sk27),n0),
inference(resolution,[status(thm)],[c15,c255]) ).
cnf(p461,plain,
( gt(succ(sk27),X0)
| ~ gt(n0,X0) ),
inference(resolution,[status(thm)],[p450,c1]) ).
cnf(p4509,plain,
gt(succ(sk27),tptp_minus_1),
inference(resolution,[status(thm)],[p461,c261]) ).
cnf(c16,plain,
( ~ gt(succ(X1),X0)
| leq(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(p4580,plain,
leq(tptp_minus_1,sk27),
inference(resolution,[status(thm)],[p4509,c16]) ).
cnf(p4582,plain,
( leq(tptp_minus_1,X0)
| ~ leq(sk27,X0) ),
inference(resolution,[status(thm)],[p4580,c4]) ).
cnf(p5797,plain,
( leq(tptp_minus_1,X0)
| ~ leq(n0,X0) ),
inference(superposition,[status(thm)],[p2618,p4582]) ).
cnf(p297,plain,
( leq(n0,X0)
| ~ leq(sk27,X0) ),
inference(resolution,[status(thm)],[c4,c255]) ).
cnf(p299,plain,
leq(n0,tptp_minus_1),
inference(resolution,[status(thm)],[p297,c256]) ).
cnf(p369,plain,
( gt(tptp_minus_1,n0)
| n0 = tptp_minus_1 ),
inference(resolution,[status(thm)],[c10,p299]) ).
cnf(p408,plain,
( n0 = tptp_minus_1
| leq(n0,pred(tptp_minus_1)) ),
inference(resolution,[status(thm)],[c12,p369]) ).
cnf(p7278,plain,
( n0 = tptp_minus_1
| leq(tptp_minus_1,pred(tptp_minus_1)) ),
inference(resolution,[status(thm)],[p5797,p408]) ).
cnf(p14580,plain,
( gt(tptp_minus_1,tptp_minus_1)
| n0 = tptp_minus_1 ),
inference(resolution,[status(thm)],[p7278,c11]) ).
cnf(p14585,plain,
n0 = tptp_minus_1,
inference(resolution,[status(thm)],[p14580,c2]) ).
cnf(p14586,plain,
gt(n0,n0),
inference(superposition,[status(thm)],[p14585,c261]) ).
cnf(p14629,plain,
$false,
inference(resolution,[status(thm)],[p14586,c2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV151+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.37 % Computer : n018.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Thu Sep 24 18:39:49 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.38 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 40.43/5.80 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 40.43/5.80 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------