%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM578+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n003.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 : Sun Sep 27 08:17:27 AM UTC 2026
% Result : Theorem 0.90s 0.53s
% Output : CNFRefutation 0.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 20 ( 8 unt; 0 def)
% Number of atoms : 50 ( 12 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 59 ( 29 ~; 16 |; 5 &)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 8 ( 0 sgn 4 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__3856,axiom,
( aElementOf0(xj,szNzAzT0)
& aElementOf0(xi,szNzAzT0) ),
file('theBenchmark.p',m__3856) ).
fof(m__3856_02,axiom,
( xi != xj
=> ( sdtlseqdt0(szszuzczcdt0(xi),xj)
| sdtlseqdt0(szszuzczcdt0(xj),xi) ) ),
file('theBenchmark.p',m__3856_02) ).
fof(m__,conjecture,
( ! [W0,W1] :
( ( aElementOf0(W1,szNzAzT0)
& aElementOf0(W0,szNzAzT0) )
=> ( sdtlseqdt0(szszuzczcdt0(W0),W1)
=> ( szmzizndt0(sdtlpdtrp0(xN,W1)) != szmzizndt0(sdtlpdtrp0(xN,W0))
& aSubsetOf0(sdtlpdtrp0(xN,W1),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
=> ( xi != xj
=> szmzizndt0(sdtlpdtrp0(xN,xi)) != szmzizndt0(sdtlpdtrp0(xN,xj)) ) ),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ ( ! [W0,W1] :
( ( aElementOf0(W1,szNzAzT0)
& aElementOf0(W0,szNzAzT0) )
=> ( sdtlseqdt0(szszuzczcdt0(W0),W1)
=> ( szmzizndt0(sdtlpdtrp0(xN,W1)) != szmzizndt0(sdtlpdtrp0(xN,W0))
& aSubsetOf0(sdtlpdtrp0(xN,W1),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
=> ( xi != xj
=> szmzizndt0(sdtlpdtrp0(xN,xi)) != szmzizndt0(sdtlpdtrp0(xN,xj)) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_245,plain,
aElementOf0(xi,szNzAzT0),
inference(clausify,[status(thm)],[m__3856]) ).
cnf(c_246,plain,
aElementOf0(xj,szNzAzT0),
inference(clausify,[status(thm)],[m__3856]) ).
cnf(c_247,plain,
( sdtlseqdt0(szszuzczcdt0(xi),xj)
| sdtlseqdt0(szszuzczcdt0(xj),xi)
| xj = xi ),
inference(clausify,[status(thm)],[m__3856_02]) ).
cnf(c_249,negated_conjecture,
( szmzizndt0(sdtlpdtrp0(xN,B)) != szmzizndt0(sdtlpdtrp0(xN,A))
| ~ sdtlseqdt0(szszuzczcdt0(A),B)
| ~ aElementOf0(B,szNzAzT0)
| ~ aElementOf0(A,szNzAzT0) ),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_250,negated_conjecture,
xj != xi,
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_251,negated_conjecture,
szmzizndt0(sdtlpdtrp0(xN,xj)) = szmzizndt0(sdtlpdtrp0(xN,xi)),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_283,negated_conjecture,
( sdtlseqdt0(szszuzczcdt0(xi),xj)
| sdtlseqdt0(szszuzczcdt0(xj),xi) ),
inference(resolve,[status(thm)],[c_250,c_247]) ).
cnf(c_1097,negated_conjecture,
( ~ sdtlseqdt0(szszuzczcdt0(xi),xj)
| ~ aElementOf0(xj,szNzAzT0)
| ~ aElementOf0(xi,szNzAzT0) ),
inference(resolve,[status(thm)],[c_251,c_249]) ).
cnf(c_1098,negated_conjecture,
( ~ sdtlseqdt0(szszuzczcdt0(xi),xj)
| ~ aElementOf0(xj,szNzAzT0) ),
inference(resolve,[status(thm)],[c_245,c_1097]) ).
cnf(c_1088,negated_conjecture,
~ sdtlseqdt0(szszuzczcdt0(xi),xj),
inference(resolve,[status(thm)],[c_246,c_1098]) ).
cnf(c_1099,negated_conjecture,
( szmzizndt0(sdtlpdtrp0(xN,A)) != szmzizndt0(sdtlpdtrp0(xN,B))
| ~ sdtlseqdt0(szszuzczcdt0(A),B)
| ~ aElementOf0(B,szNzAzT0)
| ~ aElementOf0(A,szNzAzT0) ),
inference(copy,[status(thm)],[c_249]) ).
cnf(c_1100,negated_conjecture,
( ~ sdtlseqdt0(szszuzczcdt0(xj),xi)
| ~ aElementOf0(xi,szNzAzT0)
| ~ aElementOf0(xj,szNzAzT0) ),
inference(resolve,[status(thm)],[c_251,c_1099]) ).
cnf(c_1101,negated_conjecture,
( ~ sdtlseqdt0(szszuzczcdt0(xj),xi)
| ~ aElementOf0(xi,szNzAzT0) ),
inference(resolve,[status(thm)],[c_246,c_1100]) ).
cnf(c_1091,negated_conjecture,
~ sdtlseqdt0(szszuzczcdt0(xj),xi),
inference(resolve,[status(thm)],[c_245,c_1101]) ).
cnf(c_1102,negated_conjecture,
sdtlseqdt0(szszuzczcdt0(xi),xj),
inference(resolve,[status(thm)],[c_1091,c_283]) ).
cnf(c_1096,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_1088,c_1102]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM578+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.34 % Computer : n003.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Sat Sep 26 03:20:08 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.07/0.35 % Process 1912785 was started by sandbox on n003,
% 0.07/0.35 % Sat Sep 26 03:20:08 2026
% 0.07/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.12/0.37
% 0.12/0.37 % From the command line: assign(max_seconds, 300).
% 0.90/0.53
% 0.90/0.53 % SZS status Theorem for theBenchmark
% 0.90/0.53
% 0.90/0.53 % Proof 1 at 0.10 (+ 0.04) seconds.
% 0.90/0.53 % Length of proof is 13.
% 0.90/0.53 % Level of proof is 3.
% 0.90/0.53 % Maximum clause weight is 25.000.
% 0.90/0.53 % Given clauses 166.
% 0.90/0.53
% 0.90/0.53 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------