%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM550+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 : n015.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 08:17:22 AM UTC 2026
% Result : Theorem 0.08s 0.42s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 17 ( 11 unt; 0 def)
% Number of atoms : 28 ( 19 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 22 ( 11 ~; 5 |; 4 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-1 aty)
% Number of variables : 3 ( 0 sgn 1 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mCardEmpty,axiom,
! [W0] :
( aSet0(W0)
=> ( sbrdtbr0(W0) = sz00
<=> W0 = slcrc0 ) ),
file('theBenchmark.p',mCardEmpty) ).
fof(m__2202_02,axiom,
( xk != sz00
& aSet0(xT)
& aSet0(xS) ),
file('theBenchmark.p',m__2202_02) ).
fof(m__2291,axiom,
( sbrdtbr0(xQ) = xk
& isFinite0(xQ)
& aSet0(xQ) ),
file('theBenchmark.p',m__2291) ).
fof(m__,conjecture,
xQ != slcrc0,
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ ( xQ != slcrc0 ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_62,negated_conjecture,
xQ = slcrc0,
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_63,negated_conjecture,
slcrc0 = xQ,
inference(copy,[status(thm)],[c_62]) ).
cnf(c_64,plain,
sbrdtbr0(xQ) = xk,
inference(clausify,[status(thm)],[m__2291]) ).
cnf(c_65,plain,
xk = sbrdtbr0(xQ),
inference(copy,[status(thm)],[c_64]) ).
cnf(c_67,plain,
aSet0(xQ),
inference(clausify,[status(thm)],[m__2291]) ).
cnf(c_75,plain,
xk != sz00,
inference(clausify,[status(thm)],[m__2202_02]) ).
cnf(c_76,plain,
sbrdtbr0(xQ) != sz00,
inference(paramod,[status(thm)],[c_65,c_75]) ).
cnf(c_134,plain,
( slcrc0 != A
| sbrdtbr0(A) = sz00
| ~ aSet0(A) ),
inference(clausify,[status(thm)],[mCardEmpty]) ).
cnf(c_135,plain,
( xQ != A
| sbrdtbr0(A) = sz00
| ~ aSet0(A) ),
inference(paramod,[status(thm)],[c_63,c_134]) ).
cnf(c_268,plain,
( xQ != xQ
| sbrdtbr0(xQ) = sz00 ),
inference(resolve,[status(thm)],[c_135,c_67]) ).
cnf(c_269,plain,
sbrdtbr0(xQ) = sz00,
inference(copy,[status(thm)],[c_268]) ).
cnf(c_267,plain,
$false,
inference(resolve,[status(thm)],[c_76,c_269]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM550+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n015.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sat Sep 26 03:15:12 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.37 % Process 2986347 was started by sandbox on n015,
% 0.08/0.37 % Sat Sep 26 03:15:12 2026
% 0.08/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.38
% 0.08/0.38 % From the command line: assign(max_seconds, 300).
% 0.08/0.40 --- backtrace (16 frames) ---
% 0.08/0.40 [0x41fd9f]
% 0.08/0.40 [0x484fd0]
% 0.08/0.40 [0x467349]
% 0.08/0.40 [0x46b3ab]
% 0.08/0.40 [0x416b10]
% 0.08/0.40 [0x41887f]
% 0.08/0.40 [0x466dba]
% 0.08/0.40 [0x466eb1]
% 0.08/0.40 [0x41b799]
% 0.08/0.40 [0x4039a8]
% 0.08/0.40 [0x403f27]
% 0.08/0.40 [0x4049d4]
% 0.08/0.40 [0x402997]
% 0.08/0.40 [0x482698]
% 0.08/0.40 [0x484860]
% 0.08/0.40 [0x402a35]
% 0.08/0.40 --- end backtrace ---
% 0.08/0.41 --- backtrace (16 frames) ---
% 0.08/0.41 [0x41fd9f]
% 0.08/0.41 [0x484fd0]
% 0.08/0.41 [0x467349]
% 0.08/0.41 [0x46b3ab]
% 0.08/0.41 [0x416b10]
% 0.08/0.41 [0x41887f]
% 0.08/0.41 [0x466dba]
% 0.08/0.41 [0x466eb1]
% 0.08/0.41 [0x41b799]
% 0.08/0.41 [0x4039a8]
% 0.08/0.41 [0x403f27]
% 0.08/0.41 [0x4049d4]
% 0.08/0.41 [0x402997]
% 0.08/0.41 [0x482698]
% 0.08/0.41 [0x484860]
% 0.08/0.41 [0x402a35]
% 0.08/0.41 --- end backtrace ---
% 0.08/0.41 --- backtrace (16 frames) ---
% 0.08/0.41 [0x41fd9f]
% 0.08/0.41 [0x484fd0]
% 0.08/0.41 [0x467349]
% 0.08/0.41 [0x46b3ab]
% 0.08/0.41 [0x416b10]
% 0.08/0.41 [0x41887f]
% 0.08/0.41 [0x466dba]
% 0.08/0.41 [0x466eb1]
% 0.08/0.41 [0x41b799]
% 0.08/0.41 [0x4039a8]
% 0.08/0.41 [0x40412f]
% 0.08/0.41 [0x4049d4]
% 0.08/0.41 [0x402997]
% 0.08/0.41 [0x482698]
% 0.08/0.41 [0x484860]
% 0.08/0.41 [0x402a35]
% 0.08/0.41 --- end backtrace ---
% 0.08/0.42 --- backtrace (16 frames) ---
% 0.08/0.42 [0x41fd9f]
% 0.08/0.42 [0x484fd0]
% 0.08/0.42 [0x467349]
% 0.08/0.42 [0x46b3ab]
% 0.08/0.42 [0x416b10]
% 0.08/0.42 [0x41887f]
% 0.08/0.42 [0x466dba]
% 0.08/0.42 [0x466eb1]
% 0.08/0.42 [0x41b799]
% 0.08/0.42 [0x4039a8]
% 0.08/0.42 [0x403f27]
% 0.08/0.42 [0x4049d4]
% 0.08/0.42 [0x402997]
% 0.08/0.42 [0x482698]
% 0.08/0.42 [0x484860]
% 0.08/0.42 [0x402a35]
% 0.08/0.42 --- end backtrace ---
% 0.08/0.42
% 0.08/0.42 % SZS status Theorem for theBenchmark
% 0.08/0.42
% 0.08/0.42 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.08/0.42 % Length of proof is 14.
% 0.08/0.42 % Level of proof is 4.
% 0.08/0.42 % Maximum clause weight is 9.000.
% 0.08/0.42 % Given clauses 54.
% 0.08/0.42
% 0.08/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------