%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : RNG121+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 : n007.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 08:26:42 AM UTC 2026
% Result : Theorem 24.43s 3.94s
% Output : CNFRefutation 24.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 30 ( 14 unt; 0 def)
% Number of atoms : 75 ( 22 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 73 ( 28 ~; 26 |; 12 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 37 ( 0 sgn 8 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mAddZero,axiom,
! [W0] :
( aElement0(W0)
=> ( W0 = sdtpldt0(sz00,W0)
& sdtpldt0(W0,sz00) = W0 ) ),
file('theBenchmark.p',mAddZero) ).
fof(mDefSSum,axiom,
! [W0,W1] :
( ( aSet0(W1)
& aSet0(W0) )
=> ! [W2] :
( W2 = sdtpldt1(W0,W1)
<=> ( ! [W3] :
( aElementOf0(W3,W2)
<=> ? [W4,W5] :
( sdtpldt0(W4,W5) = W3
& aElementOf0(W5,W1)
& aElementOf0(W4,W0) ) )
& aSet0(W2) ) ) ),
file('theBenchmark.p',mDefSSum) ).
fof(mDefPrIdeal,axiom,
! [W0] :
( aElement0(W0)
=> ! [W1] :
( W1 = slsdtgt0(W0)
<=> ( ! [W2] :
( aElementOf0(W2,W1)
<=> ? [W3] :
( sdtasdt0(W0,W3) = W2
& aElement0(W3) ) )
& aSet0(W1) ) ) ),
file('theBenchmark.p',mDefPrIdeal) ).
fof(m__2091,axiom,
( aElement0(xb)
& aElement0(xa) ),
file('theBenchmark.p',m__2091) ).
fof(m__2174,axiom,
( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
& aIdeal0(xI) ),
file('theBenchmark.p',m__2174) ).
fof(m__2203,axiom,
( aElementOf0(xb,slsdtgt0(xb))
& aElementOf0(sz00,slsdtgt0(xb))
& aElementOf0(xa,slsdtgt0(xa))
& aElementOf0(sz00,slsdtgt0(xa)) ),
file('theBenchmark.p',m__2203) ).
fof(m__,conjecture,
aElementOf0(xb,xI),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ aElementOf0(xb,xI),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_78,plain,
( sdtpldt0(sz00,A) = A
| ~ aElement0(A) ),
inference(clausify,[status(thm)],[mAddZero]) ).
cnf(c_105,plain,
( sdtpldt0(E,F) != D
| ~ aElementOf0(F,B)
| ~ aElementOf0(E,A)
| aElementOf0(D,C)
| sdtpldt1(A,B) != C
| ~ aSet0(B)
| ~ aSet0(A) ),
inference(clausify,[status(thm)],[mDefSSum]) ).
cnf(c_144,plain,
( aSet0(B)
| slsdtgt0(A) != B
| ~ aElement0(A) ),
inference(clausify,[status(thm)],[mDefPrIdeal]) ).
cnf(c_153,plain,
aElement0(xa),
inference(clausify,[status(thm)],[m__2091]) ).
cnf(c_154,plain,
aElement0(xb),
inference(clausify,[status(thm)],[m__2091]) ).
cnf(c_157,plain,
sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) = xI,
inference(clausify,[status(thm)],[m__2174]) ).
cnf(c_158,plain,
aElementOf0(sz00,slsdtgt0(xa)),
inference(clausify,[status(thm)],[m__2203]) ).
cnf(c_161,plain,
aElementOf0(xb,slsdtgt0(xb)),
inference(clausify,[status(thm)],[m__2203]) ).
cnf(c_181,negated_conjecture,
~ aElementOf0(xb,xI),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_20508,plain,
( aSet0(A)
| slsdtgt0(xa) != A ),
inference(resolve,[status(thm)],[c_144,c_153]) ).
cnf(c_508,plain,
aSet0(slsdtgt0(xa)),
inference(xxres,[status(thm)],[c_20508]) ).
cnf(c_626,plain,
sdtpldt0(sz00,xb) = xb,
inference(resolve,[status(thm)],[c_154,c_78]) ).
cnf(c_20509,plain,
( aSet0(A)
| slsdtgt0(xb) != A ),
inference(resolve,[status(thm)],[c_144,c_154]) ).
cnf(c_641,plain,
aSet0(slsdtgt0(xb)),
inference(xxres,[status(thm)],[c_20509]) ).
cnf(c_20510,plain,
( sdtpldt0(D,E) != C
| ~ aElementOf0(E,A)
| ~ aElementOf0(D,slsdtgt0(xa))
| aElementOf0(C,B)
| sdtpldt1(slsdtgt0(xa),A) != B
| ~ aSet0(A) ),
inference(resolve,[status(thm)],[c_105,c_508]) ).
cnf(c_20511,plain,
( sdtpldt0(C,D) != B
| ~ aElementOf0(D,slsdtgt0(xb))
| ~ aElementOf0(C,slsdtgt0(xa))
| aElementOf0(B,A)
| sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) != A ),
inference(resolve,[status(thm)],[c_20510,c_641]) ).
cnf(c_20512,plain,
( sdtpldt0(B,C) != A
| ~ aElementOf0(C,slsdtgt0(xb))
| ~ aElementOf0(B,slsdtgt0(xa))
| aElementOf0(A,xI) ),
inference(resolve,[status(thm)],[c_20511,c_157]) ).
cnf(c_20513,plain,
( sdtpldt0(sz00,B) != A
| ~ aElementOf0(B,slsdtgt0(xb))
| aElementOf0(A,xI) ),
inference(resolve,[status(thm)],[c_20512,c_158]) ).
cnf(c_20514,plain,
( sdtpldt0(sz00,xb) != A
| aElementOf0(A,xI) ),
inference(resolve,[status(thm)],[c_20513,c_161]) ).
cnf(c_20515,plain,
aElementOf0(sdtpldt0(sz00,xb),xI),
inference(xxres,[status(thm)],[c_20514]) ).
cnf(c_20516,plain,
aElementOf0(xb,xI),
inference(paramod,[status(thm)],[c_626,c_20515]) ).
cnf(c_20507,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_181,c_20516]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG121+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n007.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 : Sat Sep 26 06:08:25 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 2966257 was started by sandbox on n007,
% 0.10/0.37 % Sat Sep 26 06:08:25 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.39
% 0.10/0.39 % From the command line: assign(max_seconds, 300).
% 24.43/3.94
% 24.43/3.94 % SZS status Theorem for theBenchmark
% 24.43/3.94
% 24.43/3.94 % Proof 1 at 2.74 (+ 0.75) seconds.
% 24.43/3.94 % Length of proof is 20.
% 24.43/3.94 % Level of proof is 3.
% 24.43/3.94 % Maximum clause weight is 33.000.
% 24.43/3.94 % Given clauses 242.
% 24.43/3.94
% 24.43/3.94 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------