%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : RNG109+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.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 08:26:40 AM UTC 2026
% Result : Theorem 4.00s 0.96s
% Output : CNFRefutation 4.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 8
% Syntax : Number of formulae : 50 ( 21 unt; 0 def)
% Number of atoms : 118 ( 46 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 122 ( 54 ~; 47 |; 14 &)
% ( 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 : 57 ( 0 sgn 8 !; 5 ?)
% 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,
? [W0] :
( W0 != sz00
& aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ ? [W0] :
( W0 != sz00
& aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_72,negated_conjecture,
( sz00 = A
| ~ aElementOf0(A,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_73,plain,
aElementOf0(xb,slsdtgt0(xb)),
inference(clausify,[status(thm)],[m__2203]) ).
cnf(c_74,plain,
aElementOf0(sz00,slsdtgt0(xb)),
inference(clausify,[status(thm)],[m__2203]) ).
cnf(c_75,plain,
aElementOf0(xa,slsdtgt0(xa)),
inference(clausify,[status(thm)],[m__2203]) ).
cnf(c_76,plain,
aElementOf0(sz00,slsdtgt0(xa)),
inference(clausify,[status(thm)],[m__2203]) ).
cnf(c_77,plain,
sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) = xI,
inference(clausify,[status(thm)],[m__2174]) ).
fof(m__2110,axiom,
( xb != sz00
| xa != sz00 ),
file('theBenchmark.p',m__2110) ).
cnf(c_79,plain,
( xb != sz00
| xa != sz00 ),
inference(clausify,[status(thm)],[m__2110]) ).
cnf(c_80,plain,
aElement0(xb),
inference(clausify,[status(thm)],[m__2091]) ).
cnf(c_81,plain,
aElement0(xa),
inference(clausify,[status(thm)],[m__2091]) ).
cnf(c_90,plain,
( aSet0(B)
| slsdtgt0(A) != B
| ~ aElement0(A) ),
inference(clausify,[status(thm)],[mDefPrIdeal]) ).
cnf(c_127,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_154,plain,
( sdtpldt0(sz00,A) = A
| ~ aElement0(A) ),
inference(clausify,[status(thm)],[mAddZero]) ).
cnf(c_155,plain,
( sdtpldt0(A,sz00) = A
| ~ aElement0(A) ),
inference(clausify,[status(thm)],[mAddZero]) ).
cnf(c_178,negated_conjecture,
( sz00 = A
| ~ aElementOf0(A,xI) ),
inference(paramod,[status(thm)],[c_77,c_72]) ).
cnf(c_2438,plain,
( aSet0(A)
| slsdtgt0(xa) != A ),
inference(resolve,[status(thm)],[c_90,c_81]) ).
cnf(c_309,plain,
aSet0(slsdtgt0(xa)),
inference(xxres,[status(thm)],[c_2438]) ).
cnf(c_2439,plain,
( aSet0(A)
| slsdtgt0(xb) != A ),
inference(resolve,[status(thm)],[c_90,c_80]) ).
cnf(c_310,plain,
aSet0(slsdtgt0(xb)),
inference(xxres,[status(thm)],[c_2439]) ).
cnf(c_554,plain,
sdtpldt0(sz00,xb) = xb,
inference(resolve,[status(thm)],[c_154,c_80]) ).
cnf(c_555,plain,
sdtpldt0(xa,sz00) = xa,
inference(resolve,[status(thm)],[c_155,c_81]) ).
cnf(c_2440,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_127,c_309]) ).
cnf(c_2441,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_2440,c_310]) ).
cnf(c_2442,plain,
( sdtpldt0(B,C) != A
| ~ aElementOf0(C,slsdtgt0(xb))
| ~ aElementOf0(B,slsdtgt0(xa))
| aElementOf0(A,xI) ),
inference(resolve,[status(thm)],[c_2441,c_77]) ).
cnf(c_2443,plain,
( sdtpldt0(sz00,B) != A
| ~ aElementOf0(B,slsdtgt0(xb))
| aElementOf0(A,xI) ),
inference(resolve,[status(thm)],[c_2442,c_76]) ).
cnf(c_2444,plain,
( sdtpldt0(sz00,xb) != A
| aElementOf0(A,xI) ),
inference(resolve,[status(thm)],[c_2443,c_73]) ).
cnf(c_2445,plain,
aElementOf0(sdtpldt0(sz00,xb),xI),
inference(xxres,[status(thm)],[c_2444]) ).
cnf(c_1923,plain,
aElementOf0(xb,xI),
inference(paramod,[status(thm)],[c_554,c_2445]) ).
cnf(c_2446,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_127,c_309]) ).
cnf(c_2447,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_2446,c_310]) ).
cnf(c_2448,plain,
( sdtpldt0(B,C) != A
| ~ aElementOf0(C,slsdtgt0(xb))
| ~ aElementOf0(B,slsdtgt0(xa))
| aElementOf0(A,xI) ),
inference(resolve,[status(thm)],[c_2447,c_77]) ).
cnf(c_2449,plain,
( sdtpldt0(xa,B) != A
| ~ aElementOf0(B,slsdtgt0(xb))
| aElementOf0(A,xI) ),
inference(resolve,[status(thm)],[c_2448,c_75]) ).
cnf(c_2450,plain,
( sdtpldt0(xa,sz00) != A
| aElementOf0(A,xI) ),
inference(resolve,[status(thm)],[c_2449,c_74]) ).
cnf(c_2451,plain,
aElementOf0(sdtpldt0(xa,sz00),xI),
inference(xxres,[status(thm)],[c_2450]) ).
cnf(c_1924,plain,
aElementOf0(xa,xI),
inference(paramod,[status(thm)],[c_555,c_2451]) ).
cnf(c_2452,negated_conjecture,
sz00 = xb,
inference(resolve,[status(thm)],[c_1923,c_178]) ).
cnf(c_2054,negated_conjecture,
xb = sz00,
inference(copy,[status(thm)],[c_2452]) ).
cnf(c_2453,plain,
( sz00 != sz00
| xa != sz00 ),
inference(paramod,[status(thm)],[c_2054,c_79]) ).
cnf(c_2394,plain,
xa != sz00,
inference(copy,[status(thm)],[c_2453]) ).
cnf(c_2454,negated_conjecture,
sz00 = xa,
inference(resolve,[status(thm)],[c_1924,c_178]) ).
cnf(c_2455,negated_conjecture,
xa = sz00,
inference(copy,[status(thm)],[c_2454]) ).
cnf(c_2437,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_2394,c_2455]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG109+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n009.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sat Sep 26 06:07:14 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.37 % Process 3521570 was started by sandbox2 on n009,
% 0.11/0.37 % Sat Sep 26 06:07:14 2026
% 0.11/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.11/0.39
% 0.11/0.39 % From the command line: assign(max_seconds, 300).
% 4.00/0.96
% 4.00/0.96 % SZS status Theorem for theBenchmark
% 4.00/0.96
% 4.00/0.96 % Proof 1 at 0.46 (+ 0.09) seconds.
% 4.00/0.96 % Length of proof is 30.
% 4.00/0.96 % Level of proof is 6.
% 4.00/0.96 % Maximum clause weight is 33.000.
% 4.00/0.96 % Given clauses 212.
% 4.00/0.96
% 4.00/0.96 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------