%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : RNG091+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 : n019.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 08:26:36 AM UTC 2026
% Result : Theorem 0.08s 0.47s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of formulae : 52 ( 27 unt; 0 def)
% Number of atoms : 115 ( 33 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 110 ( 47 ~; 41 |; 15 &)
% ( 3 <=>; 4 =>; 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 : 12 ( 12 usr; 9 con; 0-2 aty)
% Number of variables : 47 ( 0 sgn 8 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
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(mDefIdeal,axiom,
! [W0] :
( aIdeal0(W0)
<=> ( ! [W1] :
( aElementOf0(W1,W0)
=> ( ! [W2] :
( aElement0(W2)
=> aElementOf0(sdtasdt0(W2,W1),W0) )
& ! [W2] :
( aElementOf0(W2,W0)
=> aElementOf0(sdtpldt0(W1,W2),W0) ) ) )
& aSet0(W0) ) ),
file('theBenchmark.p',mDefIdeal) ).
fof(m__870,axiom,
( aIdeal0(xJ)
& aIdeal0(xI) ),
file('theBenchmark.p',m__870) ).
fof(m__934,axiom,
( xx = sdtpldt0(xk,xl)
& aElementOf0(xl,xJ)
& aElementOf0(xk,xI) ),
file('theBenchmark.p',m__934) ).
fof(m__967,axiom,
( xy = sdtpldt0(xm,xn)
& aElementOf0(xn,xJ)
& aElementOf0(xm,xI) ),
file('theBenchmark.p',m__967) ).
fof(m__994,axiom,
( aElementOf0(sdtpldt0(xl,xn),xJ)
& aElementOf0(sdtpldt0(xk,xm),xI) ),
file('theBenchmark.p',m__994) ).
fof(m__1021,axiom,
( aElementOf0(sdtasdt0(xz,xl),xJ)
& aElementOf0(sdtasdt0(xz,xk),xI) ),
file('theBenchmark.p',m__1021) ).
fof(m__,conjecture,
( aElementOf0(sdtasdt0(xz,xx),sdtpldt1(xI,xJ))
& aElementOf0(sdtpldt0(xx,xy),sdtpldt1(xI,xJ)) ),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ ( aElementOf0(sdtasdt0(xz,xx),sdtpldt1(xI,xJ))
& aElementOf0(sdtpldt0(xx,xy),sdtpldt1(xI,xJ)) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_32,plain,
( aSet0(A)
| ~ aIdeal0(A) ),
inference(clausify,[status(thm)],[mDefIdeal]) ).
cnf(c_37,plain,
aIdeal0(xI),
inference(clausify,[status(thm)],[m__870]) ).
cnf(c_38,plain,
aIdeal0(xJ),
inference(clausify,[status(thm)],[m__870]) ).
cnf(c_39,plain,
aSet0(xJ),
inference(resolve,[status(thm)],[c_38,c_32]) ).
cnf(c_42,plain,
aSet0(xI),
inference(resolve,[status(thm)],[c_37,c_32]) ).
cnf(c_55,negated_conjecture,
( ~ aElementOf0(sdtasdt0(xz,xx),sdtpldt1(xI,xJ))
| ~ aElementOf0(sdtpldt0(xx,xy),sdtpldt1(xI,xJ)) ),
inference(clausify,[status(thm)],[m___neg]) ).
fof(m__1098,axiom,
sdtasdt0(xz,xx) = sdtpldt0(sdtasdt0(xz,xk),sdtasdt0(xz,xl)),
file('theBenchmark.p',m__1098) ).
cnf(c_56,plain,
sdtasdt0(xz,xx) = sdtpldt0(sdtasdt0(xz,xk),sdtasdt0(xz,xl)),
inference(clausify,[status(thm)],[m__1098]) ).
cnf(c_57,plain,
sdtpldt0(sdtasdt0(xz,xk),sdtasdt0(xz,xl)) = sdtasdt0(xz,xx),
inference(copy,[status(thm)],[c_56]) ).
fof(m__1061,axiom,
sdtpldt0(xx,xy) = sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,xn)),
file('theBenchmark.p',m__1061) ).
cnf(c_58,plain,
sdtpldt0(xx,xy) = sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,xn)),
inference(clausify,[status(thm)],[m__1061]) ).
cnf(c_59,plain,
sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,xn)) = sdtpldt0(xx,xy),
inference(copy,[status(thm)],[c_58]) ).
cnf(c_60,plain,
aElementOf0(sdtasdt0(xz,xl),xJ),
inference(clausify,[status(thm)],[m__1021]) ).
cnf(c_61,plain,
aElementOf0(sdtasdt0(xz,xk),xI),
inference(clausify,[status(thm)],[m__1021]) ).
cnf(c_62,plain,
aElementOf0(sdtpldt0(xl,xn),xJ),
inference(clausify,[status(thm)],[m__994]) ).
cnf(c_63,plain,
aElementOf0(sdtpldt0(xk,xm),xI),
inference(clausify,[status(thm)],[m__994]) ).
cnf(c_64,plain,
sdtpldt0(xm,xn) = xy,
inference(clausify,[status(thm)],[m__967]) ).
cnf(c_65,plain,
xy = sdtpldt0(xm,xn),
inference(copy,[status(thm)],[c_64]) ).
cnf(c_68,plain,
sdtpldt0(xk,xl) = xx,
inference(clausify,[status(thm)],[m__934]) ).
cnf(c_69,plain,
xx = sdtpldt0(xk,xl),
inference(copy,[status(thm)],[c_68]) ).
cnf(c_89,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_836,plain,
sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,xn)) = sdtpldt0(sdtpldt0(xk,xl),xy),
inference(paramod,[status(thm)],[c_69,c_59]) ).
cnf(c_144,plain,
sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,xn)) = sdtpldt0(sdtpldt0(xk,xl),sdtpldt0(xm,xn)),
inference(paramod,[status(thm)],[c_65,c_836]) ).
cnf(c_837,negated_conjecture,
( ~ aElementOf0(sdtasdt0(xz,xx),sdtpldt1(xI,xJ))
| ~ aElementOf0(sdtpldt0(sdtpldt0(xk,xl),xy),sdtpldt1(xI,xJ)) ),
inference(paramod,[status(thm)],[c_69,c_55]) ).
cnf(c_838,negated_conjecture,
( ~ aElementOf0(sdtasdt0(xz,xx),sdtpldt1(xI,xJ))
| ~ aElementOf0(sdtpldt0(sdtpldt0(xk,xl),sdtpldt0(xm,xn)),sdtpldt1(xI,xJ)) ),
inference(paramod,[status(thm)],[c_65,c_837]) ).
cnf(c_145,negated_conjecture,
( ~ aElementOf0(sdtasdt0(xz,sdtpldt0(xk,xl)),sdtpldt1(xI,xJ))
| ~ aElementOf0(sdtpldt0(sdtpldt0(xk,xl),sdtpldt0(xm,xn)),sdtpldt1(xI,xJ)) ),
inference(paramod,[status(thm)],[c_69,c_838]) ).
cnf(c_146,plain,
sdtpldt0(sdtasdt0(xz,xk),sdtasdt0(xz,xl)) = sdtasdt0(xz,sdtpldt0(xk,xl)),
inference(paramod,[status(thm)],[c_69,c_57]) ).
cnf(c_839,plain,
( sdtpldt0(D,E) != C
| ~ aElementOf0(E,A)
| ~ aElementOf0(D,xI)
| aElementOf0(C,B)
| sdtpldt1(xI,A) != B
| ~ aSet0(A) ),
inference(resolve,[status(thm)],[c_89,c_42]) ).
cnf(c_840,plain,
( sdtpldt0(C,D) != B
| ~ aElementOf0(D,xJ)
| ~ aElementOf0(C,xI)
| aElementOf0(B,A)
| sdtpldt1(xI,xJ) != A ),
inference(resolve,[status(thm)],[c_839,c_39]) ).
cnf(c_841,plain,
( sdtpldt0(B,C) != A
| ~ aElementOf0(C,xJ)
| ~ aElementOf0(B,xI)
| aElementOf0(A,sdtpldt1(xI,xJ)) ),
inference(xxres,[status(thm)],[c_840]) ).
cnf(c_842,plain,
( sdtpldt0(sdtpldt0(xk,xm),B) != A
| ~ aElementOf0(B,xJ)
| aElementOf0(A,sdtpldt1(xI,xJ)) ),
inference(resolve,[status(thm)],[c_841,c_63]) ).
cnf(c_843,plain,
( sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,xn)) != A
| aElementOf0(A,sdtpldt1(xI,xJ)) ),
inference(resolve,[status(thm)],[c_842,c_62]) ).
cnf(c_844,plain,
aElementOf0(sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,xn)),sdtpldt1(xI,xJ)),
inference(xxres,[status(thm)],[c_843]) ).
cnf(c_793,plain,
aElementOf0(sdtpldt0(sdtpldt0(xk,xl),sdtpldt0(xm,xn)),sdtpldt1(xI,xJ)),
inference(paramod,[status(thm)],[c_144,c_844]) ).
cnf(c_845,plain,
( sdtpldt0(D,E) != C
| ~ aElementOf0(E,A)
| ~ aElementOf0(D,xI)
| aElementOf0(C,B)
| sdtpldt1(xI,A) != B
| ~ aSet0(A) ),
inference(resolve,[status(thm)],[c_89,c_42]) ).
cnf(c_846,plain,
( sdtpldt0(C,D) != B
| ~ aElementOf0(D,xJ)
| ~ aElementOf0(C,xI)
| aElementOf0(B,A)
| sdtpldt1(xI,xJ) != A ),
inference(resolve,[status(thm)],[c_845,c_39]) ).
cnf(c_847,plain,
( sdtpldt0(B,C) != A
| ~ aElementOf0(C,xJ)
| ~ aElementOf0(B,xI)
| aElementOf0(A,sdtpldt1(xI,xJ)) ),
inference(xxres,[status(thm)],[c_846]) ).
cnf(c_848,plain,
( sdtpldt0(sdtasdt0(xz,xk),B) != A
| ~ aElementOf0(B,xJ)
| aElementOf0(A,sdtpldt1(xI,xJ)) ),
inference(resolve,[status(thm)],[c_847,c_61]) ).
cnf(c_849,plain,
( sdtpldt0(sdtasdt0(xz,xk),sdtasdt0(xz,xl)) != A
| aElementOf0(A,sdtpldt1(xI,xJ)) ),
inference(resolve,[status(thm)],[c_848,c_60]) ).
cnf(c_850,plain,
aElementOf0(sdtpldt0(sdtasdt0(xz,xk),sdtasdt0(xz,xl)),sdtpldt1(xI,xJ)),
inference(xxres,[status(thm)],[c_849]) ).
cnf(c_798,plain,
aElementOf0(sdtasdt0(xz,sdtpldt0(xk,xl)),sdtpldt1(xI,xJ)),
inference(paramod,[status(thm)],[c_146,c_850]) ).
cnf(c_851,negated_conjecture,
~ aElementOf0(sdtasdt0(xz,sdtpldt0(xk,xl)),sdtpldt1(xI,xJ)),
inference(resolve,[status(thm)],[c_793,c_145]) ).
cnf(c_835,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_798,c_851]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG091+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 : n019.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 06:02:18 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.36 % Process 563398 was started by sandbox on n019,
% 0.08/0.36 % Sat Sep 26 06:02:18 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.37
% 0.08/0.37 % From the command line: assign(max_seconds, 300).
% 0.08/0.47
% 0.08/0.47 % SZS status Theorem for theBenchmark
% 0.08/0.47
% 0.08/0.47 % Proof 1 at 0.08 (+ 0.02) seconds.
% 0.08/0.47 % Length of proof is 33.
% 0.08/0.47 % Level of proof is 5.
% 0.08/0.47 % Maximum clause weight is 50.000.
% 0.08/0.47 % Given clauses 41.
% 0.08/0.47
% 0.08/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------