%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : RNG086+2 : 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 : 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 08:26:35 AM UTC 2026
% Result : Theorem 0.12s 0.38s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 2
% Syntax : Number of formulae : 14 ( 7 unt; 0 def)
% Number of atoms : 45 ( 13 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 38 ( 7 ~; 3 |; 28 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 15 ( 0 sgn 0 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__901,axiom,
( aElement0(xz)
& aElementOf0(xy,sdtpldt1(xI,xJ))
& ? [W0,W1] :
( sdtpldt0(W0,W1) = xy
& aElementOf0(W1,xJ)
& aElementOf0(W0,xI) )
& aElementOf0(xx,sdtpldt1(xI,xJ))
& ? [W0,W1] :
( sdtpldt0(W0,W1) = xx
& aElementOf0(W1,xJ)
& aElementOf0(W0,xI) ) ),
file('theBenchmark.p',m__901) ).
fof(m__,conjecture,
? [W0,W1] :
( xx = sdtpldt0(W0,W1)
& aElementOf0(W1,xJ)
& aElementOf0(W0,xI) ),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ ? [W0,W1] :
( xx = sdtpldt0(W0,W1)
& aElementOf0(W1,xJ)
& aElementOf0(W0,xI) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_51,negated_conjecture,
( sdtpldt0(A,B) != xx
| ~ aElementOf0(B,xJ)
| ~ aElementOf0(A,xI) ),
inference(clausify,[status(thm)],[m___neg]) ).
fof(nnf_23,plain,
( aElement0(xz)
& aElementOf0(xy,sdtpldt1(xI,xJ))
& ? [W0,W1] :
( sdtpldt0(W0,W1) = xy
& aElementOf0(W1,xJ)
& aElementOf0(W0,xI) )
& aElementOf0(xx,sdtpldt1(xI,xJ))
& ? [X0,X1] :
( sdtpldt0(X0,X1) = xx
& aElementOf0(X1,xJ)
& aElementOf0(X0,xI) ) ),
inference(fof_nnf,[status(thm)],[m__901]) ).
fof(sk_m__901,plain,
( aElement0(xz)
& aElementOf0(xy,sdtpldt1(xI,xJ))
& sdtpldt0(sK2,sK3) = xy
& aElementOf0(sK3,xJ)
& aElementOf0(sK2,xI)
& aElementOf0(xx,sdtpldt1(xI,xJ))
& sdtpldt0(sK0,sK1) = xx
& aElementOf0(sK1,xJ)
& aElementOf0(sK0,xI) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(W0,sK2),skolemize(W1,sK3)],[nnf_23]) ).
cnf(c_58,plain,
sdtpldt0(sK0,sK1) = xx,
inference(split_conjunct,[status(thm)],[sk_m__901]) ).
cnf(c_59,plain,
xx = sdtpldt0(sK0,sK1),
inference(copy,[status(thm)],[c_58]) ).
cnf(c_60,plain,
aElementOf0(sK1,xJ),
inference(split_conjunct,[status(thm)],[sk_m__901]) ).
cnf(c_61,plain,
aElementOf0(sK0,xI),
inference(split_conjunct,[status(thm)],[sk_m__901]) ).
cnf(c_301,negated_conjecture,
( sdtpldt0(A,sK1) != xx
| ~ aElementOf0(A,xI) ),
inference(resolve,[status(thm)],[c_51,c_60]) ).
cnf(c_302,plain,
sdtpldt0(sK0,sK1) = xx,
inference(copy,[status(thm)],[c_59]) ).
cnf(c_303,negated_conjecture,
~ aElementOf0(sK0,xI),
inference(resolve,[status(thm)],[c_301,c_302]) ).
cnf(c_300,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_61,c_303]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG086+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n007.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 26 05:59:23 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.35 % Process 2956049 was started by sandbox2 on n007,
% 0.08/0.35 % Sat Sep 26 05:59:23 2026
% 0.08/0.35 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.12/0.36
% 0.12/0.36 % From the command line: assign(max_seconds, 300).
% 0.12/0.38
% 0.12/0.38 % SZS status Theorem for theBenchmark
% 0.12/0.38
% 0.12/0.38 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.12/0.38 % Length of proof is 8.
% 0.12/0.38 % Level of proof is 3.
% 0.12/0.38 % Maximum clause weight is 21.000.
% 0.12/0.38 % Given clauses 25.
% 0.12/0.38
% 0.12/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------