%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM533+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 : n012.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 08:17:18 AM UTC 2026
% Result : Theorem 0.04s 0.32s
% Output : CNFRefutation 0.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 29 ( 11 unt; 0 def)
% Number of atoms : 90 ( 0 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 108 ( 47 ~; 42 |; 14 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 33 ( 0 sgn 18 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mDefSub,axiom,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aSubsetOf0(W1,W0)
<=> ( ! [W2] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,W0) )
& aSet0(W1) ) ) ),
file('theBenchmark.p',mDefSub) ).
fof(m__522,axiom,
( aSet0(xC)
& aSet0(xB)
& aSet0(xA) ),
file('theBenchmark.p',m__522) ).
fof(m__,conjecture,
( ( aSubsetOf0(xB,xC)
& aSubsetOf0(xA,xB) )
=> aSubsetOf0(xA,xC) ),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ ( ( aSubsetOf0(xB,xC)
& aSubsetOf0(xA,xB) )
=> aSubsetOf0(xA,xC) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(nnf_9,plain,
! [W0] :
( ! [W1] :
( ( ? [W2] :
( ~ aElementOf0(W2,W0)
& aElementOf0(W2,W1) )
| ~ aSet0(W1)
| aSubsetOf0(W1,W0) )
& ( ( ! [X0] :
( aElementOf0(X0,W0)
| ~ aElementOf0(X0,W1) )
& aSet0(W1) )
| ~ aSubsetOf0(W1,W0) ) )
| ~ aSet0(W0) ),
inference(fof_nnf,[status(thm)],[mDefSub]) ).
fof(sk_mDefSub_sk,plain,
! [W0] :
( ! [W1] :
( ( ( ~ aElementOf0(sK0(W0,W1),W0)
& aElementOf0(sK0(W0,W1),W1) )
| ~ aSet0(W1)
| aSubsetOf0(W1,W0) )
& ( ( ! [X0] :
( aElementOf0(X0,W0)
| ~ aElementOf0(X0,W1) )
& aSet0(W1) )
| ~ aSubsetOf0(W1,W0) ) )
| ~ aSet0(W0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(W2,sK0(W0,W1))],[nnf_9]) ).
fof(sk_mDefSub,plain,
( ! [VAR_0,VAR_1] :
( ~ aElementOf0(sK0(VAR_0,VAR_1),VAR_0)
| ~ aSet0(VAR_1)
| aSubsetOf0(VAR_1,VAR_0)
| ~ aSet0(VAR_0) )
& ! [VAR_0,VAR_1] :
( aElementOf0(sK0(VAR_0,VAR_1),VAR_1)
| ~ aSet0(VAR_1)
| aSubsetOf0(VAR_1,VAR_0)
| ~ aSet0(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2] :
( aElementOf0(VAR_2,VAR_0)
| ~ aElementOf0(VAR_2,VAR_1)
| ~ aSubsetOf0(VAR_1,VAR_0)
| ~ aSet0(VAR_0) )
& ! [VAR_0,VAR_1] :
( aSet0(VAR_1)
| ~ aSubsetOf0(VAR_1,VAR_0)
| ~ aSet0(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_mDefSub_sk]) ).
cnf(c_20,plain,
( aElementOf0(C,A)
| ~ aElementOf0(C,B)
| ~ aSubsetOf0(B,A)
| ~ aSet0(A) ),
inference(split_conjunct,[status(thm)],[sk_mDefSub]) ).
cnf(c_21,plain,
( aElementOf0(sK0(A,B),B)
| ~ aSet0(B)
| aSubsetOf0(B,A)
| ~ aSet0(A) ),
inference(split_conjunct,[status(thm)],[sk_mDefSub]) ).
cnf(c_22,plain,
( ~ aElementOf0(sK0(A,B),A)
| ~ aSet0(B)
| aSubsetOf0(B,A)
| ~ aSet0(A) ),
inference(split_conjunct,[status(thm)],[sk_mDefSub]) ).
cnf(c_26,plain,
aSet0(xA),
inference(clausify,[status(thm)],[m__522]) ).
cnf(c_27,plain,
aSet0(xB),
inference(clausify,[status(thm)],[m__522]) ).
cnf(c_28,plain,
aSet0(xC),
inference(clausify,[status(thm)],[m__522]) ).
cnf(c_29,negated_conjecture,
aSubsetOf0(xA,xB),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_30,negated_conjecture,
aSubsetOf0(xB,xC),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_31,negated_conjecture,
~ aSubsetOf0(xA,xC),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_57,plain,
( ~ aElementOf0(sK0(xC,A),xC)
| ~ aSet0(A)
| aSubsetOf0(A,xC) ),
inference(resolve,[status(thm)],[c_22,c_28]) ).
cnf(c_58,negated_conjecture,
( ~ aElementOf0(sK0(xC,xA),xC)
| ~ aSet0(xA) ),
inference(resolve,[status(thm)],[c_57,c_31]) ).
cnf(c_50,negated_conjecture,
~ aElementOf0(sK0(xC,xA),xC),
inference(resolve,[status(thm)],[c_58,c_26]) ).
cnf(c_59,plain,
( aElementOf0(B,xC)
| ~ aElementOf0(B,A)
| ~ aSubsetOf0(A,xC) ),
inference(resolve,[status(thm)],[c_20,c_28]) ).
cnf(c_60,negated_conjecture,
( aElementOf0(A,xC)
| ~ aElementOf0(A,xB) ),
inference(resolve,[status(thm)],[c_59,c_30]) ).
cnf(c_54,negated_conjecture,
~ aElementOf0(sK0(xC,xA),xB),
inference(resolve,[status(thm)],[c_60,c_50]) ).
cnf(c_61,plain,
( aElementOf0(B,xB)
| ~ aElementOf0(B,A)
| ~ aSubsetOf0(A,xB) ),
inference(resolve,[status(thm)],[c_20,c_27]) ).
cnf(c_62,negated_conjecture,
( aElementOf0(A,xB)
| ~ aElementOf0(A,xA) ),
inference(resolve,[status(thm)],[c_61,c_29]) ).
cnf(c_55,negated_conjecture,
~ aElementOf0(sK0(xC,xA),xA),
inference(resolve,[status(thm)],[c_62,c_54]) ).
cnf(c_63,negated_conjecture,
( aElementOf0(sK0(xC,xA),xA)
| ~ aSet0(xA)
| ~ aSet0(xC) ),
inference(resolve,[status(thm)],[c_21,c_31]) ).
cnf(c_64,negated_conjecture,
( aElementOf0(sK0(xC,xA),xA)
| ~ aSet0(xC) ),
inference(resolve,[status(thm)],[c_63,c_26]) ).
cnf(c_65,negated_conjecture,
~ aSet0(xC),
inference(resolve,[status(thm)],[c_64,c_55]) ).
cnf(c_56,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_28,c_65]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : NUM533+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.04/0.30 % Computer : n012.cluster.edu
% 0.04/0.30 % Model : x86_64 x86_64
% 0.04/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.30 % Memory : 8046.5625MB
% 0.04/0.30 % OS : Linux 6.8.0-71-generic
% 0.04/0.30 % CPULimit : 300
% 0.04/0.30 % WCLimit : 300
% 0.04/0.30 % DateTime : Sat Sep 26 03:07:50 UTC 2026
% 0.04/0.31 % CPUTime :
% 0.04/0.31 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.04/0.31 % Process 3753061 was started by sandbox2 on n012,
% 0.04/0.31 % Sat Sep 26 03:07:50 2026
% 0.04/0.31 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.04/0.31
% 0.04/0.31 % From the command line: assign(max_seconds, 300).
% 0.04/0.32
% 0.04/0.32 % SZS status Theorem for theBenchmark
% 0.04/0.32
% 0.04/0.32 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.04/0.32 % Length of proof is 16.
% 0.04/0.32 % Level of proof is 5.
% 0.04/0.32 % Maximum clause weight is 12.000.
% 0.04/0.32 % Given clauses 22.
% 0.04/0.32
% 0.04/0.32 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------