%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : RNG126+4 : 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 : n014.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 08:26:43 AM UTC 2026
% Result : Theorem 59.08s 8.00s
% Output : CNFRefutation 59.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 9
% Syntax : Number of formulae : 65 ( 31 unt; 0 def)
% Number of atoms : 192 ( 65 equ)
% Maximal formula atoms : 18 ( 2 avg)
% Number of connectives : 185 ( 58 ~; 50 |; 55 &)
% ( 9 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 9 con; 0-2 aty)
% Number of variables : 83 ( 0 sgn 31 !; 21 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mMulComm,axiom,
! [W0,W1] :
( ( aElement0(W1)
& aElement0(W0) )
=> sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ),
file('theBenchmark.p',mMulComm) ).
fof(mAMDistr,axiom,
! [W0,W1,W2] :
( ( aElement0(W2)
& aElement0(W1)
& aElement0(W0) )
=> ( sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0))
& sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) ) ),
file('theBenchmark.p',mAMDistr) ).
fof(mEOfElem,axiom,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aElementOf0(W1,W0)
=> aElement0(W1) ) ),
file('theBenchmark.p',mEOfElem) ).
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))
& ! [W0] :
( aElementOf0(W0,xI)
<=> ? [W1,W2] :
( sdtpldt0(W1,W2) = W0
& aElementOf0(W2,slsdtgt0(xb))
& aElementOf0(W1,slsdtgt0(xa)) ) )
& ! [W0] :
( aElementOf0(W0,slsdtgt0(xb))
<=> ? [W1] :
( sdtasdt0(xb,W1) = W0
& aElement0(W1) ) )
& ! [W0] :
( aElementOf0(W0,slsdtgt0(xa))
<=> ? [W1] :
( sdtasdt0(xa,W1) = W0
& aElement0(W1) ) )
& aIdeal0(xI)
& ! [W0] :
( aElementOf0(W0,xI)
=> ( ! [W1] :
( aElement0(W1)
=> aElementOf0(sdtasdt0(W1,W0),xI) )
& ! [W1] :
( aElementOf0(W1,xI)
=> aElementOf0(sdtpldt0(W0,W1),xI) ) ) )
& aSet0(xI) ),
file('theBenchmark.p',m__2174) ).
fof(m__2273,axiom,
( ! [W0] :
( ( W0 != sz00
& ( aElementOf0(W0,xI)
| ? [W1,W2] :
( sdtpldt0(W1,W2) = W0
& aElementOf0(W2,slsdtgt0(xb))
& aElementOf0(W1,slsdtgt0(xa)) ) ) )
=> ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu)) )
& xu != sz00
& aElementOf0(xu,xI)
& ? [W0,W1] :
( sdtpldt0(W0,W1) = xu
& aElementOf0(W1,slsdtgt0(xb))
& aElementOf0(W0,slsdtgt0(xa)) ) ),
file('theBenchmark.p',m__2273) ).
fof(m__2744,axiom,
? [W0] :
( sdtasdt0(xu,W0) = xc
& aElement0(W0) ),
file('theBenchmark.p',m__2744) ).
fof(m__,conjecture,
( ! [W0] :
( aElementOf0(W0,slsdtgt0(xa))
<=> ? [W1] :
( sdtasdt0(xa,W1) = W0
& aElement0(W1) ) )
=> ( ! [W0] :
( aElementOf0(W0,slsdtgt0(xb))
<=> ? [W1] :
( sdtasdt0(xb,W1) = W0
& aElement0(W1) ) )
=> ( aElementOf0(xc,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ? [W0,W1] :
( sdtpldt0(W0,W1) = xc
& aElementOf0(W1,slsdtgt0(xb))
& aElementOf0(W0,slsdtgt0(xa)) ) ) ) ),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ ( ! [W0] :
( aElementOf0(W0,slsdtgt0(xa))
<=> ? [W1] :
( sdtasdt0(xa,W1) = W0
& aElement0(W1) ) )
=> ( ! [W0] :
( aElementOf0(W0,slsdtgt0(xb))
<=> ? [W1] :
( sdtasdt0(xb,W1) = W0
& aElement0(W1) ) )
=> ( aElementOf0(xc,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ? [W0,W1] :
( sdtpldt0(W0,W1) = xc
& aElementOf0(W1,slsdtgt0(xb))
& aElementOf0(W0,slsdtgt0(xa)) ) ) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_80,plain,
( sdtasdt0(B,A) = sdtasdt0(A,B)
| ~ aElement0(B)
| ~ aElement0(A) ),
inference(clausify,[status(thm)],[mMulComm]) ).
cnf(c_84,plain,
( sdtasdt0(A,sdtpldt0(B,C)) = sdtpldt0(sdtasdt0(A,B),sdtasdt0(A,C))
| ~ aElement0(C)
| ~ aElement0(B)
| ~ aElement0(A) ),
inference(clausify,[status(thm)],[mAMDistr]) ).
cnf(c_85,plain,
( sdtpldt0(sdtasdt0(A,B),sdtasdt0(A,C)) = sdtasdt0(A,sdtpldt0(B,C))
| ~ aElement0(C)
| ~ aElement0(B)
| ~ aElement0(A) ),
inference(copy,[status(thm)],[c_84]) ).
cnf(c_86,plain,
( sdtasdt0(sdtpldt0(B,C),A) = sdtpldt0(sdtasdt0(B,A),sdtasdt0(C,A))
| ~ aElement0(C)
| ~ aElement0(B)
| ~ aElement0(A) ),
inference(clausify,[status(thm)],[mAMDistr]) ).
cnf(c_87,plain,
( sdtpldt0(sdtasdt0(B,A),sdtasdt0(C,A)) = sdtasdt0(sdtpldt0(B,C),A)
| ~ aElement0(C)
| ~ aElement0(B)
| ~ aElement0(A) ),
inference(copy,[status(thm)],[c_86]) ).
cnf(c_95,plain,
( aElement0(B)
| ~ aElementOf0(B,A)
| ~ aSet0(A) ),
inference(clausify,[status(thm)],[mEOfElem]) ).
cnf(c_143,plain,
( aSet0(B)
| slsdtgt0(A) != B
| ~ aElement0(A) ),
inference(clausify,[status(thm)],[mDefPrIdeal]) ).
cnf(c_152,plain,
aElement0(xa),
inference(clausify,[status(thm)],[m__2091]) ).
cnf(c_153,plain,
aElement0(xb),
inference(clausify,[status(thm)],[m__2091]) ).
cnf(c_194,plain,
( aElementOf0(sdtasdt0(B,A),xI)
| ~ aElement0(B)
| ~ aElementOf0(A,xI) ),
inference(clausify,[status(thm)],[m__2174]) ).
cnf(c_206,plain,
sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) = xI,
inference(clausify,[status(thm)],[m__2174]) ).
fof(nnf_41,plain,
( ! [W0] :
( ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu))
| sz00 = W0
| ( ~ aElementOf0(W0,xI)
& ! [W1,W2] :
( sdtpldt0(W1,W2) != W0
| ~ aElementOf0(W2,slsdtgt0(xb))
| ~ aElementOf0(W1,slsdtgt0(xa)) ) ) )
& xu != sz00
& aElementOf0(xu,xI)
& ? [X3,X0] :
( sdtpldt0(X3,X0) = xu
& aElementOf0(X0,slsdtgt0(xb))
& aElementOf0(X3,slsdtgt0(xa)) ) ),
inference(fof_nnf,[status(thm)],[m__2273]) ).
fof(sk_m__2273_sk,plain,
( ! [W0] :
( ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu))
| sz00 = W0
| ( ~ aElementOf0(W0,xI)
& ! [W1,W2] :
( sdtpldt0(W1,W2) != W0
| ~ aElementOf0(W2,slsdtgt0(xb))
| ~ aElementOf0(W1,slsdtgt0(xa)) ) ) )
& xu != sz00
& aElementOf0(xu,xI)
& sdtpldt0(sK0,sK1) = xu
& aElementOf0(sK1,slsdtgt0(xb))
& aElementOf0(sK0,slsdtgt0(xa)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X3,sK0),skolemize(X0,sK1)],[nnf_41]) ).
fof(sk_m__2273,plain,
( ! [VAR_0] :
( ~ iLess0(sbrdtbr0(VAR_0),sbrdtbr0(xu))
| sz00 = VAR_0
| ~ aElementOf0(VAR_0,xI) )
& ! [VAR_0,VAR_1,VAR_2] :
( ~ iLess0(sbrdtbr0(VAR_2),sbrdtbr0(xu))
| sz00 = VAR_2
| sdtpldt0(VAR_0,VAR_1) != VAR_2
| ~ aElementOf0(VAR_1,slsdtgt0(xb))
| ~ aElementOf0(VAR_0,slsdtgt0(xa)) )
& xu != sz00
& aElementOf0(xu,xI)
& sdtpldt0(sK0,sK1) = xu
& aElementOf0(sK1,slsdtgt0(xb))
& aElementOf0(sK0,slsdtgt0(xa)) ),
inference(cnf_transformation,[status(thm)],[sk_m__2273_sk]) ).
cnf(c_230,plain,
aElementOf0(sK0,slsdtgt0(xa)),
inference(split_conjunct,[status(thm)],[sk_m__2273]) ).
cnf(c_231,plain,
aElementOf0(sK1,slsdtgt0(xb)),
inference(split_conjunct,[status(thm)],[sk_m__2273]) ).
cnf(c_232,plain,
sdtpldt0(sK0,sK1) = xu,
inference(split_conjunct,[status(thm)],[sk_m__2273]) ).
cnf(c_233,plain,
aElementOf0(xu,xI),
inference(split_conjunct,[status(thm)],[sk_m__2273]) ).
fof(nnf_43,plain,
? [W0] :
( sdtasdt0(xu,W0) = xc
& aElement0(W0) ),
inference(fof_nnf,[status(thm)],[m__2744]) ).
fof(sk_m__2744,plain,
( sdtasdt0(xu,sK2) = xc
& aElement0(sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(W0,sK2)],[nnf_43]) ).
cnf(c_245,plain,
aElement0(sK2),
inference(split_conjunct,[status(thm)],[sk_m__2744]) ).
cnf(c_246,plain,
sdtasdt0(xu,sK2) = xc,
inference(split_conjunct,[status(thm)],[sk_m__2744]) ).
cnf(c_252,negated_conjecture,
~ aElementOf0(xc,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_253,negated_conjecture,
~ aElementOf0(xc,xI),
inference(paramod,[status(thm)],[c_206,c_252]) ).
cnf(c_25659,plain,
( aSet0(A)
| slsdtgt0(xa) != A ),
inference(resolve,[status(thm)],[c_143,c_152]) ).
cnf(c_598,plain,
aSet0(slsdtgt0(xa)),
inference(xxres,[status(thm)],[c_25659]) ).
cnf(c_25660,plain,
( aSet0(A)
| slsdtgt0(xb) != A ),
inference(resolve,[status(thm)],[c_143,c_153]) ).
cnf(c_732,plain,
aSet0(slsdtgt0(xb)),
inference(xxres,[status(thm)],[c_25660]) ).
cnf(c_25661,plain,
( aElement0(sK0)
| ~ aSet0(slsdtgt0(xa)) ),
inference(resolve,[status(thm)],[c_230,c_95]) ).
cnf(c_9194,plain,
aElement0(sK0),
inference(resolve,[status(thm)],[c_598,c_25661]) ).
cnf(c_25662,plain,
( aElement0(sK1)
| ~ aSet0(slsdtgt0(xb)) ),
inference(resolve,[status(thm)],[c_231,c_95]) ).
cnf(c_9229,plain,
aElement0(sK1),
inference(resolve,[status(thm)],[c_732,c_25662]) ).
cnf(c_25663,plain,
( aElementOf0(sdtasdt0(A,xu),xI)
| ~ aElement0(A) ),
inference(resolve,[status(thm)],[c_194,c_233]) ).
cnf(c_14856,plain,
aElementOf0(sdtasdt0(sK2,xu),xI),
inference(resolve,[status(thm)],[c_25663,c_245]) ).
cnf(c_25664,plain,
( sdtasdt0(A,sK2) = sdtasdt0(sK2,A)
| ~ aElement0(A) ),
inference(resolve,[status(thm)],[c_80,c_245]) ).
cnf(c_25665,plain,
sdtasdt0(sK0,sK2) = sdtasdt0(sK2,sK0),
inference(resolve,[status(thm)],[c_25664,c_9194]) ).
cnf(c_24683,plain,
sdtasdt0(sK2,sK0) = sdtasdt0(sK0,sK2),
inference(copy,[status(thm)],[c_25665]) ).
cnf(c_25666,plain,
( sdtpldt0(sdtasdt0(A,sK2),sdtasdt0(B,sK2)) = sdtasdt0(sdtpldt0(A,B),sK2)
| ~ aElement0(B)
| ~ aElement0(A) ),
inference(resolve,[status(thm)],[c_87,c_245]) ).
cnf(c_25667,plain,
( sdtpldt0(sdtasdt0(sK0,sK2),sdtasdt0(A,sK2)) = sdtasdt0(sdtpldt0(sK0,A),sK2)
| ~ aElement0(A) ),
inference(resolve,[status(thm)],[c_25666,c_9194]) ).
cnf(c_25668,plain,
sdtpldt0(sdtasdt0(sK0,sK2),sdtasdt0(sK1,sK2)) = sdtasdt0(sdtpldt0(sK0,sK1),sK2),
inference(resolve,[status(thm)],[c_25667,c_9229]) ).
cnf(c_25669,plain,
sdtpldt0(sdtasdt0(sK0,sK2),sdtasdt0(sK1,sK2)) = sdtasdt0(xu,sK2),
inference(paramod,[status(thm)],[c_232,c_25668]) ).
cnf(c_25109,plain,
sdtpldt0(sdtasdt0(sK0,sK2),sdtasdt0(sK1,sK2)) = xc,
inference(paramod,[status(thm)],[c_246,c_25669]) ).
cnf(c_25670,plain,
( sdtpldt0(sdtasdt0(sK2,A),sdtasdt0(sK2,B)) = sdtasdt0(sK2,sdtpldt0(A,B))
| ~ aElement0(B)
| ~ aElement0(A) ),
inference(resolve,[status(thm)],[c_85,c_245]) ).
cnf(c_25671,plain,
( sdtpldt0(sdtasdt0(sK2,sK0),sdtasdt0(sK2,A)) = sdtasdt0(sK2,sdtpldt0(sK0,A))
| ~ aElement0(A) ),
inference(resolve,[status(thm)],[c_25670,c_9194]) ).
cnf(c_25672,plain,
sdtpldt0(sdtasdt0(sK2,sK0),sdtasdt0(sK2,sK1)) = sdtasdt0(sK2,sdtpldt0(sK0,sK1)),
inference(resolve,[status(thm)],[c_25671,c_9229]) ).
cnf(c_25673,plain,
sdtpldt0(sdtasdt0(sK0,sK2),sdtasdt0(sK2,sK1)) = sdtasdt0(sK2,sdtpldt0(sK0,sK1)),
inference(paramod,[status(thm)],[c_24683,c_25672]) ).
cnf(c_25342,plain,
sdtpldt0(sdtasdt0(sK0,sK2),sdtasdt0(sK2,sK1)) = sdtasdt0(sK2,xu),
inference(paramod,[status(thm)],[c_232,c_25673]) ).
cnf(c_25674,plain,
( sdtasdt0(A,sK2) = sdtasdt0(sK2,A)
| ~ aElement0(A) ),
inference(resolve,[status(thm)],[c_80,c_245]) ).
cnf(c_25675,plain,
sdtasdt0(sK1,sK2) = sdtasdt0(sK2,sK1),
inference(resolve,[status(thm)],[c_25674,c_9229]) ).
cnf(c_25546,plain,
sdtasdt0(sK2,sK1) = sdtasdt0(sK1,sK2),
inference(copy,[status(thm)],[c_25675]) ).
cnf(c_25676,plain,
sdtpldt0(sdtasdt0(sK0,sK2),sdtasdt0(sK1,sK2)) = sdtasdt0(sK2,xu),
inference(paramod,[status(thm)],[c_25546,c_25342]) ).
cnf(c_25677,plain,
xc = sdtasdt0(sK2,xu),
inference(paramod,[status(thm)],[c_25109,c_25676]) ).
cnf(c_25625,plain,
sdtasdt0(sK2,xu) = xc,
inference(copy,[status(thm)],[c_25677]) ).
cnf(c_25678,plain,
aElementOf0(xc,xI),
inference(paramod,[status(thm)],[c_25625,c_14856]) ).
cnf(c_25658,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_253,c_25678]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG126+4 : 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 : n014.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 06:12:01 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.36 % Process 2356788 was started by sandbox2 on n014,
% 0.08/0.36 % Sat Sep 26 06:12:01 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/0.38
% 0.08/0.38 % From the command line: assign(max_seconds, 300).
% 59.08/8.00
% 59.08/8.00 % SZS status Theorem for theBenchmark
% 59.08/8.00
% 59.08/8.00 % Proof 1 at 5.88 (+ 1.63) seconds.
% 59.08/8.00 % Length of proof is 39.
% 59.08/8.00 % Level of proof is 7.
% 59.08/8.00 % Maximum clause weight is 34.000.
% 59.08/8.00 % Given clauses 309.
% 59.08/8.00
% 59.08/8.00 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------