%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : RNG104+2 : 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 : n003.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 08:26:39 AM UTC 2026
% Result : Theorem 0.15s 5.57s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 34 ( 22 unt; 0 def)
% Number of atoms : 59 ( 30 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 43 ( 18 ~; 13 |; 10 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 20 ( 0 sgn 5 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mMulComm,axiom,
! [W0,W1] :
( ( aElement0(W1)
& aElement0(W0) )
=> sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ),
file('theBenchmark.p',mMulComm) ).
fof(mMulAsso,axiom,
! [W0,W1,W2] :
( ( aElement0(W2)
& aElement0(W1)
& aElement0(W0) )
=> sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) ),
file('theBenchmark.p',mMulAsso) ).
fof(m__1933,axiom,
( aElement0(xz)
& aElementOf0(xy,slsdtgt0(xc))
& ? [W0] :
( sdtasdt0(xc,W0) = xy
& aElement0(W0) )
& aElementOf0(xx,slsdtgt0(xc))
& ? [W0] :
( sdtasdt0(xc,W0) = xx
& aElement0(W0) ) ),
file('theBenchmark.p',m__1933) ).
fof(m__1956,axiom,
( sdtasdt0(xc,xu) = xx
& aElement0(xu) ),
file('theBenchmark.p',m__1956) ).
fof(m__,conjecture,
sdtasdt0(xz,xx) = sdtasdt0(xc,sdtasdt0(xu,xz)),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
sdtasdt0(xz,xx) != sdtasdt0(xc,sdtasdt0(xu,xz)),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_67,negated_conjecture,
sdtasdt0(xz,xx) != sdtasdt0(xc,sdtasdt0(xu,xz)),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_68,negated_conjecture,
sdtasdt0(xc,sdtasdt0(xu,xz)) != sdtasdt0(xz,xx),
inference(copy,[status(thm)],[c_67]) ).
cnf(c_73,plain,
sdtasdt0(xc,xu) = xx,
inference(clausify,[status(thm)],[m__1956]) ).
cnf(c_74,plain,
xx = sdtasdt0(xc,xu),
inference(copy,[status(thm)],[c_73]) ).
cnf(c_75,plain,
aElement0(xu),
inference(clausify,[status(thm)],[m__1956]) ).
cnf(c_76,plain,
aElement0(xz),
inference(clausify,[status(thm)],[m__1933]) ).
fof(m__1905,axiom,
aElement0(xc),
file('theBenchmark.p',m__1905) ).
cnf(c_85,plain,
aElement0(xc),
inference(clausify,[status(thm)],[m__1905]) ).
cnf(c_153,plain,
( sdtasdt0(sdtasdt0(A,B),C) = sdtasdt0(A,sdtasdt0(B,C))
| ~ aElement0(C)
| ~ aElement0(B)
| ~ aElement0(A) ),
inference(clausify,[status(thm)],[mMulAsso]) ).
cnf(c_154,plain,
( sdtasdt0(B,A) = sdtasdt0(A,B)
| ~ aElement0(B)
| ~ aElement0(A) ),
inference(clausify,[status(thm)],[mMulComm]) ).
cnf(c_1505,negated_conjecture,
sdtasdt0(xc,sdtasdt0(xu,xz)) != sdtasdt0(xz,sdtasdt0(xc,xu)),
inference(paramod,[status(thm)],[c_74,c_68]) ).
cnf(c_182,negated_conjecture,
sdtasdt0(xz,sdtasdt0(xc,xu)) != sdtasdt0(xc,sdtasdt0(xu,xz)),
inference(copy,[status(thm)],[c_1505]) ).
cnf(c_1506,plain,
( sdtasdt0(sdtasdt0(xc,A),B) = sdtasdt0(xc,sdtasdt0(A,B))
| ~ aElement0(B)
| ~ aElement0(A) ),
inference(resolve,[status(thm)],[c_153,c_85]) ).
cnf(c_1507,plain,
( sdtasdt0(sdtasdt0(xc,xz),A) = sdtasdt0(xc,sdtasdt0(xz,A))
| ~ aElement0(A) ),
inference(resolve,[status(thm)],[c_1506,c_76]) ).
cnf(c_1196,plain,
sdtasdt0(sdtasdt0(xc,xz),xu) = sdtasdt0(xc,sdtasdt0(xz,xu)),
inference(resolve,[status(thm)],[c_1507,c_75]) ).
cnf(c_1508,plain,
( sdtasdt0(sdtasdt0(xz,A),B) = sdtasdt0(xz,sdtasdt0(A,B))
| ~ aElement0(B)
| ~ aElement0(A) ),
inference(resolve,[status(thm)],[c_153,c_76]) ).
cnf(c_1509,plain,
( sdtasdt0(sdtasdt0(xz,xc),A) = sdtasdt0(xz,sdtasdt0(xc,A))
| ~ aElement0(A) ),
inference(resolve,[status(thm)],[c_1508,c_85]) ).
cnf(c_1286,plain,
sdtasdt0(sdtasdt0(xz,xc),xu) = sdtasdt0(xz,sdtasdt0(xc,xu)),
inference(resolve,[status(thm)],[c_1509,c_75]) ).
cnf(c_1510,plain,
( sdtasdt0(A,xc) = sdtasdt0(xc,A)
| ~ aElement0(A) ),
inference(resolve,[status(thm)],[c_154,c_85]) ).
cnf(c_1422,plain,
sdtasdt0(xz,xc) = sdtasdt0(xc,xz),
inference(resolve,[status(thm)],[c_1510,c_76]) ).
cnf(c_1511,plain,
( sdtasdt0(A,xz) = sdtasdt0(xz,A)
| ~ aElement0(A) ),
inference(resolve,[status(thm)],[c_154,c_76]) ).
cnf(c_1512,plain,
sdtasdt0(xu,xz) = sdtasdt0(xz,xu),
inference(resolve,[status(thm)],[c_1511,c_75]) ).
cnf(c_1432,plain,
sdtasdt0(xz,xu) = sdtasdt0(xu,xz),
inference(copy,[status(thm)],[c_1512]) ).
cnf(c_1513,plain,
sdtasdt0(sdtasdt0(xc,xz),xu) = sdtasdt0(xz,sdtasdt0(xc,xu)),
inference(paramod,[status(thm)],[c_1422,c_1286]) ).
cnf(c_1514,plain,
sdtasdt0(xc,sdtasdt0(xz,xu)) = sdtasdt0(xz,sdtasdt0(xc,xu)),
inference(paramod,[status(thm)],[c_1196,c_1513]) ).
cnf(c_1515,plain,
sdtasdt0(xc,sdtasdt0(xu,xz)) = sdtasdt0(xz,sdtasdt0(xc,xu)),
inference(paramod,[status(thm)],[c_1432,c_1514]) ).
cnf(c_1516,plain,
sdtasdt0(xz,sdtasdt0(xc,xu)) = sdtasdt0(xc,sdtasdt0(xu,xz)),
inference(copy,[status(thm)],[c_1515]) ).
cnf(c_1504,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_182,c_1516]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG104+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/5.37 % Computer : n003.cluster.edu
% 0.11/5.37 % Model : x86_64 x86_64
% 0.11/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.37 % Memory : 8046.5625MB
% 0.11/5.37 % OS : Linux 6.8.0-71-generic
% 0.11/5.37 % CPULimit : 300
% 0.11/5.37 % WCLimit : 300
% 0.11/5.37 % DateTime : Sat Sep 26 06:07:59 UTC 2026
% 0.11/5.38 % CPUTime :
% 0.11/5.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/5.38 % Process 2194872 was started by sandbox on n003,
% 0.11/5.38 % Sat Sep 26 06:07:59 2026
% 0.11/5.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/5.39
% 0.11/5.39 % From the command line: assign(max_seconds, 300).
% 0.15/5.57
% 0.15/5.57 % SZS status Theorem for theBenchmark
% 0.15/5.57
% 0.15/5.57 % Proof 1 at 0.13 (+ 0.04) seconds.
% 0.15/5.57 % Length of proof is 20.
% 0.15/5.57 % Level of proof is 4.
% 0.15/5.57 % Maximum clause weight is 42.000.
% 0.15/5.57 % Given clauses 80.
% 0.15/5.57
% 0.15/5.57 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------