%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM422+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 : n016.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 08:16:57 AM UTC 2026
% Result : Theorem 1.49s 0.60s
% Output : CNFRefutation 1.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 13
% Syntax : Number of formulae : 68 ( 36 unt; 0 def)
% Number of atoms : 126 ( 58 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 100 ( 42 ~; 38 |; 11 &)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 53 ( 0 sgn 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mIntNeg,axiom,
! [W0] :
( aInteger0(W0)
=> aInteger0(smndt0(W0)) ),
file('theBenchmark.p',mIntNeg) ).
fof(mIntMult,axiom,
! [W0,W1] :
( ( aInteger0(W1)
& aInteger0(W0) )
=> aInteger0(sdtasdt0(W0,W1)) ),
file('theBenchmark.p',mIntMult) ).
fof(mAddAsso,axiom,
! [W0,W1,W2] :
( ( aInteger0(W2)
& aInteger0(W1)
& aInteger0(W0) )
=> sdtpldt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtpldt0(W0,W1),W2) ),
file('theBenchmark.p',mAddAsso) ).
fof(mAddZero,axiom,
! [W0] :
( aInteger0(W0)
=> ( W0 = sdtpldt0(sz00,W0)
& sdtpldt0(W0,sz00) = W0 ) ),
file('theBenchmark.p',mAddZero) ).
fof(mAddNeg,axiom,
! [W0] :
( aInteger0(W0)
=> ( sz00 = sdtpldt0(smndt0(W0),W0)
& sdtpldt0(W0,smndt0(W0)) = sz00 ) ),
file('theBenchmark.p',mAddNeg) ).
fof(mMulComm,axiom,
! [W0,W1] :
( ( aInteger0(W1)
& aInteger0(W0) )
=> sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ),
file('theBenchmark.p',mMulComm) ).
fof(mMulOne,axiom,
! [W0] :
( aInteger0(W0)
=> ( W0 = sdtasdt0(sz10,W0)
& sdtasdt0(W0,sz10) = W0 ) ),
file('theBenchmark.p',mMulOne) ).
fof(mDistrib,axiom,
! [W0,W1,W2] :
( ( aInteger0(W2)
& aInteger0(W1)
& aInteger0(W0) )
=> ( sdtasdt0(sdtpldt0(W0,W1),W2) = sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2))
& sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) ) ),
file('theBenchmark.p',mDistrib) ).
fof(mMulZero,axiom,
! [W0] :
( aInteger0(W0)
=> ( sz00 = sdtasdt0(sz00,W0)
& sdtasdt0(W0,sz00) = sz00 ) ),
file('theBenchmark.p',mMulZero) ).
fof(m__,conjecture,
sdtasdt0(smndt0(sz10),xa) = smndt0(xa),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
sdtasdt0(smndt0(sz10),xa) != smndt0(xa),
inference(assume_negation,[status(cth)],[m__]) ).
fof(mIntZero,axiom,
aInteger0(sz00),
file('theBenchmark.p',mIntZero) ).
cnf(c_15,plain,
aInteger0(sz00),
inference(clausify,[status(thm)],[mIntZero]) ).
fof(mIntOne,axiom,
aInteger0(sz10),
file('theBenchmark.p',mIntOne) ).
cnf(c_16,plain,
aInteger0(sz10),
inference(clausify,[status(thm)],[mIntOne]) ).
cnf(c_17,plain,
( aInteger0(smndt0(A))
| ~ aInteger0(A) ),
inference(clausify,[status(thm)],[mIntNeg]) ).
cnf(c_19,plain,
( aInteger0(sdtasdt0(A,B))
| ~ aInteger0(B)
| ~ aInteger0(A) ),
inference(clausify,[status(thm)],[mIntMult]) ).
cnf(c_20,plain,
( sdtpldt0(sdtpldt0(A,B),C) = sdtpldt0(A,sdtpldt0(B,C))
| ~ aInteger0(C)
| ~ aInteger0(B)
| ~ aInteger0(A) ),
inference(clausify,[status(thm)],[mAddAsso]) ).
cnf(c_22,plain,
( sdtpldt0(A,sz00) = A
| ~ aInteger0(A) ),
inference(clausify,[status(thm)],[mAddZero]) ).
cnf(c_23,plain,
( sdtpldt0(sz00,A) = A
| ~ aInteger0(A) ),
inference(clausify,[status(thm)],[mAddZero]) ).
cnf(c_24,plain,
( sdtpldt0(A,smndt0(A)) = sz00
| ~ aInteger0(A) ),
inference(clausify,[status(thm)],[mAddNeg]) ).
cnf(c_25,plain,
( sdtpldt0(smndt0(A),A) = sz00
| ~ aInteger0(A) ),
inference(clausify,[status(thm)],[mAddNeg]) ).
cnf(c_27,plain,
( sdtasdt0(B,A) = sdtasdt0(A,B)
| ~ aInteger0(B)
| ~ aInteger0(A) ),
inference(clausify,[status(thm)],[mMulComm]) ).
cnf(c_28,plain,
( sdtasdt0(A,sz10) = A
| ~ aInteger0(A) ),
inference(clausify,[status(thm)],[mMulOne]) ).
cnf(c_30,plain,
( sdtasdt0(A,sdtpldt0(B,C)) = sdtpldt0(sdtasdt0(A,B),sdtasdt0(A,C))
| ~ aInteger0(C)
| ~ aInteger0(B)
| ~ aInteger0(A) ),
inference(clausify,[status(thm)],[mDistrib]) ).
cnf(c_31,plain,
( sdtpldt0(sdtasdt0(A,B),sdtasdt0(A,C)) = sdtasdt0(A,sdtpldt0(B,C))
| ~ aInteger0(C)
| ~ aInteger0(B)
| ~ aInteger0(A) ),
inference(copy,[status(thm)],[c_30]) ).
cnf(c_32,plain,
( sdtasdt0(sdtpldt0(A,B),C) = sdtpldt0(sdtasdt0(A,C),sdtasdt0(B,C))
| ~ aInteger0(C)
| ~ aInteger0(B)
| ~ aInteger0(A) ),
inference(clausify,[status(thm)],[mDistrib]) ).
cnf(c_33,plain,
( sdtpldt0(sdtasdt0(A,C),sdtasdt0(B,C)) = sdtasdt0(sdtpldt0(A,B),C)
| ~ aInteger0(C)
| ~ aInteger0(B)
| ~ aInteger0(A) ),
inference(copy,[status(thm)],[c_32]) ).
cnf(c_34,plain,
( sdtasdt0(A,sz00) = sz00
| ~ aInteger0(A) ),
inference(clausify,[status(thm)],[mMulZero]) ).
cnf(c_35,plain,
( sdtasdt0(sz00,A) = sz00
| ~ aInteger0(A) ),
inference(clausify,[status(thm)],[mMulZero]) ).
fof(m__446,axiom,
aInteger0(xa),
file('theBenchmark.p',m__446) ).
cnf(c_36,plain,
aInteger0(xa),
inference(clausify,[status(thm)],[m__446]) ).
cnf(c_37,negated_conjecture,
sdtasdt0(smndt0(sz10),xa) != smndt0(xa),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_38,negated_conjecture,
smndt0(xa) != sdtasdt0(smndt0(sz10),xa),
inference(copy,[status(thm)],[c_37]) ).
cnf(c_39,plain,
aInteger0(smndt0(sz10)),
inference(resolve,[status(thm)],[c_17,c_16]) ).
cnf(c_67,plain,
sdtpldt0(sz10,smndt0(sz10)) = sz00,
inference(resolve,[status(thm)],[c_24,c_16]) ).
cnf(c_98,plain,
sdtasdt0(xa,sz00) = sz00,
inference(resolve,[status(thm)],[c_34,c_36]) ).
cnf(c_136,plain,
sdtasdt0(xa,sz10) = xa,
inference(resolve,[status(thm)],[c_28,c_36]) ).
cnf(c_142,plain,
sdtpldt0(smndt0(xa),xa) = sz00,
inference(resolve,[status(thm)],[c_25,c_36]) ).
cnf(c_144,plain,
sdtpldt0(sz00,xa) = xa,
inference(resolve,[status(thm)],[c_23,c_36]) ).
cnf(c_161,plain,
aInteger0(smndt0(xa)),
inference(resolve,[status(thm)],[c_17,c_36]) ).
cnf(c_187,plain,
sdtasdt0(sz00,smndt0(sz10)) = sz00,
inference(resolve,[status(thm)],[c_35,c_39]) ).
cnf(c_1187,plain,
( sdtpldt0(sdtasdt0(sz00,B),sdtasdt0(A,B)) = sdtasdt0(sdtpldt0(sz00,A),B)
| ~ aInteger0(B)
| ~ aInteger0(A) ),
inference(resolve,[status(thm)],[c_33,c_15]) ).
cnf(c_1188,plain,
( sdtpldt0(sdtasdt0(sz00,A),sdtasdt0(xa,A)) = sdtasdt0(sdtpldt0(sz00,xa),A)
| ~ aInteger0(A) ),
inference(resolve,[status(thm)],[c_1187,c_36]) ).
cnf(c_1189,plain,
sdtpldt0(sdtasdt0(sz00,smndt0(sz10)),sdtasdt0(xa,smndt0(sz10))) = sdtasdt0(sdtpldt0(sz00,xa),smndt0(sz10)),
inference(resolve,[status(thm)],[c_1188,c_39]) ).
cnf(c_1190,plain,
sdtpldt0(sz00,sdtasdt0(xa,smndt0(sz10))) = sdtasdt0(sdtpldt0(sz00,xa),smndt0(sz10)),
inference(paramod,[status(thm)],[c_187,c_1189]) ).
cnf(c_202,plain,
sdtpldt0(sz00,sdtasdt0(xa,smndt0(sz10))) = sdtasdt0(xa,smndt0(sz10)),
inference(paramod,[status(thm)],[c_144,c_1190]) ).
cnf(c_1191,plain,
( sdtpldt0(sdtasdt0(xa,A),sdtasdt0(xa,B)) = sdtasdt0(xa,sdtpldt0(A,B))
| ~ aInteger0(B)
| ~ aInteger0(A) ),
inference(resolve,[status(thm)],[c_31,c_36]) ).
cnf(c_1192,plain,
( sdtpldt0(sdtasdt0(xa,sz10),sdtasdt0(xa,A)) = sdtasdt0(xa,sdtpldt0(sz10,A))
| ~ aInteger0(A) ),
inference(resolve,[status(thm)],[c_1191,c_16]) ).
cnf(c_1193,plain,
sdtpldt0(sdtasdt0(xa,sz10),sdtasdt0(xa,smndt0(sz10))) = sdtasdt0(xa,sdtpldt0(sz10,smndt0(sz10))),
inference(resolve,[status(thm)],[c_1192,c_39]) ).
cnf(c_1194,plain,
sdtpldt0(xa,sdtasdt0(xa,smndt0(sz10))) = sdtasdt0(xa,sdtpldt0(sz10,smndt0(sz10))),
inference(paramod,[status(thm)],[c_136,c_1193]) ).
cnf(c_1195,plain,
sdtpldt0(xa,sdtasdt0(xa,smndt0(sz10))) = sdtasdt0(xa,sz00),
inference(paramod,[status(thm)],[c_67,c_1194]) ).
cnf(c_229,plain,
sdtpldt0(xa,sdtasdt0(xa,smndt0(sz10))) = sz00,
inference(paramod,[status(thm)],[c_98,c_1195]) ).
cnf(c_1196,plain,
( sdtasdt0(A,xa) = sdtasdt0(xa,A)
| ~ aInteger0(A) ),
inference(resolve,[status(thm)],[c_27,c_36]) ).
cnf(c_259,plain,
sdtasdt0(smndt0(sz10),xa) = sdtasdt0(xa,smndt0(sz10)),
inference(resolve,[status(thm)],[c_1196,c_39]) ).
cnf(c_1197,plain,
( aInteger0(sdtasdt0(xa,A))
| ~ aInteger0(A) ),
inference(resolve,[status(thm)],[c_19,c_36]) ).
cnf(c_300,plain,
aInteger0(sdtasdt0(xa,smndt0(sz10))),
inference(resolve,[status(thm)],[c_1197,c_39]) ).
cnf(c_319,negated_conjecture,
smndt0(xa) != sdtasdt0(xa,smndt0(sz10)),
inference(paramod,[status(thm)],[c_259,c_38]) ).
cnf(c_609,plain,
sdtpldt0(smndt0(xa),sz00) = smndt0(xa),
inference(resolve,[status(thm)],[c_22,c_161]) ).
cnf(c_1198,plain,
( sdtpldt0(sdtpldt0(smndt0(xa),A),B) = sdtpldt0(smndt0(xa),sdtpldt0(A,B))
| ~ aInteger0(B)
| ~ aInteger0(A) ),
inference(resolve,[status(thm)],[c_20,c_161]) ).
cnf(c_1199,plain,
( sdtpldt0(sdtpldt0(smndt0(xa),xa),A) = sdtpldt0(smndt0(xa),sdtpldt0(xa,A))
| ~ aInteger0(A) ),
inference(resolve,[status(thm)],[c_1198,c_36]) ).
cnf(c_1200,plain,
sdtpldt0(sdtpldt0(smndt0(xa),xa),sdtasdt0(xa,smndt0(sz10))) = sdtpldt0(smndt0(xa),sdtpldt0(xa,sdtasdt0(xa,smndt0(sz10)))),
inference(resolve,[status(thm)],[c_1199,c_300]) ).
cnf(c_1201,plain,
sdtpldt0(sz00,sdtasdt0(xa,smndt0(sz10))) = sdtpldt0(smndt0(xa),sdtpldt0(xa,sdtasdt0(xa,smndt0(sz10)))),
inference(paramod,[status(thm)],[c_142,c_1200]) ).
cnf(c_1202,plain,
sdtasdt0(xa,smndt0(sz10)) = sdtpldt0(smndt0(xa),sdtpldt0(xa,sdtasdt0(xa,smndt0(sz10)))),
inference(paramod,[status(thm)],[c_202,c_1201]) ).
cnf(c_1203,plain,
sdtasdt0(xa,smndt0(sz10)) = sdtpldt0(smndt0(xa),sz00),
inference(paramod,[status(thm)],[c_229,c_1202]) ).
cnf(c_1204,plain,
sdtasdt0(xa,smndt0(sz10)) = smndt0(xa),
inference(paramod,[status(thm)],[c_609,c_1203]) ).
cnf(c_1185,plain,
smndt0(xa) = sdtasdt0(xa,smndt0(sz10)),
inference(copy,[status(thm)],[c_1204]) ).
cnf(c_1186,plain,
$false,
inference(resolve,[status(thm)],[c_1185,c_319]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM422+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n016.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sat Sep 26 02:45:30 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.38 % Process 4023438 was started by sandbox on n016,
% 0.11/0.38 % Sat Sep 26 02:45:30 2026
% 0.11/0.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/0.38
% 0.11/0.38 % From the command line: assign(max_seconds, 300).
% 1.49/0.60
% 1.49/0.60 % SZS status Theorem for theBenchmark
% 1.49/0.60
% 1.49/0.60 % Proof 1 at 0.13 (+ 0.07) seconds.
% 1.49/0.60 % Length of proof is 46.
% 1.49/0.60 % Level of proof is 6.
% 1.49/0.60 % Maximum clause weight is 27.000.
% 1.49/0.60 % Given clauses 49.
% 1.49/0.60
% 1.49/0.60 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------