%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN013-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n001.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 09:36:15 AM UTC 2026
% Result : Unsatisfiable 0.10s 0.38s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 53
% Number of leaves : 16
% Syntax : Number of formulae : 123 ( 20 unt; 0 def)
% Number of atoms : 376 ( 237 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 347 ( 94 ~; 253 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-1 aty)
% Number of variables : 53 ( 0 sgn 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(c_1,axiom,
m != n,
file('theBenchmark.p',c_1) ).
cnf(c_1_001,plain,
m != n,
inference(clausify,[status(thm)],[c_1]) ).
cnf(c_2,plain,
n != m,
inference(copy,[status(thm)],[c_1]) ).
fof(c_2_002,axiom,
n != k,
file('theBenchmark.p',c_2) ).
cnf(c_3,plain,
n != k,
inference(clausify,[status(thm)],[c_2]) ).
cnf(c_4,plain,
k != n,
inference(copy,[status(thm)],[c_3]) ).
fof(c_3_003,axiom,
k != m,
file('theBenchmark.p',c_3) ).
cnf(c_5,plain,
k != m,
inference(clausify,[status(thm)],[c_3]) ).
fof(c_4_004,axiom,
! [VAR_0] :
( f(VAR_0) != m
| ~ element(VAR_0,m)
| VAR_0 = m ),
file('theBenchmark.p',c_4) ).
cnf(c_6,plain,
( f(A) != m
| ~ element(A,m)
| A = m ),
inference(clausify,[status(thm)],[c_4]) ).
cnf(c_7,plain,
( f(A) != m
| ~ element(A,m)
| m = A ),
inference(copy,[status(thm)],[c_6]) ).
fof(c_5_005,axiom,
! [VAR_0] :
( f(VAR_0) != VAR_0
| ~ element(VAR_0,m)
| VAR_0 = m ),
file('theBenchmark.p',c_5) ).
cnf(c_8,plain,
( f(A) != A
| ~ element(A,m)
| A = m ),
inference(clausify,[status(thm)],[c_5]) ).
cnf(c_9,plain,
( f(A) != A
| ~ element(A,m)
| m = A ),
inference(copy,[status(thm)],[c_8]) ).
fof(c_6_006,axiom,
! [VAR_0] :
( element(VAR_0,f(VAR_0))
| ~ element(VAR_0,m)
| VAR_0 = m ),
file('theBenchmark.p',c_6) ).
cnf(c_10,plain,
( element(A,f(A))
| ~ element(A,m)
| A = m ),
inference(clausify,[status(thm)],[c_6]) ).
cnf(c_11,plain,
( element(A,f(A))
| ~ element(A,m)
| m = A ),
inference(copy,[status(thm)],[c_10]) ).
fof(c_7_007,axiom,
! [VAR_0] :
( element(f(VAR_0),VAR_0)
| ~ element(VAR_0,m)
| VAR_0 = m ),
file('theBenchmark.p',c_7) ).
cnf(c_12,plain,
( element(f(A),A)
| ~ element(A,m)
| A = m ),
inference(clausify,[status(thm)],[c_7]) ).
cnf(c_13,plain,
( element(f(A),A)
| ~ element(A,m)
| m = A ),
inference(copy,[status(thm)],[c_12]) ).
fof(c_8_008,axiom,
! [VAR_0,VAR_1] :
( ~ element(VAR_1,VAR_0)
| ~ element(VAR_0,VAR_1)
| VAR_1 = VAR_0
| VAR_1 = m
| element(VAR_0,m)
| VAR_0 = m ),
file('theBenchmark.p',c_8) ).
cnf(c_14,plain,
( ~ element(B,A)
| ~ element(A,B)
| B = A
| B = m
| element(A,m)
| A = m ),
inference(clausify,[status(thm)],[c_8]) ).
cnf(c_154,plain,
( ~ element(B,A)
| ~ element(A,B)
| B = A
| B = m
| element(A,m)
| m = A ),
inference(copy,[status(thm)],[c_14]) ).
cnf(c_15,plain,
( ~ element(B,A)
| ~ element(A,B)
| B = A
| m = B
| element(A,m)
| m = A ),
inference(copy,[status(thm)],[c_154]) ).
fof(c_9_009,axiom,
! [VAR_0] :
( g(VAR_0) != n
| element(VAR_0,n)
| VAR_0 = n ),
file('theBenchmark.p',c_9) ).
cnf(c_16,plain,
( g(A) != n
| element(A,n)
| A = n ),
inference(clausify,[status(thm)],[c_9]) ).
cnf(c_17,plain,
( g(A) != n
| element(A,n)
| n = A ),
inference(copy,[status(thm)],[c_16]) ).
fof(c_10_010,axiom,
! [VAR_0] :
( g(VAR_0) != VAR_0
| element(VAR_0,n)
| VAR_0 = n ),
file('theBenchmark.p',c_10) ).
cnf(c_18,plain,
( g(A) != A
| element(A,n)
| A = n ),
inference(clausify,[status(thm)],[c_10]) ).
cnf(c_19,plain,
( g(A) != A
| element(A,n)
| n = A ),
inference(copy,[status(thm)],[c_18]) ).
fof(c_11_011,axiom,
! [VAR_0] :
( element(VAR_0,g(VAR_0))
| element(VAR_0,n)
| VAR_0 = n ),
file('theBenchmark.p',c_11) ).
cnf(c_20,plain,
( element(A,g(A))
| element(A,n)
| A = n ),
inference(clausify,[status(thm)],[c_11]) ).
cnf(c_21,plain,
( element(A,g(A))
| element(A,n)
| n = A ),
inference(copy,[status(thm)],[c_20]) ).
fof(c_12_012,axiom,
! [VAR_0] :
( element(g(VAR_0),VAR_0)
| element(VAR_0,n)
| VAR_0 = n ),
file('theBenchmark.p',c_12) ).
cnf(c_22,plain,
( element(g(A),A)
| element(A,n)
| A = n ),
inference(clausify,[status(thm)],[c_12]) ).
cnf(c_23,plain,
( element(g(A),A)
| element(A,n)
| n = A ),
inference(copy,[status(thm)],[c_22]) ).
fof(c_13_013,axiom,
! [VAR_0,VAR_1] :
( ~ element(VAR_1,VAR_0)
| ~ element(VAR_0,VAR_1)
| VAR_1 = VAR_0
| VAR_1 = n
| ~ element(VAR_0,n)
| VAR_0 = n ),
file('theBenchmark.p',c_13) ).
cnf(c_24,plain,
( ~ element(B,A)
| ~ element(A,B)
| B = A
| B = n
| ~ element(A,n)
| A = n ),
inference(clausify,[status(thm)],[c_13]) ).
cnf(c_155,plain,
( ~ element(B,A)
| ~ element(A,B)
| B = A
| B = n
| ~ element(A,n)
| n = A ),
inference(copy,[status(thm)],[c_24]) ).
cnf(c_25,plain,
( ~ element(B,A)
| ~ element(A,B)
| B = A
| n = B
| ~ element(A,n)
| n = A ),
inference(copy,[status(thm)],[c_155]) ).
fof(c_14_014,axiom,
! [VAR_0] :
( element(VAR_0,k)
| VAR_0 != m
| VAR_0 = k ),
file('theBenchmark.p',c_14) ).
cnf(c_26,plain,
( element(A,k)
| A != m
| A = k ),
inference(clausify,[status(thm)],[c_14]) ).
cnf(c_156,plain,
( element(A,k)
| A != m
| k = A ),
inference(copy,[status(thm)],[c_26]) ).
cnf(c_27,plain,
( element(A,k)
| m != A
| k = A ),
inference(copy,[status(thm)],[c_156]) ).
fof(c_15_015,axiom,
! [VAR_0] :
( element(VAR_0,k)
| VAR_0 != n
| VAR_0 = k ),
file('theBenchmark.p',c_15) ).
cnf(c_28,plain,
( element(A,k)
| A != n
| A = k ),
inference(clausify,[status(thm)],[c_15]) ).
cnf(c_157,plain,
( element(A,k)
| A != n
| k = A ),
inference(copy,[status(thm)],[c_28]) ).
cnf(c_29,plain,
( element(A,k)
| n != A
| k = A ),
inference(copy,[status(thm)],[c_157]) ).
fof(c_16_016,axiom,
! [VAR_0] :
( ~ element(VAR_0,k)
| VAR_0 = n
| VAR_0 = m
| VAR_0 = k ),
file('theBenchmark.p',c_16) ).
cnf(c_30,plain,
( ~ element(A,k)
| A = n
| A = m
| A = k ),
inference(clausify,[status(thm)],[c_16]) ).
cnf(c_158,plain,
( ~ element(A,k)
| A = n
| A = m
| k = A ),
inference(copy,[status(thm)],[c_30]) ).
cnf(c_159,plain,
( ~ element(A,k)
| A = n
| m = A
| k = A ),
inference(copy,[status(thm)],[c_158]) ).
cnf(c_31,plain,
( ~ element(A,k)
| n = A
| m = A
| k = A ),
inference(copy,[status(thm)],[c_159]) ).
cnf(c_160,plain,
( element(m,k)
| k = m ),
inference(xxres,[status(thm)],[c_27]) ).
cnf(c_42,plain,
element(m,k),
inference(resolve,[status(thm)],[c_5,c_160]) ).
cnf(c_161,plain,
( element(n,k)
| k = n ),
inference(xxres,[status(thm)],[c_29]) ).
cnf(c_43,plain,
element(n,k),
inference(resolve,[status(thm)],[c_4,c_161]) ).
cnf(c_162,plain,
( element(k,n)
| n = k
| n = g(k)
| m = g(k)
| k = g(k) ),
inference(resolve,[status(thm)],[c_31,c_23]) ).
cnf(c_163,plain,
( element(k,n)
| n = k
| n = g(k)
| m = g(k)
| g(k) = k ),
inference(copy,[status(thm)],[c_162]) ).
cnf(c_164,plain,
( element(k,n)
| n = k
| n = g(k)
| g(k) = m
| g(k) = k ),
inference(copy,[status(thm)],[c_163]) ).
cnf(c_165,plain,
( element(k,n)
| n = k
| g(k) = n
| g(k) = m
| g(k) = k ),
inference(copy,[status(thm)],[c_164]) ).
cnf(c_166,plain,
( element(k,n)
| k = n
| g(k) = n
| g(k) = m
| g(k) = k ),
inference(copy,[status(thm)],[c_165]) ).
cnf(c_44,plain,
( element(k,n)
| g(k) = n
| g(k) = m
| g(k) = k ),
inference(resolve,[status(thm)],[c_4,c_166]) ).
cnf(c_167,plain,
( ~ element(k,m)
| m = k
| n = m
| ~ element(k,n)
| n = k ),
inference(resolve,[status(thm)],[c_42,c_25]) ).
cnf(c_168,plain,
( ~ element(k,m)
| m = k
| n = m
| ~ element(k,n)
| k = n ),
inference(copy,[status(thm)],[c_167]) ).
cnf(c_169,plain,
( ~ element(k,m)
| k = m
| n = m
| ~ element(k,n)
| k = n ),
inference(copy,[status(thm)],[c_168]) ).
cnf(c_170,plain,
( ~ element(k,m)
| k = m
| n = m
| ~ element(k,n) ),
inference(resolve,[status(thm)],[c_4,c_169]) ).
cnf(c_171,plain,
( ~ element(k,m)
| k = m
| ~ element(k,n) ),
inference(resolve,[status(thm)],[c_2,c_170]) ).
cnf(c_46,plain,
( ~ element(k,m)
| ~ element(k,n) ),
inference(resolve,[status(thm)],[c_5,c_171]) ).
cnf(c_172,plain,
( ~ element(k,n)
| n = k
| m = n
| element(k,m)
| m = k ),
inference(resolve,[status(thm)],[c_43,c_15]) ).
cnf(c_173,plain,
( ~ element(k,n)
| n = k
| m = n
| element(k,m)
| k = m ),
inference(copy,[status(thm)],[c_172]) ).
cnf(c_174,plain,
( ~ element(k,n)
| n = k
| n = m
| element(k,m)
| k = m ),
inference(copy,[status(thm)],[c_173]) ).
cnf(c_175,plain,
( ~ element(k,n)
| k = n
| n = m
| element(k,m)
| k = m ),
inference(copy,[status(thm)],[c_174]) ).
cnf(c_176,plain,
( ~ element(k,n)
| k = n
| n = m
| element(k,m) ),
inference(resolve,[status(thm)],[c_5,c_175]) ).
cnf(c_177,plain,
( ~ element(k,n)
| k = n
| element(k,m) ),
inference(resolve,[status(thm)],[c_2,c_176]) ).
cnf(c_48,plain,
( ~ element(k,n)
| element(k,m) ),
inference(resolve,[status(thm)],[c_4,c_177]) ).
cnf(c_60,plain,
( element(k,m)
| g(k) = n
| g(k) = m
| g(k) = k ),
inference(resolve,[status(thm)],[c_44,c_48]) ).
cnf(c_61,plain,
( ~ element(k,m)
| g(k) = n
| g(k) = m
| g(k) = k ),
inference(resolve,[status(thm)],[c_44,c_46]) ).
cnf(c_178,plain,
( g(k) = n
| g(k) = m
| g(k) = k
| g(k) = n
| g(k) = m
| g(k) = k ),
inference(resolve,[status(thm)],[c_61,c_60]) ).
cnf(c_179,plain,
( g(k) = n
| g(k) = m
| g(k) = n
| g(k) = m
| g(k) = k ),
inference(copy,[status(thm)],[c_178]) ).
cnf(c_180,plain,
( g(k) = n
| g(k) = n
| g(k) = m
| g(k) = k ),
inference(copy,[status(thm)],[c_179]) ).
cnf(c_73,plain,
( g(k) = n
| g(k) = m
| g(k) = k ),
inference(copy,[status(thm)],[c_180]) ).
cnf(c_181,plain,
( element(k,n)
| n = k
| g(k) = n
| g(k) = m ),
inference(resolve,[status(thm)],[c_73,c_19]) ).
cnf(c_182,plain,
( element(k,n)
| k = n
| g(k) = n
| g(k) = m ),
inference(copy,[status(thm)],[c_181]) ).
cnf(c_75,plain,
( element(k,n)
| g(k) = n
| g(k) = m ),
inference(resolve,[status(thm)],[c_4,c_182]) ).
cnf(c_77,plain,
( element(k,m)
| g(k) = n
| g(k) = m ),
inference(resolve,[status(thm)],[c_75,c_48]) ).
cnf(c_78,plain,
( ~ element(k,m)
| g(k) = n
| g(k) = m ),
inference(resolve,[status(thm)],[c_75,c_46]) ).
cnf(c_183,plain,
( g(k) = n
| g(k) = m
| g(k) = n
| g(k) = m ),
inference(resolve,[status(thm)],[c_78,c_77]) ).
cnf(c_184,plain,
( g(k) = n
| g(k) = n
| g(k) = m ),
inference(copy,[status(thm)],[c_183]) ).
cnf(c_95,plain,
( g(k) = n
| g(k) = m ),
inference(copy,[status(thm)],[c_184]) ).
cnf(c_185,plain,
( element(k,n)
| n = k
| g(k) = m ),
inference(resolve,[status(thm)],[c_95,c_17]) ).
cnf(c_186,plain,
( element(k,n)
| k = n
| g(k) = m ),
inference(copy,[status(thm)],[c_185]) ).
cnf(c_96,plain,
( element(k,n)
| g(k) = m ),
inference(resolve,[status(thm)],[c_4,c_186]) ).
cnf(c_99,plain,
( element(k,m)
| g(k) = m ),
inference(resolve,[status(thm)],[c_96,c_48]) ).
cnf(c_100,plain,
( ~ element(k,m)
| g(k) = m ),
inference(resolve,[status(thm)],[c_96,c_46]) ).
cnf(c_187,plain,
( g(k) = m
| g(k) = m ),
inference(resolve,[status(thm)],[c_100,c_99]) ).
cnf(c_116,plain,
g(k) = m,
inference(copy,[status(thm)],[c_187]) ).
cnf(c_188,plain,
( element(k,m)
| element(k,n)
| n = k ),
inference(paramod,[status(thm)],[c_116,c_21]) ).
cnf(c_189,plain,
( element(k,m)
| element(k,n)
| k = n ),
inference(copy,[status(thm)],[c_188]) ).
cnf(c_117,plain,
( element(k,m)
| element(k,n) ),
inference(resolve,[status(thm)],[c_4,c_189]) ).
cnf(c_190,plain,
( element(k,m)
| element(k,m) ),
inference(resolve,[status(thm)],[c_117,c_48]) ).
cnf(c_119,plain,
element(k,m),
inference(copy,[status(thm)],[c_190]) ).
cnf(c_121,plain,
~ element(k,n),
inference(resolve,[status(thm)],[c_119,c_46]) ).
cnf(c_191,plain,
( element(f(k),k)
| m = k ),
inference(resolve,[status(thm)],[c_119,c_13]) ).
cnf(c_192,plain,
( element(f(k),k)
| k = m ),
inference(copy,[status(thm)],[c_191]) ).
cnf(c_148,plain,
element(f(k),k),
inference(resolve,[status(thm)],[c_5,c_192]) ).
cnf(c_193,plain,
( element(k,f(k))
| m = k ),
inference(resolve,[status(thm)],[c_119,c_11]) ).
cnf(c_194,plain,
( element(k,f(k))
| k = m ),
inference(copy,[status(thm)],[c_193]) ).
cnf(c_149,plain,
element(k,f(k)),
inference(resolve,[status(thm)],[c_5,c_194]) ).
cnf(c_195,plain,
( f(k) != k
| m = k ),
inference(resolve,[status(thm)],[c_119,c_9]) ).
cnf(c_196,plain,
( f(k) != k
| k = m ),
inference(copy,[status(thm)],[c_195]) ).
cnf(c_150,plain,
f(k) != k,
inference(resolve,[status(thm)],[c_5,c_196]) ).
cnf(c_197,plain,
( f(k) != m
| m = k ),
inference(resolve,[status(thm)],[c_119,c_7]) ).
cnf(c_198,plain,
( f(k) != m
| k = m ),
inference(copy,[status(thm)],[c_197]) ).
cnf(c_151,plain,
f(k) != m,
inference(resolve,[status(thm)],[c_5,c_198]) ).
cnf(c_199,plain,
( n = f(k)
| m = f(k)
| k = f(k) ),
inference(resolve,[status(thm)],[c_148,c_31]) ).
cnf(c_200,plain,
( n = f(k)
| m = f(k)
| f(k) = k ),
inference(copy,[status(thm)],[c_199]) ).
cnf(c_201,plain,
( n = f(k)
| f(k) = m
| f(k) = k ),
inference(copy,[status(thm)],[c_200]) ).
cnf(c_202,plain,
( f(k) = n
| f(k) = m
| f(k) = k ),
inference(copy,[status(thm)],[c_201]) ).
cnf(c_203,plain,
( f(k) = n
| f(k) = m ),
inference(resolve,[status(thm)],[c_150,c_202]) ).
cnf(c_152,plain,
f(k) = n,
inference(resolve,[status(thm)],[c_151,c_203]) ).
cnf(c_204,plain,
element(k,n),
inference(paramod,[status(thm)],[c_152,c_149]) ).
cnf(c_153,plain,
$false,
inference(resolve,[status(thm)],[c_121,c_204]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN013-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n001.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Sat Sep 26 17:09:58 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.35 % Process 2276327 was started by sandbox on n001,
% 0.10/0.35 % Sat Sep 26 17:09:58 2026
% 0.10/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.36
% 0.10/0.36 % From the command line: assign(max_seconds, 300).
% 0.10/0.38
% 0.10/0.38 % SZS status Unsatisfiable for theBenchmark
% 0.10/0.38
% 0.10/0.38 % Proof 1 at 0.02 (+ 0.00) seconds.
% 0.10/0.38 % Length of proof is 56.
% 0.10/0.38 % Level of proof is 16.
% 0.10/0.38 % Maximum clause weight is 18.000.
% 0.10/0.38 % Given clauses 56.
% 0.10/0.38
% 0.10/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------