%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN014-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/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 0.15s 0.42s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 91
% Number of leaves : 15
% Syntax : Number of formulae : 160 ( 12 unt; 0 def)
% Number of atoms : 613 ( 497 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 535 ( 82 ~; 453 |; 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 : 6 ( 6 usr; 4 con; 0-1 aty)
% Number of variables : 55 ( 0 sgn 14 !; 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,
( m = k
| n = k ),
file('theBenchmark.p',c_2) ).
cnf(c_3,plain,
( m = k
| n = k ),
inference(clausify,[status(thm)],[c_2]) ).
cnf(c_216,plain,
( m = k
| k = n ),
inference(copy,[status(thm)],[c_3]) ).
cnf(c_4,plain,
( k = m
| k = n ),
inference(copy,[status(thm)],[c_216]) ).
fof(c_3_003,axiom,
! [VAR_0] :
( element(VAR_0,j)
| VAR_0 != k
| VAR_0 = j ),
file('theBenchmark.p',c_3) ).
cnf(c_5,plain,
( element(A,j)
| A != k
| A = j ),
inference(clausify,[status(thm)],[c_3]) ).
cnf(c_217,plain,
( element(A,j)
| A != k
| j = A ),
inference(copy,[status(thm)],[c_5]) ).
cnf(c_6,plain,
( element(A,j)
| k != A
| j = A ),
inference(copy,[status(thm)],[c_217]) ).
fof(c_4_004,axiom,
! [VAR_0] :
( ~ element(VAR_0,j)
| VAR_0 = k
| VAR_0 = j ),
file('theBenchmark.p',c_4) ).
cnf(c_7,plain,
( ~ element(A,j)
| A = k
| A = j ),
inference(clausify,[status(thm)],[c_4]) ).
cnf(c_218,plain,
( ~ element(A,j)
| A = k
| j = A ),
inference(copy,[status(thm)],[c_7]) ).
cnf(c_8,plain,
( ~ element(A,j)
| k = A
| j = A ),
inference(copy,[status(thm)],[c_218]) ).
fof(c_5_005,axiom,
! [VAR_0] :
( f(VAR_0) != m
| ~ element(VAR_0,m)
| VAR_0 = m ),
file('theBenchmark.p',c_5) ).
cnf(c_9,plain,
( f(A) != m
| ~ element(A,m)
| A = m ),
inference(clausify,[status(thm)],[c_5]) ).
cnf(c_10,plain,
( f(A) != m
| ~ element(A,m)
| m = A ),
inference(copy,[status(thm)],[c_9]) ).
fof(c_6_006,axiom,
! [VAR_0] :
( f(VAR_0) != VAR_0
| ~ element(VAR_0,m)
| VAR_0 = m ),
file('theBenchmark.p',c_6) ).
cnf(c_11,plain,
( f(A) != A
| ~ element(A,m)
| A = m ),
inference(clausify,[status(thm)],[c_6]) ).
cnf(c_12,plain,
( f(A) != A
| ~ element(A,m)
| m = A ),
inference(copy,[status(thm)],[c_11]) ).
fof(c_7_007,axiom,
! [VAR_0] :
( element(VAR_0,f(VAR_0))
| ~ element(VAR_0,m)
| VAR_0 = m ),
file('theBenchmark.p',c_7) ).
cnf(c_13,plain,
( element(A,f(A))
| ~ element(A,m)
| A = m ),
inference(clausify,[status(thm)],[c_7]) ).
cnf(c_14,plain,
( element(A,f(A))
| ~ element(A,m)
| m = A ),
inference(copy,[status(thm)],[c_13]) ).
fof(c_8_008,axiom,
! [VAR_0] :
( element(f(VAR_0),VAR_0)
| ~ element(VAR_0,m)
| VAR_0 = m ),
file('theBenchmark.p',c_8) ).
cnf(c_15,plain,
( element(f(A),A)
| ~ element(A,m)
| A = m ),
inference(clausify,[status(thm)],[c_8]) ).
cnf(c_16,plain,
( element(f(A),A)
| ~ element(A,m)
| m = A ),
inference(copy,[status(thm)],[c_15]) ).
fof(c_9_009,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_9) ).
cnf(c_17,plain,
( ~ element(B,A)
| ~ element(A,B)
| B = A
| B = m
| element(A,m)
| A = m ),
inference(clausify,[status(thm)],[c_9]) ).
cnf(c_219,plain,
( ~ element(B,A)
| ~ element(A,B)
| B = A
| B = m
| element(A,m)
| m = A ),
inference(copy,[status(thm)],[c_17]) ).
cnf(c_18,plain,
( ~ element(B,A)
| ~ element(A,B)
| B = A
| m = B
| element(A,m)
| m = A ),
inference(copy,[status(thm)],[c_219]) ).
fof(c_10_010,axiom,
! [VAR_0] :
( g(VAR_0) != n
| element(VAR_0,n)
| VAR_0 = n ),
file('theBenchmark.p',c_10) ).
cnf(c_19,plain,
( g(A) != n
| element(A,n)
| A = n ),
inference(clausify,[status(thm)],[c_10]) ).
cnf(c_20,plain,
( g(A) != n
| element(A,n)
| n = A ),
inference(copy,[status(thm)],[c_19]) ).
fof(c_11_011,axiom,
! [VAR_0] :
( g(VAR_0) != VAR_0
| element(VAR_0,n)
| VAR_0 = n ),
file('theBenchmark.p',c_11) ).
cnf(c_21,plain,
( g(A) != A
| element(A,n)
| A = n ),
inference(clausify,[status(thm)],[c_11]) ).
cnf(c_22,plain,
( g(A) != A
| element(A,n)
| n = A ),
inference(copy,[status(thm)],[c_21]) ).
fof(c_13_012,axiom,
! [VAR_0] :
( element(g(VAR_0),VAR_0)
| element(VAR_0,n)
| VAR_0 = n ),
file('theBenchmark.p',c_13) ).
cnf(c_25,plain,
( element(g(A),A)
| element(A,n)
| A = n ),
inference(clausify,[status(thm)],[c_13]) ).
cnf(c_26,plain,
( element(g(A),A)
| element(A,n)
| n = A ),
inference(copy,[status(thm)],[c_25]) ).
fof(c_15_013,axiom,
! [VAR_0] :
( element(VAR_0,k)
| VAR_0 != m
| VAR_0 = k ),
file('theBenchmark.p',c_15) ).
cnf(c_29,plain,
( element(A,k)
| A != m
| A = k ),
inference(clausify,[status(thm)],[c_15]) ).
cnf(c_220,plain,
( element(A,k)
| A != m
| k = A ),
inference(copy,[status(thm)],[c_29]) ).
cnf(c_30,plain,
( element(A,k)
| m != A
| k = A ),
inference(copy,[status(thm)],[c_220]) ).
fof(c_16_014,axiom,
! [VAR_0] :
( element(VAR_0,k)
| VAR_0 != n
| VAR_0 = k ),
file('theBenchmark.p',c_16) ).
cnf(c_31,plain,
( element(A,k)
| A != n
| A = k ),
inference(clausify,[status(thm)],[c_16]) ).
cnf(c_221,plain,
( element(A,k)
| A != n
| k = A ),
inference(copy,[status(thm)],[c_31]) ).
cnf(c_32,plain,
( element(A,k)
| n != A
| k = A ),
inference(copy,[status(thm)],[c_221]) ).
fof(c_17_015,axiom,
! [VAR_0] :
( ~ element(VAR_0,k)
| VAR_0 = n
| VAR_0 = m
| VAR_0 = k ),
file('theBenchmark.p',c_17) ).
cnf(c_33,plain,
( ~ element(A,k)
| A = n
| A = m
| A = k ),
inference(clausify,[status(thm)],[c_17]) ).
cnf(c_222,plain,
( ~ element(A,k)
| A = n
| A = m
| k = A ),
inference(copy,[status(thm)],[c_33]) ).
cnf(c_223,plain,
( ~ element(A,k)
| A = n
| m = A
| k = A ),
inference(copy,[status(thm)],[c_222]) ).
cnf(c_34,plain,
( ~ element(A,k)
| n = A
| m = A
| k = A ),
inference(copy,[status(thm)],[c_223]) ).
cnf(c_35,plain,
( k = m
| element(n,j)
| j = n ),
inference(resolve,[status(thm)],[c_6,c_4]) ).
cnf(c_224,plain,
( k = g(j)
| j = g(j)
| element(j,n)
| n = j ),
inference(resolve,[status(thm)],[c_26,c_8]) ).
cnf(c_225,plain,
( k = g(j)
| j = g(j)
| element(j,n)
| j = n ),
inference(copy,[status(thm)],[c_224]) ).
cnf(c_226,plain,
( k = g(j)
| g(j) = j
| element(j,n)
| j = n ),
inference(copy,[status(thm)],[c_225]) ).
cnf(c_46,plain,
( g(j) = k
| g(j) = j
| element(j,n)
| j = n ),
inference(copy,[status(thm)],[c_226]) ).
cnf(c_49,plain,
( element(m,k)
| k = m ),
inference(xxres,[status(thm)],[c_30]) ).
cnf(c_50,plain,
( element(n,k)
| k = n ),
inference(xxres,[status(thm)],[c_32]) ).
cnf(c_52,plain,
( ~ element(A,n)
| n = A
| m = A
| k = A
| k = m ),
inference(paramod,[status(thm)],[c_4,c_34]) ).
cnf(c_227,plain,
( element(m,n)
| k = m
| k = m ),
inference(paramod,[status(thm)],[c_4,c_49]) ).
cnf(c_60,plain,
( element(m,n)
| k = m ),
inference(copy,[status(thm)],[c_227]) ).
cnf(c_228,plain,
( g(j) = k
| g(j) = j
| j = n
| n = j
| m = j
| k = j
| k = m ),
inference(resolve,[status(thm)],[c_52,c_46]) ).
cnf(c_229,plain,
( g(j) = k
| g(j) = j
| j = n
| n = j
| m = j
| j = k
| k = m ),
inference(copy,[status(thm)],[c_228]) ).
cnf(c_230,plain,
( g(j) = k
| g(j) = j
| j = n
| n = j
| j = m
| j = k
| k = m ),
inference(copy,[status(thm)],[c_229]) ).
cnf(c_231,plain,
( g(j) = k
| g(j) = j
| j = n
| j = n
| j = m
| j = k
| k = m ),
inference(copy,[status(thm)],[c_230]) ).
cnf(c_74,plain,
( g(j) = k
| g(j) = j
| j = n
| j = m
| j = k
| k = m ),
inference(copy,[status(thm)],[c_231]) ).
cnf(c_232,plain,
( element(j,n)
| n = j
| g(j) = k
| j = n
| j = m
| j = k
| k = m ),
inference(resolve,[status(thm)],[c_74,c_22]) ).
cnf(c_233,plain,
( element(j,n)
| j = n
| g(j) = k
| j = n
| j = m
| j = k
| k = m ),
inference(copy,[status(thm)],[c_232]) ).
cnf(c_83,plain,
( element(j,n)
| g(j) = k
| j = n
| j = m
| j = k
| k = m ),
inference(copy,[status(thm)],[c_233]) ).
cnf(c_234,plain,
( n = j
| m = j
| k = j
| k = m
| g(j) = k
| j = n
| j = m
| j = k
| k = m ),
inference(resolve,[status(thm)],[c_83,c_52]) ).
cnf(c_235,plain,
( n = j
| m = j
| j = k
| k = m
| g(j) = k
| j = n
| j = m
| j = k
| k = m ),
inference(copy,[status(thm)],[c_234]) ).
cnf(c_236,plain,
( n = j
| j = m
| j = k
| k = m
| g(j) = k
| j = n
| j = m
| j = k
| k = m ),
inference(copy,[status(thm)],[c_235]) ).
cnf(c_237,plain,
( j = n
| j = m
| j = k
| k = m
| g(j) = k
| j = n
| j = m
| j = k
| k = m ),
inference(copy,[status(thm)],[c_236]) ).
cnf(c_238,plain,
( j = n
| j = m
| j = k
| g(j) = k
| j = n
| j = m
| j = k
| k = m ),
inference(copy,[status(thm)],[c_237]) ).
cnf(c_239,plain,
( j = n
| j = m
| g(j) = k
| j = n
| j = m
| j = k
| k = m ),
inference(copy,[status(thm)],[c_238]) ).
cnf(c_240,plain,
( j = n
| g(j) = k
| j = n
| j = m
| j = k
| k = m ),
inference(copy,[status(thm)],[c_239]) ).
cnf(c_87,plain,
( g(j) = k
| j = n
| j = m
| j = k
| k = m ),
inference(copy,[status(thm)],[c_240]) ).
cnf(c_241,plain,
( g(j) = n
| j = n
| j = m
| j = k
| k = m
| k = m ),
inference(paramod,[status(thm)],[c_4,c_87]) ).
cnf(c_89,plain,
( g(j) = n
| j = n
| j = m
| j = k
| k = m ),
inference(copy,[status(thm)],[c_241]) ).
cnf(c_242,plain,
( element(j,n)
| n = j
| j = n
| j = m
| j = k
| k = m ),
inference(resolve,[status(thm)],[c_89,c_20]) ).
cnf(c_243,plain,
( element(j,n)
| j = n
| j = n
| j = m
| j = k
| k = m ),
inference(copy,[status(thm)],[c_242]) ).
cnf(c_92,plain,
( element(j,n)
| j = n
| j = m
| j = k
| k = m ),
inference(copy,[status(thm)],[c_243]) ).
cnf(c_244,plain,
( n = j
| m = j
| k = j
| k = m
| j = n
| j = m
| j = k
| k = m ),
inference(resolve,[status(thm)],[c_92,c_52]) ).
cnf(c_245,plain,
( n = j
| m = j
| j = k
| k = m
| j = n
| j = m
| j = k
| k = m ),
inference(copy,[status(thm)],[c_244]) ).
cnf(c_246,plain,
( n = j
| j = m
| j = k
| k = m
| j = n
| j = m
| j = k
| k = m ),
inference(copy,[status(thm)],[c_245]) ).
cnf(c_247,plain,
( j = n
| j = m
| j = k
| k = m
| j = n
| j = m
| j = k
| k = m ),
inference(copy,[status(thm)],[c_246]) ).
cnf(c_248,plain,
( j = n
| j = m
| j = k
| j = n
| j = m
| j = k
| k = m ),
inference(copy,[status(thm)],[c_247]) ).
cnf(c_249,plain,
( j = n
| j = m
| j = n
| j = m
| j = k
| k = m ),
inference(copy,[status(thm)],[c_248]) ).
cnf(c_250,plain,
( j = n
| j = n
| j = m
| j = k
| k = m ),
inference(copy,[status(thm)],[c_249]) ).
cnf(c_96,plain,
( j = n
| j = m
| j = k
| k = m ),
inference(copy,[status(thm)],[c_250]) ).
cnf(c_251,plain,
( j = n
| j = m
| j = n
| k = m
| k = m ),
inference(paramod,[status(thm)],[c_4,c_96]) ).
cnf(c_252,plain,
( j = n
| j = m
| j = n
| k = m ),
inference(copy,[status(thm)],[c_251]) ).
cnf(c_97,plain,
( j = m
| j = n
| k = m ),
inference(copy,[status(thm)],[c_252]) ).
cnf(c_99,plain,
( ~ element(A,n)
| k = A
| j = A
| j = m
| k = m ),
inference(paramod,[status(thm)],[c_97,c_8]) ).
cnf(c_253,plain,
( ~ element(m,n)
| j = m
| j = m
| k = m ),
inference(factor,[status(thm)],[c_99]) ).
cnf(c_106,plain,
( ~ element(m,n)
| j = m
| k = m ),
inference(copy,[status(thm)],[c_253]) ).
cnf(c_254,plain,
( k = m
| j = m
| k = m ),
inference(resolve,[status(thm)],[c_106,c_60]) ).
cnf(c_107,plain,
( j = m
| k = m ),
inference(copy,[status(thm)],[c_254]) ).
cnf(c_255,plain,
( k = m
| element(n,m)
| j = n
| k = m ),
inference(paramod,[status(thm)],[c_107,c_35]) ).
cnf(c_111,plain,
( element(n,m)
| j = n
| k = m ),
inference(copy,[status(thm)],[c_255]) ).
cnf(c_256,plain,
( element(f(n),n)
| m = n
| j = n
| k = m ),
inference(resolve,[status(thm)],[c_111,c_16]) ).
cnf(c_257,plain,
( element(f(n),n)
| n = m
| j = n
| k = m ),
inference(copy,[status(thm)],[c_256]) ).
cnf(c_115,plain,
( element(f(n),n)
| j = n
| k = m ),
inference(resolve,[status(thm)],[c_2,c_257]) ).
cnf(c_258,plain,
( f(n) != n
| m = n
| j = n
| k = m ),
inference(resolve,[status(thm)],[c_111,c_12]) ).
cnf(c_259,plain,
( f(n) != n
| n = m
| j = n
| k = m ),
inference(copy,[status(thm)],[c_258]) ).
cnf(c_117,plain,
( f(n) != n
| j = n
| k = m ),
inference(resolve,[status(thm)],[c_2,c_259]) ).
cnf(c_260,plain,
( f(n) != m
| m = n
| j = n
| k = m ),
inference(resolve,[status(thm)],[c_111,c_10]) ).
cnf(c_261,plain,
( f(n) != m
| n = m
| j = n
| k = m ),
inference(copy,[status(thm)],[c_260]) ).
cnf(c_118,plain,
( f(n) != m
| j = n
| k = m ),
inference(resolve,[status(thm)],[c_2,c_261]) ).
cnf(c_262,plain,
( n = f(n)
| m = f(n)
| k = f(n)
| k = m
| j = n
| k = m ),
inference(resolve,[status(thm)],[c_115,c_52]) ).
cnf(c_263,plain,
( n = f(n)
| m = f(n)
| f(n) = k
| k = m
| j = n
| k = m ),
inference(copy,[status(thm)],[c_262]) ).
cnf(c_264,plain,
( n = f(n)
| f(n) = m
| f(n) = k
| k = m
| j = n
| k = m ),
inference(copy,[status(thm)],[c_263]) ).
cnf(c_265,plain,
( f(n) = n
| f(n) = m
| f(n) = k
| k = m
| j = n
| k = m ),
inference(copy,[status(thm)],[c_264]) ).
cnf(c_129,plain,
( f(n) = n
| f(n) = m
| f(n) = k
| j = n
| k = m ),
inference(copy,[status(thm)],[c_265]) ).
cnf(c_266,plain,
( f(n) = n
| f(n) = m
| f(n) = n
| j = n
| k = m
| k = m ),
inference(paramod,[status(thm)],[c_4,c_129]) ).
cnf(c_267,plain,
( f(n) = n
| f(n) = m
| f(n) = n
| j = n
| k = m ),
inference(copy,[status(thm)],[c_266]) ).
cnf(c_172,plain,
( f(n) = m
| f(n) = n
| j = n
| k = m ),
inference(copy,[status(thm)],[c_267]) ).
cnf(c_268,plain,
( j = n
| k = m
| f(n) = m
| j = n
| k = m ),
inference(resolve,[status(thm)],[c_172,c_117]) ).
cnf(c_269,plain,
( j = n
| f(n) = m
| j = n
| k = m ),
inference(copy,[status(thm)],[c_268]) ).
cnf(c_174,plain,
( f(n) = m
| j = n
| k = m ),
inference(copy,[status(thm)],[c_269]) ).
cnf(c_270,plain,
( j = n
| k = m
| j = n
| k = m ),
inference(resolve,[status(thm)],[c_174,c_118]) ).
cnf(c_271,plain,
( j = n
| j = n
| k = m ),
inference(copy,[status(thm)],[c_270]) ).
cnf(c_176,plain,
( j = n
| k = m ),
inference(copy,[status(thm)],[c_271]) ).
cnf(c_272,plain,
( n = m
| k = m
| k = m ),
inference(paramod,[status(thm)],[c_176,c_107]) ).
cnf(c_273,plain,
( n = m
| k = m ),
inference(copy,[status(thm)],[c_272]) ).
cnf(c_180,plain,
k = m,
inference(resolve,[status(thm)],[c_2,c_273]) ).
cnf(c_274,plain,
( element(n,k)
| m = n ),
inference(paramod,[status(thm)],[c_180,c_50]) ).
cnf(c_275,plain,
( element(n,m)
| m = n ),
inference(paramod,[status(thm)],[c_180,c_274]) ).
cnf(c_276,plain,
( element(n,m)
| n = m ),
inference(copy,[status(thm)],[c_275]) ).
cnf(c_190,plain,
element(n,m),
inference(resolve,[status(thm)],[c_2,c_276]) ).
cnf(c_277,plain,
( ~ element(A,k)
| n = A
| m = A
| m = A ),
inference(paramod,[status(thm)],[c_180,c_34]) ).
cnf(c_278,plain,
( ~ element(A,m)
| n = A
| m = A
| m = A ),
inference(paramod,[status(thm)],[c_180,c_277]) ).
cnf(c_193,plain,
( ~ element(A,m)
| n = A
| m = A ),
inference(copy,[status(thm)],[c_278]) ).
cnf(c_279,plain,
( element(f(n),n)
| m = n ),
inference(resolve,[status(thm)],[c_190,c_16]) ).
cnf(c_280,plain,
( element(f(n),n)
| n = m ),
inference(copy,[status(thm)],[c_279]) ).
cnf(c_197,plain,
element(f(n),n),
inference(resolve,[status(thm)],[c_2,c_280]) ).
cnf(c_281,plain,
( element(n,f(n))
| m = n ),
inference(resolve,[status(thm)],[c_190,c_14]) ).
cnf(c_282,plain,
( element(n,f(n))
| n = m ),
inference(copy,[status(thm)],[c_281]) ).
cnf(c_198,plain,
element(n,f(n)),
inference(resolve,[status(thm)],[c_2,c_282]) ).
cnf(c_283,plain,
( f(n) != n
| m = n ),
inference(resolve,[status(thm)],[c_190,c_12]) ).
cnf(c_284,plain,
( f(n) != n
| n = m ),
inference(copy,[status(thm)],[c_283]) ).
cnf(c_199,plain,
f(n) != n,
inference(resolve,[status(thm)],[c_2,c_284]) ).
cnf(c_285,plain,
( f(n) != m
| m = n ),
inference(resolve,[status(thm)],[c_190,c_10]) ).
cnf(c_286,plain,
( f(n) != m
| n = m ),
inference(copy,[status(thm)],[c_285]) ).
cnf(c_200,plain,
f(n) != m,
inference(resolve,[status(thm)],[c_2,c_286]) ).
cnf(c_287,plain,
( ~ element(n,f(n))
| n = f(n)
| m = n
| element(f(n),m)
| m = f(n) ),
inference(resolve,[status(thm)],[c_197,c_18]) ).
cnf(c_288,plain,
( ~ element(n,f(n))
| n = f(n)
| m = n
| element(f(n),m)
| f(n) = m ),
inference(copy,[status(thm)],[c_287]) ).
cnf(c_289,plain,
( ~ element(n,f(n))
| n = f(n)
| n = m
| element(f(n),m)
| f(n) = m ),
inference(copy,[status(thm)],[c_288]) ).
cnf(c_290,plain,
( ~ element(n,f(n))
| f(n) = n
| n = m
| element(f(n),m)
| f(n) = m ),
inference(copy,[status(thm)],[c_289]) ).
cnf(c_291,plain,
( ~ element(n,f(n))
| f(n) = n
| n = m
| element(f(n),m) ),
inference(resolve,[status(thm)],[c_200,c_290]) ).
cnf(c_292,plain,
( ~ element(n,f(n))
| f(n) = n
| element(f(n),m) ),
inference(resolve,[status(thm)],[c_2,c_291]) ).
cnf(c_293,plain,
( ~ element(n,f(n))
| element(f(n),m) ),
inference(resolve,[status(thm)],[c_199,c_292]) ).
cnf(c_202,plain,
element(f(n),m),
inference(resolve,[status(thm)],[c_198,c_293]) ).
cnf(c_294,plain,
( n = f(n)
| m = f(n) ),
inference(resolve,[status(thm)],[c_193,c_202]) ).
cnf(c_295,plain,
( n = f(n)
| f(n) = m ),
inference(copy,[status(thm)],[c_294]) ).
cnf(c_296,plain,
( f(n) = n
| f(n) = m ),
inference(copy,[status(thm)],[c_295]) ).
cnf(c_297,plain,
f(n) = n,
inference(resolve,[status(thm)],[c_200,c_296]) ).
cnf(c_215,plain,
$false,
inference(resolve,[status(thm)],[c_199,c_297]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN014-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n001.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 26 17:09:58 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 2276337 was started by sandbox2 on n001,
% 0.10/0.37 % Sat Sep 26 17:09:58 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.37
% 0.10/0.37 % From the command line: assign(max_seconds, 300).
% 0.15/0.42
% 0.15/0.42 % SZS status Unsatisfiable for theBenchmark
% 0.15/0.42
% 0.15/0.42 % Proof 1 at 0.03 (+ 0.01) seconds.
% 0.15/0.42 % Length of proof is 63.
% 0.15/0.42 % Level of proof is 23.
% 0.15/0.42 % Maximum clause weight is 20.000.
% 0.15/0.42 % Given clauses 108.
% 0.15/0.42
% 0.15/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------