%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN077+1 : TPTP v9.3.1. Released v2.0.0.
% 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 09:36:59 AM UTC 2026
% Result : Theorem 0.16s 0.48s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 2
% Syntax : Number of formulae : 43 ( 7 unt; 0 def)
% Number of atoms : 137 ( 9 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 151 ( 57 ~; 71 |; 18 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 67 ( 0 sgn 28 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(pel54_1,axiom,
! [Y] :
? [Z] :
! [X] :
( big_f(X,Z)
<=> X = Y ),
file('theBenchmark.p',pel54_1) ).
fof(pel54,conjecture,
~ ? [W] :
! [X] :
( big_f(X,W)
<=> ! [U] :
( big_f(X,U)
=> ? [Y] :
( ~ ? [Z] :
( big_f(Z,Y)
& big_f(Z,U) )
& big_f(Y,U) ) ) ),
file('theBenchmark.p',pel54) ).
fof(pel54_neg,negated_conjecture,
~ ~ ? [W] :
! [X] :
( big_f(X,W)
<=> ! [U] :
( big_f(X,U)
=> ? [Y] :
( ~ ? [Z] :
( big_f(Z,Y)
& big_f(Z,U) )
& big_f(Y,U) ) ) ),
inference(assume_negation,[status(cth)],[pel54]) ).
fof(nnf_1,plain,
! [Y] :
? [Z] :
! [X] :
( ( Y != X
| big_f(X,Z) )
& ( Y = X
| ~ big_f(X,Z) ) ),
inference(fof_nnf,[status(thm)],[pel54_1]) ).
fof(sk_pel54_1,plain,
! [Y,X] :
( ( Y != X
| big_f(X,sK0(Y)) )
& ( Y = X
| ~ big_f(X,sK0(Y)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(Z,sK0(Y))],[nnf_1]) ).
cnf(c_3,plain,
( B = A
| ~ big_f(A,sK0(B)) ),
inference(split_conjunct,[status(thm)],[sk_pel54_1]) ).
cnf(c_4,plain,
( B != A
| big_f(A,sK0(B)) ),
inference(split_conjunct,[status(thm)],[sk_pel54_1]) ).
fof(nnf_2,plain,
? [W] :
! [X] :
( ( ? [U] :
( ! [Y] :
( ? [Z] :
( big_f(Z,Y)
& big_f(Z,U) )
| ~ big_f(Y,U) )
& big_f(X,U) )
| big_f(X,W) )
& ( ! [X0] :
( ? [X1] :
( ! [X2] :
( ~ big_f(X2,X1)
| ~ big_f(X2,X0) )
& big_f(X1,X0) )
| ~ big_f(X,X0) )
| ~ big_f(X,W) ) ),
inference(fof_nnf,[status(thm)],[pel54_neg]) ).
fof(sk_pel54_neg_sk,plain,
! [X] :
( ( ( ! [Y] :
( ( big_f(sK4(X,Y),Y)
& big_f(sK4(X,Y),sK3(X)) )
| ~ big_f(Y,sK3(X)) )
& big_f(X,sK3(X)) )
| big_f(X,sK1) )
& ( ! [X0] :
( ( ! [X2] :
( ~ big_f(X2,sK2(X,X0))
| ~ big_f(X2,X0) )
& big_f(sK2(X,X0),X0) )
| ~ big_f(X,X0) )
| ~ big_f(X,sK1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4]),skolemize(W,sK1),skolemize(X1,sK2(X,X0)),skolemize(U,sK3(X)),skolemize(Z,sK4(X,Y))],[nnf_2]) ).
fof(sk_pel54_neg,plain,
( ! [VAR_0,VAR_1] :
( big_f(sK4(VAR_0,VAR_1),VAR_1)
| ~ big_f(VAR_1,sK3(VAR_0))
| big_f(VAR_0,sK1) )
& ! [VAR_0,VAR_1] :
( big_f(sK4(VAR_0,VAR_1),sK3(VAR_0))
| ~ big_f(VAR_1,sK3(VAR_0))
| big_f(VAR_0,sK1) )
& ! [VAR_0] :
( big_f(VAR_0,sK3(VAR_0))
| big_f(VAR_0,sK1) )
& ! [VAR_0,VAR_1,VAR_2] :
( ~ big_f(VAR_2,sK2(VAR_0,VAR_1))
| ~ big_f(VAR_2,VAR_1)
| ~ big_f(VAR_0,VAR_1)
| ~ big_f(VAR_0,sK1) )
& ! [VAR_0,VAR_1] :
( big_f(sK2(VAR_0,VAR_1),VAR_1)
| ~ big_f(VAR_0,VAR_1)
| ~ big_f(VAR_0,sK1) ) ),
inference(cnf_transformation,[status(thm)],[sk_pel54_neg_sk]) ).
cnf(c_5,negated_conjecture,
( big_f(sK2(A,B),B)
| ~ big_f(A,B)
| ~ big_f(A,sK1) ),
inference(split_conjunct,[status(thm)],[sk_pel54_neg]) ).
cnf(c_6,negated_conjecture,
( ~ big_f(C,sK2(A,B))
| ~ big_f(C,B)
| ~ big_f(A,B)
| ~ big_f(A,sK1) ),
inference(split_conjunct,[status(thm)],[sk_pel54_neg]) ).
cnf(c_7,negated_conjecture,
( big_f(A,sK3(A))
| big_f(A,sK1) ),
inference(split_conjunct,[status(thm)],[sk_pel54_neg]) ).
cnf(c_8,negated_conjecture,
( big_f(sK4(A,B),sK3(A))
| ~ big_f(B,sK3(A))
| big_f(A,sK1) ),
inference(split_conjunct,[status(thm)],[sk_pel54_neg]) ).
cnf(c_9,negated_conjecture,
( big_f(sK4(A,B),B)
| ~ big_f(B,sK3(A))
| big_f(A,sK1) ),
inference(split_conjunct,[status(thm)],[sk_pel54_neg]) ).
cnf(c_13,plain,
( ~ big_f(A,sK2(A,B))
| ~ big_f(A,B)
| ~ big_f(A,sK1) ),
inference(factor,[status(thm)],[c_6]) ).
cnf(c_14,plain,
big_f(A,sK0(A)),
inference(xxres,[status(thm)],[c_4]) ).
cnf(c_164,negated_conjecture,
( big_f(A,sK1)
| big_f(sK4(A,A),sK3(A))
| big_f(A,sK1) ),
inference(resolve,[status(thm)],[c_8,c_7]) ).
cnf(c_15,negated_conjecture,
( big_f(sK4(A,A),sK3(A))
| big_f(A,sK1) ),
inference(copy,[status(thm)],[c_164]) ).
cnf(c_165,negated_conjecture,
( big_f(A,sK1)
| big_f(sK4(A,A),A)
| big_f(A,sK1) ),
inference(resolve,[status(thm)],[c_9,c_7]) ).
cnf(c_16,negated_conjecture,
( big_f(sK4(A,A),A)
| big_f(A,sK1) ),
inference(copy,[status(thm)],[c_165]) ).
cnf(c_18,plain,
( big_f(sK2(A,sK0(A)),sK0(A))
| ~ big_f(A,sK1) ),
inference(resolve,[status(thm)],[c_14,c_5]) ).
cnf(c_21,plain,
( ~ big_f(B,sK2(sK4(A,A),sK3(A)))
| ~ big_f(B,sK3(A))
| ~ big_f(sK4(A,A),sK1)
| big_f(A,sK1) ),
inference(resolve,[status(thm)],[c_15,c_6]) ).
cnf(c_22,plain,
( big_f(sK2(sK4(A,A),sK3(A)),sK3(A))
| ~ big_f(sK4(A,A),sK1)
| big_f(A,sK1) ),
inference(resolve,[status(thm)],[c_15,c_5]) ).
cnf(c_166,plain,
( big_f(sK1,sK1)
| ~ big_f(A,sK2(sK4(sK1,sK1),sK3(sK1)))
| ~ big_f(A,sK3(sK1))
| big_f(sK1,sK1) ),
inference(resolve,[status(thm)],[c_21,c_16]) ).
cnf(c_64,plain,
( ~ big_f(A,sK2(sK4(sK1,sK1),sK3(sK1)))
| ~ big_f(A,sK3(sK1))
| big_f(sK1,sK1) ),
inference(copy,[status(thm)],[c_166]) ).
cnf(c_167,plain,
( big_f(sK1,sK1)
| big_f(sK2(sK4(sK1,sK1),sK3(sK1)),sK3(sK1))
| big_f(sK1,sK1) ),
inference(resolve,[status(thm)],[c_22,c_16]) ).
cnf(c_66,plain,
( big_f(sK2(sK4(sK1,sK1),sK3(sK1)),sK3(sK1))
| big_f(sK1,sK1) ),
inference(copy,[status(thm)],[c_167]) ).
cnf(c_168,negated_conjecture,
( big_f(sK4(sK1,sK2(sK4(sK1,sK1),sK3(sK1))),sK2(sK4(sK1,sK1),sK3(sK1)))
| big_f(sK1,sK1)
| big_f(sK1,sK1) ),
inference(resolve,[status(thm)],[c_66,c_9]) ).
cnf(c_67,negated_conjecture,
( big_f(sK4(sK1,sK2(sK4(sK1,sK1),sK3(sK1))),sK2(sK4(sK1,sK1),sK3(sK1)))
| big_f(sK1,sK1) ),
inference(copy,[status(thm)],[c_168]) ).
cnf(c_169,negated_conjecture,
( big_f(sK4(sK1,sK2(sK4(sK1,sK1),sK3(sK1))),sK3(sK1))
| big_f(sK1,sK1)
| big_f(sK1,sK1) ),
inference(resolve,[status(thm)],[c_66,c_8]) ).
cnf(c_68,negated_conjecture,
( big_f(sK4(sK1,sK2(sK4(sK1,sK1),sK3(sK1))),sK3(sK1))
| big_f(sK1,sK1) ),
inference(copy,[status(thm)],[c_169]) ).
cnf(c_170,plain,
( ~ big_f(sK4(sK1,sK2(sK4(sK1,sK1),sK3(sK1))),sK3(sK1))
| big_f(sK1,sK1)
| big_f(sK1,sK1) ),
inference(resolve,[status(thm)],[c_67,c_64]) ).
cnf(c_126,plain,
( ~ big_f(sK4(sK1,sK2(sK4(sK1,sK1),sK3(sK1))),sK3(sK1))
| big_f(sK1,sK1) ),
inference(copy,[status(thm)],[c_170]) ).
cnf(c_171,plain,
( big_f(sK1,sK1)
| big_f(sK1,sK1) ),
inference(resolve,[status(thm)],[c_126,c_68]) ).
cnf(c_129,plain,
big_f(sK1,sK1),
inference(copy,[status(thm)],[c_171]) ).
cnf(c_130,plain,
big_f(sK2(sK1,sK0(sK1)),sK0(sK1)),
inference(resolve,[status(thm)],[c_129,c_18]) ).
cnf(c_172,plain,
sK1 = sK2(sK1,sK0(sK1)),
inference(resolve,[status(thm)],[c_130,c_3]) ).
cnf(c_159,plain,
sK2(sK1,sK0(sK1)) = sK1,
inference(copy,[status(thm)],[c_172]) ).
cnf(c_173,plain,
( ~ big_f(sK1,sK1)
| ~ big_f(sK1,sK0(sK1))
| ~ big_f(sK1,sK1) ),
inference(paramod,[status(thm)],[c_159,c_13]) ).
cnf(c_174,plain,
( ~ big_f(sK1,sK0(sK1))
| ~ big_f(sK1,sK1) ),
inference(copy,[status(thm)],[c_173]) ).
cnf(c_175,plain,
~ big_f(sK1,sK0(sK1)),
inference(resolve,[status(thm)],[c_129,c_174]) ).
cnf(c_163,plain,
$false,
inference(resolve,[status(thm)],[c_14,c_175]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN077+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.05 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.42 % Computer : n001.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Sat Sep 26 17:15:13 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.43 % Process 2291564 was started by sandbox2 on n001,
% 0.16/0.43 % Sat Sep 26 17:15:13 2026
% 0.16/0.43 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.16/0.44
% 0.16/0.44 % From the command line: assign(max_seconds, 300).
% 0.16/0.48
% 0.16/0.48 % SZS status Theorem for theBenchmark
% 0.16/0.48
% 0.16/0.48 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.16/0.48 % Length of proof is 25.
% 0.16/0.48 % Level of proof is 10.
% 0.16/0.48 % Maximum clause weight is 38.000.
% 0.16/0.48 % Given clauses 67.
% 0.16/0.48
% 0.16/0.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------