%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN075+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 : n020.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 09:36:58 AM UTC 2026
% Result : Theorem 0.19s 0.51s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 2
% Syntax : Number of formulae : 37 ( 6 unt; 0 def)
% Number of atoms : 121 ( 77 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 140 ( 56 ~; 63 |; 16 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 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; 2 con; 0-2 aty)
% Number of variables : 74 ( 2 sgn 30 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(pel52_1,axiom,
? [Z,W] :
! [X,Y] :
( big_f(X,Y)
<=> ( Y = W
& X = Z ) ),
file('theBenchmark.p',pel52_1) ).
fof(pel52,conjecture,
? [W] :
! [Y] :
( ? [Z] :
! [X] :
( big_f(X,Y)
<=> X = Z )
<=> Y = W ),
file('theBenchmark.p',pel52) ).
fof(pel52_neg,negated_conjecture,
~ ? [W] :
! [Y] :
( ? [Z] :
! [X] :
( big_f(X,Y)
<=> X = Z )
<=> Y = W ),
inference(assume_negation,[status(cth)],[pel52]) ).
fof(nnf_1,plain,
? [Z,W] :
! [X,Y] :
( ( W != Y
| Z != X
| big_f(X,Y) )
& ( ( W = Y
& Z = X )
| ~ big_f(X,Y) ) ),
inference(fof_nnf,[status(thm)],[pel52_1]) ).
fof(sk_pel52_1_sk,plain,
! [X,Y] :
( ( sK1 != Y
| sK0 != X
| big_f(X,Y) )
& ( ( sK1 = Y
& sK0 = X )
| ~ big_f(X,Y) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(Z,sK0),skolemize(W,sK1)],[nnf_1]) ).
fof(sk_pel52_1,plain,
( ! [VAR_0,VAR_1] :
( sK1 != VAR_1
| sK0 != VAR_0
| big_f(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1] :
( sK1 = VAR_1
| ~ big_f(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1] :
( sK0 = VAR_0
| ~ big_f(VAR_0,VAR_1) ) ),
inference(cnf_transformation,[status(thm)],[sk_pel52_1_sk]) ).
cnf(c_3,plain,
( sK0 = A
| ~ big_f(A,B) ),
inference(split_conjunct,[status(thm)],[sk_pel52_1]) ).
cnf(c_4,plain,
( sK1 = B
| ~ big_f(A,B) ),
inference(split_conjunct,[status(thm)],[sk_pel52_1]) ).
cnf(c_5,plain,
( sK1 != B
| sK0 != A
| big_f(A,B) ),
inference(split_conjunct,[status(thm)],[sk_pel52_1]) ).
fof(nnf_2,plain,
! [W] :
? [Y] :
( ( W != Y
| ! [Z] :
? [X] :
( ( Z != X
| ~ big_f(X,Y) )
& ( Z = X
| big_f(X,Y) ) ) )
& ( W = Y
| ? [X0] :
! [X1] :
( ( X0 != X1
| big_f(X1,Y) )
& ( X0 = X1
| ~ big_f(X1,Y) ) ) ) ),
inference(fof_nnf,[status(thm)],[pel52_neg]) ).
fof(sk_pel52_neg_sk,plain,
! [W] :
( ( W != sK2(W)
| ! [Z] :
( ( Z != sK4(W,Z)
| ~ big_f(sK4(W,Z),sK2(W)) )
& ( Z = sK4(W,Z)
| big_f(sK4(W,Z),sK2(W)) ) ) )
& ( W = sK2(W)
| ! [X1] :
( ( sK3(W) != X1
| big_f(X1,sK2(W)) )
& ( sK3(W) = X1
| ~ big_f(X1,sK2(W)) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(Y,sK2(W)),skolemize(X0,sK3(W)),skolemize(X,sK4(W,Z))],[nnf_2]) ).
fof(sk_pel52_neg,plain,
( ! [VAR_0,VAR_1] :
( VAR_0 != sK2(VAR_0)
| VAR_1 != sK4(VAR_0,VAR_1)
| ~ big_f(sK4(VAR_0,VAR_1),sK2(VAR_0)) )
& ! [VAR_0,VAR_1] :
( VAR_0 != sK2(VAR_0)
| VAR_1 = sK4(VAR_0,VAR_1)
| big_f(sK4(VAR_0,VAR_1),sK2(VAR_0)) )
& ! [VAR_0,VAR_1] :
( VAR_1 = sK2(VAR_1)
| sK3(VAR_1) != VAR_0
| big_f(VAR_0,sK2(VAR_1)) )
& ! [VAR_0,VAR_1] :
( VAR_1 = sK2(VAR_1)
| sK3(VAR_1) = VAR_0
| ~ big_f(VAR_0,sK2(VAR_1)) ) ),
inference(cnf_transformation,[status(thm)],[sk_pel52_neg_sk]) ).
cnf(c_8,negated_conjecture,
( B = sK2(B)
| sK3(B) != A
| big_f(A,sK2(B)) ),
inference(split_conjunct,[status(thm)],[sk_pel52_neg]) ).
cnf(c_9,negated_conjecture,
( sK2(B) = B
| sK3(B) != A
| big_f(A,sK2(B)) ),
inference(copy,[status(thm)],[c_8]) ).
cnf(c_10,negated_conjecture,
( A != sK2(A)
| B = sK4(A,B)
| big_f(sK4(A,B),sK2(A)) ),
inference(split_conjunct,[status(thm)],[sk_pel52_neg]) ).
cnf(c_37,negated_conjecture,
( A != sK2(A)
| sK4(A,B) = B
| big_f(sK4(A,B),sK2(A)) ),
inference(copy,[status(thm)],[c_10]) ).
cnf(c_11,negated_conjecture,
( sK2(A) != A
| sK4(A,B) = B
| big_f(sK4(A,B),sK2(A)) ),
inference(copy,[status(thm)],[c_37]) ).
cnf(c_12,negated_conjecture,
( A != sK2(A)
| B != sK4(A,B)
| ~ big_f(sK4(A,B),sK2(A)) ),
inference(split_conjunct,[status(thm)],[sk_pel52_neg]) ).
cnf(c_38,negated_conjecture,
( A != sK2(A)
| sK4(A,B) != B
| ~ big_f(sK4(A,B),sK2(A)) ),
inference(copy,[status(thm)],[c_12]) ).
cnf(c_13,negated_conjecture,
( sK2(A) != A
| sK4(A,B) != B
| ~ big_f(sK4(A,B),sK2(A)) ),
inference(copy,[status(thm)],[c_38]) ).
cnf(c_14,plain,
( sK1 != A
| big_f(sK0,A) ),
inference(xxres,[status(thm)],[c_5]) ).
cnf(c_16,plain,
( sK2(A) = A
| big_f(sK3(A),sK2(A)) ),
inference(xxres,[status(thm)],[c_9]) ).
cnf(c_17,plain,
big_f(sK0,sK1),
inference(xxres,[status(thm)],[c_14]) ).
cnf(c_39,plain,
( sK1 = sK2(A)
| sK2(A) = A ),
inference(resolve,[status(thm)],[c_16,c_4]) ).
cnf(c_18,plain,
( sK2(A) = sK1
| sK2(A) = A ),
inference(copy,[status(thm)],[c_39]) ).
cnf(c_20,plain,
sK2(sK1) = sK1,
inference(factor,[status(thm)],[c_18]) ).
cnf(c_40,negated_conjecture,
( sK4(sK1,A) = A
| big_f(sK4(sK1,A),sK2(sK1)) ),
inference(resolve,[status(thm)],[c_20,c_11]) ).
cnf(c_21,negated_conjecture,
( sK4(sK1,A) = A
| big_f(sK4(sK1,A),sK1) ),
inference(paramod,[status(thm)],[c_20,c_40]) ).
cnf(c_41,plain,
( sK2(sK1) != sK1
| sK4(sK1,A) != A
| ~ big_f(sK4(sK1,A),sK1) ),
inference(paramod,[status(thm)],[c_20,c_13]) ).
cnf(c_42,plain,
( sK1 != sK1
| sK4(sK1,A) != A
| ~ big_f(sK4(sK1,A),sK1) ),
inference(paramod,[status(thm)],[c_20,c_41]) ).
cnf(c_22,plain,
( sK4(sK1,A) != A
| ~ big_f(sK4(sK1,A),sK1) ),
inference(copy,[status(thm)],[c_42]) ).
cnf(c_43,plain,
( sK0 = sK4(sK1,A)
| sK4(sK1,A) = A ),
inference(resolve,[status(thm)],[c_21,c_3]) ).
cnf(c_34,plain,
( sK4(sK1,A) = sK0
| sK4(sK1,A) = A ),
inference(copy,[status(thm)],[c_43]) ).
cnf(c_35,plain,
sK4(sK1,sK0) = sK0,
inference(factor,[status(thm)],[c_34]) ).
cnf(c_44,plain,
~ big_f(sK4(sK1,sK0),sK1),
inference(resolve,[status(thm)],[c_22,c_35]) ).
cnf(c_45,plain,
~ big_f(sK0,sK1),
inference(paramod,[status(thm)],[c_35,c_44]) ).
cnf(c_36,plain,
$false,
inference(resolve,[status(thm)],[c_17,c_45]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SYN075+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.46 % Computer : n020.cluster.edu
% 0.19/0.46 % Model : x86_64 x86_64
% 0.19/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.46 % Memory : 8046.5625MB
% 0.19/0.46 % OS : Linux 6.8.0-71-generic
% 0.19/0.46 % CPULimit : 300
% 0.19/0.46 % WCLimit : 300
% 0.19/0.46 % DateTime : Sat Sep 26 17:10:33 UTC 2026
% 0.19/0.46 % CPUTime :
% 0.19/0.47 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/0.47 % Process 2093315 was started by sandbox2 on n020,
% 0.19/0.47 % Sat Sep 26 17:10:33 2026
% 0.19/0.47 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.19/0.48
% 0.19/0.48 % From the command line: assign(max_seconds, 300).
% 0.19/0.51
% 0.19/0.51 % SZS status Theorem for theBenchmark
% 0.19/0.51
% 0.19/0.51 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.19/0.51 % Length of proof is 21.
% 0.19/0.51 % Level of proof is 9.
% 0.19/0.51 % Maximum clause weight is 15.000.
% 0.19/0.51 % Given clauses 20.
% 0.19/0.51
% 0.19/0.51 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------