%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : ALG040+1 : TPTP v9.3.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.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 06:49:20 AM UTC 2026
% Result : Theorem 0.16s 0.47s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 3
% Syntax : Number of formulae : 30 ( 13 unt; 0 def)
% Number of atoms : 80 ( 28 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 74 ( 24 ~; 15 |; 15 &)
% ( 0 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-2 aty)
% Number of variables : 37 ( 0 sgn 24 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax3,axiom,
? [U] :
( ! [V] :
( sorti1(V)
=> op1(V,V) = U )
& sorti1(U) ),
file('theBenchmark.p',ax3) ).
fof(ax4,axiom,
~ ? [U] :
( ! [V] :
( sorti2(V)
=> op2(V,V) = U )
& sorti2(U) ),
file('theBenchmark.p',ax4) ).
fof(co1,conjecture,
( ( ! [V] :
( sorti2(V)
=> sorti1(j(V)) )
& ! [U] :
( sorti1(U)
=> sorti2(h(U)) ) )
=> ~ ( ! [X2] :
( sorti1(X2)
=> j(h(X2)) = X2 )
& ! [X1] :
( sorti2(X1)
=> h(j(X1)) = X1 )
& ! [Y] :
( sorti2(Y)
=> ! [Z] :
( sorti2(Z)
=> j(op2(Y,Z)) = op1(j(Y),j(Z)) ) )
& ! [W] :
( sorti1(W)
=> ! [X] :
( sorti1(X)
=> h(op1(W,X)) = op2(h(W),h(X)) ) ) ) ),
file('theBenchmark.p',co1) ).
fof(co1_neg,negated_conjecture,
~ ( ( ! [V] :
( sorti2(V)
=> sorti1(j(V)) )
& ! [U] :
( sorti1(U)
=> sorti2(h(U)) ) )
=> ~ ( ! [X2] :
( sorti1(X2)
=> j(h(X2)) = X2 )
& ! [X1] :
( sorti2(X1)
=> h(j(X1)) = X1 )
& ! [Y] :
( sorti2(Y)
=> ! [Z] :
( sorti2(Z)
=> j(op2(Y,Z)) = op1(j(Y),j(Z)) ) )
& ! [W] :
( sorti1(W)
=> ! [X] :
( sorti1(X)
=> h(op1(W,X)) = op2(h(W),h(X)) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(nnf_3,plain,
? [U] :
( ! [V] :
( op1(V,V) = U
| ~ sorti1(V) )
& sorti1(U) ),
inference(fof_nnf,[status(thm)],[ax3]) ).
fof(sk_ax3,plain,
( ! [V] :
( op1(V,V) = sK0
| ~ sorti1(V) )
& sorti1(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(U,sK0)],[nnf_3]) ).
cnf(c_8,plain,
sorti1(sK0),
inference(split_conjunct,[status(thm)],[sk_ax3]) ).
cnf(c_9,plain,
( op1(A,A) = sK0
| ~ sorti1(A) ),
inference(split_conjunct,[status(thm)],[sk_ax3]) ).
fof(nnf_4,plain,
! [U] :
( ? [V] :
( op2(V,V) != U
& sorti2(V) )
| ~ sorti2(U) ),
inference(fof_nnf,[status(thm)],[ax4]) ).
fof(sk_ax4_sk,plain,
! [U] :
( ( op2(sK1(U),sK1(U)) != U
& sorti2(sK1(U)) )
| ~ sorti2(U) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(V,sK1(U))],[nnf_4]) ).
fof(sk_ax4,plain,
( ! [VAR_0] :
( op2(sK1(VAR_0),sK1(VAR_0)) != VAR_0
| ~ sorti2(VAR_0) )
& ! [VAR_0] :
( sorti2(sK1(VAR_0))
| ~ sorti2(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_ax4_sk]) ).
cnf(c_10,plain,
( sorti2(sK1(A))
| ~ sorti2(A) ),
inference(split_conjunct,[status(thm)],[sk_ax4]) ).
cnf(c_11,plain,
( op2(sK1(A),sK1(A)) != A
| ~ sorti2(A) ),
inference(split_conjunct,[status(thm)],[sk_ax4]) ).
cnf(c_12,negated_conjecture,
( sorti2(h(A))
| ~ sorti1(A) ),
inference(clausify,[status(thm)],[co1_neg]) ).
cnf(c_13,negated_conjecture,
( sorti1(j(A))
| ~ sorti2(A) ),
inference(clausify,[status(thm)],[co1_neg]) ).
cnf(c_14,negated_conjecture,
( h(op1(A,B)) = op2(h(A),h(B))
| ~ sorti1(B)
| ~ sorti1(A) ),
inference(clausify,[status(thm)],[co1_neg]) ).
cnf(c_16,negated_conjecture,
( h(j(A)) = A
| ~ sorti2(A) ),
inference(clausify,[status(thm)],[co1_neg]) ).
cnf(c_20,negated_conjecture,
sorti2(h(sK0)),
inference(resolve,[status(thm)],[c_12,c_8]) ).
cnf(c_23,plain,
sorti2(sK1(h(sK0))),
inference(resolve,[status(thm)],[c_10,c_20]) ).
cnf(c_24,plain,
op2(sK1(h(sK0)),sK1(h(sK0))) != h(sK0),
inference(resolve,[status(thm)],[c_11,c_20]) ).
cnf(c_25,negated_conjecture,
h(j(sK1(h(sK0)))) = sK1(h(sK0)),
inference(resolve,[status(thm)],[c_16,c_23]) ).
cnf(c_29,negated_conjecture,
sorti1(j(sK1(h(sK0)))),
inference(resolve,[status(thm)],[c_13,c_23]) ).
cnf(c_42,negated_conjecture,
( h(op1(j(sK1(h(sK0))),A)) = op2(h(j(sK1(h(sK0)))),h(A))
| ~ sorti1(A) ),
inference(resolve,[status(thm)],[c_14,c_29]) ).
cnf(c_43,negated_conjecture,
h(op1(j(sK1(h(sK0))),j(sK1(h(sK0))))) = op2(h(j(sK1(h(sK0)))),h(j(sK1(h(sK0))))),
inference(resolve,[status(thm)],[c_42,c_29]) ).
cnf(c_44,negated_conjecture,
h(op1(j(sK1(h(sK0))),j(sK1(h(sK0))))) = op2(sK1(h(sK0)),h(j(sK1(h(sK0))))),
inference(paramod,[status(thm)],[c_25,c_43]) ).
cnf(c_35,negated_conjecture,
h(op1(j(sK1(h(sK0))),j(sK1(h(sK0))))) = op2(sK1(h(sK0)),sK1(h(sK0))),
inference(paramod,[status(thm)],[c_25,c_44]) ).
cnf(c_38,plain,
op1(j(sK1(h(sK0))),j(sK1(h(sK0)))) = sK0,
inference(resolve,[status(thm)],[c_9,c_29]) ).
cnf(c_45,negated_conjecture,
h(sK0) = op2(sK1(h(sK0)),sK1(h(sK0))),
inference(paramod,[status(thm)],[c_38,c_35]) ).
cnf(c_46,negated_conjecture,
op2(sK1(h(sK0)),sK1(h(sK0))) = h(sK0),
inference(copy,[status(thm)],[c_45]) ).
cnf(c_41,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_24,c_46]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : ALG040+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.43 % Computer : n009.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % 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 21:01:15 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 1142714 was started by sandbox2 on n009,
% 0.16/0.43 % Sat Sep 26 21:01:15 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).
% 0.16/0.47
% 0.16/0.47 % SZS status Theorem for theBenchmark
% 0.16/0.47
% 0.16/0.47 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.16/0.47 % Length of proof is 19.
% 0.16/0.47 % Level of proof is 6.
% 0.16/0.47 % Maximum clause weight is 18.000.
% 0.16/0.47 % Given clauses 17.
% 0.16/0.47
% 0.16/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------