%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : ALG019+1 : TPTP v9.3.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n013.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 06:49:08 AM UTC 2026
% Result : Theorem 0.03s 0.38s
% Output : CNFRefutation 0.03s
% 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 : 76 ( 26 ~; 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_sk,plain,
! [U] :
( ( op1(sK0(U),sK0(U)) != U
& sorti1(sK0(U)) )
| ~ sorti1(U) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(V,sK0(U))],[nnf_3]) ).
fof(sk_ax3,plain,
( ! [VAR_0] :
( op1(sK0(VAR_0),sK0(VAR_0)) != VAR_0
| ~ sorti1(VAR_0) )
& ! [VAR_0] :
( sorti1(sK0(VAR_0))
| ~ sorti1(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_ax3_sk]) ).
cnf(c_8,plain,
( sorti1(sK0(A))
| ~ sorti1(A) ),
inference(split_conjunct,[status(thm)],[sk_ax3]) ).
cnf(c_9,plain,
( op1(sK0(A),sK0(A)) != A
| ~ 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,plain,
( ! [V] :
( op2(V,V) = sK1
| ~ sorti2(V) )
& sorti2(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U,sK1)],[nnf_4]) ).
cnf(c_10,plain,
sorti2(sK1),
inference(split_conjunct,[status(thm)],[sk_ax4]) ).
cnf(c_11,plain,
( op2(A,A) = sK1
| ~ 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_15,negated_conjecture,
( j(op2(A,B)) = op1(j(A),j(B))
| ~ sorti2(B)
| ~ sorti2(A) ),
inference(clausify,[status(thm)],[co1_neg]) ).
cnf(c_17,negated_conjecture,
( j(h(A)) = A
| ~ sorti1(A) ),
inference(clausify,[status(thm)],[co1_neg]) ).
cnf(c_20,negated_conjecture,
sorti1(j(sK1)),
inference(resolve,[status(thm)],[c_13,c_10]) ).
cnf(c_23,plain,
sorti1(sK0(j(sK1))),
inference(resolve,[status(thm)],[c_8,c_20]) ).
cnf(c_24,plain,
op1(sK0(j(sK1)),sK0(j(sK1))) != j(sK1),
inference(resolve,[status(thm)],[c_9,c_20]) ).
cnf(c_25,negated_conjecture,
j(h(sK0(j(sK1)))) = sK0(j(sK1)),
inference(resolve,[status(thm)],[c_17,c_23]) ).
cnf(c_29,negated_conjecture,
sorti2(h(sK0(j(sK1)))),
inference(resolve,[status(thm)],[c_12,c_23]) ).
cnf(c_42,negated_conjecture,
( j(op2(h(sK0(j(sK1))),A)) = op1(j(h(sK0(j(sK1)))),j(A))
| ~ sorti2(A) ),
inference(resolve,[status(thm)],[c_15,c_29]) ).
cnf(c_43,negated_conjecture,
j(op2(h(sK0(j(sK1))),h(sK0(j(sK1))))) = op1(j(h(sK0(j(sK1)))),j(h(sK0(j(sK1))))),
inference(resolve,[status(thm)],[c_42,c_29]) ).
cnf(c_44,negated_conjecture,
j(op2(h(sK0(j(sK1))),h(sK0(j(sK1))))) = op1(sK0(j(sK1)),j(h(sK0(j(sK1))))),
inference(paramod,[status(thm)],[c_25,c_43]) ).
cnf(c_35,negated_conjecture,
j(op2(h(sK0(j(sK1))),h(sK0(j(sK1))))) = op1(sK0(j(sK1)),sK0(j(sK1))),
inference(paramod,[status(thm)],[c_25,c_44]) ).
cnf(c_38,plain,
op2(h(sK0(j(sK1))),h(sK0(j(sK1)))) = sK1,
inference(resolve,[status(thm)],[c_11,c_29]) ).
cnf(c_45,negated_conjecture,
j(sK1) = op1(sK0(j(sK1)),sK0(j(sK1))),
inference(paramod,[status(thm)],[c_38,c_35]) ).
cnf(c_46,negated_conjecture,
op1(sK0(j(sK1)),sK0(j(sK1))) = j(sK1),
inference(copy,[status(thm)],[c_45]) ).
cnf(c_41,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_24,c_46]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG019+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n013.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.03/0.36 % CPULimit : 300
% 0.03/0.36 % WCLimit : 300
% 0.03/0.36 % DateTime : Sat Sep 26 20:58:54 UTC 2026
% 0.03/0.36 % CPUTime :
% 0.03/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.03/0.36 % Process 3565970 was started by sandbox on n013,
% 0.03/0.36 % Sat Sep 26 20:58:54 2026
% 0.03/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.03/0.37
% 0.03/0.37 % From the command line: assign(max_seconds, 300).
% 0.03/0.38
% 0.03/0.38 % SZS status Theorem for theBenchmark
% 0.03/0.38
% 0.03/0.38 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.03/0.38 % Length of proof is 19.
% 0.03/0.38 % Level of proof is 6.
% 0.03/0.38 % Maximum clause weight is 18.000.
% 0.03/0.38 % Given clauses 17.
% 0.03/0.38
% 0.03/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------