%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : ALG202+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 : n005.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 06:49:44 AM UTC 2026
% Result : Theorem 0.09s 5.39s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 27 ( 13 unt; 0 def)
% Number of atoms : 68 ( 25 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 57 ( 16 ~; 9 |; 10 &)
% ( 0 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 30 ( 0 sgn 20 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax2,axiom,
! [U] :
( sorti2(U)
=> ! [V] :
( sorti2(V)
=> sorti2(op2(U,V)) ) ),
file('theBenchmark.p',ax2) ).
fof(ax3,axiom,
! [U] :
( sorti1(U)
=> op1(U,U) = U ),
file('theBenchmark.p',ax3) ).
fof(ax4,axiom,
~ ! [U] :
( sorti2(U)
=> op2(U,U) = 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]) ).
cnf(c_7,plain,
( sorti2(op2(A,B))
| ~ sorti2(B)
| ~ sorti2(A) ),
inference(clausify,[status(thm)],[ax2]) ).
cnf(c_8,plain,
( op1(A,A) = A
| ~ sorti1(A) ),
inference(clausify,[status(thm)],[ax3]) ).
fof(nnf_4,plain,
? [U] :
( op2(U,U) != U
& sorti2(U) ),
inference(fof_nnf,[status(thm)],[ax4]) ).
fof(sk_ax4,plain,
( op2(sK0,sK0) != sK0
& sorti2(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(U,sK0)],[nnf_4]) ).
cnf(c_9,plain,
sorti2(sK0),
inference(split_conjunct,[status(thm)],[sk_ax4]) ).
cnf(c_10,plain,
op2(sK0,sK0) != sK0,
inference(split_conjunct,[status(thm)],[sk_ax4]) ).
cnf(c_12,negated_conjecture,
( sorti1(j(A))
| ~ sorti2(A) ),
inference(clausify,[status(thm)],[co1_neg]) ).
cnf(c_14,negated_conjecture,
( j(op2(A,B)) = op1(j(A),j(B))
| ~ sorti2(B)
| ~ sorti2(A) ),
inference(clausify,[status(thm)],[co1_neg]) ).
cnf(c_15,negated_conjecture,
( h(j(A)) = A
| ~ sorti2(A) ),
inference(clausify,[status(thm)],[co1_neg]) ).
cnf(c_35,plain,
( sorti2(op2(sK0,A))
| ~ sorti2(A) ),
inference(resolve,[status(thm)],[c_7,c_9]) ).
cnf(c_17,plain,
sorti2(op2(sK0,sK0)),
inference(resolve,[status(thm)],[c_35,c_9]) ).
cnf(c_18,negated_conjecture,
sorti1(j(sK0)),
inference(resolve,[status(thm)],[c_12,c_9]) ).
cnf(c_36,negated_conjecture,
( j(op2(sK0,A)) = op1(j(sK0),j(A))
| ~ sorti2(A) ),
inference(resolve,[status(thm)],[c_14,c_9]) ).
cnf(c_19,negated_conjecture,
j(op2(sK0,sK0)) = op1(j(sK0),j(sK0)),
inference(resolve,[status(thm)],[c_36,c_9]) ).
cnf(c_20,negated_conjecture,
h(j(sK0)) = sK0,
inference(resolve,[status(thm)],[c_15,c_9]) ).
cnf(c_37,negated_conjecture,
h(j(op2(sK0,sK0))) = op2(sK0,sK0),
inference(resolve,[status(thm)],[c_15,c_17]) ).
cnf(c_21,negated_conjecture,
h(op1(j(sK0),j(sK0))) = op2(sK0,sK0),
inference(paramod,[status(thm)],[c_19,c_37]) ).
cnf(c_29,plain,
op1(j(sK0),j(sK0)) = j(sK0),
inference(resolve,[status(thm)],[c_8,c_18]) ).
cnf(c_38,negated_conjecture,
h(j(sK0)) = op2(sK0,sK0),
inference(paramod,[status(thm)],[c_29,c_21]) ).
cnf(c_39,negated_conjecture,
sK0 = op2(sK0,sK0),
inference(paramod,[status(thm)],[c_20,c_38]) ).
cnf(c_33,negated_conjecture,
op2(sK0,sK0) = sK0,
inference(copy,[status(thm)],[c_39]) ).
cnf(c_34,plain,
$false,
inference(resolve,[status(thm)],[c_33,c_10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG202+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/5.36 % Computer : n005.cluster.edu
% 0.09/5.36 % Model : x86_64 x86_64
% 0.09/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.36 % Memory : 8046.5625MB
% 0.09/5.36 % OS : Linux 6.8.0-71-generic
% 0.09/5.37 % CPULimit : 300
% 0.09/5.37 % WCLimit : 300
% 0.09/5.37 % DateTime : Sat Sep 26 21:25:07 UTC 2026
% 0.09/5.37 % CPUTime :
% 0.09/5.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/5.37 % Process 3115275 was started by sandbox2 on n005,
% 0.09/5.37 % Sat Sep 26 21:25:07 2026
% 0.09/5.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/5.37
% 0.09/5.37 % From the command line: assign(max_seconds, 300).
% 0.09/5.39
% 0.09/5.39 % SZS status Theorem for theBenchmark
% 0.09/5.39
% 0.09/5.39 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.09/5.39 % Length of proof is 19.
% 0.09/5.39 % Level of proof is 5.
% 0.09/5.39 % Maximum clause weight is 14.000.
% 0.09/5.39 % Given clauses 13.
% 0.09/5.39
% 0.09/5.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------