%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : ALG070+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 : 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 06:49:24 AM UTC 2026
% Result : Theorem 0.13s 0.37s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 3
% Syntax : Number of formulae : 37 ( 22 unt; 0 def)
% Number of atoms : 89 ( 42 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 76 ( 24 ~; 16 |; 14 &)
% ( 0 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 33 ( 0 sgn 20 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax3,axiom,
! [U] :
( sorti1(U)
=> ! [V] :
( sorti1(V)
=> ( op1(U,V) = U
| op1(U,U) != V ) ) ),
file('theBenchmark.p',ax3) ).
fof(ax4,axiom,
~ ! [U] :
( sorti2(U)
=> ! [V] :
( sorti2(V)
=> ( op2(U,V) = U
| op2(U,U) != V ) ) ),
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_8,plain,
( op1(A,B) = A
| op1(A,A) != B
| ~ sorti1(B)
| ~ sorti1(A) ),
inference(clausify,[status(thm)],[ax3]) ).
fof(nnf_4,plain,
? [U] :
( ? [V] :
( op2(U,V) != U
& op2(U,U) = V
& sorti2(V) )
& sorti2(U) ),
inference(fof_nnf,[status(thm)],[ax4]) ).
fof(sk_ax4,plain,
( op2(sK0,sK1) != sK0
& op2(sK0,sK0) = sK1
& sorti2(sK1)
& sorti2(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(U,sK0),skolemize(V,sK1)],[nnf_4]) ).
cnf(c_9,plain,
sorti2(sK0),
inference(split_conjunct,[status(thm)],[sk_ax4]) ).
cnf(c_10,plain,
sorti2(sK1),
inference(split_conjunct,[status(thm)],[sk_ax4]) ).
cnf(c_11,plain,
op2(sK0,sK0) = sK1,
inference(split_conjunct,[status(thm)],[sk_ax4]) ).
cnf(c_12,plain,
sK1 = op2(sK0,sK0),
inference(copy,[status(thm)],[c_11]) ).
cnf(c_13,plain,
op2(sK0,sK1) != sK0,
inference(split_conjunct,[status(thm)],[sk_ax4]) ).
cnf(c_14,plain,
op2(sK0,op2(sK0,sK0)) != sK0,
inference(paramod,[status(thm)],[c_12,c_13]) ).
cnf(c_16,negated_conjecture,
( sorti1(j(A))
| ~ sorti2(A) ),
inference(clausify,[status(thm)],[co1_neg]) ).
cnf(c_17,negated_conjecture,
( h(op1(A,B)) = op2(h(A),h(B))
| ~ sorti1(B)
| ~ sorti1(A) ),
inference(clausify,[status(thm)],[co1_neg]) ).
cnf(c_18,negated_conjecture,
( j(op2(A,B)) = op1(j(A),j(B))
| ~ sorti2(B)
| ~ sorti2(A) ),
inference(clausify,[status(thm)],[co1_neg]) ).
cnf(c_19,negated_conjecture,
( h(j(A)) = A
| ~ sorti2(A) ),
inference(clausify,[status(thm)],[co1_neg]) ).
cnf(c_21,plain,
sorti2(op2(sK0,sK0)),
inference(paramod,[status(thm)],[c_12,c_10]) ).
cnf(c_22,negated_conjecture,
sorti1(j(sK0)),
inference(resolve,[status(thm)],[c_16,c_9]) ).
cnf(c_41,negated_conjecture,
( j(op2(sK0,A)) = op1(j(sK0),j(A))
| ~ sorti2(A) ),
inference(resolve,[status(thm)],[c_18,c_9]) ).
cnf(c_23,negated_conjecture,
j(op2(sK0,sK0)) = op1(j(sK0),j(sK0)),
inference(resolve,[status(thm)],[c_41,c_9]) ).
cnf(c_24,negated_conjecture,
h(j(sK0)) = sK0,
inference(resolve,[status(thm)],[c_19,c_9]) ).
cnf(c_42,negated_conjecture,
h(j(op2(sK0,sK0))) = op2(sK0,sK0),
inference(resolve,[status(thm)],[c_19,c_21]) ).
cnf(c_25,negated_conjecture,
h(op1(j(sK0),j(sK0))) = op2(sK0,sK0),
inference(paramod,[status(thm)],[c_23,c_42]) ).
cnf(c_43,negated_conjecture,
sorti1(j(op2(sK0,sK0))),
inference(resolve,[status(thm)],[c_16,c_21]) ).
cnf(c_29,negated_conjecture,
sorti1(op1(j(sK0),j(sK0))),
inference(paramod,[status(thm)],[c_23,c_43]) ).
cnf(c_44,negated_conjecture,
( h(op1(j(sK0),A)) = op2(h(j(sK0)),h(A))
| ~ sorti1(A) ),
inference(resolve,[status(thm)],[c_17,c_22]) ).
cnf(c_45,negated_conjecture,
h(op1(j(sK0),op1(j(sK0),j(sK0)))) = op2(h(j(sK0)),h(op1(j(sK0),j(sK0)))),
inference(resolve,[status(thm)],[c_44,c_29]) ).
cnf(c_46,negated_conjecture,
h(op1(j(sK0),op1(j(sK0),j(sK0)))) = op2(sK0,h(op1(j(sK0),j(sK0)))),
inference(paramod,[status(thm)],[c_24,c_45]) ).
cnf(c_34,negated_conjecture,
h(op1(j(sK0),op1(j(sK0),j(sK0)))) = op2(sK0,op2(sK0,sK0)),
inference(paramod,[status(thm)],[c_25,c_46]) ).
cnf(c_47,plain,
( op1(j(sK0),A) = j(sK0)
| op1(j(sK0),j(sK0)) != A
| ~ sorti1(A) ),
inference(resolve,[status(thm)],[c_8,c_22]) ).
cnf(c_48,plain,
( op1(j(sK0),op1(j(sK0),j(sK0))) = j(sK0)
| op1(j(sK0),j(sK0)) != op1(j(sK0),j(sK0)) ),
inference(resolve,[status(thm)],[c_47,c_29]) ).
cnf(c_36,plain,
op1(j(sK0),op1(j(sK0),j(sK0))) = j(sK0),
inference(xxres,[status(thm)],[c_48]) ).
cnf(c_49,negated_conjecture,
h(j(sK0)) = op2(sK0,op2(sK0,sK0)),
inference(paramod,[status(thm)],[c_36,c_34]) ).
cnf(c_50,negated_conjecture,
sK0 = op2(sK0,op2(sK0,sK0)),
inference(paramod,[status(thm)],[c_24,c_49]) ).
cnf(c_39,negated_conjecture,
op2(sK0,op2(sK0,sK0)) = sK0,
inference(copy,[status(thm)],[c_50]) ).
cnf(c_40,plain,
$false,
inference(resolve,[status(thm)],[c_39,c_14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG070+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.35 % Computer : n001.cluster.edu
% 0.11/0.35 % Model : x86_64 x86_64
% 0.11/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.35 % Memory : 8046.5625MB
% 0.11/0.35 % OS : Linux 6.8.0-71-generic
% 0.11/0.35 % CPULimit : 300
% 0.11/0.35 % WCLimit : 300
% 0.11/0.35 % DateTime : Sat Sep 26 21:11:00 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.36 % Process 2682516 was started by sandbox2 on n001,
% 0.11/0.36 % Sat Sep 26 21:11:00 2026
% 0.11/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.13/0.36
% 0.13/0.36 % From the command line: assign(max_seconds, 300).
% 0.13/0.37
% 0.13/0.37 % SZS status Theorem for theBenchmark
% 0.13/0.37
% 0.13/0.37 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.13/0.37 % Length of proof is 24.
% 0.13/0.37 % Level of proof is 7.
% 0.13/0.37 % Maximum clause weight is 15.000.
% 0.13/0.37 % Given clauses 16.
% 0.13/0.37
% 0.13/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------