%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : ALG203+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 : n011.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 0.03s 0.38s
% Output : CNFRefutation 0.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 3
% Syntax : Number of formulae : 40 ( 21 unt; 0 def)
% Number of atoms : 99 ( 47 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 89 ( 30 ~; 21 |; 20 &)
% ( 0 <=>; 18 =>; 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 : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 40 ( 0 sgn 16 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax3,axiom,
( ? [V] :
( op1(V,V) != V
& sorti1(V) )
& ? [U] :
( op1(U,U) = U
& sorti1(U) ) ),
file('theBenchmark.p',ax3) ).
fof(ax4,axiom,
~ ( ? [V] :
( op2(V,V) != V
& sorti2(V) )
& ? [U] :
( op2(U,U) = 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,
( ? [V] :
( op1(V,V) != V
& sorti1(V) )
& ? [U] :
( op1(U,U) = U
& sorti1(U) ) ),
inference(fof_nnf,[status(thm)],[ax3]) ).
fof(sk_ax3,plain,
( op1(sK1,sK1) != sK1
& sorti1(sK1)
& op1(sK0,sK0) = sK0
& sorti1(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(U,sK0),skolemize(V,sK1)],[nnf_3]) ).
cnf(c_8,plain,
sorti1(sK0),
inference(split_conjunct,[status(thm)],[sk_ax3]) ).
cnf(c_9,plain,
op1(sK0,sK0) = sK0,
inference(split_conjunct,[status(thm)],[sk_ax3]) ).
cnf(c_10,plain,
sorti1(sK1),
inference(split_conjunct,[status(thm)],[sk_ax3]) ).
cnf(c_11,plain,
op1(sK1,sK1) != sK1,
inference(split_conjunct,[status(thm)],[sk_ax3]) ).
cnf(c_12,plain,
( op2(B,B) = B
| ~ sorti2(B)
| op2(A,A) != A
| ~ sorti2(A) ),
inference(clausify,[status(thm)],[ax4]) ).
cnf(c_13,negated_conjecture,
( sorti2(h(A))
| ~ sorti1(A) ),
inference(clausify,[status(thm)],[co1_neg]) ).
cnf(c_15,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,
( op2(h(A),h(B)) = h(op1(A,B))
| ~ sorti1(B)
| ~ sorti1(A) ),
inference(copy,[status(thm)],[c_15]) ).
cnf(c_17,negated_conjecture,
( j(op2(A,B)) = op1(j(A),j(B))
| ~ sorti2(B)
| ~ sorti2(A) ),
inference(clausify,[status(thm)],[co1_neg]) ).
cnf(c_18,negated_conjecture,
( op1(j(A),j(B)) = j(op2(A,B))
| ~ sorti2(B)
| ~ sorti2(A) ),
inference(copy,[status(thm)],[c_17]) ).
cnf(c_20,negated_conjecture,
( j(h(A)) = A
| ~ sorti1(A) ),
inference(clausify,[status(thm)],[co1_neg]) ).
cnf(c_28,plain,
sorti2(h(sK1)),
inference(resolve,[status(thm)],[c_13,c_10]) ).
cnf(c_29,plain,
sorti2(h(sK0)),
inference(resolve,[status(thm)],[c_13,c_8]) ).
cnf(c_124,negated_conjecture,
( op2(h(sK1),h(A)) = h(op1(sK1,A))
| ~ sorti1(A) ),
inference(resolve,[status(thm)],[c_16,c_10]) ).
cnf(c_34,negated_conjecture,
op2(h(sK1),h(sK1)) = h(op1(sK1,sK1)),
inference(resolve,[status(thm)],[c_124,c_10]) ).
cnf(c_125,negated_conjecture,
( op2(h(sK0),h(A)) = h(op1(sK0,A))
| ~ sorti1(A) ),
inference(resolve,[status(thm)],[c_16,c_8]) ).
cnf(c_126,negated_conjecture,
op2(h(sK0),h(sK0)) = h(op1(sK0,sK0)),
inference(resolve,[status(thm)],[c_125,c_8]) ).
cnf(c_37,negated_conjecture,
op2(h(sK0),h(sK0)) = h(sK0),
inference(paramod,[status(thm)],[c_9,c_126]) ).
cnf(c_38,plain,
j(h(sK1)) = sK1,
inference(resolve,[status(thm)],[c_20,c_10]) ).
cnf(c_127,negated_conjecture,
( op1(j(h(sK1)),j(A)) = j(op2(h(sK1),A))
| ~ sorti2(A) ),
inference(resolve,[status(thm)],[c_18,c_28]) ).
cnf(c_128,negated_conjecture,
op1(j(h(sK1)),j(h(sK1))) = j(op2(h(sK1),h(sK1))),
inference(resolve,[status(thm)],[c_127,c_28]) ).
cnf(c_129,negated_conjecture,
op1(sK1,j(h(sK1))) = j(op2(h(sK1),h(sK1))),
inference(paramod,[status(thm)],[c_38,c_128]) ).
cnf(c_130,negated_conjecture,
op1(sK1,sK1) = j(op2(h(sK1),h(sK1))),
inference(paramod,[status(thm)],[c_38,c_129]) ).
cnf(c_131,negated_conjecture,
op1(sK1,sK1) = j(h(op1(sK1,sK1))),
inference(paramod,[status(thm)],[c_34,c_130]) ).
cnf(c_46,negated_conjecture,
j(h(op1(sK1,sK1))) = op1(sK1,sK1),
inference(copy,[status(thm)],[c_131]) ).
cnf(c_132,plain,
( op2(A,A) = A
| ~ sorti2(A)
| op2(h(sK0),h(sK0)) != h(sK0) ),
inference(resolve,[status(thm)],[c_29,c_12]) ).
cnf(c_133,plain,
( op2(A,A) = A
| ~ sorti2(A)
| h(sK0) != h(sK0) ),
inference(paramod,[status(thm)],[c_37,c_132]) ).
cnf(c_50,plain,
( op2(A,A) = A
| ~ sorti2(A) ),
inference(copy,[status(thm)],[c_133]) ).
cnf(c_134,plain,
op2(h(sK1),h(sK1)) = h(sK1),
inference(resolve,[status(thm)],[c_50,c_28]) ).
cnf(c_111,plain,
h(op1(sK1,sK1)) = h(sK1),
inference(paramod,[status(thm)],[c_34,c_134]) ).
cnf(c_135,negated_conjecture,
j(h(sK1)) = op1(sK1,sK1),
inference(paramod,[status(thm)],[c_111,c_46]) ).
cnf(c_136,negated_conjecture,
sK1 = op1(sK1,sK1),
inference(paramod,[status(thm)],[c_38,c_135]) ).
cnf(c_137,negated_conjecture,
op1(sK1,sK1) = sK1,
inference(copy,[status(thm)],[c_136]) ).
cnf(c_123,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_11,c_137]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG203+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n011.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Sat Sep 26 21:25:15 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 1569992 was started by sandbox on n011,
% 0.03/0.36 % Sat Sep 26 21:25:15 2026
% 0.03/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.03/0.36
% 0.03/0.36 % 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 23.
% 0.03/0.38 % Level of proof is 6.
% 0.03/0.38 % Maximum clause weight is 29.000.
% 0.03/0.38 % Given clauses 23.
% 0.03/0.38
% 0.03/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------