%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : ALG178+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 : 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 06:49:39 AM UTC 2026
% Result : Theorem 0.10s 0.41s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 4
% Syntax : Number of formulae : 38 ( 21 unt; 0 def)
% Number of atoms : 88 ( 32 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 71 ( 21 ~; 14 |; 12 &)
% ( 0 <=>; 24 =>; 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 : 38 ( 0 sgn 22 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax2,axiom,
! [U] :
( sorti2(U)
=> ! [V] :
( sorti2(V)
=> sorti2(op2(U,V)) ) ),
file('theBenchmark.p',ax2) ).
fof(ax3,axiom,
! [U] :
( sorti1(U)
=> ! [V] :
( sorti1(V)
=> op1(U,op1(U,V)) = V ) ),
file('theBenchmark.p',ax3) ).
fof(ax4,axiom,
~ ! [U] :
( sorti2(U)
=> ! [V] :
( sorti2(V)
=> op2(U,op2(U,V)) = 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_7,plain,
( sorti2(op2(A,B))
| ~ sorti2(B)
| ~ sorti2(A) ),
inference(clausify,[status(thm)],[ax2]) ).
cnf(c_8,plain,
( op1(A,op1(A,B)) = B
| ~ sorti1(B)
| ~ sorti1(A) ),
inference(clausify,[status(thm)],[ax3]) ).
fof(nnf_4,plain,
? [U] :
( ? [V] :
( op2(U,op2(U,V)) != V
& sorti2(V) )
& sorti2(U) ),
inference(fof_nnf,[status(thm)],[ax4]) ).
fof(sk_ax4,plain,
( op2(sK0,op2(sK0,sK1)) != 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,op2(sK0,sK1)) != sK1,
inference(split_conjunct,[status(thm)],[sk_ax4]) ).
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_15,negated_conjecture,
( j(op2(A,B)) = op1(j(A),j(B))
| ~ sorti2(B)
| ~ sorti2(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_146,plain,
( sorti2(op2(sK0,A))
| ~ sorti2(A) ),
inference(resolve,[status(thm)],[c_7,c_9]) ).
cnf(c_20,plain,
sorti2(op2(sK0,sK1)),
inference(resolve,[status(thm)],[c_146,c_10]) ).
cnf(c_22,negated_conjecture,
sorti1(j(sK1)),
inference(resolve,[status(thm)],[c_13,c_10]) ).
cnf(c_23,negated_conjecture,
sorti1(j(sK0)),
inference(resolve,[status(thm)],[c_13,c_9]) ).
cnf(c_147,negated_conjecture,
( j(op2(sK0,A)) = op1(j(sK0),j(A))
| ~ sorti2(A) ),
inference(resolve,[status(thm)],[c_15,c_9]) ).
cnf(c_26,negated_conjecture,
j(op2(sK0,sK1)) = op1(j(sK0),j(sK1)),
inference(resolve,[status(thm)],[c_147,c_10]) ).
cnf(c_28,negated_conjecture,
h(j(sK1)) = sK1,
inference(resolve,[status(thm)],[c_16,c_10]) ).
cnf(c_29,negated_conjecture,
h(j(sK0)) = sK0,
inference(resolve,[status(thm)],[c_16,c_9]) ).
cnf(c_148,negated_conjecture,
h(j(op2(sK0,sK1))) = op2(sK0,sK1),
inference(resolve,[status(thm)],[c_16,c_20]) ).
cnf(c_58,negated_conjecture,
h(op1(j(sK0),j(sK1))) = op2(sK0,sK1),
inference(paramod,[status(thm)],[c_26,c_148]) ).
cnf(c_149,negated_conjecture,
sorti1(j(op2(sK0,sK1))),
inference(resolve,[status(thm)],[c_13,c_20]) ).
cnf(c_68,negated_conjecture,
sorti1(op1(j(sK0),j(sK1))),
inference(paramod,[status(thm)],[c_26,c_149]) ).
cnf(c_150,plain,
( op1(j(sK0),op1(j(sK0),A)) = A
| ~ sorti1(A) ),
inference(resolve,[status(thm)],[c_8,c_23]) ).
cnf(c_83,plain,
op1(j(sK0),op1(j(sK0),j(sK1))) = j(sK1),
inference(resolve,[status(thm)],[c_150,c_22]) ).
cnf(c_151,negated_conjecture,
( h(op1(j(sK0),A)) = op2(h(j(sK0)),h(A))
| ~ sorti1(A) ),
inference(resolve,[status(thm)],[c_14,c_23]) ).
cnf(c_152,negated_conjecture,
h(op1(j(sK0),op1(j(sK0),j(sK1)))) = op2(h(j(sK0)),h(op1(j(sK0),j(sK1)))),
inference(resolve,[status(thm)],[c_151,c_68]) ).
cnf(c_153,negated_conjecture,
h(j(sK1)) = op2(h(j(sK0)),h(op1(j(sK0),j(sK1)))),
inference(paramod,[status(thm)],[c_83,c_152]) ).
cnf(c_154,negated_conjecture,
sK1 = op2(h(j(sK0)),h(op1(j(sK0),j(sK1)))),
inference(paramod,[status(thm)],[c_28,c_153]) ).
cnf(c_155,negated_conjecture,
sK1 = op2(sK0,h(op1(j(sK0),j(sK1)))),
inference(paramod,[status(thm)],[c_29,c_154]) ).
cnf(c_156,negated_conjecture,
sK1 = op2(sK0,op2(sK0,sK1)),
inference(paramod,[status(thm)],[c_58,c_155]) ).
cnf(c_144,negated_conjecture,
op2(sK0,op2(sK0,sK1)) = sK1,
inference(copy,[status(thm)],[c_156]) ).
cnf(c_145,plain,
$false,
inference(resolve,[status(thm)],[c_144,c_11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : ALG178+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.05 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n013.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 26 21:22:21 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.38 % Process 3584397 was started by sandbox2 on n013,
% 0.10/0.38 % Sat Sep 26 21:22:21 2026
% 0.10/0.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.38
% 0.10/0.38 % From the command line: assign(max_seconds, 300).
% 0.10/0.41
% 0.10/0.41 % SZS status Theorem for theBenchmark
% 0.10/0.41
% 0.10/0.41 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.10/0.41 % Length of proof is 24.
% 0.10/0.41 % Level of proof is 5.
% 0.10/0.41 % Maximum clause weight is 36.000.
% 0.10/0.41 % Given clauses 26.
% 0.10/0.41
% 0.10/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------