%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : ALG073+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 : n007.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 0.14s 5.40s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 4
% Syntax : Number of formulae : 45 ( 26 unt; 0 def)
% Number of atoms : 109 ( 55 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 93 ( 29 ~; 20 |; 24 &)
% ( 0 <=>; 20 =>; 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 : 37 ( 0 sgn 18 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax1,axiom,
! [U] :
( sorti1(U)
=> ! [V] :
( sorti1(V)
=> sorti1(op1(U,V)) ) ),
file('theBenchmark.p',ax1) ).
fof(ax3,axiom,
? [U] :
( ? [V] :
( op1(U,V) != U
& op1(V,V) = U
& op1(U,U) = V
& sorti1(V) )
& sorti1(U) ),
file('theBenchmark.p',ax3) ).
fof(ax4,axiom,
~ ? [U] :
( ? [V] :
( op2(U,V) != U
& op2(V,V) = U
& op2(U,U) = V
& sorti2(V) )
& 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]) ).
cnf(c_6,plain,
( sorti1(op1(A,B))
| ~ sorti1(B)
| ~ sorti1(A) ),
inference(clausify,[status(thm)],[ax1]) ).
fof(nnf_3,plain,
? [U] :
( ? [V] :
( op1(U,V) != U
& op1(V,V) = U
& op1(U,U) = V
& sorti1(V) )
& sorti1(U) ),
inference(fof_nnf,[status(thm)],[ax3]) ).
fof(sk_ax3,plain,
( op1(sK0,sK1) != sK0
& op1(sK1,sK1) = sK0
& op1(sK0,sK0) = sK1
& sorti1(sK1)
& 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,
sorti1(sK1),
inference(split_conjunct,[status(thm)],[sk_ax3]) ).
cnf(c_10,plain,
op1(sK0,sK0) = sK1,
inference(split_conjunct,[status(thm)],[sk_ax3]) ).
cnf(c_11,plain,
op1(sK1,sK1) = sK0,
inference(split_conjunct,[status(thm)],[sk_ax3]) ).
cnf(c_12,plain,
op1(sK0,sK1) != sK0,
inference(split_conjunct,[status(thm)],[sk_ax3]) ).
cnf(c_13,plain,
( op2(A,B) = A
| op2(B,B) != A
| op2(A,A) != B
| ~ sorti2(B)
| ~ sorti2(A) ),
inference(clausify,[status(thm)],[ax4]) ).
cnf(c_14,negated_conjecture,
( sorti2(h(A))
| ~ sorti1(A) ),
inference(clausify,[status(thm)],[co1_neg]) ).
cnf(c_16,negated_conjecture,
( h(op1(A,B)) = op2(h(A),h(B))
| ~ sorti1(B)
| ~ sorti1(A) ),
inference(clausify,[status(thm)],[co1_neg]) ).
cnf(c_19,negated_conjecture,
( j(h(A)) = A
| ~ sorti1(A) ),
inference(clausify,[status(thm)],[co1_neg]) ).
cnf(c_138,plain,
( sorti1(op1(sK0,A))
| ~ sorti1(A) ),
inference(resolve,[status(thm)],[c_6,c_8]) ).
cnf(c_20,plain,
sorti1(op1(sK0,sK1)),
inference(resolve,[status(thm)],[c_138,c_9]) ).
cnf(c_22,negated_conjecture,
sorti2(h(sK1)),
inference(resolve,[status(thm)],[c_14,c_9]) ).
cnf(c_23,negated_conjecture,
sorti2(h(sK0)),
inference(resolve,[status(thm)],[c_14,c_8]) ).
cnf(c_139,negated_conjecture,
( h(op1(sK1,A)) = op2(h(sK1),h(A))
| ~ sorti1(A) ),
inference(resolve,[status(thm)],[c_16,c_9]) ).
cnf(c_140,negated_conjecture,
h(op1(sK1,sK1)) = op2(h(sK1),h(sK1)),
inference(resolve,[status(thm)],[c_139,c_9]) ).
cnf(c_141,negated_conjecture,
h(sK0) = op2(h(sK1),h(sK1)),
inference(paramod,[status(thm)],[c_11,c_140]) ).
cnf(c_24,negated_conjecture,
op2(h(sK1),h(sK1)) = h(sK0),
inference(copy,[status(thm)],[c_141]) ).
cnf(c_142,negated_conjecture,
( h(op1(sK0,A)) = op2(h(sK0),h(A))
| ~ sorti1(A) ),
inference(resolve,[status(thm)],[c_16,c_8]) ).
cnf(c_26,negated_conjecture,
h(op1(sK0,sK1)) = op2(h(sK0),h(sK1)),
inference(resolve,[status(thm)],[c_142,c_9]) ).
cnf(c_143,negated_conjecture,
( h(op1(sK0,A)) = op2(h(sK0),h(A))
| ~ sorti1(A) ),
inference(resolve,[status(thm)],[c_16,c_8]) ).
cnf(c_144,negated_conjecture,
h(op1(sK0,sK0)) = op2(h(sK0),h(sK0)),
inference(resolve,[status(thm)],[c_143,c_8]) ).
cnf(c_27,negated_conjecture,
h(sK1) = op2(h(sK0),h(sK0)),
inference(paramod,[status(thm)],[c_10,c_144]) ).
cnf(c_28,negated_conjecture,
h(op1(sK0,sK1)) = op2(h(sK0),op2(h(sK0),h(sK0))),
inference(paramod,[status(thm)],[c_27,c_26]) ).
cnf(c_145,negated_conjecture,
op2(op2(h(sK0),h(sK0)),h(sK1)) = h(sK0),
inference(paramod,[status(thm)],[c_27,c_24]) ).
cnf(c_30,negated_conjecture,
op2(op2(h(sK0),h(sK0)),op2(h(sK0),h(sK0))) = h(sK0),
inference(paramod,[status(thm)],[c_27,c_145]) ).
cnf(c_31,negated_conjecture,
sorti2(op2(h(sK0),h(sK0))),
inference(paramod,[status(thm)],[c_27,c_22]) ).
cnf(c_33,negated_conjecture,
j(h(sK0)) = sK0,
inference(resolve,[status(thm)],[c_19,c_8]) ).
cnf(c_146,negated_conjecture,
j(h(op1(sK0,sK1))) = op1(sK0,sK1),
inference(resolve,[status(thm)],[c_19,c_20]) ).
cnf(c_34,negated_conjecture,
j(op2(h(sK0),op2(h(sK0),h(sK0)))) = op1(sK0,sK1),
inference(paramod,[status(thm)],[c_28,c_146]) ).
cnf(c_147,plain,
( op2(h(sK0),A) = h(sK0)
| op2(A,A) != h(sK0)
| op2(h(sK0),h(sK0)) != A
| ~ sorti2(A) ),
inference(resolve,[status(thm)],[c_13,c_23]) ).
cnf(c_148,plain,
( op2(h(sK0),op2(h(sK0),h(sK0))) = h(sK0)
| op2(op2(h(sK0),h(sK0)),op2(h(sK0),h(sK0))) != h(sK0)
| op2(h(sK0),h(sK0)) != op2(h(sK0),h(sK0)) ),
inference(resolve,[status(thm)],[c_147,c_31]) ).
cnf(c_149,plain,
( op2(h(sK0),op2(h(sK0),h(sK0))) = h(sK0)
| op2(op2(h(sK0),h(sK0)),op2(h(sK0),h(sK0))) != h(sK0) ),
inference(xxres,[status(thm)],[c_148]) ).
cnf(c_113,plain,
op2(h(sK0),op2(h(sK0),h(sK0))) = h(sK0),
inference(resolve,[status(thm)],[c_149,c_30]) ).
cnf(c_150,negated_conjecture,
j(h(sK0)) = op1(sK0,sK1),
inference(paramod,[status(thm)],[c_113,c_34]) ).
cnf(c_151,negated_conjecture,
sK0 = op1(sK0,sK1),
inference(paramod,[status(thm)],[c_33,c_150]) ).
cnf(c_136,negated_conjecture,
op1(sK0,sK1) = sK0,
inference(copy,[status(thm)],[c_151]) ).
cnf(c_137,plain,
$false,
inference(resolve,[status(thm)],[c_136,c_12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG073+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/5.37 % Computer : n007.cluster.edu
% 0.11/5.37 % Model : x86_64 x86_64
% 0.11/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.37 % Memory : 8046.5625MB
% 0.11/5.37 % OS : Linux 6.8.0-71-generic
% 0.11/5.37 % CPULimit : 300
% 0.11/5.37 % WCLimit : 300
% 0.11/5.37 % DateTime : Sat Sep 26 21:03:59 UTC 2026
% 0.11/5.38 % CPUTime :
% 0.11/5.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/5.38 % Process 478751 was started by sandbox on n007,
% 0.11/5.38 % Sat Sep 26 21:03:59 2026
% 0.11/5.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/5.38
% 0.11/5.38 % From the command line: assign(max_seconds, 300).
% 0.14/5.40
% 0.14/5.40 % SZS status Theorem for theBenchmark
% 0.14/5.40
% 0.14/5.40 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.14/5.40 % Length of proof is 28.
% 0.14/5.40 % Level of proof is 6.
% 0.14/5.40 % Maximum clause weight is 44.000.
% 0.14/5.40 % Given clauses 26.
% 0.14/5.40
% 0.14/5.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------