%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : ALG074+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 06:49:25 AM UTC 2026
% Result : Theorem 17.70s 2.75s
% Output : CNFRefutation 17.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 4
% Syntax : Number of formulae : 55 ( 30 unt; 0 def)
% Number of atoms : 126 ( 68 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 104 ( 33 ~; 27 |; 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 : 39 ( 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(op1(U,V),U) != V
& op1(op1(U,V),V) = U
& op1(V,U) != op1(U,V)
& sorti1(V) )
& sorti1(U) ),
file('theBenchmark.p',ax3) ).
fof(ax4,axiom,
~ ? [U] :
( ? [V] :
( op2(op2(U,V),U) != V
& op2(op2(U,V),V) = U
& op2(V,U) != op2(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(op1(U,V),U) != V
& op1(op1(U,V),V) = U
& op1(V,U) != op1(U,V)
& sorti1(V) )
& sorti1(U) ),
inference(fof_nnf,[status(thm)],[ax3]) ).
fof(sk_ax3,plain,
( op1(op1(sK0,sK1),sK0) != sK1
& op1(op1(sK0,sK1),sK1) = sK0
& op1(sK1,sK0) != op1(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(sK1,sK0) != op1(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_ax3]) ).
cnf(c_11,plain,
op1(op1(sK0,sK1),sK1) = sK0,
inference(split_conjunct,[status(thm)],[sk_ax3]) ).
cnf(c_12,plain,
op1(op1(sK0,sK1),sK0) != sK1,
inference(split_conjunct,[status(thm)],[sk_ax3]) ).
cnf(c_13,plain,
( op2(op2(A,B),A) = B
| op2(op2(A,B),B) != A
| op2(B,A) = op2(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_24,plain,
( sorti1(op1(A,sK0))
| ~ sorti1(A) ),
inference(resolve,[status(thm)],[c_8,c_6]) ).
cnf(c_25,plain,
( sorti1(op1(sK0,A))
| ~ sorti1(A) ),
inference(resolve,[status(thm)],[c_8,c_6]) ).
cnf(c_28,plain,
sorti2(h(sK1)),
inference(resolve,[status(thm)],[c_14,c_9]) ).
cnf(c_29,plain,
sorti2(h(sK0)),
inference(resolve,[status(thm)],[c_14,c_8]) ).
cnf(c_30,plain,
( h(op1(sK1,A)) = op2(h(sK1),h(A))
| ~ sorti1(A) ),
inference(resolve,[status(thm)],[c_16,c_9]) ).
cnf(c_31,plain,
( h(op1(sK0,A)) = op2(h(sK0),h(A))
| ~ sorti1(A) ),
inference(resolve,[status(thm)],[c_16,c_8]) ).
cnf(c_32,plain,
( h(op1(A,sK1)) = op2(h(A),h(sK1))
| ~ sorti1(A) ),
inference(resolve,[status(thm)],[c_16,c_9]) ).
cnf(c_33,plain,
( h(op1(A,sK0)) = op2(h(A),h(sK0))
| ~ sorti1(A) ),
inference(resolve,[status(thm)],[c_16,c_8]) ).
cnf(c_34,plain,
j(h(sK1)) = sK1,
inference(resolve,[status(thm)],[c_19,c_9]) ).
cnf(c_40,plain,
sorti1(op1(sK1,sK0)),
inference(resolve,[status(thm)],[c_24,c_9]) ).
cnf(c_41,plain,
sorti1(op1(sK0,sK1)),
inference(resolve,[status(thm)],[c_25,c_9]) ).
cnf(c_46,plain,
( op2(op2(A,h(sK1)),A) = h(sK1)
| op2(op2(A,h(sK1)),h(sK1)) != A
| op2(h(sK1),A) = op2(A,h(sK1))
| ~ sorti2(A) ),
inference(resolve,[status(thm)],[c_28,c_13]) ).
cnf(c_81,plain,
j(h(op1(sK1,sK0))) = op1(sK1,sK0),
inference(resolve,[status(thm)],[c_40,c_19]) ).
cnf(c_88,plain,
sorti1(op1(op1(sK0,sK1),sK0)),
inference(resolve,[status(thm)],[c_41,c_24]) ).
cnf(c_91,plain,
j(h(op1(sK0,sK1))) = op1(sK0,sK1),
inference(resolve,[status(thm)],[c_41,c_19]) ).
cnf(c_105,plain,
h(op1(sK1,sK0)) = op2(h(sK1),h(sK0)),
inference(resolve,[status(thm)],[c_30,c_8]) ).
cnf(c_110,plain,
j(op2(h(sK1),h(sK0))) = op1(sK1,sK0),
inference(paramod,[status(thm)],[c_105,c_81]) ).
cnf(c_116,plain,
h(op1(sK0,sK1)) = op2(h(sK0),h(sK1)),
inference(resolve,[status(thm)],[c_31,c_9]) ).
cnf(c_122,plain,
j(op2(h(sK0),h(sK1))) = op1(sK0,sK1),
inference(paramod,[status(thm)],[c_116,c_91]) ).
cnf(c_12416,plain,
h(op1(op1(sK0,sK1),sK1)) = op2(h(op1(sK0,sK1)),h(sK1)),
inference(resolve,[status(thm)],[c_32,c_41]) ).
cnf(c_12417,plain,
h(sK0) = op2(h(op1(sK0,sK1)),h(sK1)),
inference(paramod,[status(thm)],[c_11,c_12416]) ).
cnf(c_12418,plain,
h(sK0) = op2(op2(h(sK0),h(sK1)),h(sK1)),
inference(paramod,[status(thm)],[c_116,c_12417]) ).
cnf(c_148,plain,
op2(op2(h(sK0),h(sK1)),h(sK1)) = h(sK0),
inference(copy,[status(thm)],[c_12418]) ).
cnf(c_12419,plain,
h(op1(op1(sK0,sK1),sK0)) = op2(h(op1(sK0,sK1)),h(sK0)),
inference(resolve,[status(thm)],[c_33,c_41]) ).
cnf(c_152,plain,
h(op1(op1(sK0,sK1),sK0)) = op2(op2(h(sK0),h(sK1)),h(sK0)),
inference(paramod,[status(thm)],[c_116,c_12419]) ).
cnf(c_12420,plain,
( op2(op2(h(sK0),h(sK1)),h(sK0)) = h(sK1)
| op2(op2(h(sK0),h(sK1)),h(sK1)) != h(sK0)
| op2(h(sK1),h(sK0)) = op2(h(sK0),h(sK1)) ),
inference(resolve,[status(thm)],[c_46,c_29]) ).
cnf(c_12421,plain,
( op2(op2(h(sK0),h(sK1)),h(sK0)) = h(sK1)
| h(sK0) != h(sK0)
| op2(h(sK1),h(sK0)) = op2(h(sK0),h(sK1)) ),
inference(paramod,[status(thm)],[c_148,c_12420]) ).
cnf(c_252,plain,
( op2(op2(h(sK0),h(sK1)),h(sK0)) = h(sK1)
| op2(h(sK1),h(sK0)) = op2(h(sK0),h(sK1)) ),
inference(copy,[status(thm)],[c_12421]) ).
cnf(c_12422,negated_conjecture,
j(h(op1(op1(sK0,sK1),sK0))) = op1(op1(sK0,sK1),sK0),
inference(resolve,[status(thm)],[c_88,c_19]) ).
cnf(c_339,negated_conjecture,
j(op2(op2(h(sK0),h(sK1)),h(sK0))) = op1(op1(sK0,sK1),sK0),
inference(paramod,[status(thm)],[c_152,c_12422]) ).
cnf(c_12423,plain,
( j(h(sK1)) = op1(op1(sK0,sK1),sK0)
| op2(h(sK1),h(sK0)) = op2(h(sK0),h(sK1)) ),
inference(paramod,[status(thm)],[c_252,c_339]) ).
cnf(c_12424,plain,
( sK1 = op1(op1(sK0,sK1),sK0)
| op2(h(sK1),h(sK0)) = op2(h(sK0),h(sK1)) ),
inference(paramod,[status(thm)],[c_34,c_12423]) ).
cnf(c_12425,plain,
( op1(op1(sK0,sK1),sK0) = sK1
| op2(h(sK1),h(sK0)) = op2(h(sK0),h(sK1)) ),
inference(copy,[status(thm)],[c_12424]) ).
cnf(c_12276,plain,
op2(h(sK1),h(sK0)) = op2(h(sK0),h(sK1)),
inference(resolve,[status(thm)],[c_12,c_12425]) ).
cnf(c_12426,plain,
j(op2(h(sK0),h(sK1))) = op1(sK1,sK0),
inference(paramod,[status(thm)],[c_12276,c_110]) ).
cnf(c_12427,plain,
op1(sK0,sK1) = op1(sK1,sK0),
inference(paramod,[status(thm)],[c_122,c_12426]) ).
cnf(c_12428,plain,
op1(sK1,sK0) = op1(sK0,sK1),
inference(copy,[status(thm)],[c_12427]) ).
cnf(c_12415,plain,
$false,
inference(resolve,[status(thm)],[c_10,c_12428]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG074+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n011.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 26 21:06:44 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 1540635 was started by sandbox on n011,
% 0.09/0.36 % Sat Sep 26 21:06:44 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.36
% 0.09/0.36 % From the command line: assign(max_seconds, 300).
% 17.70/2.75
% 17.70/2.75 % given #500 (T,wt=45): 653 sorti1(op1(c1,op1(op1(c1,c2),op1(c1,c2)))). [resolve(90,a,25,a)].
% 17.70/2.75
% 17.70/2.75 % SZS status Theorem for theBenchmark
% 17.70/2.75
% 17.70/2.75 % Proof 1 at 1.68 (+ 0.47) seconds.
% 17.70/2.75 % Length of proof is 39.
% 17.70/2.75 % Level of proof is 7.
% 17.70/2.75 % Maximum clause weight is 59.000.
% 17.70/2.75 % Given clauses 516.
% 17.70/2.75
% 17.70/2.75 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------