%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : ALG071+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 : n026.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 0.15s 5.47s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 5
% Syntax : Number of formulae : 59 ( 26 unt; 0 def)
% Number of atoms : 141 ( 59 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 131 ( 49 ~; 38 |; 20 &)
% ( 0 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-2 aty)
% Number of variables : 59 ( 0 sgn 29 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax1,axiom,
! [U] :
( sorti1(U)
=> ! [V] :
( sorti1(V)
=> sorti1(op1(U,V)) ) ),
file('theBenchmark.p',ax1) ).
fof(ax2,axiom,
! [U] :
( sorti2(U)
=> ! [V] :
( sorti2(V)
=> sorti2(op2(U,V)) ) ),
file('theBenchmark.p',ax2) ).
fof(ax3,axiom,
! [U] :
( sorti1(U)
=> ? [V] :
( op1(U,op1(V,U)) = V
& op1(V,op1(V,U)) != U
& sorti1(V) ) ),
file('theBenchmark.p',ax3) ).
fof(ax4,axiom,
~ ! [U] :
( sorti2(U)
=> ? [V] :
( op2(U,op2(V,U)) = V
& op2(V,op2(V,U)) != U
& sorti2(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_6,plain,
( sorti1(op1(A,B))
| ~ sorti1(B)
| ~ sorti1(A) ),
inference(clausify,[status(thm)],[ax1]) ).
cnf(c_7,plain,
( sorti2(op2(A,B))
| ~ sorti2(B)
| ~ sorti2(A) ),
inference(clausify,[status(thm)],[ax2]) ).
fof(nnf_3,plain,
! [U] :
( ? [V] :
( op1(U,op1(V,U)) = V
& op1(V,op1(V,U)) != U
& sorti1(V) )
| ~ sorti1(U) ),
inference(fof_nnf,[status(thm)],[ax3]) ).
fof(sk_ax3_sk,plain,
! [U] :
( ( op1(U,op1(sK0(U),U)) = sK0(U)
& op1(sK0(U),op1(sK0(U),U)) != U
& sorti1(sK0(U)) )
| ~ sorti1(U) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(V,sK0(U))],[nnf_3]) ).
fof(sk_ax3,plain,
( ! [VAR_0] :
( op1(VAR_0,op1(sK0(VAR_0),VAR_0)) = sK0(VAR_0)
| ~ sorti1(VAR_0) )
& ! [VAR_0] :
( op1(sK0(VAR_0),op1(sK0(VAR_0),VAR_0)) != VAR_0
| ~ sorti1(VAR_0) )
& ! [VAR_0] :
( sorti1(sK0(VAR_0))
| ~ sorti1(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_ax3_sk]) ).
cnf(c_8,plain,
( sorti1(sK0(A))
| ~ sorti1(A) ),
inference(split_conjunct,[status(thm)],[sk_ax3]) ).
cnf(c_9,plain,
( op1(sK0(A),op1(sK0(A),A)) != A
| ~ sorti1(A) ),
inference(split_conjunct,[status(thm)],[sk_ax3]) ).
cnf(c_10,plain,
( op1(A,op1(sK0(A),A)) = sK0(A)
| ~ sorti1(A) ),
inference(split_conjunct,[status(thm)],[sk_ax3]) ).
fof(nnf_4,plain,
? [U] :
( ! [V] :
( op2(U,op2(V,U)) != V
| op2(V,op2(V,U)) = U
| ~ sorti2(V) )
& sorti2(U) ),
inference(fof_nnf,[status(thm)],[ax4]) ).
fof(sk_ax4,plain,
( ! [V] :
( op2(sK1,op2(V,sK1)) != V
| op2(V,op2(V,sK1)) = sK1
| ~ sorti2(V) )
& sorti2(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U,sK1)],[nnf_4]) ).
cnf(c_11,plain,
sorti2(sK1),
inference(split_conjunct,[status(thm)],[sk_ax4]) ).
cnf(c_12,plain,
( op2(sK1,op2(A,sK1)) != A
| op2(A,op2(A,sK1)) = sK1
| ~ sorti2(A) ),
inference(split_conjunct,[status(thm)],[sk_ax4]) ).
cnf(c_13,negated_conjecture,
( sorti2(h(A))
| ~ sorti1(A) ),
inference(clausify,[status(thm)],[co1_neg]) ).
cnf(c_14,negated_conjecture,
( sorti1(j(A))
| ~ sorti2(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_19,negated_conjecture,
( h(j(A)) = A
| ~ sorti2(A) ),
inference(clausify,[status(thm)],[co1_neg]) ).
cnf(c_20,negated_conjecture,
( j(h(A)) = A
| ~ sorti1(A) ),
inference(clausify,[status(thm)],[co1_neg]) ).
cnf(c_21,plain,
( sorti2(op2(A,sK1))
| ~ sorti2(A) ),
inference(resolve,[status(thm)],[c_11,c_7]) ).
cnf(c_24,plain,
sorti1(j(sK1)),
inference(resolve,[status(thm)],[c_14,c_11]) ).
cnf(c_28,plain,
h(j(sK1)) = sK1,
inference(resolve,[status(thm)],[c_19,c_11]) ).
cnf(c_31,plain,
op1(j(sK1),op1(sK0(j(sK1)),j(sK1))) = sK0(j(sK1)),
inference(resolve,[status(thm)],[c_24,c_10]) ).
cnf(c_32,plain,
op1(sK0(j(sK1)),op1(sK0(j(sK1)),j(sK1))) != j(sK1),
inference(resolve,[status(thm)],[c_24,c_9]) ).
cnf(c_33,plain,
sorti1(sK0(j(sK1))),
inference(resolve,[status(thm)],[c_24,c_8]) ).
cnf(c_49,plain,
j(h(sK0(j(sK1)))) = sK0(j(sK1)),
inference(resolve,[status(thm)],[c_33,c_20]) ).
cnf(c_52,plain,
sorti2(h(sK0(j(sK1)))),
inference(resolve,[status(thm)],[c_33,c_13]) ).
cnf(c_515,negated_conjecture,
( op2(h(sK0(j(sK1))),h(A)) = h(op1(sK0(j(sK1)),A))
| ~ sorti1(A) ),
inference(resolve,[status(thm)],[c_16,c_33]) ).
cnf(c_516,negated_conjecture,
op2(h(sK0(j(sK1))),h(j(sK1))) = h(op1(sK0(j(sK1)),j(sK1))),
inference(resolve,[status(thm)],[c_515,c_24]) ).
cnf(c_517,negated_conjecture,
op2(h(sK0(j(sK1))),sK1) = h(op1(sK0(j(sK1)),j(sK1))),
inference(paramod,[status(thm)],[c_28,c_516]) ).
cnf(c_60,negated_conjecture,
h(op1(sK0(j(sK1)),j(sK1))) = op2(h(sK0(j(sK1))),sK1),
inference(copy,[status(thm)],[c_517]) ).
cnf(c_518,plain,
( sorti1(op1(sK0(j(sK1)),A))
| ~ sorti1(A) ),
inference(resolve,[status(thm)],[c_6,c_33]) ).
cnf(c_63,plain,
sorti1(op1(sK0(j(sK1)),j(sK1))),
inference(resolve,[status(thm)],[c_518,c_24]) ).
cnf(c_83,plain,
sorti2(op2(h(sK0(j(sK1))),sK1)),
inference(resolve,[status(thm)],[c_52,c_21]) ).
cnf(c_86,plain,
( op2(sK1,op2(h(sK0(j(sK1))),sK1)) != h(sK0(j(sK1)))
| op2(h(sK0(j(sK1))),op2(h(sK0(j(sK1))),sK1)) = sK1 ),
inference(resolve,[status(thm)],[c_52,c_12]) ).
cnf(c_519,negated_conjecture,
( op1(j(h(sK0(j(sK1)))),j(A)) = j(op2(h(sK0(j(sK1))),A))
| ~ sorti2(A) ),
inference(resolve,[status(thm)],[c_18,c_52]) ).
cnf(c_520,negated_conjecture,
op1(j(h(sK0(j(sK1)))),j(sK1)) = j(op2(h(sK0(j(sK1))),sK1)),
inference(resolve,[status(thm)],[c_519,c_11]) ).
cnf(c_521,negated_conjecture,
op1(sK0(j(sK1)),j(sK1)) = j(op2(h(sK0(j(sK1))),sK1)),
inference(paramod,[status(thm)],[c_49,c_520]) ).
cnf(c_92,negated_conjecture,
j(op2(h(sK0(j(sK1))),sK1)) = op1(sK0(j(sK1)),j(sK1)),
inference(copy,[status(thm)],[c_521]) ).
cnf(c_522,negated_conjecture,
( op2(h(j(sK1)),h(A)) = h(op1(j(sK1),A))
| ~ sorti1(A) ),
inference(resolve,[status(thm)],[c_16,c_24]) ).
cnf(c_523,negated_conjecture,
op2(h(j(sK1)),h(op1(sK0(j(sK1)),j(sK1)))) = h(op1(j(sK1),op1(sK0(j(sK1)),j(sK1)))),
inference(resolve,[status(thm)],[c_522,c_63]) ).
cnf(c_524,negated_conjecture,
op2(sK1,h(op1(sK0(j(sK1)),j(sK1)))) = h(op1(j(sK1),op1(sK0(j(sK1)),j(sK1)))),
inference(paramod,[status(thm)],[c_28,c_523]) ).
cnf(c_525,negated_conjecture,
op2(sK1,op2(h(sK0(j(sK1))),sK1)) = h(op1(j(sK1),op1(sK0(j(sK1)),j(sK1)))),
inference(paramod,[status(thm)],[c_60,c_524]) ).
cnf(c_199,negated_conjecture,
op2(sK1,op2(h(sK0(j(sK1))),sK1)) = h(sK0(j(sK1))),
inference(paramod,[status(thm)],[c_31,c_525]) ).
cnf(c_526,plain,
( h(sK0(j(sK1))) != h(sK0(j(sK1)))
| op2(h(sK0(j(sK1))),op2(h(sK0(j(sK1))),sK1)) = sK1 ),
inference(paramod,[status(thm)],[c_199,c_86]) ).
cnf(c_214,plain,
op2(h(sK0(j(sK1))),op2(h(sK0(j(sK1))),sK1)) = sK1,
inference(copy,[status(thm)],[c_526]) ).
cnf(c_527,negated_conjecture,
( op1(j(h(sK0(j(sK1)))),j(A)) = j(op2(h(sK0(j(sK1))),A))
| ~ sorti2(A) ),
inference(resolve,[status(thm)],[c_18,c_52]) ).
cnf(c_528,negated_conjecture,
op1(j(h(sK0(j(sK1)))),j(op2(h(sK0(j(sK1))),sK1))) = j(op2(h(sK0(j(sK1))),op2(h(sK0(j(sK1))),sK1))),
inference(resolve,[status(thm)],[c_527,c_83]) ).
cnf(c_529,negated_conjecture,
op1(sK0(j(sK1)),j(op2(h(sK0(j(sK1))),sK1))) = j(op2(h(sK0(j(sK1))),op2(h(sK0(j(sK1))),sK1))),
inference(paramod,[status(thm)],[c_49,c_528]) ).
cnf(c_530,negated_conjecture,
op1(sK0(j(sK1)),op1(sK0(j(sK1)),j(sK1))) = j(op2(h(sK0(j(sK1))),op2(h(sK0(j(sK1))),sK1))),
inference(paramod,[status(thm)],[c_92,c_529]) ).
cnf(c_531,negated_conjecture,
op1(sK0(j(sK1)),op1(sK0(j(sK1)),j(sK1))) = j(sK1),
inference(paramod,[status(thm)],[c_214,c_530]) ).
cnf(c_514,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_32,c_531]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG071+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/5.38 % Computer : n026.cluster.edu
% 0.12/5.38 % Model : x86_64 x86_64
% 0.12/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.38 % Memory : 8046.5625MB
% 0.12/5.38 % OS : Linux 6.8.0-71-generic
% 0.12/5.38 % CPULimit : 300
% 0.12/5.38 % WCLimit : 300
% 0.12/5.38 % DateTime : Sat Sep 26 21:08:01 UTC 2026
% 0.12/5.39 % CPUTime :
% 0.12/5.39 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/5.39 % Process 1951117 was started by sandbox2 on n026,
% 0.12/5.39 % Sat Sep 26 21:08:01 2026
% 0.12/5.39 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.12/5.39
% 0.12/5.39 % From the command line: assign(max_seconds, 300).
% 0.15/5.47
% 0.15/5.47 % SZS status Theorem for theBenchmark
% 0.15/5.47
% 0.15/5.47 % Proof 1 at 0.04 (+ 0.02) seconds.
% 0.15/5.47 % Length of proof is 36.
% 0.15/5.47 % Level of proof is 7.
% 0.15/5.47 % Maximum clause weight is 66.000.
% 0.15/5.47 % Given clauses 56.
% 0.15/5.47
% 0.15/5.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------