%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : ALG201+1 : TPTP v9.3.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.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 : Thu Sep 24 08:11:47 AM UTC 2026
% Result : Theorem 0.28s 0.60s
% Output : Proof 0.28s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% 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)
=> op1(U,U) != U ),
file('theBenchmark.p',ax3) ).
fof(ax4,axiom,
~ ! [U] :
( sorti2(U)
=> op2(U,U) != 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(f_1_1,plain,
! [U] :
( ! [V] :
( sorti1(op1(U,V))
| ~ sorti1(V) )
| ~ sorti1(U) ),
inference(fof_nnf,[status(thm)],[ax1]) ).
fof(f_1_2,plain,
! [U_1] :
( ! [U_0] :
( sorti1(op1(U_1,U_0))
| ~ sorti1(U_0) )
| ~ sorti1(U_1) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
cnf(f_1_3,plain,
( sorti1(op1(U_1,U_0))
| ~ sorti1(U_0)
| ~ sorti1(U_1) ),
inference(clausify,[status(thm)],[f_1_2]) ).
fof(f_2_1,plain,
! [U] :
( ! [V] :
( sorti2(op2(U,V))
| ~ sorti2(V) )
| ~ sorti2(U) ),
inference(fof_nnf,[status(thm)],[ax2]) ).
fof(f_2_2,plain,
! [U_3] :
( ! [U_2] :
( sorti2(op2(U_3,U_2))
| ~ sorti2(U_2) )
| ~ sorti2(U_3) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
cnf(f_2_3,plain,
( sorti2(op2(U_3,U_2))
| ~ sorti2(U_2)
| ~ sorti2(U_3) ),
inference(clausify,[status(thm)],[f_2_2]) ).
fof(f_3_1,plain,
! [U] :
( op1(U,U) != U
| ~ sorti1(U) ),
inference(fof_nnf,[status(thm)],[ax3]) ).
fof(f_3_2,plain,
! [U_4] :
( op1(U_4,U_4) != U_4
| ~ sorti1(U_4) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
cnf(f_3_3,plain,
( op1(U_4,U_4) != U_4
| ~ sorti1(U_4) ),
inference(clausify,[status(thm)],[f_3_2]) ).
fof(f_4_1,plain,
? [U] :
( op2(U,U) = U
& sorti2(U) ),
inference(fof_nnf,[status(thm)],[ax4]) ).
fof(f_4_2,plain,
? [U_5] :
( op2(U_5,U_5) = U_5
& sorti2(U_5) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
( op2(sK1,sK1) = sK1
& sorti2(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_5,sK1)],[f_4_2]) ).
cnf(f_4_4,plain,
sorti2(sK1),
inference(clausify,[status(thm)],[f_4_3]) ).
cnf(f_4_5,plain,
op2(sK1,sK1) = sK1,
inference(clausify,[status(thm)],[f_4_3]) ).
fof(f_5_1,negated_conjecture,
( ! [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)) ) )
& ! [V] :
( sorti2(V)
=> sorti1(j(V)) )
& ! [U] :
( sorti1(U)
=> sorti2(h(U)) ) ),
inference(negate,[status(cth)],[co1]) ).
fof(f_5_2,negated_conjecture,
( ! [X2] :
( j(h(X2)) = X2
| ~ sorti1(X2) )
& ! [X1] :
( h(j(X1)) = X1
| ~ sorti2(X1) )
& ! [Y] :
( ! [Z] :
( j(op2(Y,Z)) = op1(j(Y),j(Z))
| ~ sorti2(Z) )
| ~ sorti2(Y) )
& ! [W] :
( ! [X] :
( h(op1(W,X)) = op2(h(W),h(X))
| ~ sorti1(X) )
| ~ sorti1(W) )
& ! [V] :
( sorti1(j(V))
| ~ sorti2(V) )
& ! [U] :
( sorti2(h(U))
| ~ sorti1(U) ) ),
inference(fof_nnf,[status(thm)],[f_5_1]) ).
fof(f_5_3,negated_conjecture,
( ! [U_13] :
( j(h(U_13)) = U_13
| ~ sorti1(U_13) )
& ! [U_12] :
( h(j(U_12)) = U_12
| ~ sorti2(U_12) )
& ! [U_11] :
( ! [U_10] :
( j(op2(U_11,U_10)) = op1(j(U_11),j(U_10))
| ~ sorti2(U_10) )
| ~ sorti2(U_11) )
& ! [U_9] :
( ! [U_8] :
( h(op1(U_9,U_8)) = op2(h(U_9),h(U_8))
| ~ sorti1(U_8) )
| ~ sorti1(U_9) )
& ! [U_7] :
( sorti1(j(U_7))
| ~ sorti2(U_7) )
& ! [U_6] :
( sorti2(h(U_6))
| ~ sorti1(U_6) ) ),
inference(variable_rename,[status(thm)],[f_5_2]) ).
fof(f_5_4,negated_conjecture,
( ! [U_13] :
( j(h(U_13)) = U_13
| ~ sorti1(U_13) )
& ! [U_12] :
( h(j(U_12)) = U_12
| ~ sorti2(U_12) )
& ! [U_11,U_10] :
( j(op2(U_11,U_10)) = op1(j(U_11),j(U_10))
| ~ sorti2(U_10)
| ~ sorti2(U_11) )
& ! [U_8,U_9] :
( h(op1(U_9,U_8)) = op2(h(U_9),h(U_8))
| ~ sorti1(U_8)
| ~ sorti1(U_9) )
& ! [U_7] :
( sorti1(j(U_7))
| ~ sorti2(U_7) )
& ! [U_6] :
( sorti2(h(U_6))
| ~ sorti1(U_6) ) ),
inference(definitional_conversion,[status(esa)],[f_5_3]) ).
cnf(f_5_5,negated_conjecture,
( sorti2(h(U_6))
| ~ sorti1(U_6) ),
inference(clausify,[status(thm)],[f_5_4]) ).
cnf(f_5_6,negated_conjecture,
( sorti1(j(U_7))
| ~ sorti2(U_7) ),
inference(clausify,[status(thm)],[f_5_4]) ).
cnf(f_5_7,negated_conjecture,
( h(op1(U_9,U_8)) = op2(h(U_9),h(U_8))
| ~ sorti1(U_8)
| ~ sorti1(U_9) ),
inference(clausify,[status(thm)],[f_5_4]) ).
cnf(f_5_8,negated_conjecture,
( j(op2(U_11,U_10)) = op1(j(U_11),j(U_10))
| ~ sorti2(U_10)
| ~ sorti2(U_11) ),
inference(clausify,[status(thm)],[f_5_4]) ).
cnf(f_5_9,negated_conjecture,
( h(j(U_12)) = U_12
| ~ sorti2(U_12) ),
inference(clausify,[status(thm)],[f_5_4]) ).
cnf(f_5_10,negated_conjecture,
( j(h(U_13)) = U_13
| ~ sorti1(U_13) ),
inference(clausify,[status(thm)],[f_5_4]) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(equality_2,axiom,
( Eq_x_1 = Eq_x_0
| Eq_x_0 != Eq_x_1 ),
theory(equality,[symmetry]) ).
cnf(equality_3,axiom,
( Eq_x_0 = Eq_x_2
| Eq_x_1 != Eq_x_2
| Eq_x_0 != Eq_x_1 ),
theory(equality,[transitivity]) ).
cnf(equality_4,axiom,
( op1(Eq_x_0,Eq_x_1) = op1(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_5,axiom,
( op2(Eq_x_0,Eq_x_1) = op2(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_6,axiom,
( h(Eq_x_0) = h(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,axiom,
( j(Eq_x_0) = j(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_8,axiom,
( sorti1(Eq_y_0)
| ~ sorti1(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_9,axiom,
( sorti2(Eq_y_0)
| ~ sorti2(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : ALG201+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.05 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.05 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.42 % Computer : n017.cluster.edu
% 0.17/0.42 % Model : x86_64 x86_64
% 0.17/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.42 % Memory : 8046.5625MB
% 0.17/0.42 % OS : Linux 6.8.0-71-generic
% 0.17/0.42 % CPULimit : 300
% 0.17/0.42 % WCLimit : 300
% 0.17/0.42 % DateTime : Sun Sep 20 09:35:56 UTC 2026
% 0.17/0.42 % CPUTime :
% 0.28/0.60 % SZS status Theorem for theBenchmark
% 0.28/0.60 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------