%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : ALG030+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 : n018.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 08:11:36 AM UTC 2026
% Result : Theorem 281.69s 282.03s
% Output : Proof 281.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of formulae : 88 ( 46 unt; 0 def)
% Number of atoms : 203 ( 68 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 190 ( 75 ~; 65 |; 27 &)
% ( 0 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 4 ( 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 : 67 ( 0 sgn 46 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax1,axiom,
! [U] :
( sorti1(U)
=> ! [V] :
( sorti1(V)
=> sorti1(op1(U,V)) ) ),
file('theBenchmark.p',ax1) ).
fof(ax3,axiom,
~ ! [U] :
( sorti1(U)
=> ! [V] :
( sorti1(V)
=> op1(U,V) = op1(V,U) ) ),
file('theBenchmark.p',ax3) ).
fof(ax4,axiom,
~ ~ ! [U] :
( sorti2(U)
=> ! [V] :
( sorti2(V)
=> op2(U,V) = op2(V,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_3_1,plain,
? [U] :
( ? [V] :
( op1(U,V) != op1(V,U)
& sorti1(V) )
& sorti1(U) ),
inference(fof_nnf,[status(thm)],[ax3]) ).
fof(f_3_2,plain,
? [U_5] :
( ? [U_4] :
( op1(U_5,U_4) != op1(U_4,U_5)
& sorti1(U_4) )
& sorti1(U_5) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
( ? [U_4] :
( op1(sK1,U_4) != op1(U_4,sK1)
& sorti1(U_4) )
& sorti1(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_5,sK1)],[f_3_2]) ).
fof(f_3_4,plain,
( op1(sK1,sK2) != op1(sK2,sK1)
& sorti1(sK2)
& sorti1(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_4,sK2)],[f_3_3]) ).
cnf(f_3_5,plain,
sorti1(sK1),
inference(clausify,[status(thm)],[f_3_4]) ).
cnf(f_3_6,plain,
sorti1(sK2),
inference(clausify,[status(thm)],[f_3_4]) ).
cnf(f_3_7,plain,
op1(sK1,sK2) != op1(sK2,sK1),
inference(clausify,[status(thm)],[f_3_4]) ).
fof(f_4_1,plain,
! [U] :
( ! [V] :
( op2(U,V) = op2(V,U)
| ~ sorti2(V) )
| ~ sorti2(U) ),
inference(fof_nnf,[status(thm)],[ax4]) ).
fof(f_4_2,plain,
! [U_7] :
( ! [U_6] :
( op2(U_7,U_6) = op2(U_6,U_7)
| ~ sorti2(U_6) )
| ~ sorti2(U_7) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
cnf(f_4_3,plain,
( op2(U_7,U_6) = op2(U_6,U_7)
| ~ sorti2(U_6)
| ~ sorti2(U_7) ),
inference(clausify,[status(thm)],[f_4_2]) ).
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_15] :
( j(h(U_15)) = U_15
| ~ sorti1(U_15) )
& ! [U_14] :
( h(j(U_14)) = U_14
| ~ sorti2(U_14) )
& ! [U_13] :
( ! [U_12] :
( j(op2(U_13,U_12)) = op1(j(U_13),j(U_12))
| ~ sorti2(U_12) )
| ~ sorti2(U_13) )
& ! [U_11] :
( ! [U_10] :
( h(op1(U_11,U_10)) = op2(h(U_11),h(U_10))
| ~ sorti1(U_10) )
| ~ sorti1(U_11) )
& ! [U_9] :
( sorti1(j(U_9))
| ~ sorti2(U_9) )
& ! [U_8] :
( sorti2(h(U_8))
| ~ sorti1(U_8) ) ),
inference(variable_rename,[status(thm)],[f_5_2]) ).
cnf(f_5_4,negated_conjecture,
( sorti2(h(U_8))
| ~ sorti1(U_8) ),
inference(clausify,[status(thm)],[f_5_3]) ).
cnf(f_5_6,negated_conjecture,
( h(op1(U_11,U_10)) = op2(h(U_11),h(U_10))
| ~ sorti1(U_10)
| ~ sorti1(U_11) ),
inference(clausify,[status(thm)],[f_5_3]) ).
cnf(f_5_9,negated_conjecture,
( j(h(U_15)) = U_15
| ~ sorti1(U_15) ),
inference(clausify,[status(thm)],[f_5_3]) ).
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_7,axiom,
( j(Eq_x_0) = j(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(t1,plain,
op1(sK1,sK2) != op1(sK2,sK1),
inference(start,[status(thm),parent(0:0)],[f_3_7]) ).
cnf(t2,plain,
( op1(sK1,sK2) != j(h(op1(sK2,sK1)))
| j(h(op1(sK2,sK1))) != op1(sK2,sK1)
| op1(sK1,sK2) = op1(sK2,sK1) ),
inference(extension,[status(thm),parent(t1:1)],[equality_3]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( ~ sorti1(op1(sK2,sK1))
| j(h(op1(sK2,sK1))) = op1(sK2,sK1) ),
inference(extension,[status(thm),parent(t2:2)],[f_5_9]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( ~ sorti1(sK2)
| ~ sorti1(sK1)
| sorti1(op1(sK2,sK1)) ),
inference(extension,[status(thm),parent(t4:2)],[f_1_3]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
sorti1(sK1),
inference(extension,[status(thm),parent(t6:2)],[f_3_5]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
sorti1(sK2),
inference(extension,[status(thm),parent(t6:3)],[f_3_6]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t6:3]) ).
cnf(t12,plain,
( op1(sK1,sK2) != j(op2(h(sK1),h(sK2)))
| j(op2(h(sK1),h(sK2))) != j(h(op1(sK2,sK1)))
| op1(sK1,sK2) = j(h(op1(sK2,sK1))) ),
inference(extension,[status(thm),parent(t2:3)],[equality_3]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t2:3]) ).
cnf(t14,plain,
( op2(h(sK1),h(sK2)) != h(op1(sK2,sK1))
| j(op2(h(sK1),h(sK2))) = j(h(op1(sK2,sK1))) ),
inference(extension,[status(thm),parent(t12:2)],[equality_7]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t12:2]) ).
cnf(t16,plain,
( op2(h(sK1),h(sK2)) != op2(h(sK2),h(sK1))
| op2(h(sK2),h(sK1)) != h(op1(sK2,sK1))
| op2(h(sK1),h(sK2)) = h(op1(sK2,sK1)) ),
inference(extension,[status(thm),parent(t14:2)],[equality_3]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t14:2]) ).
cnf(t18,plain,
( h(op1(sK2,sK1)) != op2(h(sK2),h(sK1))
| op2(h(sK2),h(sK1)) = h(op1(sK2,sK1)) ),
inference(extension,[status(thm),parent(t16:2)],[equality_2]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t16:2]) ).
cnf(t20,plain,
( ~ sorti1(sK2)
| ~ sorti1(sK1)
| h(op1(sK2,sK1)) = op2(h(sK2),h(sK1)) ),
inference(extension,[status(thm),parent(t18:2)],[f_5_6]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t18:2]) ).
cnf(t22,plain,
sorti1(sK1),
inference(extension,[status(thm),parent(t20:2)],[f_3_5]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t20:2]) ).
cnf(t24,plain,
sorti1(sK2),
inference(extension,[status(thm),parent(t20:3)],[f_3_6]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t20:3]) ).
cnf(t26,plain,
( ~ sorti2(h(sK2))
| ~ sorti2(h(sK1))
| op2(h(sK1),h(sK2)) = op2(h(sK2),h(sK1)) ),
inference(extension,[status(thm),parent(t16:3)],[f_4_3]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t16:3]) ).
cnf(t28,plain,
( ~ sorti1(sK1)
| sorti2(h(sK1)) ),
inference(extension,[status(thm),parent(t26:2)],[f_5_4]) ).
cnf(t29,plain,
$false,
inference(connection,[status(thm),parent(t28:1)],[t28:1,t26:2]) ).
cnf(t30,plain,
sorti1(sK1),
inference(extension,[status(thm),parent(t28:2)],[f_3_5]) ).
cnf(t31,plain,
$false,
inference(connection,[status(thm),parent(t30:1)],[t30:1,t28:2]) ).
cnf(t32,plain,
( ~ sorti1(sK2)
| sorti2(h(sK2)) ),
inference(extension,[status(thm),parent(t26:3)],[f_5_4]) ).
cnf(t33,plain,
$false,
inference(connection,[status(thm),parent(t32:1)],[t32:1,t26:3]) ).
cnf(t34,plain,
sorti1(sK2),
inference(extension,[status(thm),parent(t32:2)],[f_3_6]) ).
cnf(t35,plain,
$false,
inference(connection,[status(thm),parent(t34:1)],[t34:1,t32:2]) ).
cnf(t36,plain,
( op1(sK1,sK2) != j(h(op1(sK1,sK2)))
| j(h(op1(sK1,sK2))) != j(op2(h(sK1),h(sK2)))
| op1(sK1,sK2) = j(op2(h(sK1),h(sK2))) ),
inference(extension,[status(thm),parent(t12:3)],[equality_3]) ).
cnf(t37,plain,
$false,
inference(connection,[status(thm),parent(t36:1)],[t36:1,t12:3]) ).
cnf(t38,plain,
( h(op1(sK1,sK2)) != op2(h(sK1),h(sK2))
| j(h(op1(sK1,sK2))) = j(op2(h(sK1),h(sK2))) ),
inference(extension,[status(thm),parent(t36:2)],[equality_7]) ).
cnf(t39,plain,
$false,
inference(connection,[status(thm),parent(t38:1)],[t38:1,t36:2]) ).
cnf(t40,plain,
( h(op1(sK1,sK2)) != h(op1(sK1,sK2))
| h(op1(sK1,sK2)) != op2(h(sK1),h(sK2))
| h(op1(sK1,sK2)) = op2(h(sK1),h(sK2)) ),
inference(extension,[status(thm),parent(t38:2)],[equality_3]) ).
cnf(t41,plain,
$false,
inference(connection,[status(thm),parent(t40:1)],[t40:1,t38:2]) ).
cnf(t42,plain,
( ~ sorti1(sK1)
| ~ sorti1(sK2)
| h(op1(sK1,sK2)) = op2(h(sK1),h(sK2)) ),
inference(extension,[status(thm),parent(t40:2)],[f_5_6]) ).
cnf(t43,plain,
$false,
inference(connection,[status(thm),parent(t42:1)],[t42:1,t40:2]) ).
cnf(t44,plain,
sorti1(sK2),
inference(extension,[status(thm),parent(t42:2)],[f_3_6]) ).
cnf(t45,plain,
$false,
inference(connection,[status(thm),parent(t44:1)],[t44:1,t42:2]) ).
cnf(t46,plain,
sorti1(sK1),
inference(extension,[status(thm),parent(t42:3)],[f_3_5]) ).
cnf(t47,plain,
$false,
inference(connection,[status(thm),parent(t46:1)],[t46:1,t42:3]) ).
cnf(t48,plain,
( h(op1(sK1,sK2)) != h(op1(sK1,sK2))
| h(op1(sK1,sK2)) = h(op1(sK1,sK2)) ),
inference(extension,[status(thm),parent(t40:3)],[equality_2]) ).
cnf(t49,plain,
$false,
inference(connection,[status(thm),parent(t48:1)],[t48:1,t40:3]) ).
cnf(t50,plain,
h(op1(sK1,sK2)) = h(op1(sK1,sK2)),
inference(extension,[status(thm),parent(t48:2)],[equality_1]) ).
cnf(t51,plain,
$false,
inference(connection,[status(thm),parent(t50:1)],[t50:1,t48:2]) ).
cnf(t52,plain,
( j(h(op1(sK1,sK2))) != op1(sK1,sK2)
| op1(sK1,sK2) = j(h(op1(sK1,sK2))) ),
inference(extension,[status(thm),parent(t36:3)],[equality_2]) ).
cnf(t53,plain,
$false,
inference(connection,[status(thm),parent(t52:1)],[t52:1,t36:3]) ).
cnf(t54,plain,
( ~ sorti1(op1(sK1,sK2))
| j(h(op1(sK1,sK2))) = op1(sK1,sK2) ),
inference(extension,[status(thm),parent(t52:2)],[f_5_9]) ).
cnf(t55,plain,
$false,
inference(connection,[status(thm),parent(t54:1)],[t54:1,t52:2]) ).
cnf(t56,plain,
( ~ sorti1(sK1)
| ~ sorti1(sK2)
| sorti1(op1(sK1,sK2)) ),
inference(extension,[status(thm),parent(t54:2)],[f_1_3]) ).
cnf(t57,plain,
$false,
inference(connection,[status(thm),parent(t56:1)],[t56:1,t54:2]) ).
cnf(t58,plain,
sorti1(sK2),
inference(extension,[status(thm),parent(t56:2)],[f_3_6]) ).
cnf(t59,plain,
$false,
inference(connection,[status(thm),parent(t58:1)],[t58:1,t56:2]) ).
cnf(t60,plain,
sorti1(sK1),
inference(extension,[status(thm),parent(t56:3)],[f_3_5]) ).
cnf(t61,plain,
$false,
inference(connection,[status(thm),parent(t60:1)],[t60:1,t56:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG030+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.03 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n018.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
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 20 08:46:57 UTC 2026
% 0.09/0.36 % CPUTime :
% 281.69/282.03 % SZS status Theorem for theBenchmark
% 281.69/282.03 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------