%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : BOO016-1 : TPTP v9.3.1. Released v1.0.0.
% 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 : n016.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 08:13:59 AM UTC 2026
% Result : Unsatisfiable 208.65s 208.96s
% Output : Proof 208.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 17
% Syntax : Number of clauses : 309 ( 256 unt; 0 nHn; 285 RR)
% Number of literals : 475 ( 123 equ; 168 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 72 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(closure_of_addition,axiom,
sum(X,Y,add(X,Y)),
file('BOO002-0.ax',closure_of_addition) ).
cnf(additive_identity2,axiom,
sum(X,additive_identity,X),
file('BOO002-0.ax',additive_identity2) ).
cnf(multiplicative_identity1,axiom,
product(multiplicative_identity,X,X),
file('BOO002-0.ax',multiplicative_identity1) ).
cnf(multiplicative_identity2,axiom,
product(X,multiplicative_identity,X),
file('BOO002-0.ax',multiplicative_identity2) ).
cnf(distributivity1,axiom,
( sum(V1,V2,V4)
| ~ product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) ),
file('BOO002-0.ax',distributivity1) ).
cnf(distributivity2,axiom,
( product(X,V3,V4)
| ~ sum(V1,V2,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) ),
file('BOO002-0.ax',distributivity2) ).
cnf(distributivity7,axiom,
( product(V1,V2,V4)
| ~ sum(V3,X,V4)
| ~ product(Y,Z,V3)
| ~ sum(Z,X,V2)
| ~ sum(Y,X,V1) ),
file('BOO002-0.ax',distributivity7) ).
cnf(additive_inverse1,axiom,
sum(inverse(X),X,multiplicative_identity),
file('BOO002-0.ax',additive_inverse1) ).
cnf(additive_inverse2,axiom,
sum(X,inverse(X),multiplicative_identity),
file('BOO002-0.ax',additive_inverse2) ).
cnf(multiplicative_inverse2,axiom,
product(X,inverse(X),additive_identity),
file('BOO002-0.ax',multiplicative_inverse2) ).
cnf(addition_is_well_defined,axiom,
( U = V
| ~ sum(X,Y,V)
| ~ sum(X,Y,U) ),
file('BOO002-0.ax',addition_is_well_defined) ).
cnf(multiplication_is_well_defined,axiom,
( U = V
| ~ product(X,Y,V)
| ~ product(X,Y,U) ),
file('BOO002-0.ax',multiplication_is_well_defined) ).
cnf(x_times_y,hypothesis,
product(x,y,z),
file('theBenchmark.p',x_times_y) ).
cnf(prove_sum,negated_conjecture,
~ sum(x,z,x),
file('theBenchmark.p',prove_sum) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(equality_7,axiom,
( sum(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sum(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_8,axiom,
( product(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ product(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(t1,plain,
~ sum(x,z,x),
inference(start,[status(thm),parent(0:0)],[prove_sum]) ).
cnf(t2,plain,
( ~ sum(multiplicative_identity,add(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity)),multiplicative_identity)
| ~ product(add(x,additive_identity),multiplicative_identity,x)
| ~ product(add(x,additive_identity),add(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity)),z)
| ~ product(add(x,additive_identity),multiplicative_identity,x)
| sum(x,z,x) ),
inference(extension,[status(thm),parent(t1:1)],[distributivity1]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( multiplicative_identity != multiplicative_identity
| add(x,additive_identity) != add(x,additive_identity)
| ~ product(add(x,additive_identity),multiplicative_identity,add(x,additive_identity))
| add(x,additive_identity) != x
| product(add(x,additive_identity),multiplicative_identity,x) ),
inference(extension,[status(thm),parent(t2:2)],[equality_8]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( ~ sum(x,additive_identity,add(x,additive_identity))
| ~ sum(x,additive_identity,x)
| add(x,additive_identity) = x ),
inference(extension,[status(thm),parent(t4:2)],[addition_is_well_defined]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
sum(x,additive_identity,x),
inference(extension,[status(thm),parent(t6:2)],[additive_identity2]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
( add(x,additive_identity) != add(x,additive_identity)
| ~ sum(x,additive_identity,add(x,additive_identity))
| additive_identity != additive_identity
| x != x
| sum(x,additive_identity,add(x,additive_identity)) ),
inference(extension,[status(thm),parent(t6:3)],[equality_7]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t6:3]) ).
cnf(t12,plain,
x = x,
inference(extension,[status(thm),parent(t10:2)],[equality_1]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t10:2]) ).
cnf(t14,plain,
additive_identity = additive_identity,
inference(extension,[status(thm),parent(t10:3)],[equality_1]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t10:3]) ).
cnf(t16,plain,
sum(x,additive_identity,add(x,additive_identity)),
inference(extension,[status(thm),parent(t10:4)],[closure_of_addition]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t10:4]) ).
cnf(t18,plain,
add(x,additive_identity) = add(x,additive_identity),
inference(extension,[status(thm),parent(t10:5)],[equality_1]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t10:5]) ).
cnf(t20,plain,
( multiplicative_identity != multiplicative_identity
| add(x,additive_identity) != add(x,additive_identity)
| ~ product(add(x,additive_identity),multiplicative_identity,add(x,additive_identity))
| add(x,additive_identity) != add(x,additive_identity)
| product(add(x,additive_identity),multiplicative_identity,add(x,additive_identity)) ),
inference(extension,[status(thm),parent(t4:3)],[equality_8]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t4:3]) ).
cnf(t22,plain,
( ~ sum(x,additive_identity,add(x,additive_identity))
| ~ sum(x,additive_identity,add(x,additive_identity))
| add(x,additive_identity) = add(x,additive_identity) ),
inference(extension,[status(thm),parent(t20:2)],[addition_is_well_defined]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t20:2]) ).
cnf(t24,plain,
sum(x,additive_identity,add(x,additive_identity)),
inference(extension,[status(thm),parent(t22:2)],[closure_of_addition]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t22:2]) ).
cnf(t26,plain,
sum(x,additive_identity,add(x,additive_identity)),
inference(extension,[status(thm),parent(t22:3)],[closure_of_addition]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t22:3]) ).
cnf(t28,plain,
( multiplicative_identity != multiplicative_identity
| add(x,additive_identity) != add(x,additive_identity)
| ~ product(add(x,additive_identity),multiplicative_identity,add(x,additive_identity))
| add(x,additive_identity) != add(x,additive_identity)
| product(add(x,additive_identity),multiplicative_identity,add(x,additive_identity)) ),
inference(extension,[status(thm),parent(t20:3)],[equality_8]) ).
cnf(t29,plain,
$false,
inference(connection,[status(thm),parent(t28:1)],[t28:1,t20:3]) ).
cnf(t30,plain,
add(x,additive_identity) = add(x,additive_identity),
inference(extension,[status(thm),parent(t28:2)],[equality_1]) ).
cnf(t31,plain,
$false,
inference(connection,[status(thm),parent(t30:1)],[t30:1,t28:2]) ).
cnf(t32,plain,
product(add(x,additive_identity),multiplicative_identity,add(x,additive_identity)),
inference(extension,[status(thm),parent(t28:3)],[multiplicative_identity2]) ).
cnf(t33,plain,
$false,
inference(connection,[status(thm),parent(t32:1)],[t32:1,t28:3]) ).
cnf(t34,plain,
add(x,additive_identity) = add(x,additive_identity),
inference(extension,[status(thm),parent(t28:4)],[equality_1]) ).
cnf(t35,plain,
$false,
inference(connection,[status(thm),parent(t34:1)],[t34:1,t28:4]) ).
cnf(t36,plain,
multiplicative_identity = multiplicative_identity,
inference(extension,[status(thm),parent(t28:5)],[equality_1]) ).
cnf(t37,plain,
$false,
inference(connection,[status(thm),parent(t36:1)],[t36:1,t28:5]) ).
cnf(t38,plain,
( ~ product(add(x,additive_identity),multiplicative_identity,add(x,additive_identity))
| ~ product(add(x,additive_identity),multiplicative_identity,add(x,additive_identity))
| add(x,additive_identity) = add(x,additive_identity) ),
inference(extension,[status(thm),parent(t20:4)],[multiplication_is_well_defined]) ).
cnf(t39,plain,
$false,
inference(connection,[status(thm),parent(t38:1)],[t38:1,t20:4]) ).
cnf(t40,plain,
product(add(x,additive_identity),multiplicative_identity,add(x,additive_identity)),
inference(extension,[status(thm),parent(t38:2)],[multiplicative_identity2]) ).
cnf(t41,plain,
$false,
inference(connection,[status(thm),parent(t40:1)],[t40:1,t38:2]) ).
cnf(t42,plain,
product(add(x,additive_identity),multiplicative_identity,add(x,additive_identity)),
inference(extension,[status(thm),parent(t38:3)],[multiplicative_identity2]) ).
cnf(t43,plain,
$false,
inference(connection,[status(thm),parent(t42:1)],[t42:1,t38:3]) ).
cnf(t44,plain,
( ~ sum(U_3604,inverse(U_3604),multiplicative_identity)
| ~ sum(U_3604,inverse(U_3604),multiplicative_identity)
| multiplicative_identity = multiplicative_identity ),
inference(extension,[status(thm),parent(t20:5)],[addition_is_well_defined]) ).
cnf(t45,plain,
$false,
inference(connection,[status(thm),parent(t44:1)],[t44:1,t20:5]) ).
cnf(t46,plain,
sum(U_3604,inverse(U_3604),multiplicative_identity),
inference(extension,[status(thm),parent(t44:2)],[additive_inverse2]) ).
cnf(t47,plain,
$false,
inference(connection,[status(thm),parent(t46:1)],[t46:1,t44:2]) ).
cnf(l23,lemma,
sum(U_3604,inverse(U_3604),multiplicative_identity),
inference(lemma,[status(cth),parent(t44:2),below(t20:5)],[t44:2]) ).
cnf(t48,plain,
sum(U_3604,inverse(U_3604),multiplicative_identity),
inference(lemma_extension,[status(thm),parent(t44:3)],[l23:1]) ).
cnf(t49,plain,
$false,
inference(connection,[status(thm),parent(t48:1)],[t48:1,t44:3]) ).
cnf(t50,plain,
( ~ product(add(x,additive_identity),multiplicative_identity,add(x,additive_identity))
| ~ product(add(x,additive_identity),multiplicative_identity,add(x,additive_identity))
| add(x,additive_identity) = add(x,additive_identity) ),
inference(extension,[status(thm),parent(t4:4)],[multiplication_is_well_defined]) ).
cnf(t51,plain,
$false,
inference(connection,[status(thm),parent(t50:1)],[t50:1,t4:4]) ).
cnf(t52,plain,
( multiplicative_identity != multiplicative_identity
| add(x,additive_identity) != add(x,additive_identity)
| ~ product(add(x,additive_identity),multiplicative_identity,add(x,additive_identity))
| add(x,additive_identity) != add(x,additive_identity)
| product(add(x,additive_identity),multiplicative_identity,add(x,additive_identity)) ),
inference(extension,[status(thm),parent(t50:2)],[equality_8]) ).
cnf(t53,plain,
$false,
inference(connection,[status(thm),parent(t52:1)],[t52:1,t50:2]) ).
cnf(t54,plain,
add(x,additive_identity) = add(x,additive_identity),
inference(extension,[status(thm),parent(t52:2)],[equality_1]) ).
cnf(t55,plain,
$false,
inference(connection,[status(thm),parent(t54:1)],[t54:1,t52:2]) ).
cnf(t56,plain,
product(add(x,additive_identity),multiplicative_identity,add(x,additive_identity)),
inference(extension,[status(thm),parent(t52:3)],[multiplicative_identity2]) ).
cnf(t57,plain,
$false,
inference(connection,[status(thm),parent(t56:1)],[t56:1,t52:3]) ).
cnf(t58,plain,
add(x,additive_identity) = add(x,additive_identity),
inference(extension,[status(thm),parent(t52:4)],[equality_1]) ).
cnf(t59,plain,
$false,
inference(connection,[status(thm),parent(t58:1)],[t58:1,t52:4]) ).
cnf(t60,plain,
multiplicative_identity = multiplicative_identity,
inference(extension,[status(thm),parent(t52:5)],[equality_1]) ).
cnf(t61,plain,
$false,
inference(connection,[status(thm),parent(t60:1)],[t60:1,t52:5]) ).
cnf(t62,plain,
( multiplicative_identity != multiplicative_identity
| add(x,additive_identity) != add(x,additive_identity)
| ~ product(add(x,additive_identity),multiplicative_identity,add(x,additive_identity))
| add(x,additive_identity) != add(x,additive_identity)
| product(add(x,additive_identity),multiplicative_identity,add(x,additive_identity)) ),
inference(extension,[status(thm),parent(t50:3)],[equality_8]) ).
cnf(t63,plain,
$false,
inference(connection,[status(thm),parent(t62:1)],[t62:1,t50:3]) ).
cnf(t64,plain,
add(x,additive_identity) = add(x,additive_identity),
inference(extension,[status(thm),parent(t62:2)],[equality_1]) ).
cnf(t65,plain,
$false,
inference(connection,[status(thm),parent(t64:1)],[t64:1,t62:2]) ).
cnf(t66,plain,
product(add(x,additive_identity),multiplicative_identity,add(x,additive_identity)),
inference(extension,[status(thm),parent(t62:3)],[multiplicative_identity2]) ).
cnf(t67,plain,
$false,
inference(connection,[status(thm),parent(t66:1)],[t66:1,t62:3]) ).
cnf(t68,plain,
add(x,additive_identity) = add(x,additive_identity),
inference(extension,[status(thm),parent(t62:4)],[equality_1]) ).
cnf(t69,plain,
$false,
inference(connection,[status(thm),parent(t68:1)],[t68:1,t62:4]) ).
cnf(t70,plain,
multiplicative_identity = multiplicative_identity,
inference(extension,[status(thm),parent(t62:5)],[equality_1]) ).
cnf(t71,plain,
$false,
inference(connection,[status(thm),parent(t70:1)],[t70:1,t62:5]) ).
cnf(t72,plain,
( ~ sum(U_3633,inverse(U_3633),multiplicative_identity)
| ~ sum(U_3633,inverse(U_3633),multiplicative_identity)
| multiplicative_identity = multiplicative_identity ),
inference(extension,[status(thm),parent(t4:5)],[addition_is_well_defined]) ).
cnf(t73,plain,
$false,
inference(connection,[status(thm),parent(t72:1)],[t72:1,t4:5]) ).
cnf(t74,plain,
sum(U_3633,inverse(U_3633),multiplicative_identity),
inference(extension,[status(thm),parent(t72:2)],[additive_inverse2]) ).
cnf(t75,plain,
$false,
inference(connection,[status(thm),parent(t74:1)],[t74:1,t72:2]) ).
cnf(l36,lemma,
sum(U_3633,inverse(U_3633),multiplicative_identity),
inference(lemma,[status(cth),parent(t72:2),below(t4:5)],[t72:2]) ).
cnf(t76,plain,
sum(U_3633,inverse(U_3633),multiplicative_identity),
inference(lemma_extension,[status(thm),parent(t72:3)],[l36:1]) ).
cnf(t77,plain,
$false,
inference(connection,[status(thm),parent(t76:1)],[t76:1,t72:3]) ).
cnf(t78,plain,
( ~ sum(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity),add(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity)))
| ~ product(add(x,additive_identity),add(add(inverse(x),additive_identity),additive_identity),additive_identity)
| ~ product(add(x,additive_identity),add(y,additive_identity),z)
| ~ sum(z,additive_identity,z)
| product(add(x,additive_identity),add(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity)),z) ),
inference(extension,[status(thm),parent(t2:3)],[distributivity2]) ).
cnf(t79,plain,
$false,
inference(connection,[status(thm),parent(t78:1)],[t78:1,t2:3]) ).
cnf(t80,plain,
sum(z,additive_identity,z),
inference(extension,[status(thm),parent(t78:2)],[additive_identity2]) ).
cnf(t81,plain,
$false,
inference(connection,[status(thm),parent(t80:1)],[t80:1,t78:2]) ).
cnf(t82,plain,
( ~ product(x,y,z)
| ~ sum(y,additive_identity,add(y,additive_identity))
| ~ sum(z,additive_identity,z)
| ~ sum(x,additive_identity,add(x,additive_identity))
| product(add(x,additive_identity),add(y,additive_identity),z) ),
inference(extension,[status(thm),parent(t78:3)],[distributivity7]) ).
cnf(t83,plain,
$false,
inference(connection,[status(thm),parent(t82:1)],[t82:1,t78:3]) ).
cnf(t84,plain,
sum(x,additive_identity,add(x,additive_identity)),
inference(extension,[status(thm),parent(t82:2)],[closure_of_addition]) ).
cnf(t85,plain,
$false,
inference(connection,[status(thm),parent(t84:1)],[t84:1,t82:2]) ).
cnf(t86,plain,
sum(z,additive_identity,z),
inference(extension,[status(thm),parent(t82:3)],[additive_identity2]) ).
cnf(t87,plain,
$false,
inference(connection,[status(thm),parent(t86:1)],[t86:1,t82:3]) ).
cnf(t88,plain,
( add(y,additive_identity) != add(y,additive_identity)
| ~ sum(y,additive_identity,add(y,additive_identity))
| additive_identity != additive_identity
| y != y
| sum(y,additive_identity,add(y,additive_identity)) ),
inference(extension,[status(thm),parent(t82:4)],[equality_7]) ).
cnf(t89,plain,
$false,
inference(connection,[status(thm),parent(t88:1)],[t88:1,t82:4]) ).
cnf(t90,plain,
y = y,
inference(extension,[status(thm),parent(t88:2)],[equality_1]) ).
cnf(t91,plain,
$false,
inference(connection,[status(thm),parent(t90:1)],[t90:1,t88:2]) ).
cnf(t92,plain,
additive_identity = additive_identity,
inference(extension,[status(thm),parent(t88:3)],[equality_1]) ).
cnf(t93,plain,
$false,
inference(connection,[status(thm),parent(t92:1)],[t92:1,t88:3]) ).
cnf(t94,plain,
sum(y,additive_identity,add(y,additive_identity)),
inference(extension,[status(thm),parent(t88:4)],[closure_of_addition]) ).
cnf(t95,plain,
$false,
inference(connection,[status(thm),parent(t94:1)],[t94:1,t88:4]) ).
cnf(t96,plain,
add(y,additive_identity) = add(y,additive_identity),
inference(extension,[status(thm),parent(t88:5)],[equality_1]) ).
cnf(t97,plain,
$false,
inference(connection,[status(thm),parent(t96:1)],[t96:1,t88:5]) ).
cnf(t98,plain,
product(x,y,z),
inference(extension,[status(thm),parent(t82:5)],[x_times_y]) ).
cnf(t99,plain,
$false,
inference(connection,[status(thm),parent(t98:1)],[t98:1,t82:5]) ).
cnf(t100,plain,
( ~ product(x,add(inverse(x),additive_identity),additive_identity)
| ~ sum(add(inverse(x),additive_identity),additive_identity,add(add(inverse(x),additive_identity),additive_identity))
| ~ sum(additive_identity,additive_identity,additive_identity)
| ~ sum(x,additive_identity,add(x,additive_identity))
| product(add(x,additive_identity),add(add(inverse(x),additive_identity),additive_identity),additive_identity) ),
inference(extension,[status(thm),parent(t78:4)],[distributivity7]) ).
cnf(t101,plain,
$false,
inference(connection,[status(thm),parent(t100:1)],[t100:1,t78:4]) ).
cnf(t102,plain,
sum(x,additive_identity,add(x,additive_identity)),
inference(extension,[status(thm),parent(t100:2)],[closure_of_addition]) ).
cnf(t103,plain,
$false,
inference(connection,[status(thm),parent(t102:1)],[t102:1,t100:2]) ).
cnf(t104,plain,
sum(additive_identity,additive_identity,additive_identity),
inference(extension,[status(thm),parent(t100:3)],[additive_identity2]) ).
cnf(t105,plain,
$false,
inference(connection,[status(thm),parent(t104:1)],[t104:1,t100:3]) ).
cnf(t106,plain,
( add(add(inverse(x),additive_identity),additive_identity) != add(add(inverse(x),additive_identity),additive_identity)
| ~ sum(add(inverse(x),additive_identity),additive_identity,add(add(inverse(x),additive_identity),additive_identity))
| additive_identity != additive_identity
| add(inverse(x),additive_identity) != add(inverse(x),additive_identity)
| sum(add(inverse(x),additive_identity),additive_identity,add(add(inverse(x),additive_identity),additive_identity)) ),
inference(extension,[status(thm),parent(t100:4)],[equality_7]) ).
cnf(t107,plain,
$false,
inference(connection,[status(thm),parent(t106:1)],[t106:1,t100:4]) ).
cnf(t108,plain,
add(inverse(x),additive_identity) = add(inverse(x),additive_identity),
inference(extension,[status(thm),parent(t106:2)],[equality_1]) ).
cnf(t109,plain,
$false,
inference(connection,[status(thm),parent(t108:1)],[t108:1,t106:2]) ).
cnf(t110,plain,
additive_identity = additive_identity,
inference(extension,[status(thm),parent(t106:3)],[equality_1]) ).
cnf(t111,plain,
$false,
inference(connection,[status(thm),parent(t110:1)],[t110:1,t106:3]) ).
cnf(t112,plain,
sum(add(inverse(x),additive_identity),additive_identity,add(add(inverse(x),additive_identity),additive_identity)),
inference(extension,[status(thm),parent(t106:4)],[closure_of_addition]) ).
cnf(t113,plain,
$false,
inference(connection,[status(thm),parent(t112:1)],[t112:1,t106:4]) ).
cnf(t114,plain,
add(add(inverse(x),additive_identity),additive_identity) = add(add(inverse(x),additive_identity),additive_identity),
inference(extension,[status(thm),parent(t106:5)],[equality_1]) ).
cnf(t115,plain,
$false,
inference(connection,[status(thm),parent(t114:1)],[t114:1,t106:5]) ).
cnf(t116,plain,
( ~ product(x,inverse(x),additive_identity)
| ~ sum(inverse(x),additive_identity,add(inverse(x),additive_identity))
| ~ sum(additive_identity,additive_identity,additive_identity)
| ~ sum(x,additive_identity,x)
| product(x,add(inverse(x),additive_identity),additive_identity) ),
inference(extension,[status(thm),parent(t100:5)],[distributivity7]) ).
cnf(t117,plain,
$false,
inference(connection,[status(thm),parent(t116:1)],[t116:1,t100:5]) ).
cnf(t118,plain,
sum(x,additive_identity,x),
inference(extension,[status(thm),parent(t116:2)],[additive_identity2]) ).
cnf(t119,plain,
$false,
inference(connection,[status(thm),parent(t118:1)],[t118:1,t116:2]) ).
cnf(t120,plain,
sum(additive_identity,additive_identity,additive_identity),
inference(extension,[status(thm),parent(t116:3)],[additive_identity2]) ).
cnf(t121,plain,
$false,
inference(connection,[status(thm),parent(t120:1)],[t120:1,t116:3]) ).
cnf(t122,plain,
sum(inverse(x),additive_identity,add(inverse(x),additive_identity)),
inference(extension,[status(thm),parent(t116:4)],[closure_of_addition]) ).
cnf(t123,plain,
$false,
inference(connection,[status(thm),parent(t122:1)],[t122:1,t116:4]) ).
cnf(t124,plain,
product(x,inverse(x),additive_identity),
inference(extension,[status(thm),parent(t116:5)],[multiplicative_inverse2]) ).
cnf(t125,plain,
$false,
inference(connection,[status(thm),parent(t124:1)],[t124:1,t116:5]) ).
cnf(t126,plain,
( add(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity)) != add(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity))
| ~ sum(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity),add(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity)))
| add(add(inverse(x),additive_identity),additive_identity) != add(add(inverse(x),additive_identity),additive_identity)
| add(y,additive_identity) != add(y,additive_identity)
| sum(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity),add(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity))) ),
inference(extension,[status(thm),parent(t78:5)],[equality_7]) ).
cnf(t127,plain,
$false,
inference(connection,[status(thm),parent(t126:1)],[t126:1,t78:5]) ).
cnf(t128,plain,
( ~ sum(y,additive_identity,add(y,additive_identity))
| ~ sum(y,additive_identity,add(y,additive_identity))
| add(y,additive_identity) = add(y,additive_identity) ),
inference(extension,[status(thm),parent(t126:2)],[addition_is_well_defined]) ).
cnf(t129,plain,
$false,
inference(connection,[status(thm),parent(t128:1)],[t128:1,t126:2]) ).
cnf(t130,plain,
sum(y,additive_identity,add(y,additive_identity)),
inference(extension,[status(thm),parent(t128:2)],[closure_of_addition]) ).
cnf(t131,plain,
$false,
inference(connection,[status(thm),parent(t130:1)],[t130:1,t128:2]) ).
cnf(t132,plain,
sum(y,additive_identity,add(y,additive_identity)),
inference(extension,[status(thm),parent(t128:3)],[closure_of_addition]) ).
cnf(t133,plain,
$false,
inference(connection,[status(thm),parent(t132:1)],[t132:1,t128:3]) ).
cnf(t134,plain,
( ~ sum(add(inverse(x),additive_identity),additive_identity,add(add(inverse(x),additive_identity),additive_identity))
| ~ sum(add(inverse(x),additive_identity),additive_identity,add(add(inverse(x),additive_identity),additive_identity))
| add(add(inverse(x),additive_identity),additive_identity) = add(add(inverse(x),additive_identity),additive_identity) ),
inference(extension,[status(thm),parent(t126:3)],[addition_is_well_defined]) ).
cnf(t135,plain,
$false,
inference(connection,[status(thm),parent(t134:1)],[t134:1,t126:3]) ).
cnf(t136,plain,
sum(add(inverse(x),additive_identity),additive_identity,add(add(inverse(x),additive_identity),additive_identity)),
inference(extension,[status(thm),parent(t134:2)],[closure_of_addition]) ).
cnf(t137,plain,
$false,
inference(connection,[status(thm),parent(t136:1)],[t136:1,t134:2]) ).
cnf(t138,plain,
sum(add(inverse(x),additive_identity),additive_identity,add(add(inverse(x),additive_identity),additive_identity)),
inference(extension,[status(thm),parent(t134:3)],[closure_of_addition]) ).
cnf(t139,plain,
$false,
inference(connection,[status(thm),parent(t138:1)],[t138:1,t134:3]) ).
cnf(t140,plain,
( add(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity)) != add(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity))
| ~ sum(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity),add(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity)))
| add(add(inverse(x),additive_identity),additive_identity) != add(add(inverse(x),additive_identity),additive_identity)
| add(y,additive_identity) != add(y,additive_identity)
| sum(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity),add(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity))) ),
inference(extension,[status(thm),parent(t126:4)],[equality_7]) ).
cnf(t141,plain,
$false,
inference(connection,[status(thm),parent(t140:1)],[t140:1,t126:4]) ).
cnf(t142,plain,
add(y,additive_identity) = add(y,additive_identity),
inference(extension,[status(thm),parent(t140:2)],[equality_1]) ).
cnf(t143,plain,
$false,
inference(connection,[status(thm),parent(t142:1)],[t142:1,t140:2]) ).
cnf(t144,plain,
add(add(inverse(x),additive_identity),additive_identity) = add(add(inverse(x),additive_identity),additive_identity),
inference(extension,[status(thm),parent(t140:3)],[equality_1]) ).
cnf(t145,plain,
$false,
inference(connection,[status(thm),parent(t144:1)],[t144:1,t140:3]) ).
cnf(t146,plain,
sum(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity),add(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity))),
inference(extension,[status(thm),parent(t140:4)],[closure_of_addition]) ).
cnf(t147,plain,
$false,
inference(connection,[status(thm),parent(t146:1)],[t146:1,t140:4]) ).
cnf(t148,plain,
add(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity)) = add(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity)),
inference(extension,[status(thm),parent(t140:5)],[equality_1]) ).
cnf(t149,plain,
$false,
inference(connection,[status(thm),parent(t148:1)],[t148:1,t140:5]) ).
cnf(t150,plain,
( ~ product(add(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity)),multiplicative_identity,add(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity)))
| ~ product(add(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity)),multiplicative_identity,add(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity)))
| add(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity)) = add(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity)) ),
inference(extension,[status(thm),parent(t126:5)],[multiplication_is_well_defined]) ).
cnf(t151,plain,
$false,
inference(connection,[status(thm),parent(t150:1)],[t150:1,t126:5]) ).
cnf(t152,plain,
product(add(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity)),multiplicative_identity,add(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity))),
inference(extension,[status(thm),parent(t150:2)],[multiplicative_identity2]) ).
cnf(t153,plain,
$false,
inference(connection,[status(thm),parent(t152:1)],[t152:1,t150:2]) ).
cnf(t154,plain,
product(add(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity)),multiplicative_identity,add(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity))),
inference(extension,[status(thm),parent(t150:3)],[multiplicative_identity2]) ).
cnf(t155,plain,
$false,
inference(connection,[status(thm),parent(t154:1)],[t154:1,t150:3]) ).
cnf(t156,plain,
( multiplicative_identity != multiplicative_identity
| add(x,additive_identity) != add(x,additive_identity)
| ~ product(add(x,additive_identity),multiplicative_identity,add(x,additive_identity))
| add(x,additive_identity) != x
| product(add(x,additive_identity),multiplicative_identity,x) ),
inference(extension,[status(thm),parent(t2:4)],[equality_8]) ).
cnf(t157,plain,
$false,
inference(connection,[status(thm),parent(t156:1)],[t156:1,t2:4]) ).
cnf(t158,plain,
( ~ sum(x,additive_identity,add(x,additive_identity))
| ~ sum(x,additive_identity,x)
| add(x,additive_identity) = x ),
inference(extension,[status(thm),parent(t156:2)],[addition_is_well_defined]) ).
cnf(t159,plain,
$false,
inference(connection,[status(thm),parent(t158:1)],[t158:1,t156:2]) ).
cnf(t160,plain,
sum(x,additive_identity,x),
inference(extension,[status(thm),parent(t158:2)],[additive_identity2]) ).
cnf(t161,plain,
$false,
inference(connection,[status(thm),parent(t160:1)],[t160:1,t158:2]) ).
cnf(t162,plain,
( add(x,additive_identity) != add(x,additive_identity)
| ~ sum(x,additive_identity,add(x,additive_identity))
| additive_identity != additive_identity
| x != x
| sum(x,additive_identity,add(x,additive_identity)) ),
inference(extension,[status(thm),parent(t158:3)],[equality_7]) ).
cnf(t163,plain,
$false,
inference(connection,[status(thm),parent(t162:1)],[t162:1,t158:3]) ).
cnf(t164,plain,
x = x,
inference(extension,[status(thm),parent(t162:2)],[equality_1]) ).
cnf(t165,plain,
$false,
inference(connection,[status(thm),parent(t164:1)],[t164:1,t162:2]) ).
cnf(t166,plain,
additive_identity = additive_identity,
inference(extension,[status(thm),parent(t162:3)],[equality_1]) ).
cnf(t167,plain,
$false,
inference(connection,[status(thm),parent(t166:1)],[t166:1,t162:3]) ).
cnf(t168,plain,
sum(x,additive_identity,add(x,additive_identity)),
inference(extension,[status(thm),parent(t162:4)],[closure_of_addition]) ).
cnf(t169,plain,
$false,
inference(connection,[status(thm),parent(t168:1)],[t168:1,t162:4]) ).
cnf(t170,plain,
add(x,additive_identity) = add(x,additive_identity),
inference(extension,[status(thm),parent(t162:5)],[equality_1]) ).
cnf(t171,plain,
$false,
inference(connection,[status(thm),parent(t170:1)],[t170:1,t162:5]) ).
cnf(t172,plain,
( multiplicative_identity != multiplicative_identity
| add(x,additive_identity) != add(x,additive_identity)
| ~ product(add(x,additive_identity),multiplicative_identity,add(x,additive_identity))
| add(x,additive_identity) != add(x,additive_identity)
| product(add(x,additive_identity),multiplicative_identity,add(x,additive_identity)) ),
inference(extension,[status(thm),parent(t156:3)],[equality_8]) ).
cnf(t173,plain,
$false,
inference(connection,[status(thm),parent(t172:1)],[t172:1,t156:3]) ).
cnf(t174,plain,
( ~ sum(x,additive_identity,add(x,additive_identity))
| ~ sum(x,additive_identity,add(x,additive_identity))
| add(x,additive_identity) = add(x,additive_identity) ),
inference(extension,[status(thm),parent(t172:2)],[addition_is_well_defined]) ).
cnf(t175,plain,
$false,
inference(connection,[status(thm),parent(t174:1)],[t174:1,t172:2]) ).
cnf(t176,plain,
sum(x,additive_identity,add(x,additive_identity)),
inference(extension,[status(thm),parent(t174:2)],[closure_of_addition]) ).
cnf(t177,plain,
$false,
inference(connection,[status(thm),parent(t176:1)],[t176:1,t174:2]) ).
cnf(t178,plain,
sum(x,additive_identity,add(x,additive_identity)),
inference(extension,[status(thm),parent(t174:3)],[closure_of_addition]) ).
cnf(t179,plain,
$false,
inference(connection,[status(thm),parent(t178:1)],[t178:1,t174:3]) ).
cnf(t180,plain,
( multiplicative_identity != multiplicative_identity
| add(x,additive_identity) != add(x,additive_identity)
| ~ product(add(x,additive_identity),multiplicative_identity,add(x,additive_identity))
| add(x,additive_identity) != add(x,additive_identity)
| product(add(x,additive_identity),multiplicative_identity,add(x,additive_identity)) ),
inference(extension,[status(thm),parent(t172:3)],[equality_8]) ).
cnf(t181,plain,
$false,
inference(connection,[status(thm),parent(t180:1)],[t180:1,t172:3]) ).
cnf(t182,plain,
add(x,additive_identity) = add(x,additive_identity),
inference(extension,[status(thm),parent(t180:2)],[equality_1]) ).
cnf(t183,plain,
$false,
inference(connection,[status(thm),parent(t182:1)],[t182:1,t180:2]) ).
cnf(t184,plain,
product(add(x,additive_identity),multiplicative_identity,add(x,additive_identity)),
inference(extension,[status(thm),parent(t180:3)],[multiplicative_identity2]) ).
cnf(t185,plain,
$false,
inference(connection,[status(thm),parent(t184:1)],[t184:1,t180:3]) ).
cnf(t186,plain,
add(x,additive_identity) = add(x,additive_identity),
inference(extension,[status(thm),parent(t180:4)],[equality_1]) ).
cnf(t187,plain,
$false,
inference(connection,[status(thm),parent(t186:1)],[t186:1,t180:4]) ).
cnf(t188,plain,
multiplicative_identity = multiplicative_identity,
inference(extension,[status(thm),parent(t180:5)],[equality_1]) ).
cnf(t189,plain,
$false,
inference(connection,[status(thm),parent(t188:1)],[t188:1,t180:5]) ).
cnf(t190,plain,
( ~ product(add(x,additive_identity),multiplicative_identity,add(x,additive_identity))
| ~ product(add(x,additive_identity),multiplicative_identity,add(x,additive_identity))
| add(x,additive_identity) = add(x,additive_identity) ),
inference(extension,[status(thm),parent(t172:4)],[multiplication_is_well_defined]) ).
cnf(t191,plain,
$false,
inference(connection,[status(thm),parent(t190:1)],[t190:1,t172:4]) ).
cnf(t192,plain,
product(add(x,additive_identity),multiplicative_identity,add(x,additive_identity)),
inference(extension,[status(thm),parent(t190:2)],[multiplicative_identity2]) ).
cnf(t193,plain,
$false,
inference(connection,[status(thm),parent(t192:1)],[t192:1,t190:2]) ).
cnf(t194,plain,
product(add(x,additive_identity),multiplicative_identity,add(x,additive_identity)),
inference(extension,[status(thm),parent(t190:3)],[multiplicative_identity2]) ).
cnf(t195,plain,
$false,
inference(connection,[status(thm),parent(t194:1)],[t194:1,t190:3]) ).
cnf(t196,plain,
( ~ sum(U_3791,inverse(U_3791),multiplicative_identity)
| ~ sum(U_3791,inverse(U_3791),multiplicative_identity)
| multiplicative_identity = multiplicative_identity ),
inference(extension,[status(thm),parent(t172:5)],[addition_is_well_defined]) ).
cnf(t197,plain,
$false,
inference(connection,[status(thm),parent(t196:1)],[t196:1,t172:5]) ).
cnf(t198,plain,
sum(U_3791,inverse(U_3791),multiplicative_identity),
inference(extension,[status(thm),parent(t196:2)],[additive_inverse2]) ).
cnf(t199,plain,
$false,
inference(connection,[status(thm),parent(t198:1)],[t198:1,t196:2]) ).
cnf(l97,lemma,
sum(U_3791,inverse(U_3791),multiplicative_identity),
inference(lemma,[status(cth),parent(t196:2),below(t172:5)],[t196:2]) ).
cnf(t200,plain,
sum(U_3791,inverse(U_3791),multiplicative_identity),
inference(lemma_extension,[status(thm),parent(t196:3)],[l97:1]) ).
cnf(t201,plain,
$false,
inference(connection,[status(thm),parent(t200:1)],[t200:1,t196:3]) ).
cnf(t202,plain,
( ~ sum(x,additive_identity,add(x,additive_identity))
| ~ sum(x,additive_identity,add(x,additive_identity))
| add(x,additive_identity) = add(x,additive_identity) ),
inference(extension,[status(thm),parent(t156:4)],[addition_is_well_defined]) ).
cnf(t203,plain,
$false,
inference(connection,[status(thm),parent(t202:1)],[t202:1,t156:4]) ).
cnf(t204,plain,
sum(x,additive_identity,add(x,additive_identity)),
inference(extension,[status(thm),parent(t202:2)],[closure_of_addition]) ).
cnf(t205,plain,
$false,
inference(connection,[status(thm),parent(t204:1)],[t204:1,t202:2]) ).
cnf(l99,lemma,
sum(x,additive_identity,add(x,additive_identity)),
inference(lemma,[status(cth),parent(t202:2),below(t156:4)],[t202:2]) ).
cnf(t206,plain,
sum(x,additive_identity,add(x,additive_identity)),
inference(lemma_extension,[status(thm),parent(t202:3)],[l99:1]) ).
cnf(t207,plain,
$false,
inference(connection,[status(thm),parent(t206:1)],[t206:1,t202:3]) ).
cnf(t208,plain,
( ~ sum(U_3802,inverse(U_3802),multiplicative_identity)
| ~ sum(U_3802,inverse(U_3802),multiplicative_identity)
| multiplicative_identity = multiplicative_identity ),
inference(extension,[status(thm),parent(t156:5)],[addition_is_well_defined]) ).
cnf(t209,plain,
$false,
inference(connection,[status(thm),parent(t208:1)],[t208:1,t156:5]) ).
cnf(t210,plain,
sum(U_3802,inverse(U_3802),multiplicative_identity),
inference(extension,[status(thm),parent(t208:2)],[additive_inverse2]) ).
cnf(t211,plain,
$false,
inference(connection,[status(thm),parent(t210:1)],[t210:1,t208:2]) ).
cnf(l101,lemma,
sum(U_3802,inverse(U_3802),multiplicative_identity),
inference(lemma,[status(cth),parent(t208:2),below(t156:5)],[t208:2]) ).
cnf(t212,plain,
sum(U_3802,inverse(U_3802),multiplicative_identity),
inference(lemma_extension,[status(thm),parent(t208:3)],[l101:1]) ).
cnf(t213,plain,
$false,
inference(connection,[status(thm),parent(t212:1)],[t212:1,t208:3]) ).
cnf(t214,plain,
( add(multiplicative_identity,add(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity))) != multiplicative_identity
| ~ sum(multiplicative_identity,add(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity)),add(multiplicative_identity,add(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity))))
| add(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity)) != add(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity))
| multiplicative_identity != multiplicative_identity
| sum(multiplicative_identity,add(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity)),multiplicative_identity) ),
inference(extension,[status(thm),parent(t2:5)],[equality_7]) ).
cnf(t215,plain,
$false,
inference(connection,[status(thm),parent(t214:1)],[t214:1,t2:5]) ).
cnf(t216,plain,
( ~ sum(U_3814,inverse(U_3814),multiplicative_identity)
| ~ sum(U_3814,inverse(U_3814),multiplicative_identity)
| multiplicative_identity = multiplicative_identity ),
inference(extension,[status(thm),parent(t214:2)],[addition_is_well_defined]) ).
cnf(t217,plain,
$false,
inference(connection,[status(thm),parent(t216:1)],[t216:1,t214:2]) ).
cnf(t218,plain,
sum(U_3814,inverse(U_3814),multiplicative_identity),
inference(extension,[status(thm),parent(t216:2)],[additive_inverse2]) ).
cnf(t219,plain,
$false,
inference(connection,[status(thm),parent(t218:1)],[t218:1,t216:2]) ).
cnf(t220,plain,
sum(U_3814,inverse(U_3814),multiplicative_identity),
inference(extension,[status(thm),parent(t216:3)],[additive_inverse2]) ).
cnf(t221,plain,
$false,
inference(connection,[status(thm),parent(t220:1)],[t220:1,t216:3]) ).
cnf(t222,plain,
( ~ sum(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity),add(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity)))
| ~ sum(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity),add(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity)))
| add(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity)) = add(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity)) ),
inference(extension,[status(thm),parent(t214:3)],[addition_is_well_defined]) ).
cnf(t223,plain,
$false,
inference(connection,[status(thm),parent(t222:1)],[t222:1,t214:3]) ).
cnf(t224,plain,
sum(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity),add(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity))),
inference(extension,[status(thm),parent(t222:2)],[closure_of_addition]) ).
cnf(t225,plain,
$false,
inference(connection,[status(thm),parent(t224:1)],[t224:1,t222:2]) ).
cnf(t226,plain,
( add(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity)) != add(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity))
| ~ sum(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity),add(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity)))
| add(add(inverse(x),additive_identity),additive_identity) != add(add(inverse(x),additive_identity),additive_identity)
| add(y,additive_identity) != add(y,additive_identity)
| sum(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity),add(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity))) ),
inference(extension,[status(thm),parent(t222:3)],[equality_7]) ).
cnf(t227,plain,
$false,
inference(connection,[status(thm),parent(t226:1)],[t226:1,t222:3]) ).
cnf(t228,plain,
add(y,additive_identity) = add(y,additive_identity),
inference(extension,[status(thm),parent(t226:2)],[equality_1]) ).
cnf(t229,plain,
$false,
inference(connection,[status(thm),parent(t228:1)],[t228:1,t226:2]) ).
cnf(t230,plain,
add(add(inverse(x),additive_identity),additive_identity) = add(add(inverse(x),additive_identity),additive_identity),
inference(extension,[status(thm),parent(t226:3)],[equality_1]) ).
cnf(t231,plain,
$false,
inference(connection,[status(thm),parent(t230:1)],[t230:1,t226:3]) ).
cnf(t232,plain,
sum(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity),add(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity))),
inference(extension,[status(thm),parent(t226:4)],[closure_of_addition]) ).
cnf(t233,plain,
$false,
inference(connection,[status(thm),parent(t232:1)],[t232:1,t226:4]) ).
cnf(t234,plain,
add(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity)) = add(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity)),
inference(extension,[status(thm),parent(t226:5)],[equality_1]) ).
cnf(t235,plain,
$false,
inference(connection,[status(thm),parent(t234:1)],[t234:1,t226:5]) ).
cnf(t236,plain,
( add(multiplicative_identity,add(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity))) != add(multiplicative_identity,add(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity)))
| ~ sum(multiplicative_identity,add(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity)),add(multiplicative_identity,add(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity))))
| add(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity)) != add(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity))
| multiplicative_identity != multiplicative_identity
| sum(multiplicative_identity,add(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity)),add(multiplicative_identity,add(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity)))) ),
inference(extension,[status(thm),parent(t214:4)],[equality_7]) ).
cnf(t237,plain,
$false,
inference(connection,[status(thm),parent(t236:1)],[t236:1,t214:4]) ).
cnf(t238,plain,
( ~ sum(U_3843,inverse(U_3843),multiplicative_identity)
| ~ sum(U_3843,inverse(U_3843),multiplicative_identity)
| multiplicative_identity = multiplicative_identity ),
inference(extension,[status(thm),parent(t236:2)],[addition_is_well_defined]) ).
cnf(t239,plain,
$false,
inference(connection,[status(thm),parent(t238:1)],[t238:1,t236:2]) ).
cnf(t240,plain,
sum(U_3843,inverse(U_3843),multiplicative_identity),
inference(extension,[status(thm),parent(t238:2)],[additive_inverse2]) ).
cnf(t241,plain,
$false,
inference(connection,[status(thm),parent(t240:1)],[t240:1,t238:2]) ).
cnf(t242,plain,
sum(U_3843,inverse(U_3843),multiplicative_identity),
inference(extension,[status(thm),parent(t238:3)],[additive_inverse2]) ).
cnf(t243,plain,
$false,
inference(connection,[status(thm),parent(t242:1)],[t242:1,t238:3]) ).
cnf(t244,plain,
( ~ sum(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity),add(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity)))
| ~ sum(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity),add(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity)))
| add(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity)) = add(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity)) ),
inference(extension,[status(thm),parent(t236:3)],[addition_is_well_defined]) ).
cnf(t245,plain,
$false,
inference(connection,[status(thm),parent(t244:1)],[t244:1,t236:3]) ).
cnf(t246,plain,
sum(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity),add(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity))),
inference(extension,[status(thm),parent(t244:2)],[closure_of_addition]) ).
cnf(t247,plain,
$false,
inference(connection,[status(thm),parent(t246:1)],[t246:1,t244:2]) ).
cnf(t248,plain,
sum(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity),add(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity))),
inference(extension,[status(thm),parent(t244:3)],[closure_of_addition]) ).
cnf(t249,plain,
$false,
inference(connection,[status(thm),parent(t248:1)],[t248:1,t244:3]) ).
cnf(t250,plain,
( add(multiplicative_identity,add(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity))) != add(multiplicative_identity,add(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity)))
| ~ sum(multiplicative_identity,add(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity)),add(multiplicative_identity,add(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity))))
| add(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity)) != add(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity))
| multiplicative_identity != multiplicative_identity
| sum(multiplicative_identity,add(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity)),add(multiplicative_identity,add(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity)))) ),
inference(extension,[status(thm),parent(t236:4)],[equality_7]) ).
cnf(t251,plain,
$false,
inference(connection,[status(thm),parent(t250:1)],[t250:1,t236:4]) ).
cnf(t252,plain,
multiplicative_identity = multiplicative_identity,
inference(extension,[status(thm),parent(t250:2)],[equality_1]) ).
cnf(t253,plain,
$false,
inference(connection,[status(thm),parent(t252:1)],[t252:1,t250:2]) ).
cnf(t254,plain,
add(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity)) = add(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity)),
inference(extension,[status(thm),parent(t250:3)],[equality_1]) ).
cnf(t255,plain,
$false,
inference(connection,[status(thm),parent(t254:1)],[t254:1,t250:3]) ).
cnf(t256,plain,
sum(multiplicative_identity,add(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity)),add(multiplicative_identity,add(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity)))),
inference(extension,[status(thm),parent(t250:4)],[closure_of_addition]) ).
cnf(t257,plain,
$false,
inference(connection,[status(thm),parent(t256:1)],[t256:1,t250:4]) ).
cnf(t258,plain,
add(multiplicative_identity,add(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity))) = add(multiplicative_identity,add(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity))),
inference(extension,[status(thm),parent(t250:5)],[equality_1]) ).
cnf(t259,plain,
$false,
inference(connection,[status(thm),parent(t258:1)],[t258:1,t250:5]) ).
cnf(t260,plain,
( ~ product(add(multiplicative_identity,add(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity))),multiplicative_identity,add(multiplicative_identity,add(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity))))
| ~ product(add(multiplicative_identity,add(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity))),multiplicative_identity,add(multiplicative_identity,add(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity))))
| add(multiplicative_identity,add(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity))) = add(multiplicative_identity,add(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity))) ),
inference(extension,[status(thm),parent(t236:5)],[multiplication_is_well_defined]) ).
cnf(t261,plain,
$false,
inference(connection,[status(thm),parent(t260:1)],[t260:1,t236:5]) ).
cnf(t262,plain,
product(add(multiplicative_identity,add(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity))),multiplicative_identity,add(multiplicative_identity,add(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity)))),
inference(extension,[status(thm),parent(t260:2)],[multiplicative_identity2]) ).
cnf(t263,plain,
$false,
inference(connection,[status(thm),parent(t262:1)],[t262:1,t260:2]) ).
cnf(t264,plain,
product(add(multiplicative_identity,add(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity))),multiplicative_identity,add(multiplicative_identity,add(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity)))),
inference(extension,[status(thm),parent(t260:3)],[multiplicative_identity2]) ).
cnf(t265,plain,
$false,
inference(connection,[status(thm),parent(t264:1)],[t264:1,t260:3]) ).
cnf(t266,plain,
( ~ product(add(multiplicative_identity,add(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity))),multiplicative_identity,multiplicative_identity)
| ~ product(add(multiplicative_identity,add(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity))),multiplicative_identity,add(multiplicative_identity,add(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity))))
| add(multiplicative_identity,add(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity))) = multiplicative_identity ),
inference(extension,[status(thm),parent(t214:5)],[multiplication_is_well_defined]) ).
cnf(t267,plain,
$false,
inference(connection,[status(thm),parent(t266:1)],[t266:1,t214:5]) ).
cnf(t268,plain,
( multiplicative_identity != multiplicative_identity
| add(multiplicative_identity,add(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity))) != add(multiplicative_identity,add(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity)))
| ~ product(add(multiplicative_identity,add(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity))),multiplicative_identity,add(multiplicative_identity,add(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity))))
| add(multiplicative_identity,add(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity))) != add(multiplicative_identity,add(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity)))
| product(add(multiplicative_identity,add(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity))),multiplicative_identity,add(multiplicative_identity,add(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity)))) ),
inference(extension,[status(thm),parent(t266:2)],[equality_8]) ).
cnf(t269,plain,
$false,
inference(connection,[status(thm),parent(t268:1)],[t268:1,t266:2]) ).
cnf(t270,plain,
add(multiplicative_identity,add(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity))) = add(multiplicative_identity,add(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity))),
inference(extension,[status(thm),parent(t268:2)],[equality_1]) ).
cnf(t271,plain,
$false,
inference(connection,[status(thm),parent(t270:1)],[t270:1,t268:2]) ).
cnf(t272,plain,
product(add(multiplicative_identity,add(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity))),multiplicative_identity,add(multiplicative_identity,add(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity)))),
inference(extension,[status(thm),parent(t268:3)],[multiplicative_identity2]) ).
cnf(t273,plain,
$false,
inference(connection,[status(thm),parent(t272:1)],[t272:1,t268:3]) ).
cnf(t274,plain,
add(multiplicative_identity,add(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity))) = add(multiplicative_identity,add(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity))),
inference(extension,[status(thm),parent(t268:4)],[equality_1]) ).
cnf(t275,plain,
$false,
inference(connection,[status(thm),parent(t274:1)],[t274:1,t268:4]) ).
cnf(t276,plain,
multiplicative_identity = multiplicative_identity,
inference(extension,[status(thm),parent(t268:5)],[equality_1]) ).
cnf(t277,plain,
$false,
inference(connection,[status(thm),parent(t276:1)],[t276:1,t268:5]) ).
cnf(t278,plain,
( ~ product(multiplicative_identity,inverse(add(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity))),inverse(add(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity))))
| ~ sum(inverse(add(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity))),add(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity)),multiplicative_identity)
| ~ sum(inverse(add(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity))),add(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity)),multiplicative_identity)
| ~ sum(multiplicative_identity,add(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity)),add(multiplicative_identity,add(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity))))
| product(add(multiplicative_identity,add(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity))),multiplicative_identity,multiplicative_identity) ),
inference(extension,[status(thm),parent(t266:3)],[distributivity7]) ).
cnf(t279,plain,
$false,
inference(connection,[status(thm),parent(t278:1)],[t278:1,t266:3]) ).
cnf(t280,plain,
sum(multiplicative_identity,add(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity)),add(multiplicative_identity,add(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity)))),
inference(extension,[status(thm),parent(t278:2)],[closure_of_addition]) ).
cnf(t281,plain,
$false,
inference(connection,[status(thm),parent(t280:1)],[t280:1,t278:2]) ).
cnf(t282,plain,
sum(inverse(add(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity))),add(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity)),multiplicative_identity),
inference(extension,[status(thm),parent(t278:3)],[additive_inverse1]) ).
cnf(t283,plain,
$false,
inference(connection,[status(thm),parent(t282:1)],[t282:1,t278:3]) ).
cnf(t284,plain,
sum(inverse(add(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity))),add(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity)),multiplicative_identity),
inference(extension,[status(thm),parent(t278:4)],[additive_inverse1]) ).
cnf(t285,plain,
$false,
inference(connection,[status(thm),parent(t284:1)],[t284:1,t278:4]) ).
cnf(t286,plain,
product(multiplicative_identity,inverse(add(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity))),inverse(add(add(y,additive_identity),add(add(inverse(x),additive_identity),additive_identity)))),
inference(extension,[status(thm),parent(t278:5)],[multiplicative_identity1]) ).
cnf(t287,plain,
$false,
inference(connection,[status(thm),parent(t286:1)],[t286:1,t278:5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO016-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 This is a CNF_UNS_RFO_SEQ_HRN problem
% 0.00/0.04 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n016.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Sun Sep 20 13:41:53 UTC 2026
% 0.10/0.35 % CPUTime :
% 208.65/208.96 % SZS status Unsatisfiable for theBenchmark
% 208.65/208.96 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------