%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : FLD060-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 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 : n005.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 08:39:00 AM UTC 2026
% Result : Unsatisfiable 118.80s 119.17s
% Output : Proof 118.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 12
% Syntax : Number of clauses : 116 ( 87 unt; 4 nHn; 116 RR)
% Number of literals : 182 ( 0 equ; 64 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 25 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(associativity_addition_2,axiom,
( ~ sum(X,V,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(U,Z,W) ),
file('FLD002-0.ax',associativity_addition_2) ).
cnf(commutativity_addition,axiom,
( ~ sum(X,Y,Z)
| sum(Y,X,Z) ),
file('FLD002-0.ax',commutativity_addition) ).
cnf(well_definedness_of_addition,axiom,
( ~ defined(Y)
| ~ defined(X)
| defined(add(X,Y)) ),
file('FLD002-0.ax',well_definedness_of_addition) ).
cnf(totality_of_addition,axiom,
( ~ defined(Y)
| ~ defined(X)
| sum(X,Y,add(X,Y)) ),
file('FLD002-0.ax',totality_of_addition) ).
cnf(antisymmetry_of_order_relation,axiom,
( ~ less_or_equal(Y,X)
| ~ less_or_equal(X,Y)
| sum(additive_identity,X,Y) ),
file('FLD002-0.ax',antisymmetry_of_order_relation) ).
cnf(transitivity_of_order_relation,axiom,
( ~ less_or_equal(Y,Z)
| ~ less_or_equal(X,Y)
| less_or_equal(X,Z) ),
file('FLD002-0.ax',transitivity_of_order_relation) ).
cnf(totality_of_order_relation,axiom,
( ~ defined(Y)
| ~ defined(X)
| less_or_equal(Y,X)
| less_or_equal(X,Y) ),
file('FLD002-0.ax',totality_of_order_relation) ).
cnf(compatibility_of_order_relation_and_addition,axiom,
( ~ sum(Y,Z,V)
| ~ sum(X,Z,U)
| ~ less_or_equal(X,Y)
| less_or_equal(U,V) ),
file('FLD002-0.ax',compatibility_of_order_relation_and_addition) ).
cnf(a_is_defined,hypothesis,
defined(a),
file('theBenchmark.p',a_is_defined) ).
cnf(b_is_defined,hypothesis,
defined(b),
file('theBenchmark.p',b_is_defined) ).
cnf(less_or_equal_3,negated_conjecture,
less_or_equal(a,b),
file('theBenchmark.p',less_or_equal_3) ).
cnf(not_less_or_equal_4,negated_conjecture,
~ less_or_equal(add(a,a),add(b,b)),
file('theBenchmark.p',not_less_or_equal_4) ).
cnf(t1,plain,
~ less_or_equal(add(a,a),add(b,b)),
inference(start,[status(thm),parent(0:0)],[not_less_or_equal_4]) ).
cnf(t2,plain,
( ~ defined(add(a,a))
| ~ defined(add(b,b))
| less_or_equal(add(b,b),add(a,a))
| less_or_equal(add(a,a),add(b,b)) ),
inference(extension,[status(thm),parent(t1:1)],[totality_of_order_relation]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( ~ less_or_equal(add(a,a),add(b,a))
| less_or_equal(add(b,b),add(b,a))
| ~ less_or_equal(add(b,b),add(a,a)) ),
inference(extension,[status(thm),parent(t2:2)],[transitivity_of_order_relation]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( ~ less_or_equal(add(b,a),add(b,a))
| less_or_equal(add(b,b),add(b,a))
| ~ less_or_equal(add(b,b),add(b,a)) ),
inference(extension,[status(thm),parent(t4:2)],[transitivity_of_order_relation]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
( ~ less_or_equal(add(b,a),add(b,b))
| sum(additive_identity,add(b,a),add(b,b))
| ~ less_or_equal(add(b,b),add(b,a)) ),
inference(extension,[status(thm),parent(t6:2)],[antisymmetry_of_order_relation]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
( ~ sum(additive_identity,b,b)
| ~ sum(b,a,add(b,a))
| sum(b,a,add(b,b))
| ~ sum(additive_identity,add(b,a),add(b,b)) ),
inference(extension,[status(thm),parent(t8:2)],[associativity_addition_2]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(t12,plain,
( ~ less_or_equal(a,b)
| ~ sum(a,a,add(a,a))
| less_or_equal(add(a,a),add(b,b))
| ~ sum(b,a,add(b,b)) ),
inference(extension,[status(thm),parent(t10:2)],[compatibility_of_order_relation_and_addition]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t10:2]) ).
cnf(t14,plain,
$false,
inference(reduction,[status(thm),parent(t12:2)],[t12:2,t1:1]) ).
cnf(t15,plain,
( ~ defined(a)
| ~ defined(a)
| sum(a,a,add(a,a)) ),
inference(extension,[status(thm),parent(t12:3)],[totality_of_addition]) ).
cnf(t16,plain,
$false,
inference(connection,[status(thm),parent(t15:1)],[t15:1,t12:3]) ).
cnf(t17,plain,
defined(a),
inference(extension,[status(thm),parent(t15:2)],[a_is_defined]) ).
cnf(t18,plain,
$false,
inference(connection,[status(thm),parent(t17:1)],[t17:1,t15:2]) ).
cnf(l9,lemma,
defined(a),
inference(lemma,[status(cth),parent(t15:2),below(t12:3)],[t15:2]) ).
cnf(t19,plain,
defined(a),
inference(lemma_extension,[status(thm),parent(t15:3)],[l9:1]) ).
cnf(t20,plain,
$false,
inference(connection,[status(thm),parent(t19:1)],[t19:1,t15:3]) ).
cnf(t21,plain,
less_or_equal(a,b),
inference(extension,[status(thm),parent(t12:4)],[less_or_equal_3]) ).
cnf(t22,plain,
$false,
inference(connection,[status(thm),parent(t21:1)],[t21:1,t12:4]) ).
cnf(t23,plain,
( ~ defined(b)
| ~ defined(a)
| sum(b,a,add(b,a)) ),
inference(extension,[status(thm),parent(t10:3)],[totality_of_addition]) ).
cnf(t24,plain,
$false,
inference(connection,[status(thm),parent(t23:1)],[t23:1,t10:3]) ).
cnf(t25,plain,
defined(a),
inference(extension,[status(thm),parent(t23:2)],[a_is_defined]) ).
cnf(t26,plain,
$false,
inference(connection,[status(thm),parent(t25:1)],[t25:1,t23:2]) ).
cnf(t27,plain,
defined(b),
inference(extension,[status(thm),parent(t23:3)],[b_is_defined]) ).
cnf(t28,plain,
$false,
inference(connection,[status(thm),parent(t27:1)],[t27:1,t23:3]) ).
cnf(t29,plain,
( ~ less_or_equal(b,b)
| ~ less_or_equal(b,b)
| sum(additive_identity,b,b) ),
inference(extension,[status(thm),parent(t10:4)],[antisymmetry_of_order_relation]) ).
cnf(t30,plain,
$false,
inference(connection,[status(thm),parent(t29:1)],[t29:1,t10:4]) ).
cnf(t31,plain,
( ~ defined(b)
| ~ defined(b)
| less_or_equal(b,b)
| less_or_equal(b,b) ),
inference(extension,[status(thm),parent(t29:2)],[totality_of_order_relation]) ).
cnf(t32,plain,
$false,
inference(connection,[status(thm),parent(t31:1)],[t31:1,t29:2]) ).
cnf(t33,plain,
$false,
inference(reduction,[status(thm),parent(t31:2)],[t31:2,t29:2]) ).
cnf(t34,plain,
defined(b),
inference(extension,[status(thm),parent(t31:3)],[b_is_defined]) ).
cnf(t35,plain,
$false,
inference(connection,[status(thm),parent(t34:1)],[t34:1,t31:3]) ).
cnf(l17,lemma,
defined(b),
inference(lemma,[status(cth),parent(t31:3),below(t29:2)],[t31:3]) ).
cnf(t36,plain,
defined(b),
inference(lemma_extension,[status(thm),parent(t31:4)],[l17:1]) ).
cnf(t37,plain,
$false,
inference(connection,[status(thm),parent(t36:1)],[t36:1,t31:4]) ).
cnf(l15,lemma,
less_or_equal(b,b),
inference(lemma,[status(cth),parent(t29:2),below(t10:4)],[t29:2]) ).
cnf(t38,plain,
less_or_equal(b,b),
inference(lemma_extension,[status(thm),parent(t29:3)],[l15:1]) ).
cnf(t39,plain,
$false,
inference(connection,[status(thm),parent(t38:1)],[t38:1,t29:3]) ).
cnf(t40,plain,
( ~ less_or_equal(a,b)
| ~ sum(a,b,add(b,a))
| ~ sum(b,b,add(b,b))
| less_or_equal(add(b,a),add(b,b)) ),
inference(extension,[status(thm),parent(t8:3)],[compatibility_of_order_relation_and_addition]) ).
cnf(t41,plain,
$false,
inference(connection,[status(thm),parent(t40:1)],[t40:1,t8:3]) ).
cnf(t42,plain,
( ~ defined(b)
| ~ defined(b)
| sum(b,b,add(b,b)) ),
inference(extension,[status(thm),parent(t40:2)],[totality_of_addition]) ).
cnf(t43,plain,
$false,
inference(connection,[status(thm),parent(t42:1)],[t42:1,t40:2]) ).
cnf(t44,plain,
defined(b),
inference(extension,[status(thm),parent(t42:2)],[b_is_defined]) ).
cnf(t45,plain,
$false,
inference(connection,[status(thm),parent(t44:1)],[t44:1,t42:2]) ).
cnf(l20,lemma,
defined(b),
inference(lemma,[status(cth),parent(t42:2),below(t40:2)],[t42:2]) ).
cnf(t46,plain,
defined(b),
inference(lemma_extension,[status(thm),parent(t42:3)],[l20:1]) ).
cnf(t47,plain,
$false,
inference(connection,[status(thm),parent(t46:1)],[t46:1,t42:3]) ).
cnf(t48,plain,
( ~ sum(b,a,add(b,a))
| sum(a,b,add(b,a)) ),
inference(extension,[status(thm),parent(t40:3)],[commutativity_addition]) ).
cnf(t49,plain,
$false,
inference(connection,[status(thm),parent(t48:1)],[t48:1,t40:3]) ).
cnf(t50,plain,
( ~ defined(b)
| ~ defined(a)
| sum(b,a,add(b,a)) ),
inference(extension,[status(thm),parent(t48:2)],[totality_of_addition]) ).
cnf(t51,plain,
$false,
inference(connection,[status(thm),parent(t50:1)],[t50:1,t48:2]) ).
cnf(t52,plain,
defined(a),
inference(extension,[status(thm),parent(t50:2)],[a_is_defined]) ).
cnf(t53,plain,
$false,
inference(connection,[status(thm),parent(t52:1)],[t52:1,t50:2]) ).
cnf(t54,plain,
defined(b),
inference(extension,[status(thm),parent(t50:3)],[b_is_defined]) ).
cnf(t55,plain,
$false,
inference(connection,[status(thm),parent(t54:1)],[t54:1,t50:3]) ).
cnf(t56,plain,
less_or_equal(a,b),
inference(extension,[status(thm),parent(t40:4)],[less_or_equal_3]) ).
cnf(t57,plain,
$false,
inference(connection,[status(thm),parent(t56:1)],[t56:1,t40:4]) ).
cnf(t58,plain,
( ~ defined(add(b,a))
| ~ defined(add(b,a))
| less_or_equal(add(b,a),add(b,a))
| less_or_equal(add(b,a),add(b,a)) ),
inference(extension,[status(thm),parent(t6:3)],[totality_of_order_relation]) ).
cnf(t59,plain,
$false,
inference(connection,[status(thm),parent(t58:1)],[t58:1,t6:3]) ).
cnf(t60,plain,
$false,
inference(reduction,[status(thm),parent(t58:2)],[t58:2,t6:3]) ).
cnf(t61,plain,
( ~ defined(b)
| ~ defined(a)
| defined(add(b,a)) ),
inference(extension,[status(thm),parent(t58:3)],[well_definedness_of_addition]) ).
cnf(t62,plain,
$false,
inference(connection,[status(thm),parent(t61:1)],[t61:1,t58:3]) ).
cnf(t63,plain,
defined(a),
inference(extension,[status(thm),parent(t61:2)],[a_is_defined]) ).
cnf(t64,plain,
$false,
inference(connection,[status(thm),parent(t63:1)],[t63:1,t61:2]) ).
cnf(t65,plain,
defined(b),
inference(extension,[status(thm),parent(t61:3)],[b_is_defined]) ).
cnf(t66,plain,
$false,
inference(connection,[status(thm),parent(t65:1)],[t65:1,t61:3]) ).
cnf(l28,lemma,
defined(add(b,a)),
inference(lemma,[status(cth),parent(t58:3),below(t6:3)],[t58:3]) ).
cnf(t67,plain,
defined(add(b,a)),
inference(lemma_extension,[status(thm),parent(t58:4)],[l28:1]) ).
cnf(t68,plain,
$false,
inference(connection,[status(thm),parent(t67:1)],[t67:1,t58:4]) ).
cnf(t69,plain,
( ~ less_or_equal(a,b)
| ~ sum(a,a,add(a,a))
| ~ sum(b,a,add(b,a))
| less_or_equal(add(a,a),add(b,a)) ),
inference(extension,[status(thm),parent(t4:3)],[compatibility_of_order_relation_and_addition]) ).
cnf(t70,plain,
$false,
inference(connection,[status(thm),parent(t69:1)],[t69:1,t4:3]) ).
cnf(t71,plain,
( ~ defined(b)
| ~ defined(a)
| sum(b,a,add(b,a)) ),
inference(extension,[status(thm),parent(t69:2)],[totality_of_addition]) ).
cnf(t72,plain,
$false,
inference(connection,[status(thm),parent(t71:1)],[t71:1,t69:2]) ).
cnf(t73,plain,
defined(a),
inference(extension,[status(thm),parent(t71:2)],[a_is_defined]) ).
cnf(t74,plain,
$false,
inference(connection,[status(thm),parent(t73:1)],[t73:1,t71:2]) ).
cnf(t75,plain,
defined(b),
inference(extension,[status(thm),parent(t71:3)],[b_is_defined]) ).
cnf(t76,plain,
$false,
inference(connection,[status(thm),parent(t75:1)],[t75:1,t71:3]) ).
cnf(t77,plain,
( ~ defined(a)
| ~ defined(a)
| sum(a,a,add(a,a)) ),
inference(extension,[status(thm),parent(t69:3)],[totality_of_addition]) ).
cnf(t78,plain,
$false,
inference(connection,[status(thm),parent(t77:1)],[t77:1,t69:3]) ).
cnf(t79,plain,
defined(a),
inference(extension,[status(thm),parent(t77:2)],[a_is_defined]) ).
cnf(t80,plain,
$false,
inference(connection,[status(thm),parent(t79:1)],[t79:1,t77:2]) ).
cnf(l36,lemma,
defined(a),
inference(lemma,[status(cth),parent(t77:2),below(t69:3)],[t77:2]) ).
cnf(t81,plain,
defined(a),
inference(lemma_extension,[status(thm),parent(t77:3)],[l36:1]) ).
cnf(t82,plain,
$false,
inference(connection,[status(thm),parent(t81:1)],[t81:1,t77:3]) ).
cnf(t83,plain,
less_or_equal(a,b),
inference(extension,[status(thm),parent(t69:4)],[less_or_equal_3]) ).
cnf(t84,plain,
$false,
inference(connection,[status(thm),parent(t83:1)],[t83:1,t69:4]) ).
cnf(t85,plain,
( ~ defined(b)
| ~ defined(b)
| defined(add(b,b)) ),
inference(extension,[status(thm),parent(t2:3)],[well_definedness_of_addition]) ).
cnf(t86,plain,
$false,
inference(connection,[status(thm),parent(t85:1)],[t85:1,t2:3]) ).
cnf(t87,plain,
defined(b),
inference(extension,[status(thm),parent(t85:2)],[b_is_defined]) ).
cnf(t88,plain,
$false,
inference(connection,[status(thm),parent(t87:1)],[t87:1,t85:2]) ).
cnf(l39,lemma,
defined(b),
inference(lemma,[status(cth),parent(t85:2),below(t2:3)],[t85:2]) ).
cnf(t89,plain,
defined(b),
inference(lemma_extension,[status(thm),parent(t85:3)],[l39:1]) ).
cnf(t90,plain,
$false,
inference(connection,[status(thm),parent(t89:1)],[t89:1,t85:3]) ).
cnf(t91,plain,
( ~ defined(a)
| ~ defined(a)
| defined(add(a,a)) ),
inference(extension,[status(thm),parent(t2:4)],[well_definedness_of_addition]) ).
cnf(t92,plain,
$false,
inference(connection,[status(thm),parent(t91:1)],[t91:1,t2:4]) ).
cnf(t93,plain,
defined(a),
inference(extension,[status(thm),parent(t91:2)],[a_is_defined]) ).
cnf(t94,plain,
$false,
inference(connection,[status(thm),parent(t93:1)],[t93:1,t91:2]) ).
cnf(l41,lemma,
defined(a),
inference(lemma,[status(cth),parent(t91:2),below(t2:4)],[t91:2]) ).
cnf(t95,plain,
defined(a),
inference(lemma_extension,[status(thm),parent(t91:3)],[l41:1]) ).
cnf(t96,plain,
$false,
inference(connection,[status(thm),parent(t95:1)],[t95:1,t91:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : FLD060-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 This is a CNF_UNS_RFO_NEQ_NHN problem
% 0.00/0.07 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.44 % Computer : n005.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Sun Sep 20 19:06:49 UTC 2026
% 0.17/0.44 % CPUTime :
% 118.80/119.17 % SZS status Unsatisfiable for theBenchmark
% 118.80/119.17 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------