%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : FLD050-4 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/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 08:38:58 AM UTC 2026
% Result : Unsatisfiable 249.04s 249.38s
% Output : Proof 250.34s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
cnf(associativity_addition_1,axiom,
( ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(X,V,W) ),
file('FLD002-0.ax',associativity_addition_1) ).
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(existence_of_identity_addition,axiom,
( ~ defined(X)
| sum(additive_identity,X,X) ),
file('FLD002-0.ax',existence_of_identity_addition) ).
cnf(existence_of_inverse_addition,axiom,
( ~ defined(X)
| sum(additive_inverse(X),X,additive_identity) ),
file('FLD002-0.ax',existence_of_inverse_addition) ).
cnf(commutativity_addition,axiom,
( ~ sum(X,Y,Z)
| sum(Y,X,Z) ),
file('FLD002-0.ax',commutativity_addition) ).
cnf(associativity_multiplication_1,axiom,
( ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| product(X,V,W) ),
file('FLD002-0.ax',associativity_multiplication_1) ).
cnf(associativity_multiplication_2,axiom,
( ~ product(X,V,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| product(U,Z,W) ),
file('FLD002-0.ax',associativity_multiplication_2) ).
cnf(existence_of_identity_multiplication,axiom,
( ~ defined(X)
| product(multiplicative_identity,X,X) ),
file('FLD002-0.ax',existence_of_identity_multiplication) ).
cnf(existence_of_inverse_multiplication,axiom,
( ~ defined(X)
| sum(additive_identity,X,additive_identity)
| product(multiplicative_inverse(X),X,multiplicative_identity) ),
file('FLD002-0.ax',existence_of_inverse_multiplication) ).
cnf(commutativity_multiplication,axiom,
( ~ product(X,Y,Z)
| product(Y,X,Z) ),
file('FLD002-0.ax',commutativity_multiplication) ).
cnf(distributivity_1,axiom,
( ~ product(Y,Z,D)
| ~ product(X,Z,C)
| ~ product(A,Z,B)
| ~ sum(X,Y,A)
| sum(C,D,B) ),
file('FLD002-0.ax',distributivity_1) ).
cnf(distributivity_2,axiom,
( ~ sum(C,D,B)
| ~ product(Y,Z,D)
| ~ product(X,Z,C)
| ~ sum(X,Y,A)
| product(A,Z,B) ),
file('FLD002-0.ax',distributivity_2) ).
cnf(well_definedness_of_addition,axiom,
( ~ defined(Y)
| ~ defined(X)
| defined(add(X,Y)) ),
file('FLD002-0.ax',well_definedness_of_addition) ).
cnf(well_definedness_of_additive_identity,axiom,
defined(additive_identity),
file('FLD002-0.ax',well_definedness_of_additive_identity) ).
cnf(well_definedness_of_additive_inverse,axiom,
( ~ defined(X)
| defined(additive_inverse(X)) ),
file('FLD002-0.ax',well_definedness_of_additive_inverse) ).
cnf(well_definedness_of_multiplication,axiom,
( ~ defined(Y)
| ~ defined(X)
| defined(multiply(X,Y)) ),
file('FLD002-0.ax',well_definedness_of_multiplication) ).
cnf(well_definedness_of_multiplicative_identity,axiom,
defined(multiplicative_identity),
file('FLD002-0.ax',well_definedness_of_multiplicative_identity) ).
cnf(well_definedness_of_multiplicative_inverse,axiom,
( sum(additive_identity,X,additive_identity)
| ~ defined(X)
| defined(multiplicative_inverse(X)) ),
file('FLD002-0.ax',well_definedness_of_multiplicative_inverse) ).
cnf(totality_of_addition,axiom,
( ~ defined(Y)
| ~ defined(X)
| sum(X,Y,add(X,Y)) ),
file('FLD002-0.ax',totality_of_addition) ).
cnf(totality_of_multiplication,axiom,
( ~ defined(Y)
| ~ defined(X)
| product(X,Y,multiply(X,Y)) ),
file('FLD002-0.ax',totality_of_multiplication) ).
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(compatibility_of_order_relation_and_multiplication,axiom,
( ~ product(X,Y,Z)
| ~ less_or_equal(additive_identity,Y)
| ~ less_or_equal(additive_identity,X)
| less_or_equal(additive_identity,Z) ),
file('FLD002-0.ax',compatibility_of_order_relation_and_multiplication) ).
cnf(different_identities,axiom,
~ sum(additive_identity,additive_identity,multiplicative_identity),
file('FLD002-0.ax',different_identities) ).
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(c_is_defined,hypothesis,
defined(c),
file('theBenchmark.p',c_is_defined) ).
cnf(d_is_defined,hypothesis,
defined(d),
file('theBenchmark.p',d_is_defined) ).
cnf(k_is_defined,hypothesis,
defined(k),
file('theBenchmark.p',k_is_defined) ).
cnf(s_is_defined,hypothesis,
defined(s),
file('theBenchmark.p',s_is_defined) ).
cnf(not_sum_7,negated_conjecture,
~ sum(additive_identity,b,additive_identity),
file('theBenchmark.p',not_sum_7) ).
cnf(not_sum_8,negated_conjecture,
~ sum(additive_identity,d,additive_identity),
file('theBenchmark.p',not_sum_8) ).
cnf(product_9,negated_conjecture,
product(a,multiplicative_inverse(b),s),
file('theBenchmark.p',product_9) ).
cnf(product_10,negated_conjecture,
product(a,d,k),
file('theBenchmark.p',product_10) ).
cnf(product_11,negated_conjecture,
product(b,c,k),
file('theBenchmark.p',product_11) ).
cnf(not_product_12,negated_conjecture,
~ product(c,multiplicative_inverse(d),s),
file('theBenchmark.p',not_product_12) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD050-4 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.03 This is a CNF_UNS_RFO_NEQ_NHN problem
% 0.00/0.04 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n005.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % 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 19:02:18 UTC 2026
% 0.09/0.36 % CPUTime :
% 249.04/249.38 % SZS status Unsatisfiable for theBenchmark
% 249.04/249.38 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------