%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : FLD030-2 : TPTP v9.2.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 04:18:17 PM UTC 2026
% Result : Unsatisfiable 0.47s 1.62s
% Output : CNFRefutation 0.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 34
% Syntax : Number of clauses : 75 ( 24 unt; 6 nHn; 75 RR)
% Number of literals : 171 ( 0 equ; 95 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 106 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(distributivity,axiom,
( equalish(add(multiply(X1,X2),multiply(X3,X2)),multiply(add(X1,X3),X2))
| ~ defined(X1)
| ~ defined(X3)
| ~ defined(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',distributivity) ).
cnf(associativity_multiplication,axiom,
( equalish(multiply(X1,multiply(X2,X3)),multiply(multiply(X1,X2),X3))
| ~ defined(X1)
| ~ defined(X2)
| ~ defined(X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',associativity_multiplication) ).
cnf(associativity_addition,axiom,
( equalish(add(X1,add(X2,X3)),add(add(X1,X2),X3))
| ~ defined(X1)
| ~ defined(X2)
| ~ defined(X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',associativity_addition) ).
cnf(compatibility_of_order_relation_and_addition,axiom,
( less_or_equal(add(X1,X2),add(X3,X2))
| ~ defined(X2)
| ~ less_or_equal(X1,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',compatibility_of_order_relation_and_addition) ).
cnf(compatibility_of_equality_and_multiplication,axiom,
( equalish(multiply(X1,X2),multiply(X3,X2))
| ~ defined(X2)
| ~ equalish(X1,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',compatibility_of_equality_and_multiplication) ).
cnf(compatibility_of_equality_and_addition,axiom,
( equalish(add(X1,X2),add(X3,X2))
| ~ defined(X2)
| ~ equalish(X1,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',compatibility_of_equality_and_addition) ).
cnf(commutativity_multiplication,axiom,
( equalish(multiply(X1,X2),multiply(X2,X1))
| ~ defined(X1)
| ~ defined(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',commutativity_multiplication) ).
cnf(commutativity_addition,axiom,
( equalish(add(X1,X2),add(X2,X1))
| ~ defined(X1)
| ~ defined(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',commutativity_addition) ).
cnf(compatibility_of_order_relation_and_multiplication,axiom,
( less_or_equal(additive_identity,multiply(X1,X2))
| ~ less_or_equal(additive_identity,X1)
| ~ less_or_equal(additive_identity,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',compatibility_of_order_relation_and_multiplication) ).
cnf(existence_of_inverse_multiplication,axiom,
( equalish(multiply(X1,multiplicative_inverse(X1)),multiplicative_identity)
| equalish(X1,additive_identity)
| ~ defined(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',existence_of_inverse_multiplication) ).
cnf(transitivity_of_order_relation,axiom,
( less_or_equal(X1,X2)
| ~ less_or_equal(X1,X3)
| ~ less_or_equal(X3,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',transitivity_of_order_relation) ).
cnf(compatibility_of_equality_and_order_relation,axiom,
( less_or_equal(X1,X2)
| ~ less_or_equal(X3,X2)
| ~ equalish(X3,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',compatibility_of_equality_and_order_relation) ).
cnf(antisymmetry_of_order_relation,axiom,
( equalish(X1,X2)
| ~ less_or_equal(X1,X2)
| ~ less_or_equal(X2,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',antisymmetry_of_order_relation) ).
cnf(transitivity_of_equality,axiom,
( equalish(X1,X2)
| ~ equalish(X1,X3)
| ~ equalish(X3,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',transitivity_of_equality) ).
cnf(existence_of_inverse_addition,axiom,
( equalish(add(X1,additive_inverse(X1)),additive_identity)
| ~ defined(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',existence_of_inverse_addition) ).
cnf(multiply_not_equal_to_c_7,negated_conjecture,
~ equalish(multiply(d,b),c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply_not_equal_to_c_7) ).
cnf(well_definedness_of_multiplication,axiom,
( defined(multiply(X1,X2))
| ~ defined(X1)
| ~ defined(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',well_definedness_of_multiplication) ).
cnf(well_definedness_of_addition,axiom,
( defined(add(X1,X2))
| ~ defined(X1)
| ~ defined(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',well_definedness_of_addition) ).
cnf(existence_of_identity_multiplication,axiom,
( equalish(multiply(multiplicative_identity,X1),X1)
| ~ defined(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',existence_of_identity_multiplication) ).
cnf(existence_of_identity_addition,axiom,
( equalish(add(additive_identity,X1),X1)
| ~ defined(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',existence_of_identity_addition) ).
cnf(totality_of_order_relation,axiom,
( less_or_equal(X1,X2)
| less_or_equal(X2,X1)
| ~ defined(X1)
| ~ defined(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',totality_of_order_relation) ).
cnf(symmetry_of_equality,axiom,
( equalish(X1,X2)
| ~ equalish(X2,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',symmetry_of_equality) ).
cnf(multiply_equals_c_5,negated_conjecture,
equalish(multiply(a,b),c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply_equals_c_5) ).
cnf(well_definedness_of_multiplicative_inverse,axiom,
( defined(multiplicative_inverse(X1))
| equalish(X1,additive_identity)
| ~ defined(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',well_definedness_of_multiplicative_inverse) ).
cnf(reflexivity_of_equality,axiom,
( equalish(X1,X1)
| ~ defined(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',reflexivity_of_equality) ).
cnf(different_identities,axiom,
~ equalish(additive_identity,multiplicative_identity),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',different_identities) ).
cnf(well_definedness_of_additive_inverse,axiom,
( defined(additive_inverse(X1))
| ~ defined(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',well_definedness_of_additive_inverse) ).
cnf(a_equals_d_6,negated_conjecture,
equalish(a,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_equals_d_6) ).
cnf(d_is_defined,hypothesis,
defined(d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d_is_defined) ).
cnf(c_is_defined,hypothesis,
defined(c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_is_defined) ).
cnf(b_is_defined,hypothesis,
defined(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_is_defined) ).
cnf(a_is_defined,hypothesis,
defined(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_is_defined) ).
cnf(well_definedness_of_multiplicative_identity,axiom,
defined(multiplicative_identity),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',well_definedness_of_multiplicative_identity) ).
cnf(well_definedness_of_additive_identity,axiom,
defined(additive_identity),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',well_definedness_of_additive_identity) ).
cnf(i_0_34,axiom,
( equalish(add(multiply(X1,X2),multiply(X3,X2)),multiply(add(X1,X3),X2))
| ~ defined(X1)
| ~ defined(X3)
| ~ defined(X2) ),
distributivity,
[final] ).
cnf(i_0_35,axiom,
( equalish(multiply(X1,multiply(X2,X3)),multiply(multiply(X1,X2),X3))
| ~ defined(X1)
| ~ defined(X2)
| ~ defined(X3) ),
associativity_multiplication,
[final] ).
cnf(i_0_36,axiom,
( equalish(add(X1,add(X2,X3)),add(add(X1,X2),X3))
| ~ defined(X1)
| ~ defined(X2)
| ~ defined(X3) ),
associativity_addition,
[final] ).
cnf(i_0_37,axiom,
( less_or_equal(add(X1,X2),add(X3,X2))
| ~ defined(X2)
| ~ less_or_equal(X1,X3) ),
compatibility_of_order_relation_and_addition,
[final] ).
cnf(i_0_38,axiom,
( equalish(multiply(X1,X2),multiply(X3,X2))
| ~ defined(X2)
| ~ equalish(X1,X3) ),
compatibility_of_equality_and_multiplication,
[final] ).
cnf(i_0_39,axiom,
( equalish(add(X1,X2),add(X3,X2))
| ~ defined(X2)
| ~ equalish(X1,X3) ),
compatibility_of_equality_and_addition,
[final] ).
cnf(i_0_40,axiom,
( equalish(multiply(X1,X2),multiply(X2,X1))
| ~ defined(X1)
| ~ defined(X2) ),
commutativity_multiplication,
[final] ).
cnf(i_0_41,axiom,
( equalish(add(X1,X2),add(X2,X1))
| ~ defined(X1)
| ~ defined(X2) ),
commutativity_addition,
[final] ).
cnf(i_0_42,axiom,
( less_or_equal(additive_identity,multiply(X1,X2))
| ~ less_or_equal(additive_identity,X1)
| ~ less_or_equal(additive_identity,X2) ),
compatibility_of_order_relation_and_multiplication,
[final] ).
cnf(i_0_43,axiom,
( equalish(multiply(X1,multiplicative_inverse(X1)),multiplicative_identity)
| equalish(X1,additive_identity)
| ~ defined(X1) ),
existence_of_inverse_multiplication,
[final] ).
cnf(i_0_44,axiom,
( less_or_equal(X1,X2)
| ~ less_or_equal(X1,X3)
| ~ less_or_equal(X3,X2) ),
transitivity_of_order_relation,
[final] ).
cnf(i_0_45,axiom,
( less_or_equal(X1,X2)
| ~ less_or_equal(X3,X2)
| ~ equalish(X3,X1) ),
compatibility_of_equality_and_order_relation,
[final] ).
cnf(i_0_46,axiom,
( equalish(X1,X2)
| ~ less_or_equal(X1,X2)
| ~ less_or_equal(X2,X1) ),
antisymmetry_of_order_relation,
[final] ).
cnf(i_0_47,axiom,
( equalish(X1,X2)
| ~ equalish(X1,X3)
| ~ equalish(X3,X2) ),
transitivity_of_equality,
[final] ).
cnf(i_0_48,axiom,
( equalish(add(X1,additive_inverse(X1)),additive_identity)
| ~ defined(X1) ),
existence_of_inverse_addition,
[final] ).
cnf(i_0_49,negated_conjecture,
~ equalish(multiply(d,b),c),
multiply_not_equal_to_c_7,
[final] ).
cnf(i_0_50,axiom,
( defined(multiply(X1,X2))
| ~ defined(X1)
| ~ defined(X2) ),
well_definedness_of_multiplication,
[final] ).
cnf(i_0_51,axiom,
( defined(add(X1,X2))
| ~ defined(X1)
| ~ defined(X2) ),
well_definedness_of_addition,
[final] ).
cnf(i_0_52,axiom,
( equalish(multiply(multiplicative_identity,X1),X1)
| ~ defined(X1) ),
existence_of_identity_multiplication,
[final] ).
cnf(i_0_53,axiom,
( equalish(add(additive_identity,X1),X1)
| ~ defined(X1) ),
existence_of_identity_addition,
[final] ).
cnf(i_0_54,axiom,
( less_or_equal(X1,X2)
| less_or_equal(X2,X1)
| ~ defined(X1)
| ~ defined(X2) ),
totality_of_order_relation,
[final] ).
cnf(i_0_55,axiom,
( equalish(X1,X2)
| ~ equalish(X2,X1) ),
symmetry_of_equality,
[final] ).
cnf(i_0_56,negated_conjecture,
equalish(multiply(a,b),c),
multiply_equals_c_5,
[final] ).
cnf(i_0_57,axiom,
( defined(multiplicative_inverse(X1))
| equalish(X1,additive_identity)
| ~ defined(X1) ),
well_definedness_of_multiplicative_inverse,
[final] ).
cnf(i_0_58,axiom,
( equalish(X1,X1)
| ~ defined(X1) ),
reflexivity_of_equality,
[final] ).
cnf(i_0_59,axiom,
~ equalish(additive_identity,multiplicative_identity),
different_identities,
[final] ).
cnf(i_0_60,axiom,
( defined(additive_inverse(X1))
| ~ defined(X1) ),
well_definedness_of_additive_inverse,
[final] ).
cnf(i_0_61,negated_conjecture,
equalish(a,d),
a_equals_d_6,
[final] ).
cnf(i_0_62,hypothesis,
defined(d),
d_is_defined,
[final] ).
cnf(i_0_63,hypothesis,
defined(c),
c_is_defined,
[final] ).
cnf(i_0_64,hypothesis,
defined(b),
b_is_defined,
[final] ).
cnf(i_0_65,hypothesis,
defined(a),
a_is_defined,
[final] ).
cnf(i_0_66,axiom,
defined(multiplicative_identity),
well_definedness_of_multiplicative_identity,
[final] ).
cnf(i_0_67,axiom,
defined(additive_identity),
well_definedness_of_additive_identity,
[final] ).
cnf(i_0_68,plain,
equalish(d,a),
inference(scs_inference,[],[i_0_61,i_0_55]) ).
cnf(i_0_69,plain,
( ~ equalish(X1,X2)
| equalish(X2,X1) ),
inference(rename_variables,[],[i_0_55]) ).
cnf(i_0_70,plain,
equalish(d,d),
inference(scs_inference,[],[i_0_61,i_0_62,i_0_55,i_0_58]) ).
cnf(i_0_71,plain,
( ~ defined(X1)
| equalish(X1,X1) ),
inference(rename_variables,[],[i_0_58]) ).
cnf(i_0_72,plain,
~ equalish(multiply(d,b),multiply(a,b)),
inference(scs_inference,[],[i_0_49,i_0_61,i_0_56,i_0_62,i_0_55,i_0_58,i_0_47]) ).
cnf(i_0_73,plain,
( ~ equalish(X1,X2)
| equalish(X3,X2)
| ~ equalish(X3,X1) ),
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_74,plain,
$false,
inference(scs_inference,[],[i_0_49,i_0_61,i_0_56,i_0_62,i_0_64,i_0_55,i_0_58,i_0_47,i_0_38]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : FLD030-2 : TPTP v9.2.1. Bugfixed v2.1.0.
% 0.00/0.13 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.34 % Computer : n008.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Mon May 4 17:27:28 EDT 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.35 % start to proof: theBenchmark
% 0.47/1.62 % Version : CSE_E---1.7
% 0.47/1.62 % Problem : theBenchmark.p
% 0.47/1.62 % SZS status Unsatisfiable for theBenchmark.p
% 0.47/1.62 % SZS output start CNFRefutation
% See solution above
% 0.47/1.65 % Total time : 1.270s
%------------------------------------------------------------------------------