%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : FLD010-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n014.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 : Fri Sep 25 01:14:53 PM UTC 2026
% Result : Unsatisfiable 10.65s 7.01s
% Output : Proof 10.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 8
% Syntax : Number of formulae : 49 ( 41 unt; 0 def)
% Number of atoms : 61 ( 25 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 34 ( 22 ~; 12 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-4 aty)
% Number of variables : 32 ( 2 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f9,axiom,
( ~ product(X,Y,Z)
| product(Y,X,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_multiplication) ).
fof(f9_nnf,plain,
! [Y,X,Z] :
( ~ product(X,Y,Z)
| product(Y,X,Z) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [Y,X,Z] :
( ~ product(X,Y,Z)
| product(Y,X,Z) ),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
( ~ product(X1,X0,X2)
| product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(t17,plain,
ifeq(product(X1,X2,X3),true,product(X2,X1,X3),true) = true,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(t61,plain,
ifeq(product(X1,X2,X3),true,product(X2,X1,X3),true) = true,
inference(orient,[status(thm)],[t17]) ).
cnf(f8,axiom,
( ~ defined(X)
| sum(additive_identity,X,additive_identity)
| product(multiplicative_inverse(X),X,multiplicative_identity) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_inverse_multiplication) ).
fof(f8_nnf,plain,
! [X] :
( ~ defined(X)
| sum(additive_identity,X,additive_identity)
| product(multiplicative_inverse(X),X,multiplicative_identity) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [X] :
( ~ defined(X)
| sum(additive_identity,X,additive_identity)
| product(multiplicative_inverse(X),X,multiplicative_identity) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
( ~ defined(X0)
| sum(additive_identity,X0,additive_identity)
| product(multiplicative_inverse(X0),X0,multiplicative_identity) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(t22,plain,
ifeq(defined(X1),true,or(product(multiplicative_inverse(X1),X1,multiplicative_identity),sum(additive_identity,X1,additive_identity)),true) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t58,plain,
ifeq(defined(X1),true,or(product(multiplicative_inverse(X1),X1,multiplicative_identity),sum(additive_identity,X1,additive_identity)),true) = true,
inference(orient,[status(thm)],[t22]) ).
cnf(f26,negated_conjecture,
~ sum(additive_identity,multiplicative_identity,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_sum_1) ).
fof(f26_nnf,plain,
~ sum(additive_identity,multiplicative_identity,additive_identity),
inference(nnf_transformation,[status(thm)],[f26]) ).
fof(f26_sk,plain,
~ sum(additive_identity,multiplicative_identity,additive_identity),
inference(skolemisation,[status(esa)],[f26_nnf]) ).
cnf(c26,plain,
~ sum(additive_identity,multiplicative_identity,additive_identity),
inference(cnf_transformation,[status(esa)],[f26_sk]) ).
cnf(t7,plain,
sum(additive_identity,multiplicative_identity,additive_identity) = false,
inference(equality_encoding,[status(esa)],[c26]) ).
cnf(t124,plain,
sum(additive_identity,multiplicative_identity,additive_identity) = false,
inference(orient,[status(thm)],[t7]) ).
cnf(t134,plain,
true = ifeq(defined(multiplicative_identity),true,or(product(multiplicative_inverse(multiplicative_identity),multiplicative_identity,multiplicative_identity),false),true),
inference(cp,[status(thm)],[t58,t124]) ).
cnf(f16,axiom,
defined(multiplicative_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',well_definedness_of_multiplicative_identity) ).
fof(f16_nnf,plain,
defined(multiplicative_identity),
inference(nnf_transformation,[status(thm)],[f16]) ).
cnf(c16,plain,
defined(multiplicative_identity),
inference(cnf_transformation,[status(esa)],[f16_nnf]) ).
cnf(t1,plain,
defined(multiplicative_identity) = true,
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(t86,plain,
defined(multiplicative_identity) = true,
inference(orient,[status(thm)],[t1]) ).
cnf(t456,plain,
true = ifeq(true,true,or(product(multiplicative_inverse(multiplicative_identity),multiplicative_identity,multiplicative_identity),false),true),
inference(step,[status(thm)],[t134,t86]) ).
cnf(t8,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t36,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t8]) ).
cnf(t457,plain,
true = or(product(multiplicative_inverse(multiplicative_identity),multiplicative_identity,multiplicative_identity),false),
inference(step,[status(thm)],[t456,t36]) ).
cnf(t2,plain,
or(X1,false) = X1,
introduced(definition) ).
cnf(t37,plain,
or(X1,false) = X1,
inference(orient,[status(thm)],[t2]) ).
cnf(t458,plain,
true = product(multiplicative_inverse(multiplicative_identity),multiplicative_identity,multiplicative_identity),
inference(step,[status(thm)],[t457,t37]) ).
cnf(t409,plain,
product(multiplicative_inverse(multiplicative_identity),multiplicative_identity,multiplicative_identity) = true,
inference(orient,[status(thm)],[t458]) ).
cnf(t410,plain,
true = ifeq(true,true,product(multiplicative_identity,multiplicative_inverse(multiplicative_identity),multiplicative_identity),true),
inference(cp,[status(thm)],[t61,t409]) ).
cnf(t459,plain,
true = product(multiplicative_identity,multiplicative_inverse(multiplicative_identity),multiplicative_identity),
inference(step,[status(thm)],[t410,t36]) ).
cnf(f27,negated_conjecture,
~ product(multiplicative_identity,multiplicative_inverse(multiplicative_identity),multiplicative_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_product_2) ).
fof(f27_nnf,plain,
~ product(multiplicative_identity,multiplicative_inverse(multiplicative_identity),multiplicative_identity),
inference(nnf_transformation,[status(thm)],[f27]) ).
fof(f27_sk,plain,
~ product(multiplicative_identity,multiplicative_inverse(multiplicative_identity),multiplicative_identity),
inference(skolemisation,[status(esa)],[f27_nnf]) ).
cnf(c27,plain,
~ product(multiplicative_identity,multiplicative_inverse(multiplicative_identity),multiplicative_identity),
inference(cnf_transformation,[status(esa)],[f27_sk]) ).
cnf(t9,plain,
product(multiplicative_identity,multiplicative_inverse(multiplicative_identity),multiplicative_identity) = false,
inference(equality_encoding,[status(esa)],[c27]) ).
cnf(t145,plain,
product(multiplicative_identity,multiplicative_inverse(multiplicative_identity),multiplicative_identity) = false,
inference(orient,[status(thm)],[t9]) ).
cnf(t460,plain,
true = false,
inference(step,[status(thm)],[t459,t145]) ).
cnf(t427,plain,
false = true,
inference(orient,[status(thm)],[t460]) ).
cnf(f25,axiom,
~ sum(additive_identity,additive_identity,multiplicative_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',different_identities) ).
fof(f25_nnf,plain,
~ sum(additive_identity,additive_identity,multiplicative_identity),
inference(nnf_transformation,[status(thm)],[f25]) ).
fof(f25_sk,plain,
~ sum(additive_identity,additive_identity,multiplicative_identity),
inference(skolemisation,[status(esa)],[f25_nnf]) ).
cnf(c25,plain,
~ sum(additive_identity,additive_identity,multiplicative_identity),
inference(cnf_transformation,[status(esa)],[f25_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c25,c26,c27]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t427]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD010-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/5.38 % Computer : n014.cluster.edu
% 0.09/5.38 % Model : x86_64 x86_64
% 0.09/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.38 % Memory : 8046.5625MB
% 0.09/5.38 % OS : Linux 6.8.0-71-generic
% 0.09/5.38 % CPULimit : 300
% 0.09/5.38 % WCLimit : 300
% 0.09/5.38 % DateTime : Fri Sep 25 10:35:24 UTC 2026
% 0.09/5.38 % CPUTime :
% 0.09/5.38 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 10.65/7.01 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.65/7.01 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------