%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : FLD027-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n008.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 01:14:58 PM UTC 2026
% Result : Unsatisfiable 27.68s 4.75s
% Output : Proof 27.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 11
% Syntax : Number of formulae : 57 ( 26 unt; 0 def)
% Number of atoms : 115 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 112 ( 54 ~; 58 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-1 aty)
% Number of variables : 76 ( 0 sgn 34 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(f26,hypothesis,
defined(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_defined) ).
fof(f26_nnf,plain,
defined(a),
inference(nnf_transformation,[status(thm)],[f26]) ).
cnf(c26,plain,
defined(a),
inference(cnf_transformation,[status(esa)],[f26_nnf]) ).
cnf(p133,plain,
( sum(additive_identity,a,additive_identity)
| product(multiplicative_inverse(a),a,multiplicative_identity) ),
inference(resolution,[status(thm)],[c8,c26]) ).
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(f30,negated_conjecture,
product(multiplicative_identity,multiplicative_inverse(a),multiplicative_inverse(b)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_5) ).
fof(f30_nnf,plain,
product(multiplicative_identity,multiplicative_inverse(a),multiplicative_inverse(b)),
inference(nnf_transformation,[status(thm)],[f30]) ).
cnf(c30,plain,
product(multiplicative_identity,multiplicative_inverse(a),multiplicative_inverse(b)),
inference(cnf_transformation,[status(esa)],[f30_nnf]) ).
cnf(p159,plain,
product(multiplicative_inverse(a),multiplicative_identity,multiplicative_inverse(b)),
inference(resolution,[status(thm)],[c9,c30]) ).
cnf(f6,axiom,
( ~ product(X,V,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| product(U,Z,W) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_multiplication_2) ).
fof(f6_nnf,plain,
! [U,Z,W,X,Y,V] :
( ~ product(X,V,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| product(U,Z,W) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [U,Z,W,X,Y,V] :
( ~ product(X,V,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| product(U,Z,W) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
( ~ product(X3,X5,X2)
| ~ product(X4,X1,X5)
| ~ product(X3,X4,X0)
| product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p164,plain,
( ~ product(multiplicative_inverse(a),X2,X1)
| ~ product(multiplicative_identity,X0,X2)
| product(multiplicative_inverse(b),X0,X1) ),
inference(resolution,[status(thm)],[p159,c6]) ).
cnf(f7,axiom,
( ~ defined(X)
| product(multiplicative_identity,X,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_identity_multiplication) ).
fof(f7_nnf,plain,
! [X] :
( ~ defined(X)
| product(multiplicative_identity,X,X) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [X] :
( ~ defined(X)
| product(multiplicative_identity,X,X) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
( ~ defined(X0)
| product(multiplicative_identity,X0,X0) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p112,plain,
product(multiplicative_identity,a,a),
inference(resolution,[status(thm)],[c7,c26]) ).
cnf(p186,plain,
( ~ product(multiplicative_inverse(a),a,X0)
| product(multiplicative_inverse(b),a,X0) ),
inference(resolution,[status(thm)],[p164,p112]) ).
cnf(p4014,plain,
( product(multiplicative_inverse(b),a,multiplicative_identity)
| sum(additive_identity,a,additive_identity) ),
inference(resolution,[status(thm)],[p133,p186]) ).
cnf(p4018,plain,
( product(a,multiplicative_inverse(b),multiplicative_identity)
| sum(additive_identity,a,additive_identity) ),
inference(resolution,[status(thm)],[p4014,c9]) ).
cnf(f5,axiom,
( ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| product(X,V,W) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_multiplication_1) ).
fof(f5_nnf,plain,
! [X,V,W,Y,U,Z] :
( ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| product(X,V,W) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [X,V,W,Y,U,Z] :
( ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| product(X,V,W) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
( ~ product(X4,X5,X2)
| ~ product(X3,X5,X1)
| ~ product(X0,X3,X4)
| product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p4019,plain,
( ~ product(multiplicative_identity,X2,X1)
| ~ product(multiplicative_inverse(b),X2,X0)
| product(a,X0,X1)
| sum(additive_identity,a,additive_identity) ),
inference(resolution,[status(thm)],[p4018,c5]) ).
cnf(f27,hypothesis,
defined(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_is_defined) ).
fof(f27_nnf,plain,
defined(b),
inference(nnf_transformation,[status(thm)],[f27]) ).
cnf(c27,plain,
defined(b),
inference(cnf_transformation,[status(esa)],[f27_nnf]) ).
cnf(p134,plain,
( sum(additive_identity,b,additive_identity)
| product(multiplicative_inverse(b),b,multiplicative_identity) ),
inference(resolution,[status(thm)],[c8,c27]) ).
cnf(p4051,plain,
( sum(additive_identity,b,additive_identity)
| ~ product(multiplicative_identity,b,X0)
| product(a,multiplicative_identity,X0)
| sum(additive_identity,a,additive_identity) ),
inference(resolution,[status(thm)],[p4019,p134]) ).
cnf(p113,plain,
product(multiplicative_identity,b,b),
inference(resolution,[status(thm)],[c7,c27]) ).
cnf(p4052,plain,
( sum(additive_identity,b,additive_identity)
| product(a,multiplicative_identity,b)
| sum(additive_identity,a,additive_identity) ),
inference(resolution,[status(thm)],[p4051,p113]) ).
cnf(p4055,plain,
( product(multiplicative_identity,a,b)
| sum(additive_identity,b,additive_identity)
| sum(additive_identity,a,additive_identity) ),
inference(resolution,[status(thm)],[p4052,c9]) ).
cnf(f31,negated_conjecture,
~ product(multiplicative_identity,a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_product_6) ).
fof(f31_nnf,plain,
~ product(multiplicative_identity,a,b),
inference(nnf_transformation,[status(thm)],[f31]) ).
fof(f31_sk,plain,
~ product(multiplicative_identity,a,b),
inference(skolemisation,[status(esa)],[f31_nnf]) ).
cnf(c31,plain,
~ product(multiplicative_identity,a,b),
inference(cnf_transformation,[status(esa)],[f31_sk]) ).
cnf(p4057,plain,
( sum(additive_identity,b,additive_identity)
| sum(additive_identity,a,additive_identity) ),
inference(resolution,[status(thm)],[p4055,c31]) ).
cnf(f29,negated_conjecture,
~ sum(additive_identity,b,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_sum_4) ).
fof(f29_nnf,plain,
~ sum(additive_identity,b,additive_identity),
inference(nnf_transformation,[status(thm)],[f29]) ).
fof(f29_sk,plain,
~ sum(additive_identity,b,additive_identity),
inference(skolemisation,[status(esa)],[f29_nnf]) ).
cnf(c29,plain,
~ sum(additive_identity,b,additive_identity),
inference(cnf_transformation,[status(esa)],[f29_sk]) ).
cnf(p4062,plain,
sum(additive_identity,a,additive_identity),
inference(resolution,[status(thm)],[p4057,c29]) ).
cnf(f28,negated_conjecture,
~ sum(additive_identity,a,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_sum_3) ).
fof(f28_nnf,plain,
~ sum(additive_identity,a,additive_identity),
inference(nnf_transformation,[status(thm)],[f28]) ).
fof(f28_sk,plain,
~ sum(additive_identity,a,additive_identity),
inference(skolemisation,[status(esa)],[f28_nnf]) ).
cnf(c28,plain,
~ sum(additive_identity,a,additive_identity),
inference(cnf_transformation,[status(esa)],[f28_sk]) ).
cnf(p4063,plain,
$false,
inference(resolution,[status(thm)],[p4062,c28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD027-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.37 % Computer : n008.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Fri Sep 25 10:43:24 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 27.68/4.75 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 27.68/4.75 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------