%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : FLD049-4 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n017.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 01:15:03 PM UTC 2026
% Result : Unsatisfiable 31.13s 5.01s
% Output : Proof 31.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 15
% Syntax : Number of formulae : 72 ( 39 unt; 0 def)
% Number of atoms : 134 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 119 ( 57 ~; 62 |; 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 : 9 ( 9 usr; 8 con; 0-1 aty)
% Number of variables : 80 ( 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(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(p115,plain,
( sum(additive_identity,b,additive_identity)
| product(multiplicative_inverse(b),b,multiplicative_identity) ),
inference(resolution,[status(thm)],[c8,c27]) ).
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(f34,negated_conjecture,
product(a,multiplicative_inverse(b),s),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_9) ).
fof(f34_nnf,plain,
product(a,multiplicative_inverse(b),s),
inference(nnf_transformation,[status(thm)],[f34]) ).
cnf(c34,plain,
product(a,multiplicative_inverse(b),s),
inference(cnf_transformation,[status(esa)],[f34_nnf]) ).
cnf(p92,plain,
( ~ product(a,X2,X1)
| ~ product(multiplicative_inverse(b),X0,X2)
| product(s,X0,X1) ),
inference(resolution,[status(thm)],[c6,c34]) ).
cnf(p2419,plain,
( ~ product(a,multiplicative_identity,X0)
| product(s,b,X0)
| sum(additive_identity,b,additive_identity) ),
inference(resolution,[status(thm)],[p115,p92]) ).
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(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(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(p99,plain,
product(multiplicative_identity,a,a),
inference(resolution,[status(thm)],[c7,c26]) ).
cnf(p132,plain,
product(a,multiplicative_identity,a),
inference(resolution,[status(thm)],[c9,p99]) ).
cnf(p2422,plain,
( product(s,b,a)
| sum(additive_identity,b,additive_identity) ),
inference(resolution,[status(thm)],[p2419,p132]) ).
cnf(p2425,plain,
( product(b,s,a)
| sum(additive_identity,b,additive_identity) ),
inference(resolution,[status(thm)],[p2422,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(p2427,plain,
( ~ product(a,X2,X1)
| ~ product(s,X2,X0)
| product(b,X0,X1)
| sum(additive_identity,b,additive_identity) ),
inference(resolution,[status(thm)],[p2425,c5]) ).
cnf(f29,hypothesis,
defined(d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d_is_defined) ).
fof(f29_nnf,plain,
defined(d),
inference(nnf_transformation,[status(thm)],[f29]) ).
cnf(c29,plain,
defined(d),
inference(cnf_transformation,[status(esa)],[f29_nnf]) ).
cnf(p117,plain,
( sum(additive_identity,d,additive_identity)
| product(multiplicative_inverse(d),d,multiplicative_identity) ),
inference(resolution,[status(thm)],[c8,c29]) ).
cnf(f35,negated_conjecture,
product(c,multiplicative_inverse(d),s),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_10) ).
fof(f35_nnf,plain,
product(c,multiplicative_inverse(d),s),
inference(nnf_transformation,[status(thm)],[f35]) ).
cnf(c35,plain,
product(c,multiplicative_inverse(d),s),
inference(cnf_transformation,[status(esa)],[f35_nnf]) ).
cnf(p94,plain,
( ~ product(c,X2,X1)
| ~ product(multiplicative_inverse(d),X0,X2)
| product(s,X0,X1) ),
inference(resolution,[status(thm)],[c6,c35]) ).
cnf(p2437,plain,
( ~ product(c,multiplicative_identity,X0)
| product(s,d,X0)
| sum(additive_identity,d,additive_identity) ),
inference(resolution,[status(thm)],[p117,p94]) ).
cnf(f28,hypothesis,
defined(c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_is_defined) ).
fof(f28_nnf,plain,
defined(c),
inference(nnf_transformation,[status(thm)],[f28]) ).
cnf(c28,plain,
defined(c),
inference(cnf_transformation,[status(esa)],[f28_nnf]) ).
cnf(p101,plain,
product(multiplicative_identity,c,c),
inference(resolution,[status(thm)],[c7,c28]) ).
cnf(p190,plain,
product(c,multiplicative_identity,c),
inference(resolution,[status(thm)],[p101,c9]) ).
cnf(p2440,plain,
( product(s,d,c)
| sum(additive_identity,d,additive_identity) ),
inference(resolution,[status(thm)],[p2437,p190]) ).
cnf(p2469,plain,
( sum(additive_identity,d,additive_identity)
| ~ product(a,d,X0)
| product(b,c,X0)
| sum(additive_identity,b,additive_identity) ),
inference(resolution,[status(thm)],[p2427,p2440]) ).
cnf(f36,negated_conjecture,
product(a,d,k),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_11) ).
fof(f36_nnf,plain,
product(a,d,k),
inference(nnf_transformation,[status(thm)],[f36]) ).
cnf(c36,plain,
product(a,d,k),
inference(cnf_transformation,[status(esa)],[f36_nnf]) ).
cnf(p2478,plain,
( sum(additive_identity,d,additive_identity)
| product(b,c,k)
| sum(additive_identity,b,additive_identity) ),
inference(resolution,[status(thm)],[p2469,c36]) ).
cnf(f37,negated_conjecture,
~ product(b,c,k),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_product_12) ).
fof(f37_nnf,plain,
~ product(b,c,k),
inference(nnf_transformation,[status(thm)],[f37]) ).
fof(f37_sk,plain,
~ product(b,c,k),
inference(skolemisation,[status(esa)],[f37_nnf]) ).
cnf(c37,plain,
~ product(b,c,k),
inference(cnf_transformation,[status(esa)],[f37_sk]) ).
cnf(p2479,plain,
( sum(additive_identity,d,additive_identity)
| sum(additive_identity,b,additive_identity) ),
inference(resolution,[status(thm)],[p2478,c37]) ).
cnf(f33,negated_conjecture,
~ sum(additive_identity,d,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_sum_8) ).
fof(f33_nnf,plain,
~ sum(additive_identity,d,additive_identity),
inference(nnf_transformation,[status(thm)],[f33]) ).
fof(f33_sk,plain,
~ sum(additive_identity,d,additive_identity),
inference(skolemisation,[status(esa)],[f33_nnf]) ).
cnf(c33,plain,
~ sum(additive_identity,d,additive_identity),
inference(cnf_transformation,[status(esa)],[f33_sk]) ).
cnf(p2482,plain,
sum(additive_identity,b,additive_identity),
inference(resolution,[status(thm)],[p2479,c33]) ).
cnf(f32,negated_conjecture,
~ sum(additive_identity,b,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_sum_7) ).
fof(f32_nnf,plain,
~ sum(additive_identity,b,additive_identity),
inference(nnf_transformation,[status(thm)],[f32]) ).
fof(f32_sk,plain,
~ sum(additive_identity,b,additive_identity),
inference(skolemisation,[status(esa)],[f32_nnf]) ).
cnf(c32,plain,
~ sum(additive_identity,b,additive_identity),
inference(cnf_transformation,[status(esa)],[f32_sk]) ).
cnf(p2484,plain,
$false,
inference(resolution,[status(thm)],[p2482,c32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD049-4 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/0.36 % Computer : n017.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Fri Sep 25 10:48:47 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 31.13/5.01 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 31.13/5.01 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------