%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : BOO012-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/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 12:59:35 PM UTC 2026
% Result : Unsatisfiable 9.68s 1.78s
% Output : Proof 9.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of formulae : 58 ( 46 unt; 0 def)
% Number of atoms : 98 ( 25 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 86 ( 46 ~; 40 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-4 aty)
% Number of variables : 125 ( 0 sgn 50 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f6,axiom,
product(multiplicative_identity,X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_identity1) ).
fof(f6_nnf,plain,
! [X] : product(multiplicative_identity,X,X),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [X] : product(multiplicative_identity,X,X),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
product(multiplicative_identity,X0,X0),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(hi6,axiom,
product(multiplicative_identity,X0,X0) = true,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(h3,plain,
product(multiplicative_identity,x,x) = true,
inference(hyper_resolution,[status(thm)],[hi6]) ).
cnf(f10,axiom,
( sum(V1,V2,V4)
| ~ product(V3,X,V4)
| ~ sum(Y,Z,V3)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity3) ).
fof(f10_nnf,plain,
! [Y,X,V1,Z,V2,V3,V4] :
( sum(V1,V2,V4)
| ~ product(V3,X,V4)
| ~ sum(Y,Z,V3)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [Y,X,V1,Z,V2,V3,V4] :
( sum(V1,V2,V4)
| ~ product(V3,X,V4)
| ~ sum(Y,Z,V3)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) ),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
( sum(X2,X4,X6)
| ~ product(X5,X1,X6)
| ~ sum(X0,X3,X5)
| ~ product(X3,X1,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(hi10,axiom,
ifeq(product(X0,X1,X2),true,ifeq(product(X3,X1,X4),true,ifeq(sum(X0,X3,X5),true,ifeq(product(X5,X1,X6),true,sum(X2,X4,X6),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(f1,axiom,
product(X,Y,multiply(X,Y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_of_multiplication) ).
fof(f1_nnf,plain,
! [X,Y] : product(X,Y,multiply(X,Y)),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X,Y] : product(X,Y,multiply(X,Y)),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
product(X0,X1,multiply(X0,X1)),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(hi1,axiom,
product(X0,X1,multiply(X0,X1)) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(f18,axiom,
product(inverse(X),X,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_inverse1) ).
fof(f18_nnf,plain,
! [X] : product(inverse(X),X,additive_identity),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
! [X] : product(inverse(X),X,additive_identity),
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c18,plain,
product(inverse(X0),X0,additive_identity),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(hi18,axiom,
product(inverse(X0),X0,additive_identity) = true,
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(f16,axiom,
sum(inverse(X),X,multiplicative_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_inverse1) ).
fof(f16_nnf,plain,
! [X] : sum(inverse(X),X,multiplicative_identity),
inference(nnf_transformation,[status(thm)],[f16]) ).
fof(f16_sk,plain,
! [X] : sum(inverse(X),X,multiplicative_identity),
inference(skolemisation,[status(esa)],[f16_nnf]) ).
cnf(c16,plain,
sum(inverse(X0),X0,multiplicative_identity),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(hi16,axiom,
sum(inverse(X0),X0,multiplicative_identity) = true,
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(h6,plain,
sum(multiply(inverse(inverse(x)),x),additive_identity,x) = true,
inference(hyper_resolution,[status(thm)],[hi10,hi1,hi18,hi16,h3]) ).
cnf(f17,axiom,
sum(X,inverse(X),multiplicative_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_inverse2) ).
fof(f17_nnf,plain,
! [X] : sum(X,inverse(X),multiplicative_identity),
inference(nnf_transformation,[status(thm)],[f17]) ).
fof(f17_sk,plain,
! [X] : sum(X,inverse(X),multiplicative_identity),
inference(skolemisation,[status(esa)],[f17_nnf]) ).
cnf(c17,plain,
sum(X0,inverse(X0),multiplicative_identity),
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
cnf(hi17,axiom,
sum(X0,inverse(X0),multiplicative_identity) = true,
inference(equality_encoding,[status(esa)],[c17]) ).
cnf(h4,plain,
sum(x,inverse(x),multiplicative_identity) = true,
inference(hyper_resolution,[status(thm)],[hi17]) ).
cnf(f8,axiom,
( sum(V1,V2,V4)
| ~ product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity1) ).
fof(f8_nnf,plain,
! [X,Y,V1,Z,V2,V3,V4] :
( sum(V1,V2,V4)
| ~ product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [X,Y,V1,Z,V2,V3,V4] :
( sum(V1,V2,V4)
| ~ product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
( sum(X2,X4,X6)
| ~ product(X0,X5,X6)
| ~ sum(X1,X3,X5)
| ~ product(X0,X3,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(hi8,axiom,
ifeq(product(X0,X1,X2),true,ifeq(product(X0,X3,X4),true,ifeq(sum(X1,X3,X5),true,ifeq(product(X0,X5,X6),true,sum(X2,X4,X6),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(f7,axiom,
product(X,multiplicative_identity,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_identity2) ).
fof(f7_nnf,plain,
! [X] : product(X,multiplicative_identity,X),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [X] : product(X,multiplicative_identity,X),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
product(X0,multiplicative_identity,X0),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(hi7,axiom,
product(X0,multiplicative_identity,X0) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(h5,plain,
sum(multiply(inverse(inverse(x)),x),additive_identity,inverse(inverse(x))) = true,
inference(hyper_resolution,[status(thm)],[hi8,hi1,hi18,h4,hi7]) ).
cnf(f20,axiom,
( U = V
| ~ sum(X,Y,V)
| ~ sum(X,Y,U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',addition_is_well_defined) ).
fof(f20_nnf,plain,
! [X,Y,U,V] :
( U = V
| ~ sum(X,Y,V)
| ~ sum(X,Y,U) ),
inference(nnf_transformation,[status(thm)],[f20]) ).
fof(f20_sk,plain,
! [X,Y,U,V] :
( U = V
| ~ sum(X,Y,V)
| ~ sum(X,Y,U) ),
inference(skolemisation,[status(esa)],[f20_nnf]) ).
cnf(c20,plain,
( X2 = X3
| ~ sum(X0,X1,X3)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(hi20,axiom,
ifeq(sum(X0,X1,X2),true,ifeq(sum(X0,X1,X3),true,X2,X3),X3) = X3,
inference(equality_encoding,[status(esa)],[c20]) ).
cnf(t0,plain,
inverse(inverse(x)) = x,
inference(hyper_resolution,[status(thm)],[hi20,h5,h6]) ).
cnf(t552,plain,
inverse(inverse(x)) = x,
inference(orient,[status(thm)],[t0]) ).
cnf(f34,negated_conjecture,
inverse(inverse(x)) != x,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_inverse_is_an_involution) ).
fof(f34_nnf,plain,
inverse(inverse(x)) != x,
inference(nnf_transformation,[status(thm)],[f34]) ).
fof(f34_sk,plain,
inverse(inverse(x)) != x,
inference(skolemisation,[status(esa)],[f34_nnf]) ).
cnf(c34,plain,
inverse(inverse(x)) != x,
inference(cnf_transformation,[status(esa)],[f34_sk]) ).
cnf(goal_0,negated_conjecture,
inverse(inverse(x)) != x,
inference(equality_encoding,[status(esa)],[c34]) ).
cnf(g0_0,plain,
x != x,
inference(rw,[status(thm)],[goal_0,t552]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : BOO012-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.06 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.42 % Computer : n008.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Fri Sep 25 06:31:54 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.42 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 9.68/1.78 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.68/1.78 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------