%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : BOO003-1 : TPTP v9.3.1. Released v1.0.0.
% 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 12:59:31 PM UTC 2026
% Result : Unsatisfiable 13.35s 7.30s
% Output : Proof 13.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 46 ( 38 unt; 0 def)
% Number of atoms : 78 ( 13 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 70 ( 38 ~; 32 |; 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 : 100 ( 0 sgn 40 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f7,axiom,
product(X,multiplicative_identity,X),
file('/export/starexec/sandbox2/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(h3,plain,
product(x,multiplicative_identity,x) = true,
inference(hyper_resolution,[status(thm)],[hi7]) ).
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/sandbox2/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(f19,axiom,
product(X,inverse(X),additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_inverse2) ).
fof(f19_nnf,plain,
! [X] : product(X,inverse(X),additive_identity),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
! [X] : product(X,inverse(X),additive_identity),
inference(skolemisation,[status(esa)],[f19_nnf]) ).
cnf(c19,plain,
product(X0,inverse(X0),additive_identity),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(hi19,axiom,
product(X0,inverse(X0),additive_identity) = true,
inference(equality_encoding,[status(esa)],[c19]) ).
cnf(f1,axiom,
product(X,Y,multiply(X,Y)),
file('/export/starexec/sandbox2/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(f16,axiom,
sum(inverse(X),X,multiplicative_identity),
file('/export/starexec/sandbox2/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(h13,plain,
sum(additive_identity,multiply(x,x),x) = true,
inference(hyper_resolution,[status(thm)],[hi8,hi19,hi1,hi16,h3]) ).
cnf(f12,axiom,
( product(V1,V2,V4)
| ~ sum(X,V3,V4)
| ~ product(Y,Z,V3)
| ~ sum(X,Z,V2)
| ~ sum(X,Y,V1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity5) ).
fof(f12_nnf,plain,
! [X,Y,V1,Z,V2,V3,V4] :
( product(V1,V2,V4)
| ~ sum(X,V3,V4)
| ~ product(Y,Z,V3)
| ~ sum(X,Z,V2)
| ~ sum(X,Y,V1) ),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [X,Y,V1,Z,V2,V3,V4] :
( product(V1,V2,V4)
| ~ sum(X,V3,V4)
| ~ product(Y,Z,V3)
| ~ sum(X,Z,V2)
| ~ sum(X,Y,V1) ),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c12,plain,
( product(X2,X4,X6)
| ~ sum(X0,X5,X6)
| ~ product(X1,X3,X5)
| ~ sum(X0,X3,X4)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(hi12,axiom,
ifeq(sum(X0,X1,X2),true,ifeq(sum(X0,X3,X4),true,ifeq(product(X1,X3,X5),true,ifeq(sum(X0,X5,X6),true,product(X2,X4,X6),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(f4,axiom,
sum(additive_identity,X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity1) ).
fof(f4_nnf,plain,
! [X] : sum(additive_identity,X,X),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [X] : sum(additive_identity,X,X),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
sum(additive_identity,X0,X0),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(hi4,axiom,
sum(additive_identity,X0,X0) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t2,plain,
product(x,x,x) = true,
inference(hyper_resolution,[status(thm)],[hi12,hi4,hi4,hi1,h13]) ).
cnf(t170,plain,
product(x,x,x) = true,
inference(orient,[status(thm)],[t2]) ).
cnf(f22,negated_conjecture,
~ product(x,x,x),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_both_equalities) ).
fof(f22_nnf,plain,
~ product(x,x,x),
inference(nnf_transformation,[status(thm)],[f22]) ).
fof(f22_sk,plain,
~ product(x,x,x),
inference(skolemisation,[status(esa)],[f22_nnf]) ).
cnf(c22,plain,
~ product(x,x,x),
inference(cnf_transformation,[status(esa)],[f22_sk]) ).
cnf(goal_0,negated_conjecture,
product(x,x,x) != true,
inference(equality_encoding,[status(esa)],[c22]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t170]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO003-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/5.39 % Computer : n014.cluster.edu
% 0.10/5.39 % Model : x86_64 x86_64
% 0.10/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.39 % Memory : 8046.5625MB
% 0.10/5.39 % OS : Linux 6.8.0-71-generic
% 0.10/5.39 % CPULimit : 300
% 0.10/5.39 % WCLimit : 300
% 0.10/5.39 % DateTime : Fri Sep 25 06:27:37 UTC 2026
% 0.10/5.39 % CPUTime :
% 0.10/5.39 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 13.35/7.30 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.35/7.30 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------