%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : BOO013-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n007.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 12:59:36 PM UTC 2026
% Result : Unsatisfiable 12.86s 2.15s
% Output : Proof 12.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 17
% Syntax : Number of formulae : 93 ( 69 unt; 0 def)
% Number of atoms : 169 ( 36 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 158 ( 82 ~; 76 |; 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 : 9 ( 9 usr; 6 con; 0-4 aty)
% Number of variables : 211 ( 0 sgn 84 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f15,axiom,
( sum(V3,X,V4)
| ~ product(V1,V2,V4)
| ~ product(Y,Z,V3)
| ~ sum(Z,X,V2)
| ~ sum(Y,X,V1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity8) ).
fof(f15_nnf,plain,
! [Y,X,V1,Z,V2,V3,V4] :
( sum(V3,X,V4)
| ~ product(V1,V2,V4)
| ~ product(Y,Z,V3)
| ~ sum(Z,X,V2)
| ~ sum(Y,X,V1) ),
inference(nnf_transformation,[status(thm)],[f15]) ).
fof(f15_sk,plain,
! [Y,X,V1,Z,V2,V3,V4] :
( sum(V3,X,V4)
| ~ product(V1,V2,V4)
| ~ product(Y,Z,V3)
| ~ sum(Z,X,V2)
| ~ sum(Y,X,V1) ),
inference(skolemisation,[status(esa)],[f15_nnf]) ).
cnf(c15,plain,
( sum(X5,X1,X6)
| ~ product(X2,X4,X6)
| ~ product(X0,X3,X5)
| ~ sum(X3,X1,X4)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(hi15,axiom,
ifeq(sum(X0,X1,X2),true,ifeq(sum(X3,X1,X4),true,ifeq(product(X0,X3,X5),true,ifeq(product(X2,X4,X6),true,sum(X5,X1,X6),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(f5,axiom,
sum(X,additive_identity,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity2) ).
fof(f5_nnf,plain,
! [X] : sum(X,additive_identity,X),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [X] : sum(X,additive_identity,X),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
sum(X0,additive_identity,X0),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(hi5,axiom,
sum(X0,additive_identity,X0) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
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(f18,axiom,
product(inverse(X),X,additive_identity),
file('/export/starexec/sandbox2/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(h9,plain,
sum(inverse(multiplicative_identity),additive_identity,additive_identity) = true,
inference(hyper_resolution,[status(thm)],[hi15,hi5,hi5,hi7,hi18]) ).
cnf(f14,axiom,
( product(V1,V2,V4)
| ~ sum(V3,X,V4)
| ~ product(Y,Z,V3)
| ~ sum(Z,X,V2)
| ~ sum(Y,X,V1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity7) ).
fof(f14_nnf,plain,
! [Y,X,V1,Z,V2,V3,V4] :
( product(V1,V2,V4)
| ~ sum(V3,X,V4)
| ~ product(Y,Z,V3)
| ~ sum(Z,X,V2)
| ~ sum(Y,X,V1) ),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [Y,X,V1,Z,V2,V3,V4] :
( product(V1,V2,V4)
| ~ sum(V3,X,V4)
| ~ product(Y,Z,V3)
| ~ sum(Z,X,V2)
| ~ sum(Y,X,V1) ),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c14,plain,
( product(X2,X4,X6)
| ~ sum(X5,X1,X6)
| ~ product(X0,X3,X5)
| ~ sum(X3,X1,X4)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(hi14,axiom,
ifeq(sum(X0,X1,X2),true,ifeq(sum(X3,X1,X4),true,ifeq(product(X0,X3,X5),true,ifeq(sum(X5,X1,X6),true,product(X2,X4,X6),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(f6,axiom,
product(multiplicative_identity,X,X),
file('/export/starexec/sandbox2/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(h41,plain,
product(multiplicative_identity,additive_identity,inverse(multiplicative_identity)) = true,
inference(hyper_resolution,[status(thm)],[hi14,hi5,h9,hi6,hi5]) ).
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(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(h68,plain,
sum(inverse(multiplicative_identity),V0,V0) = true,
inference(hyper_resolution,[status(thm)],[hi8,h41,hi6,hi4,hi6]) ).
cnf(h12,plain,
sum(additive_identity,additive_identity,inverse(multiplicative_identity)) = true,
inference(hyper_resolution,[status(thm)],[hi15,hi5,hi5,hi18,hi7]) ).
cnf(f25,negated_conjecture,
product(x,y,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_to_additive_identity1) ).
fof(f25_nnf,plain,
product(x,y,additive_identity),
inference(nnf_transformation,[status(thm)],[f25]) ).
cnf(c25,plain,
product(x,y,additive_identity),
inference(cnf_transformation,[status(esa)],[f25_nnf]) ).
cnf(hi25,negated_conjecture,
product(x,y,additive_identity) = true,
inference(equality_encoding,[status(esa)],[c25]) ).
cnf(h53,plain,
product(x,y,inverse(multiplicative_identity)) = true,
inference(hyper_resolution,[status(thm)],[hi14,hi5,hi5,hi25,h12]) ).
cnf(f24,negated_conjecture,
sum(x,z,multiplicative_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_to_multiplicative_identity2) ).
fof(f24_nnf,plain,
sum(x,z,multiplicative_identity),
inference(nnf_transformation,[status(thm)],[f24]) ).
cnf(c24,plain,
sum(x,z,multiplicative_identity),
inference(cnf_transformation,[status(esa)],[f24_nnf]) ).
cnf(hi24,negated_conjecture,
sum(x,z,multiplicative_identity) = true,
inference(equality_encoding,[status(esa)],[c24]) ).
cnf(f0,axiom,
sum(X,Y,add(X,Y)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure_of_addition) ).
fof(f0_nnf,plain,
! [X,Y] : sum(X,Y,add(X,Y)),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X,Y] : sum(X,Y,add(X,Y)),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
sum(X0,X1,add(X0,X1)),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi0,axiom,
sum(X0,X1,add(X0,X1)) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(h304,plain,
product(multiplicative_identity,add(y,z),z) = true,
inference(hyper_resolution,[status(thm)],[hi14,hi24,hi0,h53,h68]) ).
cnf(f2,axiom,
( sum(Y,X,Z)
| ~ sum(X,Y,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_addition) ).
fof(f2_nnf,plain,
! [X,Y,Z] :
( sum(Y,X,Z)
| ~ sum(X,Y,Z) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X,Y,Z] :
( sum(Y,X,Z)
| ~ sum(X,Y,Z) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( sum(X1,X0,X2)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi2,axiom,
ifeq(sum(X0,X1,X2),true,sum(X1,X0,X2),true) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(f23,negated_conjecture,
sum(x,y,multiplicative_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_to_multiplicative_identity1) ).
fof(f23_nnf,plain,
sum(x,y,multiplicative_identity),
inference(nnf_transformation,[status(thm)],[f23]) ).
cnf(c23,plain,
sum(x,y,multiplicative_identity),
inference(cnf_transformation,[status(esa)],[f23_nnf]) ).
cnf(hi23,negated_conjecture,
sum(x,y,multiplicative_identity) = true,
inference(equality_encoding,[status(esa)],[c23]) ).
cnf(h0,plain,
sum(y,x,multiplicative_identity) = true,
inference(hyper_resolution,[status(thm)],[hi2,hi23]) ).
cnf(f13,axiom,
( sum(X,V3,V4)
| ~ product(V1,V2,V4)
| ~ product(Y,Z,V3)
| ~ sum(X,Z,V2)
| ~ sum(X,Y,V1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity6) ).
fof(f13_nnf,plain,
! [X,Y,V1,Z,V2,V3,V4] :
( sum(X,V3,V4)
| ~ product(V1,V2,V4)
| ~ product(Y,Z,V3)
| ~ sum(X,Z,V2)
| ~ sum(X,Y,V1) ),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [X,Y,V1,Z,V2,V3,V4] :
( sum(X,V3,V4)
| ~ product(V1,V2,V4)
| ~ product(Y,Z,V3)
| ~ sum(X,Z,V2)
| ~ sum(X,Y,V1) ),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c13,plain,
( sum(X0,X5,X6)
| ~ product(X2,X4,X6)
| ~ product(X1,X3,X5)
| ~ sum(X0,X3,X4)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(hi13,axiom,
ifeq(sum(X0,X1,X2),true,ifeq(sum(X0,X3,X4),true,ifeq(product(X1,X3,X5),true,ifeq(product(X2,X4,X6),true,sum(X0,X5,X6),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(f26,negated_conjecture,
product(x,z,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_to_additive_identity2) ).
fof(f26_nnf,plain,
product(x,z,additive_identity),
inference(nnf_transformation,[status(thm)],[f26]) ).
cnf(c26,plain,
product(x,z,additive_identity),
inference(cnf_transformation,[status(esa)],[f26_nnf]) ).
cnf(hi26,negated_conjecture,
product(x,z,additive_identity) = true,
inference(equality_encoding,[status(esa)],[c26]) ).
cnf(h3696,plain,
sum(y,additive_identity,z) = true,
inference(hyper_resolution,[status(thm)],[hi13,h0,hi0,hi26,h304]) ).
cnf(f20,axiom,
( U = V
| ~ sum(X,Y,V)
| ~ sum(X,Y,U) ),
file('/export/starexec/sandbox2/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,
z = y,
inference(hyper_resolution,[status(thm)],[hi20,hi5,h3696]) ).
cnf(t280,plain,
y = z,
inference(orient,[status(thm)],[t0]) ).
cnf(f27,negated_conjecture,
y != z,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_both_inverse_are_equal) ).
fof(f27_nnf,plain,
y != z,
inference(nnf_transformation,[status(thm)],[f27]) ).
fof(f27_sk,plain,
y != z,
inference(skolemisation,[status(esa)],[f27_nnf]) ).
cnf(c27,plain,
y != z,
inference(cnf_transformation,[status(esa)],[f27_sk]) ).
cnf(goal_0,negated_conjecture,
z != y,
inference(equality_encoding,[status(esa)],[c27]) ).
cnf(g0_0,plain,
z != z,
inference(rw,[status(thm)],[goal_0,t280]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : BOO013-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.35 % Computer : n007.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Fri Sep 25 06:29:22 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 12.86/2.15 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.86/2.15 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------