%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : BOO016-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n019.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 12:59:38 PM UTC 2026
% Result : Unsatisfiable 12.85s 2.22s
% Output : Proof 12.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 15
% Syntax : Number of formulae : 88 ( 64 unt; 0 def)
% Number of atoms : 172 ( 28 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 174 ( 90 ~; 84 |; 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 : 236 ( 2 sgn 92 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(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(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(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(h208,plain,
product(multiplicative_identity,add(multiplicative_identity,V0),multiplicative_identity) = true,
inference(hyper_resolution,[status(thm)],[hi14,hi16,hi0,hi7,hi16]) ).
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(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(h207,plain,
product(multiplicative_identity,add(V0,V0),V0) = true,
inference(hyper_resolution,[status(thm)],[hi14,hi16,hi0,hi18,hi4]) ).
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(h6,plain,
sum(inverse(multiplicative_identity),additive_identity,additive_identity) = true,
inference(hyper_resolution,[status(thm)],[hi15,hi5,hi5,hi7,hi18]) ).
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(h34,plain,
product(multiplicative_identity,additive_identity,inverse(multiplicative_identity)) = true,
inference(hyper_resolution,[status(thm)],[hi14,hi5,h6,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(h57,plain,
sum(inverse(multiplicative_identity),V0,V0) = true,
inference(hyper_resolution,[status(thm)],[hi8,h34,hi6,hi4,hi6]) ).
cnf(h171,plain,
product(V0,add(multiplicative_identity,V0),V0) = true,
inference(hyper_resolution,[status(thm)],[hi14,h57,hi0,hi18,hi4]) ).
cnf(h1670,plain,
sum(multiplicative_identity,multiplicative_identity,multiplicative_identity) = true,
inference(hyper_resolution,[status(thm)],[hi8,hi7,hi7,hi0,h171]) ).
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/sandbox2/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(h1779,plain,
sum(V0,V0,V0) = true,
inference(hyper_resolution,[status(thm)],[hi10,hi6,hi6,h1670,hi6]) ).
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(h2025,plain,
sum(multiplicative_identity,V0,multiplicative_identity) = true,
inference(hyper_resolution,[status(thm)],[hi13,h1779,hi0,h207,h208]) ).
cnf(f3,axiom,
( product(Y,X,Z)
| ~ product(X,Y,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_multiplication) ).
fof(f3_nnf,plain,
! [X,Y,Z] :
( product(Y,X,Z)
| ~ product(X,Y,Z) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [X,Y,Z] :
( product(Y,X,Z)
| ~ product(X,Y,Z) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
( product(X1,X0,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(hi3,axiom,
ifeq(product(X0,X1,X2),true,product(X1,X0,X2),true) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(f22,hypothesis,
product(x,y,z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_times_y) ).
fof(f22_nnf,plain,
product(x,y,z),
inference(nnf_transformation,[status(thm)],[f22]) ).
cnf(c22,plain,
product(x,y,z),
inference(cnf_transformation,[status(esa)],[f22_nnf]) ).
cnf(hi22,axiom,
product(x,y,z) = true,
inference(equality_encoding,[status(esa)],[c22]) ).
cnf(h0,plain,
product(y,x,z) = true,
inference(hyper_resolution,[status(thm)],[hi3,hi22]) ).
cnf(t37,plain,
sum(x,z,x) = true,
inference(hyper_resolution,[status(thm)],[hi10,hi6,h0,h2025,hi6]) ).
cnf(t421,plain,
sum(x,z,x) = true,
inference(orient,[status(thm)],[t37]) ).
cnf(f23,negated_conjecture,
~ sum(x,z,x),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_sum) ).
fof(f23_nnf,plain,
~ sum(x,z,x),
inference(nnf_transformation,[status(thm)],[f23]) ).
fof(f23_sk,plain,
~ sum(x,z,x),
inference(skolemisation,[status(esa)],[f23_nnf]) ).
cnf(c23,plain,
~ sum(x,z,x),
inference(cnf_transformation,[status(esa)],[f23_sk]) ).
cnf(goal_0,negated_conjecture,
sum(x,z,x) != true,
inference(equality_encoding,[status(esa)],[c23]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t421]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO016-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.58 % Computer : n019.cluster.edu
% 0.09/0.58 % Model : x86_64 x86_64
% 0.09/0.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.58 % Memory : 8046.5625MB
% 0.09/0.58 % OS : Linux 6.8.0-71-generic
% 0.09/0.58 % CPULimit : 300
% 0.09/0.58 % WCLimit : 300
% 0.09/0.58 % DateTime : Fri Sep 25 06:33:22 UTC 2026
% 0.09/0.58 % CPUTime :
% 0.09/0.58 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 12.85/2.22 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.85/2.22 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------