%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : BOO006-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n016.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 12:59:32 PM UTC 2026
% Result : Unsatisfiable 37.13s 10.10s
% Output : Proof 37.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 11
% Syntax : Number of formulae : 75 ( 55 unt; 0 def)
% Number of atoms : 127 ( 38 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 110 ( 58 ~; 52 |; 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; 3 con; 0-4 aty)
% Number of variables : 183 ( 5 sgn 64 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(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(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(h14,plain,
product(V0,V1,add(additive_identity,multiply(V0,V1))) = true,
inference(hyper_resolution,[status(thm)],[hi12,hi4,hi4,hi1,hi0]) ).
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(t108,plain,
product(X1,X2,add(additive_identity,multiply(X2,X1))) = true,
inference(hyper_resolution,[status(thm)],[hi3,h14]) ).
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(t3,plain,
add(additive_identity,X1) = X1,
inference(hyper_resolution,[status(thm)],[hi20,hi4,hi0]) ).
cnf(t257,plain,
add(additive_identity,X1) = X1,
inference(orient,[status(thm)],[t3]) ).
cnf(t1818,plain,
product(X1,X2,multiply(X2,X1)) = true,
inference(step,[status(thm)],[t108,t257]) ).
cnf(t592,plain,
product(X1,X2,multiply(X2,X1)) = true,
inference(orient,[status(thm)],[t1818]) ).
cnf(f11,axiom,
( product(V3,X,V4)
| ~ sum(V1,V2,V4)
| ~ sum(Y,Z,V3)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity4) ).
fof(f11_nnf,plain,
! [Y,X,V1,Z,V2,V3,V4] :
( product(V3,X,V4)
| ~ sum(V1,V2,V4)
| ~ sum(Y,Z,V3)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) ),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [Y,X,V1,Z,V2,V3,V4] :
( product(V3,X,V4)
| ~ sum(V1,V2,V4)
| ~ sum(Y,Z,V3)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) ),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
( product(X5,X1,X6)
| ~ sum(X2,X4,X6)
| ~ sum(X0,X3,X5)
| ~ product(X3,X1,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(hi11,axiom,
ifeq(product(X0,X1,X2),true,ifeq(product(X3,X1,X4),true,ifeq(sum(X0,X3,X5),true,ifeq(sum(X2,X4,X6),true,product(X5,X1,X6),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(h21,plain,
product(V0,V1,add(multiply(additive_identity,V1),multiply(V0,V1))) = true,
inference(hyper_resolution,[status(thm)],[hi11,hi1,hi1,hi4,hi0]) ).
cnf(f21,axiom,
( U = V
| ~ product(X,Y,V)
| ~ product(X,Y,U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplication_is_well_defined) ).
fof(f21_nnf,plain,
! [X,Y,U,V] :
( U = V
| ~ product(X,Y,V)
| ~ product(X,Y,U) ),
inference(nnf_transformation,[status(thm)],[f21]) ).
fof(f21_sk,plain,
! [X,Y,U,V] :
( U = V
| ~ product(X,Y,V)
| ~ product(X,Y,U) ),
inference(skolemisation,[status(esa)],[f21_nnf]) ).
cnf(c21,plain,
( X2 = X3
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(hi21,axiom,
ifeq(product(X0,X1,X2),true,ifeq(product(X0,X1,X3),true,X2,X3),X3) = X3,
inference(equality_encoding,[status(esa)],[c21]) ).
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(t104,plain,
add(multiply(additive_identity,X1),multiply(inverse(X1),X1)) = additive_identity,
inference(hyper_resolution,[status(thm)],[hi21,hi18,h21]) ).
cnf(t27,plain,
add(additive_identity,multiply(inverse(X1),X1)) = additive_identity,
inference(hyper_resolution,[status(thm)],[hi21,hi18,h14]) ).
cnf(t1796,plain,
multiply(inverse(X1),X1) = additive_identity,
inference(step,[status(thm)],[t27,t257]) ).
cnf(t269,plain,
multiply(inverse(X1),X1) = additive_identity,
inference(orient,[status(thm)],[t1796]) ).
cnf(t1797,plain,
add(multiply(additive_identity,X1),additive_identity) = additive_identity,
inference(step,[status(thm)],[t104,t269]) ).
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(t2,plain,
add(X1,additive_identity) = X1,
inference(hyper_resolution,[status(thm)],[hi20,hi0,hi5]) ).
cnf(t256,plain,
add(X1,additive_identity) = X1,
inference(orient,[status(thm)],[t2]) ).
cnf(t1798,plain,
multiply(additive_identity,X1) = additive_identity,
inference(step,[status(thm)],[t1797,t256]) ).
cnf(t282,plain,
multiply(additive_identity,X1) = additive_identity,
inference(orient,[status(thm)],[t1798]) ).
cnf(t599,plain,
true = product(X1,additive_identity,additive_identity),
inference(cp,[status(thm)],[t592,t282]) ).
cnf(t1767,plain,
product(X1,additive_identity,additive_identity) = true,
inference(orient,[status(thm)],[t599]) ).
cnf(f22,negated_conjecture,
~ product(x,additive_identity,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_equations) ).
fof(f22_nnf,plain,
~ product(x,additive_identity,additive_identity),
inference(nnf_transformation,[status(thm)],[f22]) ).
fof(f22_sk,plain,
~ product(x,additive_identity,additive_identity),
inference(skolemisation,[status(esa)],[f22_nnf]) ).
cnf(c22,plain,
~ product(x,additive_identity,additive_identity),
inference(cnf_transformation,[status(esa)],[f22_sk]) ).
cnf(goal_0,negated_conjecture,
product(x,additive_identity,additive_identity) != true,
inference(equality_encoding,[status(esa)],[c22]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t1767]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO006-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/5.37 % Computer : n016.cluster.edu
% 0.10/5.37 % Model : x86_64 x86_64
% 0.10/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.37 % Memory : 8046.5625MB
% 0.10/5.37 % OS : Linux 6.8.0-71-generic
% 0.10/5.37 % CPULimit : 300
% 0.10/5.37 % WCLimit : 300
% 0.10/5.37 % DateTime : Fri Sep 25 06:31:19 UTC 2026
% 0.10/5.37 % CPUTime :
% 0.10/5.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 37.13/10.10 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 37.13/10.10 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------