%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : RNG001-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n005.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 02:37:22 PM UTC 2026
% Result : Unsatisfiable 14.85s 2.40s
% Output : Proof 14.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 8
% Syntax : Number of formulae : 60 ( 44 unt; 0 def)
% Number of atoms : 116 ( 27 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 118 ( 62 ~; 56 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-4 aty)
% Number of variables : 167 ( 6 sgn 60 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f2,axiom,
( sum(X,V,W)
| ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_addition1) ).
fof(f2_nnf,plain,
! [X,Y,U,Z,V,W] :
( sum(X,V,W)
| ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X,Y,U,Z,V,W] :
( sum(X,V,W)
| ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( sum(X0,X4,X5)
| ~ sum(X2,X3,X5)
| ~ sum(X1,X3,X4)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi2,axiom,
ifeq(sum(X0,X1,X2),true,ifeq(sum(X1,X3,X4),true,ifeq(sum(X2,X3,X5),true,sum(X0,X4,X5),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(f1,axiom,
sum(additive_inverse(X),X,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_inverse1) ).
fof(f1_nnf,plain,
! [X] : sum(additive_inverse(X),X,additive_identity),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X] : sum(additive_inverse(X),X,additive_identity),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
sum(additive_inverse(X0),X0,additive_identity),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(hi1,axiom,
sum(additive_inverse(X0),X0,additive_identity) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(f0,axiom,
sum(additive_identity,X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity1) ).
fof(f0_nnf,plain,
! [X] : sum(additive_identity,X,X),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X] : sum(additive_identity,X,X),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
sum(additive_identity,X0,X0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi0,axiom,
sum(additive_identity,X0,X0) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(h0,plain,
sum(additive_inverse(additive_inverse(V0)),additive_identity,V0) = true,
inference(hyper_resolution,[status(thm)],[hi2,hi1,hi1,hi0]) ).
cnf(f3,axiom,
( sum(U,Z,W)
| ~ sum(X,V,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_addition2) ).
fof(f3_nnf,plain,
! [X,Y,U,Z,V,W] :
( sum(U,Z,W)
| ~ sum(X,V,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [X,Y,U,Z,V,W] :
( sum(U,Z,W)
| ~ sum(X,V,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
( sum(X2,X3,X5)
| ~ sum(X0,X4,X5)
| ~ sum(X1,X3,X4)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(hi3,axiom,
ifeq(sum(X0,X1,X2),true,ifeq(sum(X1,X3,X4),true,ifeq(sum(X0,X4,X5),true,sum(X2,X3,X5),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(h12,plain,
sum(V0,additive_inverse(V0),additive_identity) = true,
inference(hyper_resolution,[status(thm)],[hi3,h0,hi0,hi1]) ).
cnf(h11,plain,
sum(V0,additive_identity,V0) = true,
inference(hyper_resolution,[status(thm)],[hi3,h0,hi0,h0]) ).
cnf(h21,plain,
sum(additive_identity,V0,additive_inverse(additive_inverse(V0))) = true,
inference(hyper_resolution,[status(thm)],[hi3,hi1,hi1,h11]) ).
cnf(h18,plain,
sum(V0,additive_identity,additive_inverse(additive_inverse(V0))) = true,
inference(hyper_resolution,[status(thm)],[hi3,h0,h11,h11]) ).
cnf(h94,plain,
sum(V0,additive_inverse(additive_inverse(additive_inverse(additive_inverse(additive_inverse(V0))))),additive_identity) = true,
inference(hyper_resolution,[status(thm)],[hi2,h18,h21,h12]) ).
cnf(f5,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(f5_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)],[f5]) ).
fof(f5_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)],[f5_nnf]) ).
cnf(c5,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)],[f5_sk]) ).
cnf(hi5,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)],[c5]) ).
cnf(f4,axiom,
product(X,Y,multiply(X,Y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_of_multiplication) ).
fof(f4_nnf,plain,
! [X,Y] : product(X,Y,multiply(X,Y)),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [X,Y] : product(X,Y,multiply(X,Y)),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
product(X0,X1,multiply(X0,X1)),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(hi4,axiom,
product(X0,X1,multiply(X0,X1)) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(h49,plain,
sum(multiply(V0,V1),multiply(V0,additive_identity),multiply(V0,V1)) = true,
inference(hyper_resolution,[status(thm)],[hi5,hi4,hi4,h11,hi4]) ).
cnf(h247,plain,
sum(multiply(V0,additive_identity),additive_identity,additive_identity) = true,
inference(hyper_resolution,[status(thm)],[hi2,h49,h94,h94]) ).
cnf(h92,plain,
sum(additive_inverse(additive_inverse(additive_inverse(additive_inverse(additive_inverse(V0))))),V0,additive_identity) = true,
inference(hyper_resolution,[status(thm)],[hi3,h18,h21,hi1]) ).
cnf(h222,plain,
sum(additive_identity,multiply(V0,additive_identity),additive_identity) = true,
inference(hyper_resolution,[status(thm)],[hi3,h92,h49,h92]) ).
cnf(h380,plain,
sum(multiply(V0,additive_identity),multiply(V1,additive_identity),additive_identity) = true,
inference(hyper_resolution,[status(thm)],[hi3,h11,h222,h247]) ).
cnf(h1,plain,
sum(additive_inverse(additive_identity),V0,V0) = true,
inference(hyper_resolution,[status(thm)],[hi2,hi1,hi0,hi0]) ).
cnf(h2,plain,
sum(additive_identity,additive_inverse(additive_identity),additive_identity) = true,
inference(hyper_resolution,[status(thm)],[hi3,hi1,h1,hi1]) ).
cnf(h4,plain,
sum(additive_inverse(additive_identity),additive_inverse(additive_identity),additive_identity) = true,
inference(hyper_resolution,[status(thm)],[hi3,hi0,h1,h2]) ).
cnf(h7,plain,
sum(additive_identity,additive_identity,additive_inverse(additive_identity)) = true,
inference(hyper_resolution,[status(thm)],[hi2,hi0,h2,hi0]) ).
cnf(f6,axiom,
( product(X,V3,V4)
| ~ sum(V1,V2,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity2) ).
fof(f6_nnf,plain,
! [X,Y,V1,Z,V2,V3,V4] :
( product(X,V3,V4)
| ~ sum(V1,V2,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [X,Y,V1,Z,V2,V3,V4] :
( product(X,V3,V4)
| ~ sum(V1,V2,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
( product(X0,X5,X6)
| ~ sum(X2,X4,X6)
| ~ sum(X1,X3,X5)
| ~ product(X0,X3,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(hi6,axiom,
ifeq(product(X0,X1,X2),true,ifeq(product(X0,X3,X4),true,ifeq(sum(X1,X3,X5),true,ifeq(sum(X2,X4,X6),true,product(X0,X5,X6),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(h216,plain,
product(V0,additive_inverse(additive_identity),multiply(V0,additive_identity)) = true,
inference(hyper_resolution,[status(thm)],[hi6,hi4,hi4,h7,h49]) ).
cnf(t0,plain,
product(X1,additive_identity,additive_identity) = true,
inference(hyper_resolution,[status(thm)],[hi6,h216,h216,h4,h380]) ).
cnf(t473,plain,
product(X1,additive_identity,additive_identity) = true,
inference(orient,[status(thm)],[t0]) ).
cnf(f7,negated_conjecture,
~ product(a,additive_identity,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_a_times_additive_id_is_additive_id) ).
fof(f7_nnf,plain,
~ product(a,additive_identity,additive_identity),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
~ product(a,additive_identity,additive_identity),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
~ product(a,additive_identity,additive_identity),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(goal_0,negated_conjecture,
product(a,additive_identity,additive_identity) != true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t473]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG001-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.35 % Computer : n005.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Thu Sep 24 07:40:17 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 14.85/2.40 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 14.85/2.40 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------