%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : RNG038-1 : 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 02:37:34 PM UTC 2026
% Result : Unsatisfiable 24.47s 4.16s
% Output : Proof 24.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 11
% Syntax : Number of formulae : 84 ( 60 unt; 0 def)
% Number of atoms : 140 ( 55 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 123 ( 67 ~; 56 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 7 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-4 aty)
% Number of variables : 205 ( 9 sgn 64 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f15,axiom,
( U = V
| ~ sum(X,Y,V)
| ~ sum(X,Y,U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',addition_is_well_defined) ).
fof(f15_nnf,plain,
! [X,Y,U,V] :
( U = V
| ~ sum(X,Y,V)
| ~ sum(X,Y,U) ),
inference(nnf_transformation,[status(thm)],[f15]) ).
fof(f15_sk,plain,
! [X,Y,U,V] :
( U = V
| ~ sum(X,Y,V)
| ~ sum(X,Y,U) ),
inference(skolemisation,[status(esa)],[f15_nnf]) ).
cnf(c15,plain,
( X2 = X3
| ~ sum(X0,X1,X3)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(hi15,axiom,
ifeq(sum(X0,X1,X2),true,ifeq(sum(X0,X1,X3),true,X2,X3),X3) = X3,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(f1,axiom,
sum(X,additive_identity,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity2) ).
fof(f1_nnf,plain,
! [X] : sum(X,additive_identity,X),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X] : sum(X,additive_identity,X),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
sum(X0,additive_identity,X0),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(hi1,axiom,
sum(X0,additive_identity,X0) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(f3,axiom,
sum(X,Y,add(X,Y)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure_of_addition) ).
fof(f3_nnf,plain,
! [X,Y] : sum(X,Y,add(X,Y)),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [X,Y] : sum(X,Y,add(X,Y)),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
sum(X0,X1,add(X0,X1)),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(hi3,axiom,
sum(X0,X1,add(X0,X1)) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(h7,plain,
V0 = add(V0,additive_identity),
inference(hyper_resolution,[status(thm)],[hi15,hi1,hi3]) ).
cnf(f17,hypothesis,
( product(X,h(X,Y),Y)
| X != additive_identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',some_property) ).
fof(f17_nnf,plain,
! [X,Y] :
( product(X,h(X,Y),Y)
| X != additive_identity ),
inference(nnf_transformation,[status(thm)],[f17]) ).
fof(f17_sk,plain,
! [X,Y] :
( product(X,h(X,Y),Y)
| X != additive_identity ),
inference(skolemisation,[status(esa)],[f17_nnf]) ).
cnf(c17,plain,
( product(X0,h(X0,X1),X1)
| X0 != additive_identity ),
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
cnf(hi17,axiom,
ifeq(X0,additive_identity,product(X0,h(X0,X1),X1),true) = true,
inference(equality_encoding,[status(esa)],[c17]) ).
cnf(h40,plain,
product(add(additive_identity,additive_identity),h(add(additive_identity,additive_identity),V0),V0) = true,
inference(hyper_resolution,[status(thm)],[hi17,h7]) ).
cnf(f6,axiom,
( sum(X,V,W)
| ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_addition1) ).
fof(f6_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)],[f6]) ).
fof(f6_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)],[f6_nnf]) ).
cnf(c6,plain,
( sum(X0,X4,X5)
| ~ sum(X2,X3,X5)
| ~ sum(X1,X3,X4)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(hi6,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)],[c6]) ).
cnf(h37,plain,
sum(V0,add(additive_identity,additive_identity),V0) = true,
inference(hyper_resolution,[status(thm)],[hi6,hi1,hi3,hi1]) ).
cnf(f13,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(f13_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)],[f13]) ).
fof(f13_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)],[f13_nnf]) ).
cnf(c13,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)],[f13_sk]) ).
cnf(hi13,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)],[c13]) ).
cnf(h83588,plain,
sum(V0,V0,V0) = true,
inference(hyper_resolution,[status(thm)],[hi13,h40,h40,h37,h40]) ).
cnf(f8,axiom,
( sum(Y,X,Z)
| ~ sum(X,Y,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_addition) ).
fof(f8_nnf,plain,
! [X,Y,Z] :
( sum(Y,X,Z)
| ~ sum(X,Y,Z) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [X,Y,Z] :
( sum(Y,X,Z)
| ~ sum(X,Y,Z) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
( sum(X1,X0,X2)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(hi8,axiom,
ifeq(sum(X0,X1,X2),true,sum(X1,X0,X2),true) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(h17,plain,
sum(V0,V1,add(V1,V0)) = true,
inference(hyper_resolution,[status(thm)],[hi8,hi3]) ).
cnf(t1,plain,
add(X1,X1) = X1,
inference(hyper_resolution,[status(thm)],[hi15,h17,h83588]) ).
cnf(t256,plain,
add(X1,X1) = X1,
inference(orient,[status(thm)],[t1]) ).
cnf(f7,axiom,
( sum(U,Z,W)
| ~ sum(X,V,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_addition2) ).
fof(f7_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)],[f7]) ).
fof(f7_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)],[f7_nnf]) ).
cnf(c7,plain,
( sum(X2,X3,X5)
| ~ sum(X0,X4,X5)
| ~ sum(X1,X3,X4)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(hi7,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)],[c7]) ).
cnf(h18,plain,
sum(add(V0,V1),V2,add(V0,add(V1,V2))) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi3,hi3,hi3]) ).
cnf(f5,axiom,
sum(X,additive_inverse(X),additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_inverse) ).
fof(f5_nnf,plain,
! [X] : sum(X,additive_inverse(X),additive_identity),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [X] : sum(X,additive_inverse(X),additive_identity),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
sum(X0,additive_inverse(X0),additive_identity),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(hi5,axiom,
sum(X0,additive_inverse(X0),additive_identity) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t102,plain,
add(X1,add(X2,additive_inverse(add(X1,X2)))) = additive_identity,
inference(hyper_resolution,[status(thm)],[hi15,hi5,h18]) ).
cnf(t324,plain,
add(X1,add(X2,additive_inverse(add(X1,X2)))) = additive_identity,
inference(orient,[status(thm)],[t102]) ).
cnf(t147,plain,
add(X1,add(X2,add(X1,X2))) = add(X1,X2),
inference(hyper_resolution,[status(thm)],[hi15,h18,h83588]) ).
cnf(t267,plain,
add(X1,add(X2,add(X1,X2))) = add(X1,X2),
inference(orient,[status(thm)],[t147]) ).
cnf(t331,plain,
additive_identity = add(X1,add(add(X2,add(X1,X2)),additive_inverse(add(X1,X2)))),
inference(cp,[status(thm)],[t324,t267]) ).
cnf(t148,plain,
add(add(X1,X2),X3) = add(X1,add(X2,X3)),
inference(hyper_resolution,[status(thm)],[hi15,hi3,h18]) ).
cnf(t306,plain,
add(add(X1,X2),X3) = add(X1,add(X2,X3)),
inference(orient,[status(thm)],[t148]) ).
cnf(t2135,plain,
additive_identity = add(X1,add(X2,add(add(X1,X2),additive_inverse(add(X1,X2))))),
inference(step,[status(thm)],[t331,t306]) ).
cnf(t2136,plain,
additive_identity = add(X1,add(X2,add(X1,add(X2,additive_inverse(add(X1,X2)))))),
inference(step,[status(thm)],[t2135,t306]) ).
cnf(t2137,plain,
additive_identity = add(X1,add(X2,additive_identity)),
inference(step,[status(thm)],[t2136,t324]) ).
cnf(h21,plain,
sum(V0,V1,add(V0,add(additive_identity,V1))) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi1,hi3,hi3]) ).
cnf(t15,plain,
add(X1,add(additive_identity,additive_identity)) = X1,
inference(hyper_resolution,[status(thm)],[hi15,hi1,h21]) ).
cnf(t2102,plain,
add(X1,additive_identity) = X1,
inference(step,[status(thm)],[t15,t256]) ).
cnf(t258,plain,
add(X1,additive_identity) = X1,
inference(orient,[status(thm)],[t2102]) ).
cnf(t2138,plain,
additive_identity = add(X1,X2),
inference(step,[status(thm)],[t2137,t258]) ).
cnf(t2029,plain,
add(X1,X2) = additive_identity,
inference(orient,[status(thm)],[t2138]) ).
cnf(t2139,plain,
additive_identity = X1,
inference(step,[status(thm)],[t256,t2029]) ).
cnf(t2030,plain,
additive_identity = X1,
inference(rw,[status(thm)],[t2139]) ).
cnf(t2063,plain,
additive_identity = X1,
inference(orient,[status(thm)],[t2030]) ).
cnf(f19,negated_conjecture,
a != additive_identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_not_additive_identity) ).
fof(f19_nnf,plain,
a != additive_identity,
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
a != additive_identity,
inference(skolemisation,[status(esa)],[f19_nnf]) ).
cnf(c19,plain,
a != additive_identity,
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(f20,negated_conjecture,
b != additive_identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_b_is_additive_identity) ).
fof(f20_nnf,plain,
b != additive_identity,
inference(nnf_transformation,[status(thm)],[f20]) ).
fof(f20_sk,plain,
b != additive_identity,
inference(skolemisation,[status(esa)],[f20_nnf]) ).
cnf(c20,plain,
b != additive_identity,
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c19,c20]) ).
cnf(g0_0,plain,
additive_identity != false,
inference(rw,[status(thm)],[goal_0,t2063]) ).
cnf(g0_1,plain,
additive_identity != additive_identity,
inference(rw,[status(thm)],[g0_0,t2063]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG038-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.35 % Computer : n014.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 : Thu Sep 24 07:55:18 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 24.47/4.16 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 24.47/4.16 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------