%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : RNG037-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n026.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 7.43s 1.41s
% Output : Proof 7.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 39 ( 31 unt; 0 def)
% Number of atoms : 59 ( 12 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 46 ( 26 ~; 20 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-4 aty)
% Number of variables : 60 ( 3 sgn 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f25,axiom,
product(X,additive_identity,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_identity2) ).
fof(f25_nnf,plain,
! [X] : product(X,additive_identity,additive_identity),
inference(nnf_transformation,[status(thm)],[f25]) ).
fof(f25_sk,plain,
! [X] : product(X,additive_identity,additive_identity),
inference(skolemisation,[status(esa)],[f25_nnf]) ).
cnf(c25,plain,
product(X0,additive_identity,additive_identity),
inference(cnf_transformation,[status(esa)],[f25_sk]) ).
cnf(hi25,axiom,
product(X0,additive_identity,additive_identity) = true,
inference(equality_encoding,[status(esa)],[c25]) ).
cnf(h1,plain,
product(a,additive_identity,additive_identity) = true,
inference(hyper_resolution,[status(thm)],[hi25]) ).
cnf(f18,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(f18_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)],[f18]) ).
fof(f18_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)],[f18_nnf]) ).
cnf(c18,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)],[f18_sk]) ).
cnf(hi18,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)],[c18]) ).
cnf(f26,hypothesis,
product(a,b,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_b) ).
fof(f26_nnf,plain,
product(a,b,d),
inference(nnf_transformation,[status(thm)],[f26]) ).
cnf(c26,plain,
product(a,b,d),
inference(cnf_transformation,[status(esa)],[f26_nnf]) ).
cnf(hi26,axiom,
product(a,b,d) = true,
inference(equality_encoding,[status(esa)],[c26]) ).
cnf(f27,hypothesis,
product(a,additive_inverse(b),c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_inverse_times_b) ).
fof(f27_nnf,plain,
product(a,additive_inverse(b),c),
inference(nnf_transformation,[status(thm)],[f27]) ).
cnf(c27,plain,
product(a,additive_inverse(b),c),
inference(cnf_transformation,[status(esa)],[f27_nnf]) ).
cnf(hi27,axiom,
product(a,additive_inverse(b),c) = true,
inference(equality_encoding,[status(esa)],[c27]) ).
cnf(f12,axiom,
sum(X,additive_inverse(X),additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_inverse2) ).
fof(f12_nnf,plain,
! [X] : sum(X,additive_inverse(X),additive_identity),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [X] : sum(X,additive_inverse(X),additive_identity),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c12,plain,
sum(X0,additive_inverse(X0),additive_identity),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(hi12,axiom,
sum(X0,additive_inverse(X0),additive_identity) = true,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(h3,plain,
sum(d,c,additive_identity) = true,
inference(hyper_resolution,[status(thm)],[hi18,hi26,hi27,hi12,h1]) ).
cnf(f15,axiom,
( sum(Y,X,Z)
| ~ sum(X,Y,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_addition) ).
fof(f15_nnf,plain,
! [X,Y,Z] :
( sum(Y,X,Z)
| ~ sum(X,Y,Z) ),
inference(nnf_transformation,[status(thm)],[f15]) ).
fof(f15_sk,plain,
! [X,Y,Z] :
( sum(Y,X,Z)
| ~ sum(X,Y,Z) ),
inference(skolemisation,[status(esa)],[f15_nnf]) ).
cnf(c15,plain,
( sum(X1,X0,X2)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(hi15,axiom,
ifeq(sum(X0,X1,X2),true,sum(X1,X0,X2),true) = true,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(t4,plain,
sum(c,d,additive_identity) = true,
inference(hyper_resolution,[status(thm)],[hi15,h3]) ).
cnf(t282,plain,
sum(c,d,additive_identity) = true,
inference(orient,[status(thm)],[t4]) ).
cnf(f28,negated_conjecture,
~ sum(c,d,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_sum_is_additive_identity) ).
fof(f28_nnf,plain,
~ sum(c,d,additive_identity),
inference(nnf_transformation,[status(thm)],[f28]) ).
fof(f28_sk,plain,
~ sum(c,d,additive_identity),
inference(skolemisation,[status(esa)],[f28_nnf]) ).
cnf(c28,plain,
~ sum(c,d,additive_identity),
inference(cnf_transformation,[status(esa)],[f28_sk]) ).
cnf(goal_0,negated_conjecture,
sum(c,d,additive_identity) != true,
inference(equality_encoding,[status(esa)],[c28]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t282]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG037-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n026.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Thu Sep 24 07:58:09 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 7.43/1.41 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.43/1.41 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------