%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : RNG038-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n001.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 3.72s 1.13s
% Output : Proof 3.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 8
% Syntax : Number of formulae : 46 ( 34 unt; 0 def)
% Number of atoms : 66 ( 17 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 50 ( 30 ~; 20 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-4 aty)
% Number of variables : 70 ( 7 sgn 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f28,negated_conjecture,
~ equalish(a,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_not_additive_identity) ).
fof(f28_nnf,plain,
~ equalish(a,additive_identity),
inference(nnf_transformation,[status(thm)],[f28]) ).
fof(f28_sk,plain,
~ equalish(a,additive_identity),
inference(skolemisation,[status(esa)],[f28_nnf]) ).
cnf(c28,plain,
~ equalish(a,additive_identity),
inference(cnf_transformation,[status(esa)],[f28_sk]) ).
cnf(t106,plain,
ifeq(equalish(a,additive_identity),true,false,true) = true,
inference(equality_encoding,[status(esa)],[c28]) ).
cnf(f22,axiom,
( equalish(U,V)
| ~ sum(X,Y,V)
| ~ sum(X,Y,U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',addition_is_well_defined) ).
fof(f22_nnf,plain,
! [X,Y,U,V] :
( equalish(U,V)
| ~ sum(X,Y,V)
| ~ sum(X,Y,U) ),
inference(nnf_transformation,[status(thm)],[f22]) ).
fof(f22_sk,plain,
! [X,Y,U,V] :
( equalish(U,V)
| ~ sum(X,Y,V)
| ~ sum(X,Y,U) ),
inference(skolemisation,[status(esa)],[f22_nnf]) ).
cnf(c22,plain,
( equalish(X2,X3)
| ~ sum(X0,X1,X3)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f22_sk]) ).
cnf(hi22,axiom,
ifeq(sum(X0,X1,X2),true,ifeq(sum(X0,X1,X3),true,equalish(X2,X3),true),true) = true,
inference(equality_encoding,[status(esa)],[c22]) ).
cnf(f9,axiom,
sum(X,additive_identity,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity2) ).
fof(f9_nnf,plain,
! [X] : sum(X,additive_identity,X),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [X] : sum(X,additive_identity,X),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
sum(X0,additive_identity,X0),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(hi9,axiom,
sum(X0,additive_identity,X0) = true,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(h0,plain,
equalish(V0,V0) = true,
inference(hyper_resolution,[status(thm)],[hi22,hi9,hi9]) ).
cnf(f26,hypothesis,
( product(X,h(X,Y),Y)
| ~ equalish(X,additive_identity) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',some_property) ).
fof(f26_nnf,plain,
! [X,Y] :
( product(X,h(X,Y),Y)
| ~ equalish(X,additive_identity) ),
inference(nnf_transformation,[status(thm)],[f26]) ).
fof(f26_sk,plain,
! [X,Y] :
( product(X,h(X,Y),Y)
| ~ equalish(X,additive_identity) ),
inference(skolemisation,[status(esa)],[f26_nnf]) ).
cnf(c26,plain,
( product(X0,h(X0,X1),X1)
| ~ equalish(X0,additive_identity) ),
inference(cnf_transformation,[status(esa)],[f26_sk]) ).
cnf(hi26,axiom,
ifeq(equalish(X0,additive_identity),true,product(X0,h(X0,X1),X1),true) = true,
inference(equality_encoding,[status(esa)],[c26]) ).
cnf(h2,plain,
product(additive_identity,h(additive_identity,V0),V0) = true,
inference(hyper_resolution,[status(thm)],[hi26,h0]) ).
cnf(f23,axiom,
( equalish(U,V)
| ~ product(X,Y,V)
| ~ product(X,Y,U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplication_is_well_defined) ).
fof(f23_nnf,plain,
! [X,Y,U,V] :
( equalish(U,V)
| ~ product(X,Y,V)
| ~ product(X,Y,U) ),
inference(nnf_transformation,[status(thm)],[f23]) ).
fof(f23_sk,plain,
! [X,Y,U,V] :
( equalish(U,V)
| ~ product(X,Y,V)
| ~ product(X,Y,U) ),
inference(skolemisation,[status(esa)],[f23_nnf]) ).
cnf(c23,plain,
( equalish(X2,X3)
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f23_sk]) ).
cnf(hi23,axiom,
ifeq(product(X0,X1,X2),true,ifeq(product(X0,X1,X3),true,equalish(X2,X3),true),true) = true,
inference(equality_encoding,[status(esa)],[c23]) ).
cnf(f24,axiom,
product(additive_identity,X,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_identity1) ).
fof(f24_nnf,plain,
! [X] : product(additive_identity,X,additive_identity),
inference(nnf_transformation,[status(thm)],[f24]) ).
fof(f24_sk,plain,
! [X] : product(additive_identity,X,additive_identity),
inference(skolemisation,[status(esa)],[f24_nnf]) ).
cnf(c24,plain,
product(additive_identity,X0,additive_identity),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
cnf(hi24,axiom,
product(additive_identity,X0,additive_identity) = true,
inference(equality_encoding,[status(esa)],[c24]) ).
cnf(t2,plain,
equalish(X1,additive_identity) = true,
inference(hyper_resolution,[status(thm)],[hi23,h2,hi24]) ).
cnf(t422,plain,
equalish(X1,additive_identity) = true,
inference(orient,[status(thm)],[t2]) ).
cnf(t5064,plain,
ifeq(true,true,false,true) = true,
inference(step,[status(thm)],[t106,t422]) ).
cnf(t27,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t256,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t27]) ).
cnf(t5065,plain,
false = true,
inference(step,[status(thm)],[t5064,t256]) ).
cnf(t5061,plain,
false = true,
inference(orient,[status(thm)],[t5065]) ).
cnf(f29,negated_conjecture,
~ equalish(b,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_b_is_additive_identity) ).
fof(f29_nnf,plain,
~ equalish(b,additive_identity),
inference(nnf_transformation,[status(thm)],[f29]) ).
fof(f29_sk,plain,
~ equalish(b,additive_identity),
inference(skolemisation,[status(esa)],[f29_nnf]) ).
cnf(c29,plain,
~ equalish(b,additive_identity),
inference(cnf_transformation,[status(esa)],[f29_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c28,c29]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t5061]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG038-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.37 % Computer : n001.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Thu Sep 24 08:01:21 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 3.72/1.13 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.72/1.13 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------