%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : RNG001-10 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/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 02:37:22 PM UTC 2026
% Result : Unsatisfiable 60.34s 10.71s
% Output : CNFRefutation 60.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 14
% Syntax : Number of clauses : 48 ( 48 unt; 0 nHn; 9 RR)
% Number of literals : 48 ( 47 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-4 aty)
% Number of variables : 86 ( 6 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(hi11,axiom,
ifeq(product(X,V3,V4),true,ifeq(product(X,Z,V2),true,ifeq(product(X,Y,V1),true,ifeq(sum(Y,Z,V3),true,sum(V1,V2,V4),true),true),true),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(hi2,axiom,
product(X,Y,multiply(X,Y)) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(hi3,axiom,
sum(X,Y,add(X,Y)) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(h16,plain,
sum(multiply(V0,V1),multiply(V0,V2),multiply(V0,add(V1,V2))) = true,
inference(hyper_resolution,[status(thm)],[hi11,hi2,hi2,hi2,hi3]) ).
cnf(hi12,axiom,
ifeq(product(X,Z,V2),true,ifeq(product(X,Y,V1),true,ifeq(sum(V1,V2,V4),true,ifeq(sum(Y,Z,V3),true,product(X,V3,V4),true),true),true),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(hi5,axiom,
sum(X,additive_inverse(X),additive_identity) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t167,plain,
product(X1,additive_identity,multiply(X1,add(X2,additive_inverse(X2)))) = true,
inference(hyper_resolution,[status(thm)],[hi12,hi2,hi2,h16,hi5]) ).
cnf(hi15,axiom,
ifeq2(sum(X,Y,V),true,ifeq2(sum(X,Y,U),true,U,V),V) = V,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t8,plain,
add(X1,additive_inverse(X1)) = additive_identity,
inference(hyper_resolution,[status(thm)],[hi15,hi3,hi5]) ).
cnf(t291,plain,
add(X1,additive_inverse(X1)) = additive_identity,
inference(orient,[status(thm)],[t8]) ).
cnf(t536,plain,
product(X1,additive_identity,multiply(X1,additive_identity)) = true,
inference(step,[status(thm)],[t167,t291]) ).
cnf(hi4,axiom,
sum(additive_inverse(X),X,additive_identity) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(h45,plain,
sum(multiply(V0,additive_inverse(V1)),multiply(V0,V1),multiply(V0,additive_identity)) = true,
inference(hyper_resolution,[status(thm)],[hi11,hi2,hi2,hi2,hi4]) ).
cnf(hi7,axiom,
ifeq(sum(Y,Z,V),true,ifeq(sum(X,V,W),true,ifeq(sum(X,Y,U),true,sum(U,Z,W),true),true),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(hi0,axiom,
sum(additive_identity,X,X) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(h24,plain,
sum(add(additive_identity,additive_identity),V0,V0) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi0,hi0,hi3]) ).
cnf(hi18,axiom,
ifeq2(sum(W,Y,Z),true,ifeq2(sum(X,Y,Z),true,X,W),W) = W,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t48,plain,
multiply(X1,additive_inverse(additive_identity)) = add(additive_identity,additive_identity),
inference(hyper_resolution,[status(thm)],[hi18,h24,h45]) ).
cnf(hi1,axiom,
sum(X,additive_identity,X) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(h50,plain,
sum(additive_identity,additive_identity,additive_inverse(additive_identity)) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi1,hi1,hi4]) ).
cnf(hi6,axiom,
ifeq(sum(U,Z,W),true,ifeq(sum(Y,Z,V),true,ifeq(sum(X,Y,U),true,sum(X,V,W),true),true),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(h32,plain,
sum(V0,V1,add(add(V0,additive_identity),V1)) = true,
inference(hyper_resolution,[status(thm)],[hi6,hi3,hi0,hi3]) ).
cnf(t45,plain,
add(add(additive_identity,additive_identity),additive_identity) = additive_inverse(additive_identity),
inference(hyper_resolution,[status(thm)],[hi15,h32,h50]) ).
cnf(h25,plain,
sum(V0,V1,add(V0,add(additive_identity,V1))) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi3,hi3,hi1]) ).
cnf(h18,plain,
sum(add(V0,V1),V2,add(V0,add(V1,V2))) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi3,hi3,hi3]) ).
cnf(t179,plain,
add(add(X1,X2),add(additive_identity,X3)) = add(X1,add(X2,X3)),
inference(hyper_resolution,[status(thm)],[hi15,h18,h25]) ).
cnf(h21,plain,
sum(add(V0,additive_identity),additive_identity,V0) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi1,hi1,hi3]) ).
cnf(hi8,axiom,
ifeq(sum(X,Y,Z),true,sum(Y,X,Z),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(h17,plain,
sum(V0,V1,add(V1,V0)) = true,
inference(hyper_resolution,[status(thm)],[hi8,hi3]) ).
cnf(t20,plain,
add(add(additive_identity,X1),additive_identity) = X1,
inference(hyper_resolution,[status(thm)],[hi18,h17,h21]) ).
cnf(t1,plain,
add(X1,additive_identity) = X1,
inference(hyper_resolution,[status(thm)],[hi18,hi1,hi3]) ).
cnf(t257,plain,
add(X1,additive_identity) = X1,
inference(orient,[status(thm)],[t1]) ).
cnf(t507,plain,
add(additive_identity,X1) = X1,
inference(step,[status(thm)],[t20,t257]) ).
cnf(t258,plain,
add(additive_identity,X1) = X1,
inference(orient,[status(thm)],[t507]) ).
cnf(t511,plain,
add(add(X1,X2),X3) = add(X1,add(X2,X3)),
inference(step,[status(thm)],[t179,t258]) ).
cnf(t273,plain,
add(add(X1,X2),X3) = add(X1,add(X2,X3)),
inference(orient,[status(thm)],[t511]) ).
cnf(t512,plain,
add(additive_identity,add(additive_identity,additive_identity)) = additive_inverse(additive_identity),
inference(step,[status(thm)],[t45,t273]) ).
cnf(t513,plain,
add(additive_identity,additive_identity) = additive_inverse(additive_identity),
inference(step,[status(thm)],[t512,t258]) ).
cnf(t514,plain,
additive_identity = additive_inverse(additive_identity),
inference(step,[status(thm)],[t513,t258]) ).
cnf(t296,plain,
additive_inverse(additive_identity) = additive_identity,
inference(orient,[status(thm)],[t514]) ).
cnf(t521,plain,
multiply(X1,additive_identity) = add(additive_identity,additive_identity),
inference(step,[status(thm)],[t48,t296]) ).
cnf(t522,plain,
multiply(X1,additive_identity) = additive_identity,
inference(step,[status(thm)],[t521,t258]) ).
cnf(t309,plain,
multiply(X1,additive_identity) = additive_identity,
inference(orient,[status(thm)],[t522]) ).
cnf(t537,plain,
product(X1,additive_identity,additive_identity) = true,
inference(step,[status(thm)],[t536,t309]) ).
cnf(t504,plain,
product(X1,additive_identity,additive_identity) = true,
inference(orient,[status(thm)],[t537]) ).
cnf(goal_0,negated_conjecture,
product(a,additive_identity,additive_identity) != true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t504]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : RNG001-10 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.06 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.44 % Computer : n016.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.45 % CPULimit : 300
% 0.17/0.45 % WCLimit : 300
% 0.17/0.45 % DateTime : Thu Sep 24 07:44:41 UTC 2026
% 0.17/0.45 % CPUTime :
% 0.17/0.45 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 60.34/10.71 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 60.34/10.71 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------