%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : RNG004-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n004.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 02:37:23 PM UTC 2026
% Result : Unsatisfiable 27.85s 3.94s
% Output : Proof 27.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 20
% Syntax : Number of formulae : 185 ( 145 unt; 0 def)
% Number of atoms : 293 ( 130 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 222 ( 114 ~; 108 |; 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 : 10 ( 10 usr; 6 con; 0-4 aty)
% Number of variables : 433 ( 6 sgn 120 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f7,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(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(f3,axiom,
sum(X,Y,add(X,Y)),
file('/export/starexec/sandbox/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(h18,plain,
sum(add(V0,V1),V2,add(V0,add(V1,V2))) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi3,hi3,hi3]) ).
cnf(f15,axiom,
( U = V
| ~ sum(X,Y,V)
| ~ sum(X,Y,U) ),
file('/export/starexec/sandbox/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(t108,plain,
add(add(X1,X2),X3) = add(X1,add(X2,X3)),
inference(hyper_resolution,[status(thm)],[hi15,hi3,h18]) ).
cnf(t290,plain,
add(add(X1,X2),X3) = add(X1,add(X2,X3)),
inference(orient,[status(thm)],[t108]) ).
cnf(f1,axiom,
sum(X,additive_identity,X),
file('/export/starexec/sandbox/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(h21,plain,
sum(V0,V1,add(V0,add(additive_identity,V1))) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi1,hi3,hi3]) ).
cnf(f5,axiom,
sum(X,additive_inverse(X),additive_identity),
file('/export/starexec/sandbox/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(t33,plain,
add(X1,add(additive_identity,additive_inverse(X1))) = additive_identity,
inference(hyper_resolution,[status(thm)],[hi15,hi5,h21]) ).
cnf(h27,plain,
sum(add(V0,additive_identity),additive_identity,V0) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi3,hi1,hi1]) ).
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(h24,plain,
sum(V0,additive_identity,add(additive_identity,V0)) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi0,hi1,hi3]) ).
cnf(f18,axiom,
( X = W
| ~ sum(W,Y,Z)
| ~ sum(X,Y,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cancellation2) ).
fof(f18_nnf,plain,
! [X,Y,Z,W] :
( X = W
| ~ sum(W,Y,Z)
| ~ sum(X,Y,Z) ),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
! [X,Y,Z,W] :
( X = W
| ~ sum(W,Y,Z)
| ~ sum(X,Y,Z) ),
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c18,plain,
( X0 = X3
| ~ sum(X3,X1,X2)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(hi18,axiom,
ifeq(sum(X0,X1,X2),true,ifeq(sum(X3,X1,X2),true,X0,X3),X3) = X3,
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(t22,plain,
add(add(additive_identity,X1),additive_identity) = X1,
inference(hyper_resolution,[status(thm)],[hi18,h24,h27]) ).
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(t2920,plain,
add(additive_identity,X1) = X1,
inference(step,[status(thm)],[t22,t257]) ).
cnf(t258,plain,
add(additive_identity,X1) = X1,
inference(orient,[status(thm)],[t2920]) ).
cnf(t2921,plain,
add(X1,additive_inverse(X1)) = additive_identity,
inference(step,[status(thm)],[t33,t258]) ).
cnf(t315,plain,
add(X1,additive_inverse(X1)) = additive_identity,
inference(orient,[status(thm)],[t2921]) ).
cnf(t318,plain,
add(X1,add(additive_inverse(X1),X2)) = add(additive_identity,X2),
inference(cp,[status(thm)],[t290,t315]) ).
cnf(t2970,plain,
add(X1,add(additive_inverse(X1),X2)) = X2,
inference(step,[status(thm)],[t318,t258]) ).
cnf(t1426,plain,
add(X1,add(additive_inverse(X1),X2)) = X2,
inference(orient,[status(thm)],[t2970]) ).
cnf(t79,plain,
add(X1,add(X2,additive_inverse(add(X1,X2)))) = additive_identity,
inference(hyper_resolution,[status(thm)],[hi15,hi5,h18]) ).
cnf(t299,plain,
add(X1,add(X2,additive_inverse(add(X1,X2)))) = additive_identity,
inference(orient,[status(thm)],[t79]) ).
cnf(t1428,plain,
add(X1,additive_inverse(add(additive_inverse(X2),X1))) = add(X2,additive_identity),
inference(cp,[status(thm)],[t1426,t299]) ).
cnf(t2979,plain,
add(X1,additive_inverse(add(additive_inverse(X2),X1))) = X2,
inference(step,[status(thm)],[t1428,t257]) ).
cnf(t1628,plain,
add(X1,additive_inverse(add(additive_inverse(X2),X1))) = X2,
inference(orient,[status(thm)],[t2979]) ).
cnf(f4,axiom,
sum(additive_inverse(X),X,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_inverse) ).
fof(f4_nnf,plain,
! [X] : sum(additive_inverse(X),X,additive_identity),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [X] : sum(additive_inverse(X),X,additive_identity),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
sum(additive_inverse(X0),X0,additive_identity),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(hi4,axiom,
sum(additive_inverse(X0),X0,additive_identity) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t4,plain,
additive_inverse(additive_inverse(X1)) = X1,
inference(hyper_resolution,[status(thm)],[hi18,hi4,hi5]) ).
cnf(t259,plain,
additive_inverse(additive_inverse(X1)) = X1,
inference(orient,[status(thm)],[t4]) ).
cnf(t1633,plain,
additive_inverse(X1) = add(X2,additive_inverse(add(X1,X2))),
inference(cp,[status(thm)],[t1628,t259]) ).
cnf(t1650,plain,
add(X1,additive_inverse(add(X2,X1))) = additive_inverse(X2),
inference(orient,[status(thm)],[t1633]) ).
cnf(f8,axiom,
( sum(Y,X,Z)
| ~ sum(X,Y,Z) ),
file('/export/starexec/sandbox/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(t19,plain,
add(X1,X2) = add(X2,X1),
inference(hyper_resolution,[status(thm)],[hi15,hi3,h17]) ).
cnf(t275,plain,
add(X1,X2) = add(X2,X1),
inference(orient,[status(thm)],[t19]) ).
cnf(t1657,plain,
additive_inverse(X1) = add(X2,additive_inverse(add(X2,X1))),
inference(cp,[status(thm)],[t1650,t275]) ).
cnf(t1717,plain,
add(X1,additive_inverse(add(X1,X2))) = additive_inverse(X2),
inference(orient,[status(thm)],[t1657]) ).
cnf(f6,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(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(h31,plain,
sum(V0,V1,add(add(V0,V1),additive_identity)) = true,
inference(hyper_resolution,[status(thm)],[hi6,hi3,hi1,hi3]) ).
cnf(f11,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(f11_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)],[f11]) ).
fof(f11_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)],[f11_nnf]) ).
cnf(c11,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)],[f11_sk]) ).
cnf(hi11,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)],[c11]) ).
cnf(f2,axiom,
product(X,Y,multiply(X,Y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_of_multiplication) ).
fof(f2_nnf,plain,
! [X,Y] : product(X,Y,multiply(X,Y)),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X,Y] : product(X,Y,multiply(X,Y)),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
product(X0,X1,multiply(X0,X1)),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi2,axiom,
product(X0,X1,multiply(X0,X1)) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(h16,plain,
sum(multiply(V0,V1),multiply(V0,V2),multiply(V0,add(V1,V2))) = true,
inference(hyper_resolution,[status(thm)],[hi11,hi2,hi2,hi3,hi2]) ).
cnf(t218,plain,
add(add(multiply(X1,X2),multiply(X1,X3)),additive_identity) = multiply(X1,add(X2,X3)),
inference(hyper_resolution,[status(thm)],[hi15,h16,h31]) ).
cnf(t2925,plain,
add(multiply(X1,X2),add(multiply(X1,X3),additive_identity)) = multiply(X1,add(X2,X3)),
inference(step,[status(thm)],[t218,t290]) ).
cnf(t107,plain,
add(X1,add(X2,X3)) = add(X3,add(X1,X2)),
inference(hyper_resolution,[status(thm)],[hi15,h17,h18]) ).
cnf(t276,plain,
add(X1,add(X2,X3)) = add(X3,add(X1,X2)),
inference(orient,[status(thm)],[t107]) ).
cnf(t2926,plain,
add(additive_identity,add(multiply(X1,X2),multiply(X1,X3))) = multiply(X1,add(X2,X3)),
inference(step,[status(thm)],[t2925,t276]) ).
cnf(t2927,plain,
add(multiply(X1,X2),multiply(X1,X3)) = multiply(X1,add(X2,X3)),
inference(step,[status(thm)],[t2926,t258]) ).
cnf(t328,plain,
add(multiply(X1,X2),multiply(X1,X3)) = multiply(X1,add(X2,X3)),
inference(orient,[status(thm)],[t2927]) ).
cnf(f14,axiom,
( product(V3,X,V4)
| ~ sum(V1,V2,V4)
| ~ sum(Y,Z,V3)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity4) ).
fof(f14_nnf,plain,
! [Y,X,V1,Z,V2,V3,V4] :
( product(V3,X,V4)
| ~ sum(V1,V2,V4)
| ~ sum(Y,Z,V3)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) ),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [Y,X,V1,Z,V2,V3,V4] :
( product(V3,X,V4)
| ~ sum(V1,V2,V4)
| ~ sum(Y,Z,V3)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) ),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c14,plain,
( product(X5,X1,X6)
| ~ sum(X2,X4,X6)
| ~ sum(X0,X3,X5)
| ~ product(X3,X1,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(hi14,axiom,
ifeq(product(X0,X1,X2),true,ifeq(product(X3,X1,X4),true,ifeq(sum(X0,X3,X5),true,ifeq(sum(X2,X4,X6),true,product(X5,X1,X6),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(h11,plain,
product(V0,V1,add(multiply(additive_identity,V1),multiply(V0,V1))) = true,
inference(hyper_resolution,[status(thm)],[hi14,hi2,hi2,hi0,hi3]) ).
cnf(f16,axiom,
( U = V
| ~ product(X,Y,V)
| ~ product(X,Y,U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplication_is_well_defined) ).
fof(f16_nnf,plain,
! [X,Y,U,V] :
( U = V
| ~ product(X,Y,V)
| ~ product(X,Y,U) ),
inference(nnf_transformation,[status(thm)],[f16]) ).
fof(f16_sk,plain,
! [X,Y,U,V] :
( U = V
| ~ product(X,Y,V)
| ~ product(X,Y,U) ),
inference(skolemisation,[status(esa)],[f16_nnf]) ).
cnf(c16,plain,
( X2 = X3
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(hi16,axiom,
ifeq(product(X0,X1,X2),true,ifeq(product(X0,X1,X3),true,X2,X3),X3) = X3,
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(f20,hypothesis,
product(additive_inverse(a),additive_inverse(b),d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_inverse_times_b_inverse) ).
fof(f20_nnf,plain,
product(additive_inverse(a),additive_inverse(b),d),
inference(nnf_transformation,[status(thm)],[f20]) ).
cnf(c20,plain,
product(additive_inverse(a),additive_inverse(b),d),
inference(cnf_transformation,[status(esa)],[f20_nnf]) ).
cnf(hi20,axiom,
product(additive_inverse(a),additive_inverse(b),d) = true,
inference(equality_encoding,[status(esa)],[c20]) ).
cnf(t122,plain,
add(multiply(additive_identity,additive_inverse(b)),multiply(additive_inverse(a),additive_inverse(b))) = d,
inference(hyper_resolution,[status(thm)],[hi16,hi20,h11]) ).
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/sandbox/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(h12,plain,
sum(multiply(V0,V1),multiply(V2,V1),multiply(add(V0,V2),V1)) = true,
inference(hyper_resolution,[status(thm)],[hi13,hi2,hi2,hi3,hi2]) ).
cnf(t219,plain,
add(add(multiply(X1,X2),multiply(X3,X2)),additive_identity) = multiply(add(X1,X3),X2),
inference(hyper_resolution,[status(thm)],[hi15,h12,h31]) ).
cnf(t2922,plain,
add(multiply(X1,X2),add(multiply(X3,X2),additive_identity)) = multiply(add(X1,X3),X2),
inference(step,[status(thm)],[t219,t290]) ).
cnf(t2923,plain,
add(additive_identity,add(multiply(X1,X2),multiply(X3,X2))) = multiply(add(X1,X3),X2),
inference(step,[status(thm)],[t2922,t276]) ).
cnf(t2924,plain,
add(multiply(X1,X2),multiply(X3,X2)) = multiply(add(X1,X3),X2),
inference(step,[status(thm)],[t2923,t258]) ).
cnf(t322,plain,
add(multiply(X1,X2),multiply(X3,X2)) = multiply(add(X1,X3),X2),
inference(orient,[status(thm)],[t2924]) ).
cnf(t2933,plain,
multiply(add(additive_identity,additive_inverse(a)),additive_inverse(b)) = d,
inference(step,[status(thm)],[t122,t322]) ).
cnf(t2934,plain,
multiply(additive_inverse(a),additive_inverse(b)) = d,
inference(step,[status(thm)],[t2933,t258]) ).
cnf(t356,plain,
multiply(additive_inverse(a),additive_inverse(b)) = d,
inference(orient,[status(thm)],[t2934]) ).
cnf(t358,plain,
multiply(additive_inverse(a),add(additive_inverse(b),X1)) = add(d,multiply(additive_inverse(a),X1)),
inference(cp,[status(thm)],[t328,t356]) ).
cnf(t2826,plain,
multiply(additive_inverse(a),add(additive_inverse(b),X1)) = add(d,multiply(additive_inverse(a),X1)),
inference(orient,[status(thm)],[t358]) ).
cnf(t2830,plain,
add(d,multiply(additive_inverse(a),additive_inverse(additive_inverse(b)))) = multiply(additive_inverse(a),additive_identity),
inference(cp,[status(thm)],[t2826,t315]) ).
cnf(t3023,plain,
add(d,multiply(additive_inverse(a),b)) = multiply(additive_inverse(a),additive_identity),
inference(step,[status(thm)],[t2830,t259]) ).
cnf(f17,axiom,
( Y = W
| ~ sum(X,W,Z)
| ~ sum(X,Y,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cancellation1) ).
fof(f17_nnf,plain,
! [X,Y,Z,W] :
( Y = W
| ~ sum(X,W,Z)
| ~ sum(X,Y,Z) ),
inference(nnf_transformation,[status(thm)],[f17]) ).
fof(f17_sk,plain,
! [X,Y,Z,W] :
( Y = W
| ~ sum(X,W,Z)
| ~ sum(X,Y,Z) ),
inference(skolemisation,[status(esa)],[f17_nnf]) ).
cnf(c17,plain,
( X1 = X3
| ~ sum(X0,X3,X2)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
cnf(t244,plain,
ifeq(sum(X1,X2,X3),true,ifeq(sum(X1,X4,X3),true,X2,X4),X4) = X4,
inference(equality_encoding,[status(esa)],[c17]) ).
cnf(t263,plain,
ifeq(sum(X1,X2,X3),true,ifeq(sum(X1,X4,X3),true,X2,X4),X4) = X4,
inference(orient,[status(thm)],[t244]) ).
cnf(t31,plain,
sum(X1,additive_inverse(X1),additive_identity) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t428,plain,
sum(X1,additive_inverse(X1),additive_identity) = true,
inference(orient,[status(thm)],[t31]) ).
cnf(t434,plain,
X1 = ifeq(true,true,ifeq(sum(X2,X1,additive_identity),true,additive_inverse(X2),X1),X1),
inference(cp,[status(thm)],[t263,t428]) ).
cnf(t29,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t260,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t29]) ).
cnf(t3011,plain,
X1 = ifeq(sum(X2,X1,additive_identity),true,additive_inverse(X2),X1),
inference(step,[status(thm)],[t434,t260]) ).
cnf(t2499,plain,
ifeq(sum(X1,X2,additive_identity),true,additive_inverse(X1),X2) = X2,
inference(orient,[status(thm)],[t3011]) ).
cnf(h9,plain,
product(add(V0,V1),V2,add(multiply(V0,V2),multiply(V1,V2))) = true,
inference(hyper_resolution,[status(thm)],[hi14,hi2,hi2,hi3,hi3]) ).
cnf(f19,hypothesis,
product(a,b,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_b) ).
fof(f19_nnf,plain,
product(a,b,c),
inference(nnf_transformation,[status(thm)],[f19]) ).
cnf(c19,plain,
product(a,b,c),
inference(cnf_transformation,[status(esa)],[f19_nnf]) ).
cnf(hi19,axiom,
product(a,b,c) = true,
inference(equality_encoding,[status(esa)],[c19]) ).
cnf(t208,plain,
sum(c,multiply(X1,b),add(multiply(a,b),multiply(X1,b))) = true,
inference(hyper_resolution,[status(thm)],[hi13,hi19,hi2,hi3,h9]) ).
cnf(t2945,plain,
sum(c,multiply(X1,b),multiply(add(a,X1),b)) = true,
inference(step,[status(thm)],[t208,t322]) ).
cnf(t570,plain,
sum(c,multiply(X1,b),multiply(add(a,X1),b)) = true,
inference(orient,[status(thm)],[t2945]) ).
cnf(t575,plain,
true = sum(c,multiply(additive_inverse(a),b),multiply(additive_identity,b)),
inference(cp,[status(thm)],[t570,t315]) ).
cnf(h1,plain,
sum(multiply(V0,V1),multiply(additive_identity,V1),multiply(V0,V1)) = true,
inference(hyper_resolution,[status(thm)],[hi13,hi2,hi2,hi1,hi2]) ).
cnf(t8,plain,
multiply(additive_identity,X1) = additive_identity,
inference(hyper_resolution,[status(thm)],[hi18,hi0,h1]) ).
cnf(t403,plain,
multiply(additive_identity,X1) = additive_identity,
inference(orient,[status(thm)],[t8]) ).
cnf(t2977,plain,
true = sum(c,multiply(additive_inverse(a),b),additive_identity),
inference(step,[status(thm)],[t575,t403]) ).
cnf(t1582,plain,
sum(c,multiply(additive_inverse(a),b),additive_identity) = true,
inference(orient,[status(thm)],[t2977]) ).
cnf(t2503,plain,
multiply(additive_inverse(a),b) = ifeq(true,true,additive_inverse(c),multiply(additive_inverse(a),b)),
inference(cp,[status(thm)],[t2499,t1582]) ).
cnf(t3013,plain,
multiply(additive_inverse(a),b) = additive_inverse(c),
inference(step,[status(thm)],[t2503,t260]) ).
cnf(t2517,plain,
multiply(additive_inverse(a),b) = additive_inverse(c),
inference(orient,[status(thm)],[t3013]) ).
cnf(t3024,plain,
add(d,additive_inverse(c)) = multiply(additive_inverse(a),additive_identity),
inference(step,[status(thm)],[t3023,t2517]) ).
cnf(h3,plain,
sum(multiply(V0,V1),multiply(V0,additive_identity),multiply(V0,V1)) = true,
inference(hyper_resolution,[status(thm)],[hi11,hi2,hi2,hi1,hi2]) ).
cnf(t6,plain,
multiply(X1,additive_identity) = additive_identity,
inference(hyper_resolution,[status(thm)],[hi18,hi0,h3]) ).
cnf(t390,plain,
multiply(X1,additive_identity) = additive_identity,
inference(orient,[status(thm)],[t6]) ).
cnf(t3025,plain,
add(d,additive_inverse(c)) = additive_identity,
inference(step,[status(thm)],[t3024,t390]) ).
cnf(t2845,plain,
add(d,additive_inverse(c)) = additive_identity,
inference(orient,[status(thm)],[t3025]) ).
cnf(t2863,plain,
additive_inverse(additive_inverse(c)) = add(d,additive_inverse(additive_identity)),
inference(cp,[status(thm)],[t1717,t2845]) ).
cnf(t3026,plain,
c = add(d,additive_inverse(additive_identity)),
inference(step,[status(thm)],[t2863,t259]) ).
cnf(t10,plain,
add(additive_identity,additive_identity) = additive_inverse(additive_identity),
inference(hyper_resolution,[status(thm)],[hi18,hi4,h27]) ).
cnf(t2935,plain,
additive_identity = additive_inverse(additive_identity),
inference(step,[status(thm)],[t10,t258]) ).
cnf(t362,plain,
additive_inverse(additive_identity) = additive_identity,
inference(orient,[status(thm)],[t2935]) ).
cnf(t3027,plain,
c = add(d,additive_identity),
inference(step,[status(thm)],[t3026,t362]) ).
cnf(t3028,plain,
c = d,
inference(step,[status(thm)],[t3027,t257]) ).
cnf(t2872,plain,
c = d,
inference(orient,[status(thm)],[t3028]) ).
cnf(f21,negated_conjecture,
c != d,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_c_equals_d) ).
fof(f21_nnf,plain,
c != d,
inference(nnf_transformation,[status(thm)],[f21]) ).
fof(f21_sk,plain,
c != d,
inference(skolemisation,[status(esa)],[f21_nnf]) ).
cnf(c21,plain,
c != d,
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(goal_0,negated_conjecture,
d != c,
inference(equality_encoding,[status(esa)],[c21]) ).
cnf(g0_0,plain,
d != d,
inference(rw,[status(thm)],[goal_0,t2872]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG004-2 : 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 : n004.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 07:41:22 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 27.85/3.94 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 27.85/3.94 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------