%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : RNG004-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : 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 30.23s 19.58s
% Output : Proof 30.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 42
% Number of leaves : 17
% Syntax : Number of formulae : 203 ( 171 unt; 0 def)
% Number of atoms : 295 ( 148 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 196 ( 104 ~; 92 |; 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 : 397 ( 16 sgn 104 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(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(h17,plain,
sum(V0,V1,add(V1,V0)) = true,
inference(hyper_resolution,[status(thm)],[hi8,hi3]) ).
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(t11,plain,
add(X1,X2) = add(X2,X1),
inference(hyper_resolution,[status(thm)],[hi15,hi3,h17]) ).
cnf(t264,plain,
add(X1,X2) = add(X2,X1),
inference(orient,[status(thm)],[t11]) ).
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(t97,plain,
add(add(X1,X2),X3) = add(X1,add(X2,X3)),
inference(hyper_resolution,[status(thm)],[hi15,hi3,h18]) ).
cnf(t279,plain,
add(add(X1,X2),X3) = add(X1,add(X2,X3)),
inference(orient,[status(thm)],[t97]) ).
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(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/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(t24,plain,
add(X1,add(additive_identity,additive_inverse(X1))) = additive_identity,
inference(hyper_resolution,[status(thm)],[hi15,hi5,h21]) ).
cnf(f0,axiom,
sum(additive_identity,X,X),
file('/export/starexec/sandbox2/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(h28,plain,
sum(add(additive_identity,V0),additive_identity,V0) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi3,hi1,hi0]) ).
cnf(h22,plain,
sum(V0,additive_identity,add(V0,additive_identity)) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi1,hi1,hi3]) ).
cnf(t14,plain,
add(add(additive_identity,X1),additive_identity) = X1,
inference(hyper_resolution,[status(thm)],[hi15,h22,h28]) ).
cnf(t1,plain,
add(X1,additive_identity) = X1,
inference(hyper_resolution,[status(thm)],[hi15,hi1,hi3]) ).
cnf(t257,plain,
add(X1,additive_identity) = X1,
inference(orient,[status(thm)],[t1]) ).
cnf(t2998,plain,
add(additive_identity,X1) = X1,
inference(step,[status(thm)],[t14,t257]) ).
cnf(t258,plain,
add(additive_identity,X1) = X1,
inference(orient,[status(thm)],[t2998]) ).
cnf(t2999,plain,
add(X1,additive_inverse(X1)) = additive_identity,
inference(step,[status(thm)],[t24,t258]) ).
cnf(t304,plain,
add(X1,additive_inverse(X1)) = additive_identity,
inference(orient,[status(thm)],[t2999]) ).
cnf(t306,plain,
add(X1,add(additive_inverse(X1),X2)) = add(additive_identity,X2),
inference(cp,[status(thm)],[t279,t304]) ).
cnf(t3055,plain,
add(X1,add(additive_inverse(X1),X2)) = X2,
inference(step,[status(thm)],[t306,t258]) ).
cnf(t1462,plain,
add(X1,add(additive_inverse(X1),X2)) = X2,
inference(orient,[status(thm)],[t3055]) ).
cnf(t1464,plain,
additive_inverse(additive_inverse(X1)) = add(X1,additive_identity),
inference(cp,[status(thm)],[t1462,t304]) ).
cnf(t3056,plain,
additive_inverse(additive_inverse(X1)) = X1,
inference(step,[status(thm)],[t1464,t257]) ).
cnf(t1479,plain,
additive_inverse(additive_inverse(X1)) = X1,
inference(orient,[status(thm)],[t3056]) ).
cnf(t70,plain,
add(X1,add(X2,additive_inverse(add(X1,X2)))) = additive_identity,
inference(hyper_resolution,[status(thm)],[hi15,hi5,h18]) ).
cnf(t288,plain,
add(X1,add(X2,additive_inverse(add(X1,X2)))) = additive_identity,
inference(orient,[status(thm)],[t70]) ).
cnf(t1465,plain,
add(X1,additive_inverse(add(additive_inverse(X2),X1))) = add(X2,additive_identity),
inference(cp,[status(thm)],[t1462,t288]) ).
cnf(t3061,plain,
add(X1,additive_inverse(add(additive_inverse(X2),X1))) = X2,
inference(step,[status(thm)],[t1465,t257]) ).
cnf(t1568,plain,
add(X1,additive_inverse(add(additive_inverse(X2),X1))) = X2,
inference(orient,[status(thm)],[t3061]) ).
cnf(t1573,plain,
additive_inverse(X1) = add(X2,additive_inverse(add(X1,X2))),
inference(cp,[status(thm)],[t1568,t1479]) ).
cnf(t1590,plain,
add(X1,additive_inverse(add(X2,X1))) = additive_inverse(X2),
inference(orient,[status(thm)],[t1573]) ).
cnf(t1597,plain,
additive_inverse(X1) = add(X2,additive_inverse(add(X2,X1))),
inference(cp,[status(thm)],[t1590,t264]) ).
cnf(t1658,plain,
add(X1,additive_inverse(add(X1,X2))) = additive_inverse(X2),
inference(orient,[status(thm)],[t1597]) ).
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(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/sandbox2/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/sandbox2/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(t217,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(t3003,plain,
add(multiply(X1,X2),add(multiply(X1,X3),additive_identity)) = multiply(X1,add(X2,X3)),
inference(step,[status(thm)],[t217,t279]) ).
cnf(t96,plain,
add(X1,add(X2,X3)) = add(X3,add(X1,X2)),
inference(hyper_resolution,[status(thm)],[hi15,h17,h18]) ).
cnf(t265,plain,
add(X1,add(X2,X3)) = add(X3,add(X1,X2)),
inference(orient,[status(thm)],[t96]) ).
cnf(t3004,plain,
add(additive_identity,add(multiply(X1,X2),multiply(X1,X3))) = multiply(X1,add(X2,X3)),
inference(step,[status(thm)],[t3003,t265]) ).
cnf(t3005,plain,
add(multiply(X1,X2),multiply(X1,X3)) = multiply(X1,add(X2,X3)),
inference(step,[status(thm)],[t3004,t258]) ).
cnf(t316,plain,
add(multiply(X1,X2),multiply(X1,X3)) = multiply(X1,add(X2,X3)),
inference(orient,[status(thm)],[t3005]) ).
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/sandbox2/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/sandbox2/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(f18,hypothesis,
product(additive_inverse(a),additive_inverse(b),d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_inverse_times_b_inverse) ).
fof(f18_nnf,plain,
product(additive_inverse(a),additive_inverse(b),d),
inference(nnf_transformation,[status(thm)],[f18]) ).
cnf(c18,plain,
product(additive_inverse(a),additive_inverse(b),d),
inference(cnf_transformation,[status(esa)],[f18_nnf]) ).
cnf(hi18,axiom,
product(additive_inverse(a),additive_inverse(b),d) = true,
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(t116,plain,
add(multiply(additive_identity,additive_inverse(b)),multiply(additive_inverse(a),additive_inverse(b))) = d,
inference(hyper_resolution,[status(thm)],[hi16,hi18,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/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(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(t218,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(t3000,plain,
add(multiply(X1,X2),add(multiply(X3,X2),additive_identity)) = multiply(add(X1,X3),X2),
inference(step,[status(thm)],[t218,t279]) ).
cnf(t3001,plain,
add(additive_identity,add(multiply(X1,X2),multiply(X3,X2))) = multiply(add(X1,X3),X2),
inference(step,[status(thm)],[t3000,t265]) ).
cnf(t3002,plain,
add(multiply(X1,X2),multiply(X3,X2)) = multiply(add(X1,X3),X2),
inference(step,[status(thm)],[t3001,t258]) ).
cnf(t310,plain,
add(multiply(X1,X2),multiply(X3,X2)) = multiply(add(X1,X3),X2),
inference(orient,[status(thm)],[t3002]) ).
cnf(t3014,plain,
multiply(add(additive_identity,additive_inverse(a)),additive_inverse(b)) = d,
inference(step,[status(thm)],[t116,t310]) ).
cnf(t3015,plain,
multiply(additive_inverse(a),additive_inverse(b)) = d,
inference(step,[status(thm)],[t3014,t258]) ).
cnf(t345,plain,
multiply(additive_inverse(a),additive_inverse(b)) = d,
inference(orient,[status(thm)],[t3015]) ).
cnf(t347,plain,
multiply(additive_inverse(a),add(additive_inverse(b),X1)) = add(d,multiply(additive_inverse(a),X1)),
inference(cp,[status(thm)],[t316,t345]) ).
cnf(t2717,plain,
multiply(additive_inverse(a),add(additive_inverse(b),X1)) = add(d,multiply(additive_inverse(a),X1)),
inference(orient,[status(thm)],[t347]) ).
cnf(t2724,plain,
add(d,multiply(additive_inverse(a),additive_identity)) = multiply(additive_inverse(a),additive_inverse(b)),
inference(cp,[status(thm)],[t2717,t257]) ).
cnf(t3088,plain,
add(d,multiply(additive_inverse(a),additive_identity)) = d,
inference(step,[status(thm)],[t2724,t345]) ).
cnf(t2737,plain,
add(d,multiply(additive_inverse(a),additive_identity)) = d,
inference(orient,[status(thm)],[t3088]) ).
cnf(t2751,plain,
additive_inverse(multiply(additive_inverse(a),additive_identity)) = add(d,additive_inverse(d)),
inference(cp,[status(thm)],[t1658,t2737]) ).
cnf(t3089,plain,
additive_inverse(multiply(additive_inverse(a),additive_identity)) = additive_identity,
inference(step,[status(thm)],[t2751,t304]) ).
cnf(t2757,plain,
additive_inverse(multiply(additive_inverse(a),additive_identity)) = additive_identity,
inference(orient,[status(thm)],[t3089]) ).
cnf(t2764,plain,
multiply(additive_inverse(a),additive_identity) = additive_inverse(additive_identity),
inference(cp,[status(thm)],[t1479,t2757]) ).
cnf(f4,axiom,
sum(additive_inverse(X),X,additive_identity),
file('/export/starexec/sandbox2/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(h60,plain,
sum(additive_identity,additive_identity,additive_inverse(additive_identity)) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi4,hi1,hi1]) ).
cnf(t29,plain,
add(add(additive_identity,additive_identity),additive_identity) = additive_inverse(additive_identity),
inference(hyper_resolution,[status(thm)],[hi15,h60,h31]) ).
cnf(t3006,plain,
add(additive_identity,add(additive_identity,additive_identity)) = additive_inverse(additive_identity),
inference(step,[status(thm)],[t29,t279]) ).
cnf(t3007,plain,
add(additive_identity,additive_identity) = additive_inverse(additive_identity),
inference(step,[status(thm)],[t3006,t258]) ).
cnf(t3008,plain,
additive_identity = additive_inverse(additive_identity),
inference(step,[status(thm)],[t3007,t258]) ).
cnf(t323,plain,
additive_inverse(additive_identity) = additive_identity,
inference(orient,[status(thm)],[t3008]) ).
cnf(t3090,plain,
multiply(additive_inverse(a),additive_identity) = additive_identity,
inference(step,[status(thm)],[t2764,t323]) ).
cnf(t2792,plain,
multiply(additive_inverse(a),additive_identity) = additive_identity,
inference(orient,[status(thm)],[t3090]) ).
cnf(f17,hypothesis,
product(a,b,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_b) ).
fof(f17_nnf,plain,
product(a,b,c),
inference(nnf_transformation,[status(thm)],[f17]) ).
cnf(c17,plain,
product(a,b,c),
inference(cnf_transformation,[status(esa)],[f17_nnf]) ).
cnf(hi17,axiom,
product(a,b,c) = true,
inference(equality_encoding,[status(esa)],[c17]) ).
cnf(t59,plain,
add(multiply(additive_identity,b),multiply(a,b)) = c,
inference(hyper_resolution,[status(thm)],[hi16,hi17,h11]) ).
cnf(t3012,plain,
multiply(add(additive_identity,a),b) = c,
inference(step,[status(thm)],[t59,t310]) ).
cnf(t3013,plain,
multiply(a,b) = c,
inference(step,[status(thm)],[t3012,t258]) ).
cnf(t339,plain,
multiply(a,b) = c,
inference(orient,[status(thm)],[t3013]) ).
cnf(t343,plain,
multiply(add(a,X1),b) = add(c,multiply(X1,b)),
inference(cp,[status(thm)],[t310,t339]) ).
cnf(t1555,plain,
add(c,multiply(X1,b)) = multiply(add(a,X1),b),
inference(orient,[status(thm)],[t343]) ).
cnf(t2721,plain,
add(d,multiply(additive_inverse(a),additive_inverse(additive_inverse(b)))) = multiply(additive_inverse(a),additive_identity),
inference(cp,[status(thm)],[t2717,t304]) ).
cnf(t3099,plain,
add(d,multiply(additive_inverse(a),b)) = multiply(additive_inverse(a),additive_identity),
inference(step,[status(thm)],[t2721,t1479]) ).
cnf(t3100,plain,
add(d,multiply(additive_inverse(a),b)) = additive_identity,
inference(step,[status(thm)],[t3099,t2792]) ).
cnf(t2934,plain,
add(d,multiply(additive_inverse(a),b)) = additive_identity,
inference(orient,[status(thm)],[t3100]) ).
cnf(t2951,plain,
additive_inverse(d) = add(multiply(additive_inverse(a),b),additive_inverse(additive_identity)),
inference(cp,[status(thm)],[t1590,t2934]) ).
cnf(t3101,plain,
additive_inverse(d) = add(additive_inverse(additive_identity),multiply(additive_inverse(a),b)),
inference(step,[status(thm)],[t2951,t264]) ).
cnf(t3102,plain,
additive_inverse(d) = add(additive_identity,multiply(additive_inverse(a),b)),
inference(step,[status(thm)],[t3101,t323]) ).
cnf(t3103,plain,
additive_inverse(d) = multiply(additive_inverse(a),b),
inference(step,[status(thm)],[t3102,t258]) ).
cnf(t2956,plain,
multiply(additive_inverse(a),b) = additive_inverse(d),
inference(orient,[status(thm)],[t3103]) ).
cnf(t2957,plain,
multiply(add(a,additive_inverse(a)),b) = add(c,additive_inverse(d)),
inference(cp,[status(thm)],[t1555,t2956]) ).
cnf(t3106,plain,
multiply(additive_identity,b) = add(c,additive_inverse(d)),
inference(step,[status(thm)],[t2957,t304]) ).
cnf(h2,plain,
sum(multiply(additive_identity,V0),multiply(V1,V0),multiply(V1,V0)) = true,
inference(hyper_resolution,[status(thm)],[hi13,hi2,hi2,hi0,hi2]) ).
cnf(t65,plain,
multiply(additive_identity,add(X1,X1)) = multiply(additive_identity,X1),
inference(hyper_resolution,[status(thm)],[hi15,h2,h16]) ).
cnf(t378,plain,
multiply(additive_identity,add(X1,X1)) = multiply(additive_identity,X1),
inference(orient,[status(thm)],[t65]) ).
cnf(t385,plain,
multiply(additive_identity,add(add(X1,X1),X2)) = add(multiply(additive_identity,X1),multiply(additive_identity,X2)),
inference(cp,[status(thm)],[t316,t378]) ).
cnf(t3068,plain,
multiply(additive_identity,add(X1,add(X1,X2))) = add(multiply(additive_identity,X1),multiply(additive_identity,X2)),
inference(step,[status(thm)],[t385,t279]) ).
cnf(t3069,plain,
multiply(additive_identity,add(X1,add(X1,X2))) = multiply(additive_identity,add(X1,X2)),
inference(step,[status(thm)],[t3068,t316]) ).
cnf(t2141,plain,
multiply(additive_identity,add(X1,add(X1,X2))) = multiply(additive_identity,add(X1,X2)),
inference(orient,[status(thm)],[t3069]) ).
cnf(t1466,plain,
X1 = add(X2,add(X1,additive_inverse(X2))),
inference(cp,[status(thm)],[t1462,t264]) ).
cnf(t1508,plain,
add(X1,add(X2,additive_inverse(X1))) = X2,
inference(orient,[status(thm)],[t1466]) ).
cnf(t2142,plain,
multiply(additive_identity,add(X1,additive_inverse(X1))) = multiply(additive_identity,X1),
inference(cp,[status(thm)],[t2141,t1508]) ).
cnf(t3070,plain,
multiply(additive_identity,additive_identity) = multiply(additive_identity,X1),
inference(step,[status(thm)],[t2142,t304]) ).
cnf(t2166,plain,
multiply(additive_identity,additive_identity) = multiply(additive_identity,X1),
inference(orient,[status(thm)],[t3070]) ).
cnf(t2174,plain,
multiply(additive_identity,X1) = multiply(additive_identity,X2),
inference(cp,[status(thm)],[t2166,t2166]) ).
cnf(t2192,plain,
multiply(additive_identity,X1) = multiply(additive_identity,X2),
inference(orient,[status(thm)],[t2174]) ).
cnf(t2195,plain,
multiply(add(a,additive_identity),b) = add(c,multiply(additive_identity,X1)),
inference(cp,[status(thm)],[t1555,t2192]) ).
cnf(t3071,plain,
multiply(a,b) = add(c,multiply(additive_identity,X1)),
inference(step,[status(thm)],[t2195,t257]) ).
cnf(t3072,plain,
c = add(c,multiply(additive_identity,X1)),
inference(step,[status(thm)],[t3071,t339]) ).
cnf(t2211,plain,
add(c,multiply(additive_identity,X1)) = c,
inference(orient,[status(thm)],[t3072]) ).
cnf(t2223,plain,
additive_inverse(multiply(additive_identity,X1)) = add(c,additive_inverse(c)),
inference(cp,[status(thm)],[t1658,t2211]) ).
cnf(t3073,plain,
additive_inverse(multiply(additive_identity,X1)) = additive_identity,
inference(step,[status(thm)],[t2223,t304]) ).
cnf(t2229,plain,
additive_inverse(multiply(additive_identity,X1)) = additive_identity,
inference(orient,[status(thm)],[t3073]) ).
cnf(t2236,plain,
multiply(additive_identity,X1) = additive_inverse(additive_identity),
inference(cp,[status(thm)],[t1479,t2229]) ).
cnf(t3074,plain,
multiply(additive_identity,X1) = additive_identity,
inference(step,[status(thm)],[t2236,t323]) ).
cnf(t2252,plain,
multiply(additive_identity,X1) = additive_identity,
inference(orient,[status(thm)],[t3074]) ).
cnf(t3107,plain,
additive_identity = add(c,additive_inverse(d)),
inference(step,[status(thm)],[t3106,t2252]) ).
cnf(t2971,plain,
add(c,additive_inverse(d)) = additive_identity,
inference(orient,[status(thm)],[t3107]) ).
cnf(f19,negated_conjecture,
c != d,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_c_equals_d) ).
fof(f19_nnf,plain,
c != d,
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
c != d,
inference(skolemisation,[status(esa)],[f19_nnf]) ).
cnf(c19,plain,
c != d,
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(goal_0,negated_conjecture,
d != c,
inference(equality_encoding,[status(esa)],[c19]) ).
cnf(g0_0,plain,
d != add(d,multiply(additive_inverse(a),additive_identity)),
inference(rw,[status(thm)],[goal_0]) ).
cnf(g0_1,plain,
d != add(multiply(additive_inverse(a),additive_identity),d),
inference(rw,[status(thm)],[g0_0,t264]) ).
cnf(g0_2,plain,
d != add(additive_identity,d),
inference(rw,[status(thm)],[g0_1,t2792]) ).
cnf(g0_3,plain,
d != add(add(c,additive_inverse(d)),d),
inference(rw,[status(thm)],[g0_2,t2971]) ).
cnf(g0_4,plain,
d != add(add(additive_inverse(d),c),d),
inference(rw,[status(thm)],[g0_3,t264]) ).
cnf(g0_5,plain,
d != add(d,add(additive_inverse(d),c)),
inference(rw,[status(thm)],[g0_4,t264]) ).
cnf(g0_6,plain,
d != c,
inference(rw,[status(thm)],[g0_5,t1462]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : RNG004-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.14/15.62 % Computer : n004.cluster.edu
% 0.14/15.62 % Model : x86_64 x86_64
% 0.14/15.62 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/15.62 % Memory : 8046.5625MB
% 0.14/15.62 % OS : Linux 6.8.0-71-generic
% 0.14/15.63 % CPULimit : 300
% 0.14/15.63 % WCLimit : 300
% 0.14/15.63 % DateTime : Thu Sep 24 07:41:08 UTC 2026
% 0.14/15.63 % CPUTime :
% 0.14/15.63 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 30.23/19.58 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 30.23/19.58 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------