%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : RNG041-1 : 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 02:37:35 PM UTC 2026
% Result : Unsatisfiable 14.99s 2.41s
% Output : Proof 14.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 12
% Syntax : Number of formulae : 91 ( 79 unt; 0 def)
% Number of atoms : 115 ( 71 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 54 ( 30 ~; 24 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-4 aty)
% Number of variables : 133 ( 9 sgn 30 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f25,negated_conjecture,
b != additive_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_b_is_additive_identity) ).
fof(f25_nnf,plain,
b != additive_identity,
inference(nnf_transformation,[status(thm)],[f25]) ).
fof(f25_sk,plain,
b != additive_identity,
inference(skolemisation,[status(esa)],[f25_nnf]) ).
cnf(c25,plain,
b != additive_identity,
inference(cnf_transformation,[status(esa)],[f25_sk]) ).
cnf(t2,plain,
eq(b,additive_identity) = false,
inference(equality_encoding,[status(esa)],[c25]) ).
cnf(t313,plain,
eq(b,additive_identity) = false,
inference(orient,[status(thm)],[t2]) ).
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(t25,plain,
ifeq(product(X1,X2,X3),true,ifeq(product(X1,X2,X4),true,X3,X4),X4) = X4,
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(t36,plain,
ifeq(product(X1,X2,X3),true,ifeq(product(X1,X2,X4),true,X3,X4),X4) = X4,
inference(orient,[status(thm)],[t25]) ).
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(t19,plain,
product(X1,X2,multiply(X1,X2)) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t65,plain,
product(X1,X2,multiply(X1,X2)) = true,
inference(orient,[status(thm)],[t19]) ).
cnf(t67,plain,
multiply(X1,X2) = ifeq(product(X1,X2,X3),true,ifeq(true,true,X3,multiply(X1,X2)),multiply(X1,X2)),
inference(cp,[status(thm)],[t36,t65]) ).
cnf(t14,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t35,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t14]) ).
cnf(t830,plain,
multiply(X1,X2) = ifeq(product(X1,X2,X3),true,X3,multiply(X1,X2)),
inference(step,[status(thm)],[t67,t35]) ).
cnf(t522,plain,
ifeq(product(X1,X2,X3),true,X3,multiply(X1,X2)) = multiply(X1,X2),
inference(orient,[status(thm)],[t830]) ).
cnf(f10,axiom,
( product(U,Z,W)
| ~ product(X,V,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_multiplication2) ).
fof(f10_nnf,plain,
! [X,Y,U,Z,V,W] :
( product(U,Z,W)
| ~ product(X,V,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [X,Y,U,Z,V,W] :
( product(U,Z,W)
| ~ product(X,V,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) ),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
( product(X2,X3,X5)
| ~ product(X0,X4,X5)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(t27,plain,
ifeq(product(X1,X2,X3),true,ifeq(product(X2,X4,X5),true,ifeq(product(X1,X5,X6),true,product(X3,X4,X6),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(t49,plain,
ifeq(product(X1,X2,X3),true,ifeq(product(X2,X4,X5),true,ifeq(product(X1,X5,X6),true,product(X3,X4,X6),true),true),true) = true,
inference(orient,[status(thm)],[t27]) ).
cnf(f18,hypothesis,
product(A,additive_identity,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_identity2) ).
fof(f18_nnf,plain,
! [A] : product(A,additive_identity,additive_identity),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
! [A] : product(A,additive_identity,additive_identity),
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c18,plain,
product(X0,additive_identity,additive_identity),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(t7,plain,
product(X1,additive_identity,additive_identity) = true,
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(t88,plain,
product(X1,additive_identity,additive_identity) = true,
inference(orient,[status(thm)],[t7]) ).
cnf(t97,plain,
true = ifeq(product(X1,X2,X3),true,ifeq(product(X2,X4,additive_identity),true,ifeq(true,true,product(X3,X4,additive_identity),true),true),true),
inference(cp,[status(thm)],[t49,t88]) ).
cnf(t868,plain,
true = ifeq(product(X1,X2,X3),true,ifeq(product(X2,X4,additive_identity),true,product(X3,X4,additive_identity),true),true),
inference(step,[status(thm)],[t97,t35]) ).
cnf(t675,plain,
ifeq(product(X1,X2,X3),true,ifeq(product(X2,X4,additive_identity),true,product(X3,X4,additive_identity),true),true) = true,
inference(orient,[status(thm)],[t868]) ).
cnf(f22,hypothesis,
( A = additive_identity
| product(h(A),A,multiplicative_identity) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause42) ).
fof(f22_nnf,plain,
! [A] :
( A = additive_identity
| product(h(A),A,multiplicative_identity) ),
inference(nnf_transformation,[status(thm)],[f22]) ).
fof(f22_sk,plain,
! [A] :
( A = additive_identity
| product(h(A),A,multiplicative_identity) ),
inference(skolemisation,[status(esa)],[f22_nnf]) ).
cnf(c22,plain,
( X0 = additive_identity
| product(h(X0),X0,multiplicative_identity) ),
inference(cnf_transformation,[status(esa)],[f22_sk]) ).
cnf(t23,plain,
or(product(h(X1),X1,multiplicative_identity),eq(X1,additive_identity)) = true,
inference(equality_encoding,[status(esa)],[c22]) ).
cnf(t307,plain,
or(product(h(X1),X1,multiplicative_identity),eq(X1,additive_identity)) = true,
inference(orient,[status(thm)],[t23]) ).
cnf(f24,negated_conjecture,
a != additive_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_not_additive_identity) ).
fof(f24_nnf,plain,
a != additive_identity,
inference(nnf_transformation,[status(thm)],[f24]) ).
fof(f24_sk,plain,
a != additive_identity,
inference(skolemisation,[status(esa)],[f24_nnf]) ).
cnf(c24,plain,
a != additive_identity,
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
cnf(t1,plain,
eq(a,additive_identity) = false,
inference(equality_encoding,[status(esa)],[c24]) ).
cnf(t309,plain,
eq(a,additive_identity) = false,
inference(orient,[status(thm)],[t1]) ).
cnf(t311,plain,
true = or(product(h(a),a,multiplicative_identity),false),
inference(cp,[status(thm)],[t307,t309]) ).
cnf(t3,plain,
or(X1,false) = X1,
introduced(definition) ).
cnf(t41,plain,
or(X1,false) = X1,
inference(orient,[status(thm)],[t3]) ).
cnf(t781,plain,
true = product(h(a),a,multiplicative_identity),
inference(step,[status(thm)],[t311,t41]) ).
cnf(t318,plain,
product(h(a),a,multiplicative_identity) = true,
inference(orient,[status(thm)],[t781]) ).
cnf(t679,plain,
true = ifeq(true,true,ifeq(product(a,X1,additive_identity),true,product(multiplicative_identity,X1,additive_identity),true),true),
inference(cp,[status(thm)],[t675,t318]) ).
cnf(t870,plain,
true = ifeq(product(a,X1,additive_identity),true,product(multiplicative_identity,X1,additive_identity),true),
inference(step,[status(thm)],[t679,t35]) ).
cnf(t687,plain,
ifeq(product(a,X1,additive_identity),true,product(multiplicative_identity,X1,additive_identity),true) = true,
inference(orient,[status(thm)],[t870]) ).
cnf(f23,negated_conjecture,
product(a,b,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_b) ).
fof(f23_nnf,plain,
product(a,b,additive_identity),
inference(nnf_transformation,[status(thm)],[f23]) ).
cnf(c23,plain,
product(a,b,additive_identity),
inference(cnf_transformation,[status(esa)],[f23_nnf]) ).
cnf(t9,plain,
product(a,b,additive_identity) = true,
inference(equality_encoding,[status(esa)],[c23]) ).
cnf(t180,plain,
product(a,b,additive_identity) = true,
inference(orient,[status(thm)],[t9]) ).
cnf(t688,plain,
true = ifeq(true,true,product(multiplicative_identity,b,additive_identity),true),
inference(cp,[status(thm)],[t687,t180]) ).
cnf(t871,plain,
true = product(multiplicative_identity,b,additive_identity),
inference(step,[status(thm)],[t688,t35]) ).
cnf(t689,plain,
product(multiplicative_identity,b,additive_identity) = true,
inference(orient,[status(thm)],[t871]) ).
cnf(t691,plain,
multiply(multiplicative_identity,b) = ifeq(true,true,additive_identity,multiply(multiplicative_identity,b)),
inference(cp,[status(thm)],[t522,t689]) ).
cnf(f20,hypothesis,
product(multiplicative_identity,A,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_multiplicative_identity) ).
fof(f20_nnf,plain,
! [A] : product(multiplicative_identity,A,A),
inference(nnf_transformation,[status(thm)],[f20]) ).
fof(f20_sk,plain,
! [A] : product(multiplicative_identity,A,A),
inference(skolemisation,[status(esa)],[f20_nnf]) ).
cnf(c20,plain,
product(multiplicative_identity,X0,X0),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(t11,plain,
product(multiplicative_identity,X1,X1) = true,
inference(equality_encoding,[status(esa)],[c20]) ).
cnf(t157,plain,
product(multiplicative_identity,X1,X1) = true,
inference(orient,[status(thm)],[t11]) ).
cnf(t158,plain,
X1 = ifeq(true,true,ifeq(product(multiplicative_identity,X2,X1),true,X2,X1),X1),
inference(cp,[status(thm)],[t36,t157]) ).
cnf(t795,plain,
X1 = ifeq(product(multiplicative_identity,X2,X1),true,X2,X1),
inference(step,[status(thm)],[t158,t35]) ).
cnf(t449,plain,
ifeq(product(multiplicative_identity,X1,X2),true,X1,X2) = X2,
inference(orient,[status(thm)],[t795]) ).
cnf(t450,plain,
multiply(multiplicative_identity,X1) = ifeq(true,true,X1,multiply(multiplicative_identity,X1)),
inference(cp,[status(thm)],[t449,t65]) ).
cnf(t796,plain,
multiply(multiplicative_identity,X1) = X1,
inference(step,[status(thm)],[t450,t35]) ).
cnf(t455,plain,
multiply(multiplicative_identity,X1) = X1,
inference(orient,[status(thm)],[t796]) ).
cnf(t872,plain,
b = ifeq(true,true,additive_identity,multiply(multiplicative_identity,b)),
inference(step,[status(thm)],[t691,t455]) ).
cnf(t873,plain,
b = additive_identity,
inference(step,[status(thm)],[t872,t35]) ).
cnf(t716,plain,
additive_identity = b,
inference(orient,[status(thm)],[t873]) ).
cnf(t890,plain,
eq(b,b) = false,
inference(step,[status(thm)],[t313,t716]) ).
cnf(t0,plain,
eq(X1,X1) = true,
introduced(definition) ).
cnf(t308,plain,
eq(X1,X1) = true,
inference(orient,[status(thm)],[t0]) ).
cnf(t891,plain,
true = false,
inference(step,[status(thm)],[t890,t308]) ).
cnf(t728,plain,
true = false,
inference(rw,[status(thm)],[t891]) ).
cnf(t778,plain,
false = true,
inference(orient,[status(thm)],[t728]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c24,c25]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t778]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG041-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.36 % 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
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Thu Sep 24 07:58:54 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 14.99/2.41 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 14.99/2.41 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------