%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : NUM228-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n019.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 02:18:51 PM UTC 2026
% Result : Unsatisfiable 6.33s 1.45s
% Output : Proof 6.33s
% Verified :
% Comments :
%------------------------------------------------------------------------------
cnf(t156,axiom,
sF3 = ifeq(function(z),true,false,true),
introduced(definition) ).
cnf(f158,negated_conjecture,
~ function(z),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_1) ).
fof(f158_nnf,plain,
~ function(z),
inference(nnf_transformation,[status(thm)],[f158]) ).
fof(f158_sk,plain,
~ function(z),
inference(skolemisation,[status(esa)],[f158_nnf]) ).
cnf(c158,plain,
~ function(z),
inference(cnf_transformation,[status(esa)],[f158_sk]) ).
cnf(t1,plain,
function(z) = false,
inference(equality_encoding,[status(esa)],[c158]) ).
cnf(t159,plain,
function(z) = false,
inference(orient,[status(thm)],[t1]) ).
cnf(t153,axiom,
sF0 = function(z),
introduced(definition) ).
cnf(t454,plain,
sF0 = false,
inference(step,[status(thm)],[t153,t159]) ).
cnf(t163,plain,
false = sF0,
inference(orient,[status(thm)],[t454]) ).
cnf(t455,plain,
function(z) = sF0,
inference(step,[status(thm)],[t159,t163]) ).
cnf(t164,plain,
function(z) = sF0,
inference(orient,[status(thm)],[t455]) ).
cnf(t472,plain,
sF3 = ifeq(sF0,true,false,true),
inference(step,[status(thm)],[t156,t164]) ).
cnf(t473,plain,
sF3 = ifeq(sF0,true,sF0,true),
inference(step,[status(thm)],[t472,t163]) ).
cnf(t21,plain,
ifeq(function(z),true,false,true) = true,
inference(equality_encoding,[status(esa)],[c158]) ).
cnf(t466,plain,
ifeq(sF0,true,false,true) = true,
inference(step,[status(thm)],[t21,t164]) ).
cnf(t467,plain,
ifeq(sF0,true,sF0,true) = true,
inference(step,[status(thm)],[t466,t163]) ).
cnf(t188,plain,
ifeq(sF0,true,sF0,true) = true,
inference(orient,[status(thm)],[t467]) ).
cnf(t474,plain,
sF3 = true,
inference(step,[status(thm)],[t473,t188]) ).
cnf(t195,plain,
true = sF3,
inference(orient,[status(thm)],[t474]) ).
cnf(f146,axiom,
( function(Z)
| ~ member(X,recursion_equation_functions(Z)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',recursion_equation_functions1) ).
fof(f146_nnf,plain,
! [X,Z] :
( function(Z)
| ~ member(X,recursion_equation_functions(Z)) ),
inference(nnf_transformation,[status(thm)],[f146]) ).
fof(f146_sk,plain,
! [X,Z] :
( function(Z)
| ~ member(X,recursion_equation_functions(Z)) ),
inference(skolemisation,[status(esa)],[f146_nnf]) ).
cnf(c146,plain,
( function(X1)
| ~ member(X0,recursion_equation_functions(X1)) ),
inference(cnf_transformation,[status(esa)],[f146_sk]) ).
cnf(t50,plain,
ifeq(member(X1,recursion_equation_functions(X2)),true,function(X2),true) = true,
inference(equality_encoding,[status(esa)],[c146]) ).
cnf(t562,plain,
ifeq(member(X1,recursion_equation_functions(X2)),sF3,function(X2),true) = true,
inference(step,[status(thm)],[t50,t195]) ).
cnf(t563,plain,
ifeq(member(X1,recursion_equation_functions(X2)),sF3,function(X2),sF3) = true,
inference(step,[status(thm)],[t562,t195]) ).
cnf(t564,plain,
ifeq(member(X1,recursion_equation_functions(X2)),sF3,function(X2),sF3) = sF3,
inference(step,[status(thm)],[t563,t195]) ).
cnf(t342,plain,
ifeq(member(X1,recursion_equation_functions(X2)),sF3,function(X2),sF3) = sF3,
inference(orient,[status(thm)],[t564]) ).
cnf(t344,plain,
sF3 = ifeq(member(X1,recursion_equation_functions(z)),sF3,sF0,sF3),
inference(cp,[status(thm)],[t342,t164]) ).
cnf(t154,axiom,
sF1 = recursion_equation_functions(z),
introduced(definition) ).
cnf(t169,plain,
recursion_equation_functions(z) = sF1,
inference(orient,[status(thm)],[t154]) ).
cnf(t565,plain,
sF3 = ifeq(member(X1,sF1),sF3,sF0,sF3),
inference(step,[status(thm)],[t344,t169]) ).
cnf(t345,plain,
ifeq(member(X1,sF1),sF3,sF0,sF3) = sF3,
inference(orient,[status(thm)],[t565]) ).
cnf(f65,axiom,
( member(regular(X),X)
| X = null_class ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',regularity1) ).
fof(f65_nnf,plain,
! [X] :
( member(regular(X),X)
| X = null_class ),
inference(nnf_transformation,[status(thm)],[f65]) ).
fof(f65_sk,plain,
! [X] :
( member(regular(X),X)
| X = null_class ),
inference(skolemisation,[status(esa)],[f65_nnf]) ).
cnf(c65,plain,
( member(regular(X0),X0)
| X0 = null_class ),
inference(cnf_transformation,[status(esa)],[f65_sk]) ).
cnf(t39,plain,
or(eq(X1,null_class),member(regular(X1),X1)) = true,
inference(equality_encoding,[status(esa)],[c65]) ).
cnf(t538,plain,
or(eq(X1,null_class),member(regular(X1),X1)) = sF3,
inference(step,[status(thm)],[t39,t195]) ).
cnf(t304,plain,
or(eq(X1,null_class),member(regular(X1),X1)) = sF3,
inference(orient,[status(thm)],[t538]) ).
cnf(f159,negated_conjecture,
recursion_equation_functions(z) != null_class,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_2) ).
fof(f159_nnf,plain,
recursion_equation_functions(z) != null_class,
inference(nnf_transformation,[status(thm)],[f159]) ).
fof(f159_sk,plain,
recursion_equation_functions(z) != null_class,
inference(skolemisation,[status(esa)],[f159_nnf]) ).
cnf(c159,plain,
recursion_equation_functions(z) != null_class,
inference(cnf_transformation,[status(esa)],[f159_sk]) ).
cnf(t12,plain,
eq(recursion_equation_functions(z),null_class) = false,
inference(equality_encoding,[status(esa)],[c159]) ).
cnf(t462,plain,
eq(sF1,null_class) = false,
inference(step,[status(thm)],[t12,t169]) ).
cnf(t463,plain,
eq(sF1,null_class) = sF0,
inference(step,[status(thm)],[t462,t163]) ).
cnf(t178,plain,
eq(sF1,null_class) = sF0,
inference(orient,[status(thm)],[t463]) ).
cnf(t305,plain,
sF3 = or(sF0,member(regular(sF1),sF1)),
inference(cp,[status(thm)],[t304,t178]) ).
cnf(t9,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t461,plain,
or(sF0,X1) = X1,
inference(step,[status(thm)],[t9,t163]) ).
cnf(t175,plain,
or(sF0,X1) = X1,
inference(orient,[status(thm)],[t461]) ).
cnf(t539,plain,
sF3 = member(regular(sF1),sF1),
inference(step,[status(thm)],[t305,t175]) ).
cnf(t306,plain,
member(regular(sF1),sF1) = sF3,
inference(orient,[status(thm)],[t539]) ).
cnf(t347,plain,
sF3 = ifeq(sF3,sF3,sF0,sF3),
inference(cp,[status(thm)],[t345,t306]) ).
cnf(t14,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t181,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t14]) ).
cnf(t567,plain,
sF3 = sF0,
inference(step,[status(thm)],[t347,t181]) ).
cnf(t348,plain,
sF3 = sF0,
inference(orient,[status(thm)],[t567]) ).
cnf(t596,plain,
true = sF0,
inference(step,[status(thm)],[t195,t348]) ).
cnf(t377,plain,
true = sF0,
inference(orient,[status(thm)],[t596]) ).
cnf(f23,axiom,
( ~ member(Z,X)
| ~ member(Z,complement(X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement1) ).
fof(f23_nnf,plain,
! [Z,X] :
( ~ member(Z,X)
| ~ member(Z,complement(X)) ),
inference(nnf_transformation,[status(thm)],[f23]) ).
fof(f23_sk,plain,
! [Z,X] :
( ~ member(Z,X)
| ~ member(Z,complement(X)) ),
inference(skolemisation,[status(esa)],[f23_nnf]) ).
cnf(c23,plain,
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
inference(cnf_transformation,[status(esa)],[f23_sk]) ).
cnf(f29,axiom,
( ~ member(Z,domain_of(X))
| restrict(X,singleton(Z),universal_class) != null_class ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain1) ).
fof(f29_nnf,plain,
! [X,Z] :
( ~ member(Z,domain_of(X))
| restrict(X,singleton(Z),universal_class) != null_class ),
inference(nnf_transformation,[status(thm)],[f29]) ).
fof(f29_sk,plain,
! [X,Z] :
( ~ member(Z,domain_of(X))
| restrict(X,singleton(Z),universal_class) != null_class ),
inference(skolemisation,[status(esa)],[f29_nnf]) ).
cnf(c29,plain,
( ~ member(X1,domain_of(X0))
| restrict(X0,singleton(X1),universal_class) != null_class ),
inference(cnf_transformation,[status(esa)],[f29_sk]) ).
cnf(f126,axiom,
( ~ member(ordered_pair(V,least(Xr,U)),Xr)
| ~ member(V,U)
| ~ subclass(U,Y)
| ~ well_ordering(Xr,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',well_ordering5) ).
fof(f126_nnf,plain,
! [Xr,Y,U,V] :
( ~ member(ordered_pair(V,least(Xr,U)),Xr)
| ~ member(V,U)
| ~ subclass(U,Y)
| ~ well_ordering(Xr,Y) ),
inference(nnf_transformation,[status(thm)],[f126]) ).
fof(f126_sk,plain,
! [Xr,Y,U,V] :
( ~ member(ordered_pair(V,least(Xr,U)),Xr)
| ~ member(V,U)
| ~ subclass(U,Y)
| ~ well_ordering(Xr,Y) ),
inference(skolemisation,[status(esa)],[f126_nnf]) ).
cnf(c126,plain,
( ~ member(ordered_pair(X3,least(X0,X2)),X0)
| ~ member(X3,X2)
| ~ subclass(X2,X1)
| ~ well_ordering(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f126_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c23,c29,c126,c158,c159]) ).
cnf(g0_0,plain,
sF0 != false,
inference(rw,[status(thm)],[goal_0,t377]) ).
cnf(g0_1,plain,
sF0 != sF0,
inference(rw,[status(thm)],[g0_0,t163]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM228-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.59 % Computer : n019.cluster.edu
% 0.11/0.59 % Model : x86_64 x86_64
% 0.11/0.59 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.59 % Memory : 8046.5625MB
% 0.11/0.59 % OS : Linux 6.8.0-71-generic
% 0.11/0.59 % CPULimit : 300
% 0.11/0.59 % WCLimit : 300
% 0.11/0.59 % DateTime : Thu Sep 24 03:16:22 UTC 2026
% 0.11/0.59 % CPUTime :
% 0.11/0.59 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 6.33/1.45 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.33/1.45 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------