%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : RNG050+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n002.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 02:37:36 PM UTC 2026
% Result : Theorem 61.91s 13.49s
% Output : Proof 61.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 9
% Syntax : Number of formulae : 65 ( 48 unt; 0 def)
% Number of atoms : 101 ( 61 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 66 ( 30 ~; 21 |; 7 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-4 aty)
% Number of variables : 35 ( 2 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f38,conjecture,
( ( aDimensionOf0(xs) != sz00
=> sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)) )
=> sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f38_neg,negated_conjecture,
~ ( ( aDimensionOf0(xs) != sz00
=> sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)) )
=> sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)) ),
inference(negated_conjecture,[status(cth)],[f38]) ).
fof(f38_nnf,plain,
( ~ sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs))
& ( sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs))
| aDimensionOf0(xs) = sz00 ) ),
inference(nnf_transformation,[status(thm)],[f38_neg]) ).
fof(f38_sk,plain,
( ~ sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs))
& ( sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs))
| aDimensionOf0(xs) = sz00 ) ),
inference(skolemisation,[status(esa)],[f38_nnf]) ).
cnf(c58,plain,
~ sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)),
inference(cnf_transformation,[status(esa)],[f38_sk]) ).
cnf(t51,plain,
sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)) = false,
inference(equality_encoding,[status(esa)],[c58]) ).
cnf(t1483,plain,
sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)) = false,
inference(orient,[status(thm)],[t51]) ).
fof(f34,axiom,
! [W0,W1] :
( ( aVector0(W1)
& aVector0(W0) )
=> ( ( aDimensionOf0(W1) = sz00
& aDimensionOf0(W0) = aDimensionOf0(W1) )
=> sdtasasdt0(W0,W1) = sz0z00 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSPZ) ).
fof(f34_nnf,plain,
! [W0,W1] :
( sdtasasdt0(W0,W1) = sz0z00
| aDimensionOf0(W1) != sz00
| aDimensionOf0(W0) != aDimensionOf0(W1)
| ~ aVector0(W1)
| ~ aVector0(W0) ),
inference(nnf_transformation,[status(thm)],[f34]) ).
fof(f34_sk,plain,
! [W0,W1] :
( sdtasasdt0(W0,W1) = sz0z00
| aDimensionOf0(W1) != sz00
| aDimensionOf0(W0) != aDimensionOf0(W1)
| ~ aVector0(W1)
| ~ aVector0(W0) ),
inference(skolemisation,[status(esa)],[f34_nnf]) ).
cnf(c53,plain,
( sdtasasdt0(X0,X1) = sz0z00
| aDimensionOf0(X1) != sz00
| aDimensionOf0(X0) != aDimensionOf0(X1)
| ~ aVector0(X1)
| ~ aVector0(X0) ),
inference(cnf_transformation,[status(esa)],[f34_sk]) ).
cnf(t237,plain,
ifeq(aVector0(X1),true,ifeq(aVector0(X2),true,ifeq(aDimensionOf0(X1),aDimensionOf0(X2),ifeq(aDimensionOf0(X2),sz00,sdtasasdt0(X1,X2),sz0z00),sz0z00),sz0z00),sz0z00) = sz0z00,
inference(equality_encoding,[status(esa)],[c53]) ).
cnf(t295,plain,
ifeq(aVector0(X1),true,ifeq(aVector0(X2),true,ifeq(aDimensionOf0(X1),aDimensionOf0(X2),ifeq(aDimensionOf0(X2),sz00,sdtasasdt0(X1,X2),sz0z00),sz0z00),sz0z00),sz0z00) = sz0z00,
inference(orient,[status(thm)],[t237]) ).
cnf(t41,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t256,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t41]) ).
cnf(t296,plain,
sz0z00 = ifeq(aVector0(X1),true,ifeq(aVector0(X1),true,ifeq(aDimensionOf0(X1),sz00,sdtasasdt0(X1,X1),sz0z00),sz0z00),sz0z00),
inference(cp,[status(thm)],[t295,t256]) ).
cnf(t10112,plain,
ifeq(aVector0(X1),true,ifeq(aVector0(X1),true,ifeq(aDimensionOf0(X1),sz00,sdtasasdt0(X1,X1),sz0z00),sz0z00),sz0z00) = sz0z00,
inference(orient,[status(thm)],[t296]) ).
fof(f36,hypothesis,
aVector0(xs),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1542) ).
fof(f36_nnf,plain,
aVector0(xs),
inference(nnf_transformation,[status(thm)],[f36]) ).
cnf(c55,plain,
aVector0(xs),
inference(cnf_transformation,[status(esa)],[f36_nnf]) ).
cnf(t2,plain,
aVector0(xs) = true,
inference(equality_encoding,[status(esa)],[c55]) ).
cnf(t838,plain,
aVector0(xs) = true,
inference(orient,[status(thm)],[t2]) ).
cnf(t10113,plain,
sz0z00 = ifeq(true,true,ifeq(aVector0(xs),true,ifeq(aDimensionOf0(xs),sz00,sdtasasdt0(xs,xs),sz0z00),sz0z00),sz0z00),
inference(cp,[status(thm)],[t10112,t838]) ).
cnf(t10523,plain,
sz0z00 = ifeq(aVector0(xs),true,ifeq(aDimensionOf0(xs),sz00,sdtasasdt0(xs,xs),sz0z00),sz0z00),
inference(step,[status(thm)],[t10113,t256]) ).
cnf(t10524,plain,
sz0z00 = ifeq(true,true,ifeq(aDimensionOf0(xs),sz00,sdtasasdt0(xs,xs),sz0z00),sz0z00),
inference(step,[status(thm)],[t10523,t838]) ).
cnf(t10525,plain,
sz0z00 = ifeq(aDimensionOf0(xs),sz00,sdtasasdt0(xs,xs),sz0z00),
inference(step,[status(thm)],[t10524,t256]) ).
cnf(t99,plain,
ifeq(eq(X1,X2),true,X1,X2) = X2,
introduced(definition) ).
cnf(t263,plain,
ifeq(eq(X1,X2),true,X1,X2) = X2,
inference(orient,[status(thm)],[t99]) ).
cnf(c57,plain,
( sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs))
| aDimensionOf0(xs) = sz00 ),
inference(cnf_transformation,[status(esa)],[f38_sk]) ).
cnf(t196,plain,
or(eq(aDimensionOf0(xs),sz00),sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs))) = true,
inference(equality_encoding,[status(esa)],[c57]) ).
cnf(t725,plain,
or(eq(aDimensionOf0(xs),sz00),sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs))) = true,
inference(orient,[status(thm)],[t196]) ).
cnf(t10158,plain,
or(eq(aDimensionOf0(xs),sz00),false) = true,
inference(step,[status(thm)],[t725,t1483]) ).
cnf(t10,plain,
or(X1,false) = X1,
introduced(definition) ).
cnf(t266,plain,
or(X1,false) = X1,
inference(orient,[status(thm)],[t10]) ).
cnf(t10159,plain,
eq(aDimensionOf0(xs),sz00) = true,
inference(step,[status(thm)],[t10158,t266]) ).
cnf(t1503,plain,
eq(aDimensionOf0(xs),sz00) = true,
inference(rw,[status(thm)],[t10159]) ).
cnf(t1507,plain,
eq(aDimensionOf0(xs),sz00) = true,
inference(orient,[status(thm)],[t1503]) ).
cnf(t1508,plain,
sz00 = ifeq(true,true,aDimensionOf0(xs),sz00),
inference(cp,[status(thm)],[t263,t1507]) ).
cnf(t10161,plain,
sz00 = aDimensionOf0(xs),
inference(step,[status(thm)],[t1508,t256]) ).
cnf(t1516,plain,
aDimensionOf0(xs) = sz00,
inference(orient,[status(thm)],[t10161]) ).
cnf(t10526,plain,
sz0z00 = ifeq(sz00,sz00,sdtasasdt0(xs,xs),sz0z00),
inference(step,[status(thm)],[t10525,t1516]) ).
cnf(t10527,plain,
sz0z00 = sdtasasdt0(xs,xs),
inference(step,[status(thm)],[t10526,t256]) ).
cnf(t10116,plain,
sdtasasdt0(xs,xs) = sz0z00,
inference(orient,[status(thm)],[t10527]) ).
cnf(t10528,plain,
sdtlseqdt0(sz0z00,sz0z00) = false,
inference(step,[status(thm)],[t1483,t10116]) ).
fof(f19,axiom,
! [W0] :
( aScalar0(W0)
=> sdtlseqdt0(W0,W0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLERef) ).
fof(f19_nnf,plain,
! [W0] :
( sdtlseqdt0(W0,W0)
| ~ aScalar0(W0) ),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
! [W0] :
( sdtlseqdt0(W0,W0)
| ~ aScalar0(W0) ),
inference(skolemisation,[status(esa)],[f19_nnf]) ).
cnf(c33,plain,
( sdtlseqdt0(X0,X0)
| ~ aScalar0(X0) ),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(hi28,axiom,
ifeq(aScalar0(X0),true,sdtlseqdt0(X0,X0),true) = true,
inference(equality_encoding,[status(esa)],[c33]) ).
fof(f8,axiom,
aScalar0(sz0z00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSZeroSc) ).
fof(f8_nnf,plain,
aScalar0(sz0z00),
inference(nnf_transformation,[status(thm)],[f8]) ).
cnf(c10,plain,
aScalar0(sz0z00),
inference(cnf_transformation,[status(esa)],[f8_nnf]) ).
cnf(hi6,axiom,
aScalar0(sz0z00) = true,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(t15,plain,
sdtlseqdt0(sz0z00,sz0z00) = true,
inference(hyper_resolution,[status(thm)],[hi28,hi6]) ).
cnf(t656,plain,
sdtlseqdt0(sz0z00,sz0z00) = true,
inference(orient,[status(thm)],[t15]) ).
cnf(t10529,plain,
true = false,
inference(step,[status(thm)],[t10528,t656]) ).
cnf(t10117,plain,
true = false,
inference(rw,[status(thm)],[t10529]) ).
cnf(t10118,plain,
false = true,
inference(orient,[status(thm)],[t10117]) ).
fof(f2,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> ( szszuzczcdt0(W0) != sz00
& aNaturalNumber0(szszuzczcdt0(W0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSuccNat) ).
fof(f2_nnf,plain,
! [W0] :
( ( szszuzczcdt0(W0) != sz00
& aNaturalNumber0(szszuzczcdt0(W0)) )
| ~ aNaturalNumber0(W0) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [W0] :
( ( szszuzczcdt0(W0) != sz00
& aNaturalNumber0(szszuzczcdt0(W0)) )
| ~ aNaturalNumber0(W0) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c3,plain,
( szszuzczcdt0(X0) != sz00
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c3,c58]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t10118]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG050+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/5.57 % Computer : n002.cluster.edu
% 0.09/5.57 % Model : x86_64 x86_64
% 0.09/5.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.57 % Memory : 8046.5625MB
% 0.09/5.57 % OS : Linux 6.8.0-71-generic
% 0.09/5.57 % CPULimit : 300
% 0.09/5.57 % WCLimit : 300
% 0.09/5.57 % DateTime : Thu Sep 24 08:01:14 UTC 2026
% 0.09/5.58 % CPUTime :
% 0.09/5.58 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 61.91/13.49 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 61.91/13.49 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------