%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : RNG101+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 : n014.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 02:37:43 PM UTC 2026
% Result : Theorem 68.44s 9.34s
% Output : Proof 68.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 6
% Syntax : Number of formulae : 55 ( 42 unt; 1 def)
% Number of atoms : 109 ( 59 equ)
% Maximal formula atoms : 17 ( 1 avg)
% Number of connectives : 91 ( 37 ~; 27 |; 24 &)
% ( 2 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 2 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 8 con; 0-4 aty)
% Number of variables : 55 ( 2 sgn 14 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f39,conjecture,
? [W0] :
( sdtasdt0(xc,W0) = xx
& aElement0(W0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f39_neg,negated_conjecture,
~ ? [W0] :
( sdtasdt0(xc,W0) = xx
& aElement0(W0) ),
inference(negated_conjecture,[status(cth)],[f39]) ).
fof(f39_nnf,plain,
! [W0] :
( sdtasdt0(xc,W0) != xx
| ~ aElement0(W0) ),
inference(nnf_transformation,[status(thm)],[f39_neg]) ).
fof(f39_sk,plain,
! [W0] :
( sdtasdt0(xc,W0) != xx
| ~ aElement0(W0) ),
inference(skolemisation,[status(esa)],[f39_nnf]) ).
cnf(c106,plain,
( sdtasdt0(xc,X0) != xx
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(esa)],[f39_sk]) ).
cnf(t176,plain,
ifeq(aElement0(X1),true,ifeq(sdtasdt0(xc,X1),xx,false,true),true) = true,
inference(equality_encoding,[status(esa)],[c106]) ).
cnf(t296,plain,
ifeq(aElement0(X1),true,ifeq(sdtasdt0(xc,X1),xx,false,true),true) = true,
inference(orient,[status(thm)],[t176]) ).
fof(f36,definition,
! [W0] :
( aElement0(W0)
=> ! [W1] :
( W1 = slsdtgt0(W0)
<=> ( ! [W2] :
( aElementOf0(W2,W1)
<=> ? [W3] :
( sdtasdt0(W0,W3) = W2
& aElement0(W3) ) )
& aSet0(W1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefPrIdeal) ).
fof(f36_nnf,plain,
! [W0] :
( ! [W1] :
( ( ? [W2] :
( ( ? [W3] :
( sdtasdt0(W0,W3) = W2
& aElement0(W3) )
& ~ aElementOf0(W2,W1) )
| ( ! [W3] :
( sdtasdt0(W0,W3) != W2
| ~ aElement0(W3) )
& aElementOf0(W2,W1) ) )
| ~ aSet0(W1)
| W1 = slsdtgt0(W0) )
& ( ( ! [W2] :
( ( ! [W3] :
( sdtasdt0(W0,W3) != W2
| ~ aElement0(W3) )
| aElementOf0(W2,W1) )
& ( ? [W3] :
( sdtasdt0(W0,W3) = W2
& aElement0(W3) )
| ~ aElementOf0(W2,W1) ) )
& aSet0(W1) )
| W1 != slsdtgt0(W0) ) )
| ~ aElement0(W0) ),
inference(nnf_transformation,[status(thm)],[f36]) ).
fof(f36_sk,plain,
! [W0,W1,W2,W3] :
( ( ( ( sdtasdt0(W0,sk19(W0,W1)) = sk18(W0,W1)
& aElement0(sk19(W0,W1))
& ~ aElementOf0(sk18(W0,W1),W1) )
| ( ( sdtasdt0(W0,W3) != sk18(W0,W1)
| ~ aElement0(W3) )
& aElementOf0(sk18(W0,W1),W1) )
| ~ aSet0(W1)
| W1 = slsdtgt0(W0) )
& ( ( ( sdtasdt0(W0,W3) != W2
| ~ aElement0(W3)
| aElementOf0(W2,W1) )
& ( ( sdtasdt0(W0,sk17(W0,W1,W2)) = W2
& aElement0(sk17(W0,W1,W2)) )
| ~ aElementOf0(W2,W1) )
& aSet0(W1) )
| W1 != slsdtgt0(W0) ) )
| ~ aElement0(W0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk17,sk18,sk19])],[f36_nnf]) ).
cnf(c94,plain,
( sdtasdt0(X0,sk17(X0,X1,X2)) = X2
| ~ aElementOf0(X2,X1)
| X1 != slsdtgt0(X0)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(esa)],[f36_sk]) ).
cnf(t205,plain,
ifeq(aElement0(X1),true,ifeq(X2,slsdtgt0(X1),ifeq(aElementOf0(X3,X2),true,sdtasdt0(X1,sk17(X1,X2,X3)),X3),X3),X3) = X3,
inference(equality_encoding,[status(esa)],[c94]) ).
cnf(t257,plain,
ifeq(aElement0(X1),true,ifeq(X2,slsdtgt0(X1),ifeq(aElementOf0(X3,X2),true,sdtasdt0(X1,sk17(X1,X2,X3)),X3),X3),X3) = X3,
inference(orient,[status(thm)],[t205]) ).
cnf(t94,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t256,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t94]) ).
cnf(t258,plain,
X1 = ifeq(aElement0(X2),true,ifeq(aElementOf0(X1,slsdtgt0(X2)),true,sdtasdt0(X2,sk17(X2,slsdtgt0(X2),X1)),X1),X1),
inference(cp,[status(thm)],[t257,t256]) ).
cnf(t5793,plain,
ifeq(aElement0(X1),true,ifeq(aElementOf0(X2,slsdtgt0(X1)),true,sdtasdt0(X1,sk17(X1,slsdtgt0(X1),X2)),X2),X2) = X2,
inference(orient,[status(thm)],[t258]) ).
fof(f38,hypothesis,
( aElement0(xz)
& aElementOf0(xy,slsdtgt0(xc))
& aElementOf0(xx,slsdtgt0(xc)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1933) ).
fof(f38_nnf,plain,
( aElement0(xz)
& aElementOf0(xy,slsdtgt0(xc))
& aElementOf0(xx,slsdtgt0(xc)) ),
inference(nnf_transformation,[status(thm)],[f38]) ).
fof(f38_sk,plain,
( aElement0(xz)
& aElementOf0(xy,slsdtgt0(xc))
& aElementOf0(xx,slsdtgt0(xc)) ),
inference(skolemisation,[status(esa)],[f38_nnf]) ).
cnf(c103,plain,
aElementOf0(xx,slsdtgt0(xc)),
inference(cnf_transformation,[status(esa)],[f38_sk]) ).
cnf(t64,plain,
aElementOf0(xx,slsdtgt0(xc)) = true,
inference(equality_encoding,[status(esa)],[c103]) ).
cnf(t2083,plain,
aElementOf0(xx,slsdtgt0(xc)) = true,
inference(orient,[status(thm)],[t64]) ).
cnf(t5819,plain,
xx = ifeq(aElement0(xc),true,ifeq(true,true,sdtasdt0(xc,sk17(xc,slsdtgt0(xc),xx)),xx),xx),
inference(cp,[status(thm)],[t5793,t2083]) ).
fof(f37,hypothesis,
aElement0(xc),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1905) ).
fof(f37_nnf,plain,
aElement0(xc),
inference(nnf_transformation,[status(thm)],[f37]) ).
cnf(c102,plain,
aElement0(xc),
inference(cnf_transformation,[status(esa)],[f37_nnf]) ).
cnf(t2,plain,
aElement0(xc) = true,
inference(equality_encoding,[status(esa)],[c102]) ).
cnf(t740,plain,
aElement0(xc) = true,
inference(orient,[status(thm)],[t2]) ).
cnf(t18885,plain,
xx = ifeq(true,true,ifeq(true,true,sdtasdt0(xc,sk17(xc,slsdtgt0(xc),xx)),xx),xx),
inference(step,[status(thm)],[t5819,t740]) ).
cnf(t18886,plain,
xx = ifeq(true,true,sdtasdt0(xc,sk17(xc,slsdtgt0(xc),xx)),xx),
inference(step,[status(thm)],[t18885,t256]) ).
cnf(t18887,plain,
xx = sdtasdt0(xc,sk17(xc,slsdtgt0(xc),xx)),
inference(step,[status(thm)],[t18886,t256]) ).
cnf(t18380,plain,
sdtasdt0(xc,sk17(xc,slsdtgt0(xc),xx)) = xx,
inference(orient,[status(thm)],[t18887]) ).
cnf(t18384,plain,
true = ifeq(aElement0(sk17(xc,slsdtgt0(xc),xx)),true,ifeq(xx,xx,false,true),true),
inference(cp,[status(thm)],[t296,t18380]) ).
cnf(c93,plain,
( aElement0(sk17(X0,X1,X2))
| ~ aElementOf0(X2,X1)
| X1 != slsdtgt0(X0)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(esa)],[f36_sk]) ).
cnf(t201,plain,
ifeq(aElement0(X1),true,ifeq(X2,slsdtgt0(X1),ifeq(aElementOf0(X3,X2),true,aElement0(sk17(X1,X2,X3)),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c93]) ).
cnf(t271,plain,
ifeq(aElement0(X1),true,ifeq(X2,slsdtgt0(X1),ifeq(aElementOf0(X3,X2),true,aElement0(sk17(X1,X2,X3)),true),true),true) = true,
inference(orient,[status(thm)],[t201]) ).
cnf(t272,plain,
true = ifeq(aElement0(X1),true,ifeq(aElementOf0(X2,slsdtgt0(X1)),true,aElement0(sk17(X1,slsdtgt0(X1),X2)),true),true),
inference(cp,[status(thm)],[t271,t256]) ).
cnf(t13167,plain,
ifeq(aElement0(X1),true,ifeq(aElementOf0(X2,slsdtgt0(X1)),true,aElement0(sk17(X1,slsdtgt0(X1),X2)),true),true) = true,
inference(orient,[status(thm)],[t272]) ).
cnf(t13223,plain,
true = ifeq(aElement0(xc),true,ifeq(true,true,aElement0(sk17(xc,slsdtgt0(xc),xx)),true),true),
inference(cp,[status(thm)],[t13167,t2083]) ).
cnf(t18767,plain,
true = ifeq(true,true,ifeq(true,true,aElement0(sk17(xc,slsdtgt0(xc),xx)),true),true),
inference(step,[status(thm)],[t13223,t740]) ).
cnf(t18768,plain,
true = ifeq(true,true,aElement0(sk17(xc,slsdtgt0(xc),xx)),true),
inference(step,[status(thm)],[t18767,t256]) ).
cnf(t18769,plain,
true = aElement0(sk17(xc,slsdtgt0(xc),xx)),
inference(step,[status(thm)],[t18768,t256]) ).
cnf(t13342,plain,
aElement0(sk17(xc,slsdtgt0(xc),xx)) = true,
inference(orient,[status(thm)],[t18769]) ).
cnf(t18888,plain,
true = ifeq(true,true,ifeq(xx,xx,false,true),true),
inference(step,[status(thm)],[t18384,t13342]) ).
cnf(t18889,plain,
true = ifeq(xx,xx,false,true),
inference(step,[status(thm)],[t18888,t256]) ).
cnf(t18890,plain,
true = false,
inference(step,[status(thm)],[t18889,t256]) ).
cnf(t18412,plain,
false = true,
inference(orient,[status(thm)],[t18890]) ).
fof(f17,axiom,
sz10 != sz00,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mUnNeZr) ).
fof(f17_nnf,plain,
sz10 != sz00,
inference(nnf_transformation,[status(thm)],[f17]) ).
fof(f17_sk,plain,
sz10 != sz00,
inference(skolemisation,[status(esa)],[f17_nnf]) ).
cnf(c23,plain,
sz10 != sz00,
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c23,c106]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t18412]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG101+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.37 % Computer : n014.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 08:14:33 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 68.44/9.34 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 68.44/9.34 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------