%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : RNG109+4 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/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 02:37:45 PM UTC 2026
% Result : Theorem 59.99s 8.12s
% Output : Proof 59.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 49 ( 29 unt; 0 def)
% Number of atoms : 152 ( 72 equ)
% Maximal formula atoms : 17 ( 3 avg)
% Number of connectives : 147 ( 44 ~; 31 |; 63 &)
% ( 4 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 10 con; 0-4 aty)
% Number of variables : 47 ( 0 sgn 17 !; 20 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
! [W0] :
( aElement0(W0)
=> ( W0 = sdtpldt0(sz00,W0)
& sdtpldt0(W0,sz00) = W0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddZero) ).
fof(f8_nnf,plain,
! [W0] :
( ( W0 = sdtpldt0(sz00,W0)
& sdtpldt0(W0,sz00) = W0 )
| ~ aElement0(W0) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [W0] :
( ( W0 = sdtpldt0(sz00,W0)
& sdtpldt0(W0,sz00) = W0 )
| ~ aElement0(W0) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c9,plain,
( X0 = sdtpldt0(sz00,X0)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(hi8,axiom,
ifeq(aElement0(X0),true,X0,sdtpldt0(sz00,X0)) = sdtpldt0(sz00,X0),
inference(equality_encoding,[status(esa)],[c9]) ).
fof(f38,hypothesis,
( aElement0(xb)
& aElement0(xa) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2091) ).
fof(f38_nnf,plain,
( aElement0(xb)
& aElement0(xa) ),
inference(nnf_transformation,[status(thm)],[f38]) ).
fof(f38_sk,plain,
( aElement0(xb)
& aElement0(xa) ),
inference(skolemisation,[status(esa)],[f38_nnf]) ).
cnf(c104,plain,
aElement0(xb),
inference(cnf_transformation,[status(esa)],[f38_sk]) ).
cnf(hi94,axiom,
aElement0(xb) = true,
inference(equality_encoding,[status(esa)],[c104]) ).
cnf(h322,plain,
xb = sdtpldt0(sz00,xb),
inference(hyper_resolution,[status(thm)],[hi8,hi94]) ).
fof(f43,conjecture,
? [W0] :
( W0 != sz00
& ( ! [W1] :
( aElementOf0(W1,slsdtgt0(xa))
<=> ? [W2] :
( sdtasdt0(xa,W2) = W1
& aElement0(W2) ) )
=> ( ! [W1] :
( aElementOf0(W1,slsdtgt0(xb))
<=> ? [W2] :
( sdtasdt0(xb,W2) = W1
& aElement0(W2) ) )
=> ( aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ? [W1,W2] :
( sdtpldt0(W1,W2) = W0
& aElementOf0(W2,slsdtgt0(xb))
& aElementOf0(W1,slsdtgt0(xa)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f43_neg,negated_conjecture,
~ ? [W0] :
( W0 != sz00
& ( ! [W1] :
( aElementOf0(W1,slsdtgt0(xa))
<=> ? [W2] :
( sdtasdt0(xa,W2) = W1
& aElement0(W2) ) )
=> ( ! [W1] :
( aElementOf0(W1,slsdtgt0(xb))
<=> ? [W2] :
( sdtasdt0(xb,W2) = W1
& aElement0(W2) ) )
=> ( aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ? [W1,W2] :
( sdtpldt0(W1,W2) = W0
& aElementOf0(W2,slsdtgt0(xb))
& aElementOf0(W1,slsdtgt0(xa)) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f43]) ).
fof(f43_nnf,plain,
! [W0] :
( W0 = sz00
| ( ~ aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& ! [W1,W2] :
( sdtpldt0(W1,W2) != W0
| ~ aElementOf0(W2,slsdtgt0(xb))
| ~ aElementOf0(W1,slsdtgt0(xa)) )
& ! [W1] :
( ( ! [W2] :
( sdtasdt0(xb,W2) != W1
| ~ aElement0(W2) )
| aElementOf0(W1,slsdtgt0(xb)) )
& ( ? [W2] :
( sdtasdt0(xb,W2) = W1
& aElement0(W2) )
| ~ aElementOf0(W1,slsdtgt0(xb)) ) )
& ! [W1] :
( ( ! [W2] :
( sdtasdt0(xa,W2) != W1
| ~ aElement0(W2) )
| aElementOf0(W1,slsdtgt0(xa)) )
& ( ? [W2] :
( sdtasdt0(xa,W2) = W1
& aElement0(W2) )
| ~ aElementOf0(W1,slsdtgt0(xa)) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f43_neg]) ).
fof(f43_sk,plain,
! [W1,W0,W2] :
( W0 = sz00
| ( ~ aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& ( sdtpldt0(W1,W2) != W0
| ~ aElementOf0(W2,slsdtgt0(xb))
| ~ aElementOf0(W1,slsdtgt0(xa)) )
& ( sdtasdt0(xb,W2) != W1
| ~ aElement0(W2)
| aElementOf0(W1,slsdtgt0(xb)) )
& ( ( sdtasdt0(xb,sk32(W0,W1)) = W1
& aElement0(sk32(W0,W1)) )
| ~ aElementOf0(W1,slsdtgt0(xb)) )
& ( sdtasdt0(xa,W2) != W1
| ~ aElement0(W2)
| aElementOf0(W1,slsdtgt0(xa)) )
& ( ( sdtasdt0(xa,sk31(W0,W1)) = W1
& aElement0(sk31(W0,W1)) )
| ~ aElementOf0(W1,slsdtgt0(xa)) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk31,sk32])],[f43_nnf]) ).
cnf(c177,plain,
( X0 = sz00
| sdtpldt0(X1,X2) != X0
| ~ aElementOf0(X2,slsdtgt0(xb))
| ~ aElementOf0(X1,slsdtgt0(xa)) ),
inference(cnf_transformation,[status(esa)],[f43_sk]) ).
cnf(hi166,negated_conjecture,
ifeq(aElementOf0(X0,slsdtgt0(xa)),true,ifeq(aElementOf0(X1,slsdtgt0(xb)),true,ifeq(sdtpldt0(X0,X1),X2,X2,sz00),sz00),sz00) = sz00,
inference(equality_encoding,[status(esa)],[c177]) ).
fof(f42,hypothesis,
( aElementOf0(xb,slsdtgt0(xb))
& ? [W0] :
( sdtasdt0(xb,W0) = xb
& aElement0(W0) )
& aElementOf0(sz00,slsdtgt0(xb))
& ? [W0] :
( sdtasdt0(xb,W0) = sz00
& aElement0(W0) )
& aElementOf0(xa,slsdtgt0(xa))
& ? [W0] :
( sdtasdt0(xa,W0) = xa
& aElement0(W0) )
& aElementOf0(sz00,slsdtgt0(xa))
& ? [W0] :
( sdtasdt0(xa,W0) = sz00
& aElement0(W0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2203) ).
fof(f42_nnf,plain,
( aElementOf0(xb,slsdtgt0(xb))
& ? [W0] :
( sdtasdt0(xb,W0) = xb
& aElement0(W0) )
& aElementOf0(sz00,slsdtgt0(xb))
& ? [W0] :
( sdtasdt0(xb,W0) = sz00
& aElement0(W0) )
& aElementOf0(xa,slsdtgt0(xa))
& ? [W0] :
( sdtasdt0(xa,W0) = xa
& aElement0(W0) )
& aElementOf0(sz00,slsdtgt0(xa))
& ? [W0] :
( sdtasdt0(xa,W0) = sz00
& aElement0(W0) ) ),
inference(nnf_transformation,[status(thm)],[f42]) ).
fof(f42_sk,plain,
( aElementOf0(xb,slsdtgt0(xb))
& sdtasdt0(xb,sk30) = xb
& aElement0(sk30)
& aElementOf0(sz00,slsdtgt0(xb))
& sdtasdt0(xb,sk29) = sz00
& aElement0(sk29)
& aElementOf0(xa,slsdtgt0(xa))
& sdtasdt0(xa,sk28) = xa
& aElement0(sk28)
& aElementOf0(sz00,slsdtgt0(xa))
& sdtasdt0(xa,sk27) = sz00
& aElement0(sk27) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk27,sk28,sk29,sk30])],[f42_nnf]) ).
cnf(c161,plain,
aElementOf0(sz00,slsdtgt0(xa)),
inference(cnf_transformation,[status(esa)],[f42_sk]) ).
cnf(hi150,axiom,
aElementOf0(sz00,slsdtgt0(xa)) = true,
inference(equality_encoding,[status(esa)],[c161]) ).
cnf(c170,plain,
aElementOf0(xb,slsdtgt0(xb)),
inference(cnf_transformation,[status(esa)],[f42_sk]) ).
cnf(hi159,axiom,
aElementOf0(xb,slsdtgt0(xb)) = true,
inference(equality_encoding,[status(esa)],[c170]) ).
cnf(h24038,plain,
xb = sz00,
inference(hyper_resolution,[status(thm)],[hi166,hi150,hi159,h322]) ).
cnf(c8,plain,
( sdtpldt0(X0,sz00) = X0
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(hi7,axiom,
ifeq(aElement0(X0),true,sdtpldt0(X0,sz00),X0) = X0,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(c103,plain,
aElement0(xa),
inference(cnf_transformation,[status(esa)],[f38_sk]) ).
cnf(hi93,axiom,
aElement0(xa) = true,
inference(equality_encoding,[status(esa)],[c103]) ).
cnf(h151,plain,
sdtpldt0(xa,sz00) = xa,
inference(hyper_resolution,[status(thm)],[hi7,hi93]) ).
cnf(c164,plain,
aElementOf0(xa,slsdtgt0(xa)),
inference(cnf_transformation,[status(esa)],[f42_sk]) ).
cnf(hi153,axiom,
aElementOf0(xa,slsdtgt0(xa)) = true,
inference(equality_encoding,[status(esa)],[c164]) ).
cnf(c167,plain,
aElementOf0(sz00,slsdtgt0(xb)),
inference(cnf_transformation,[status(esa)],[f42_sk]) ).
cnf(hi156,axiom,
aElementOf0(sz00,slsdtgt0(xb)) = true,
inference(equality_encoding,[status(esa)],[c167]) ).
cnf(h22806,plain,
xa = sz00,
inference(hyper_resolution,[status(thm)],[hi166,hi153,hi156,h151]) ).
fof(f39,hypothesis,
( xb != sz00
| xa != sz00 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2110) ).
fof(f39_nnf,plain,
( xb != sz00
| xa != sz00 ),
inference(nnf_transformation,[status(thm)],[f39]) ).
fof(f39_sk,plain,
( xb != sz00
| xa != sz00 ),
inference(skolemisation,[status(esa)],[f39_nnf]) ).
cnf(c105,plain,
( xb != sz00
| xa != sz00 ),
inference(cnf_transformation,[status(esa)],[f39_sk]) ).
cnf(hi169,axiom,
ifeq(xa,sz00,ifeq(xb,sz00,false,true),true) = true,
inference(equality_encoding,[status(esa)],[c105]) ).
cnf(t0,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi169,h22806,h24038]) ).
cnf(t2757,plain,
false = true,
inference(orient,[status(thm)],[t0]) ).
fof(f17,axiom,
sz10 != sz00,
file('/export/starexec/sandbox2/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,c105]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t2757]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG109+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.36 % Computer : n002.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Thu Sep 24 08:19:48 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 59.99/8.12 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 59.99/8.12 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------