%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : RNG095+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n009.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 02:37:42 PM UTC 2026
% Result : Theorem 13.65s 2.24s
% Output : Proof 13.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 31 ( 20 unt; 0 def)
% Number of atoms : 56 ( 25 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 46 ( 21 ~; 11 |; 13 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-4 aty)
% Number of variables : 25 ( 0 sgn 7 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f28,hypothesis,
! [W0] :
( aElement0(W0)
=> ( aElementOf0(W0,sdtpldt1(xI,xJ))
& ? [W1,W2] :
( sdtpldt0(W1,W2) = W0
& aElementOf0(W2,xJ)
& aElementOf0(W1,xI) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1205_03) ).
fof(f28_nnf,plain,
! [W0] :
( ( aElementOf0(W0,sdtpldt1(xI,xJ))
& ? [W1,W2] :
( sdtpldt0(W1,W2) = W0
& aElementOf0(W2,xJ)
& aElementOf0(W1,xI) ) )
| ~ aElement0(W0) ),
inference(nnf_transformation,[status(thm)],[f28]) ).
fof(f28_sk,plain,
! [W0] :
( ( aElementOf0(W0,sdtpldt1(xI,xJ))
& sdtpldt0(sk11(W0),sk12(W0)) = W0
& aElementOf0(sk12(W0),xJ)
& aElementOf0(sk11(W0),xI) )
| ~ aElement0(W0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk11,sk12])],[f28_nnf]) ).
cnf(c75,plain,
( sdtpldt0(sk11(X0),sk12(X0)) = X0
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(esa)],[f28_sk]) ).
cnf(hi68,axiom,
ifeq(aElement0(X0),true,sdtpldt0(sk11(X0),sk12(X0)),X0) = X0,
inference(equality_encoding,[status(esa)],[c75]) ).
fof(f2,axiom,
aElement0(sz10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC_01) ).
fof(f2_nnf,plain,
aElement0(sz10),
inference(nnf_transformation,[status(thm)],[f2]) ).
cnf(c2,plain,
aElement0(sz10),
inference(cnf_transformation,[status(esa)],[f2_nnf]) ).
cnf(hi1,axiom,
aElement0(sz10) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(h20,plain,
sdtpldt0(sk11(sz10),sk12(sz10)) = sz10,
inference(hyper_resolution,[status(thm)],[hi68,hi1]) ).
cnf(c74,plain,
( aElementOf0(sk12(X0),xJ)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(esa)],[f28_sk]) ).
cnf(hi67,axiom,
ifeq(aElement0(X0),true,aElementOf0(sk12(X0),xJ),true) = true,
inference(equality_encoding,[status(esa)],[c74]) ).
cnf(h21,plain,
aElementOf0(sk12(sz10),xJ) = true,
inference(hyper_resolution,[status(thm)],[hi67,hi1]) ).
cnf(c73,plain,
( aElementOf0(sk11(X0),xI)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(esa)],[f28_sk]) ).
cnf(hi66,axiom,
ifeq(aElement0(X0),true,aElementOf0(sk11(X0),xI),true) = true,
inference(equality_encoding,[status(esa)],[c73]) ).
cnf(h22,plain,
aElementOf0(sk11(sz10),xI) = true,
inference(hyper_resolution,[status(thm)],[hi66,hi1]) ).
fof(f30,conjecture,
? [W0,W1] :
( sdtpldt0(W0,W1) = sz10
& aElementOf0(W1,xJ)
& aElementOf0(W0,xI) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f30_neg,negated_conjecture,
~ ? [W0,W1] :
( sdtpldt0(W0,W1) = sz10
& aElementOf0(W1,xJ)
& aElementOf0(W0,xI) ),
inference(negated_conjecture,[status(cth)],[f30]) ).
fof(f30_nnf,plain,
! [W0,W1] :
( sdtpldt0(W0,W1) != sz10
| ~ aElementOf0(W1,xJ)
| ~ aElementOf0(W0,xI) ),
inference(nnf_transformation,[status(thm)],[f30_neg]) ).
fof(f30_sk,plain,
! [W0,W1] :
( sdtpldt0(W0,W1) != sz10
| ~ aElementOf0(W1,xJ)
| ~ aElementOf0(W0,xI) ),
inference(skolemisation,[status(esa)],[f30_nnf]) ).
cnf(c79,plain,
( sdtpldt0(X0,X1) != sz10
| ~ aElementOf0(X1,xJ)
| ~ aElementOf0(X0,xI) ),
inference(cnf_transformation,[status(esa)],[f30_sk]) ).
cnf(hi73,negated_conjecture,
ifeq(aElementOf0(X0,xI),true,ifeq(aElementOf0(X1,xJ),true,ifeq(sdtpldt0(X0,X1),sz10,false,true),true),true) = true,
inference(equality_encoding,[status(esa)],[c79]) ).
cnf(t0,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi73,h22,h21,h20]) ).
cnf(t1776,plain,
false = true,
inference(orient,[status(thm)],[t0]) ).
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,c79]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t1776]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG095+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.36 % Computer : n009.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Thu Sep 24 08:12:14 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 13.65/2.24 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 13.65/2.24 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------