%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : RNG089+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 : n016.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 02:37:41 PM UTC 2026
% Result : Theorem 57.10s 13.21s
% Output : Proof 57.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 41 ( 23 unt; 1 def)
% Number of atoms : 96 ( 20 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 85 ( 30 ~; 20 |; 31 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 11 con; 0-4 aty)
% Number of variables : 20 ( 0 sgn 11 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f23,definition,
! [W0] :
( aIdeal0(W0)
<=> ( ! [W1] :
( aElementOf0(W1,W0)
=> ( ! [W2] :
( aElement0(W2)
=> aElementOf0(sdtasdt0(W2,W1),W0) )
& ! [W2] :
( aElementOf0(W2,W0)
=> aElementOf0(sdtpldt0(W1,W2),W0) ) ) )
& aSet0(W0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefIdeal) ).
fof(f23_nnf,plain,
! [W0] :
( ( ? [W1] :
( ( ? [W2] :
( ~ aElementOf0(sdtasdt0(W2,W1),W0)
& aElement0(W2) )
| ? [W2] :
( ~ aElementOf0(sdtpldt0(W1,W2),W0)
& aElementOf0(W2,W0) ) )
& aElementOf0(W1,W0) )
| ~ aSet0(W0)
| aIdeal0(W0) )
& ( ( ! [W1] :
( ( ! [W2] :
( aElementOf0(sdtasdt0(W2,W1),W0)
| ~ aElement0(W2) )
& ! [W2] :
( aElementOf0(sdtpldt0(W1,W2),W0)
| ~ aElementOf0(W2,W0) ) )
| ~ aElementOf0(W1,W0) )
& aSet0(W0) )
| ~ aIdeal0(W0) ) ),
inference(nnf_transformation,[status(thm)],[f23]) ).
fof(f23_sk,plain,
! [W0,W1,W2] :
( ( ( ( ( ~ aElementOf0(sdtasdt0(sk10(W0),sk8(W0)),W0)
& aElement0(sk10(W0)) )
| ( ~ aElementOf0(sdtpldt0(sk8(W0),sk9(W0)),W0)
& aElementOf0(sk9(W0),W0) ) )
& aElementOf0(sk8(W0),W0) )
| ~ aSet0(W0)
| aIdeal0(W0) )
& ( ( ( ( ( aElementOf0(sdtasdt0(W2,W1),W0)
| ~ aElement0(W2) )
& ( aElementOf0(sdtpldt0(W1,W2),W0)
| ~ aElementOf0(W2,W0) ) )
| ~ aElementOf0(W1,W0) )
& aSet0(W0) )
| ~ aIdeal0(W0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk8,sk9,sk10])],[f23_nnf]) ).
cnf(c55,plain,
( aElementOf0(sdtasdt0(X2,X1),X0)
| ~ aElement0(X2)
| ~ aElementOf0(X1,X0)
| ~ aIdeal0(X0) ),
inference(cnf_transformation,[status(esa)],[f23_sk]) ).
cnf(hi48,axiom,
ifeq(aIdeal0(X0),true,ifeq(aElementOf0(X1,X0),true,ifeq(aElement0(X2),true,aElementOf0(sdtasdt0(X2,X1),X0),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c55]) ).
fof(f24,hypothesis,
( aIdeal0(xJ)
& aIdeal0(xI) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__870) ).
fof(f24_nnf,plain,
( aIdeal0(xJ)
& aIdeal0(xI) ),
inference(nnf_transformation,[status(thm)],[f24]) ).
fof(f24_sk,plain,
( aIdeal0(xJ)
& aIdeal0(xI) ),
inference(skolemisation,[status(esa)],[f24_nnf]) ).
cnf(c62,plain,
aIdeal0(xJ),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
cnf(hi55,axiom,
aIdeal0(xJ) = true,
inference(equality_encoding,[status(esa)],[c62]) ).
fof(f26,hypothesis,
( xx = sdtpldt0(xk,xl)
& aElementOf0(xl,xJ)
& aElementOf0(xk,xI) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__934) ).
fof(f26_nnf,plain,
( xx = sdtpldt0(xk,xl)
& aElementOf0(xl,xJ)
& aElementOf0(xk,xI) ),
inference(nnf_transformation,[status(thm)],[f26]) ).
fof(f26_sk,plain,
( xx = sdtpldt0(xk,xl)
& aElementOf0(xl,xJ)
& aElementOf0(xk,xI) ),
inference(skolemisation,[status(esa)],[f26_nnf]) ).
cnf(c67,plain,
aElementOf0(xl,xJ),
inference(cnf_transformation,[status(esa)],[f26_sk]) ).
cnf(hi60,axiom,
aElementOf0(xl,xJ) = true,
inference(equality_encoding,[status(esa)],[c67]) ).
fof(f25,hypothesis,
( aElement0(xz)
& aElementOf0(xy,sdtpldt1(xI,xJ))
& aElementOf0(xx,sdtpldt1(xI,xJ)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__901) ).
fof(f25_nnf,plain,
( aElement0(xz)
& aElementOf0(xy,sdtpldt1(xI,xJ))
& aElementOf0(xx,sdtpldt1(xI,xJ)) ),
inference(nnf_transformation,[status(thm)],[f25]) ).
fof(f25_sk,plain,
( aElement0(xz)
& aElementOf0(xy,sdtpldt1(xI,xJ))
& aElementOf0(xx,sdtpldt1(xI,xJ)) ),
inference(skolemisation,[status(esa)],[f25_nnf]) ).
cnf(c65,plain,
aElement0(xz),
inference(cnf_transformation,[status(esa)],[f25_sk]) ).
cnf(hi58,axiom,
aElement0(xz) = true,
inference(equality_encoding,[status(esa)],[c65]) ).
cnf(h166,plain,
aElementOf0(sdtasdt0(xz,xl),xJ) = true,
inference(hyper_resolution,[status(thm)],[hi48,hi55,hi60,hi58]) ).
cnf(c61,plain,
aIdeal0(xI),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
cnf(hi54,axiom,
aIdeal0(xI) = true,
inference(equality_encoding,[status(esa)],[c61]) ).
cnf(c66,plain,
aElementOf0(xk,xI),
inference(cnf_transformation,[status(esa)],[f26_sk]) ).
cnf(hi59,axiom,
aElementOf0(xk,xI) = true,
inference(equality_encoding,[status(esa)],[c66]) ).
cnf(h162,plain,
aElementOf0(sdtasdt0(xz,xk),xI) = true,
inference(hyper_resolution,[status(thm)],[hi48,hi54,hi59,hi58]) ).
fof(f29,conjecture,
( aElementOf0(sdtasdt0(xz,xl),xJ)
& aElementOf0(sdtasdt0(xz,xk),xI) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f29_neg,negated_conjecture,
~ ( aElementOf0(sdtasdt0(xz,xl),xJ)
& aElementOf0(sdtasdt0(xz,xk),xI) ),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f29_nnf,plain,
( ~ aElementOf0(sdtasdt0(xz,xl),xJ)
| ~ aElementOf0(sdtasdt0(xz,xk),xI) ),
inference(nnf_transformation,[status(thm)],[f29_neg]) ).
fof(f29_sk,plain,
( ~ aElementOf0(sdtasdt0(xz,xl),xJ)
| ~ aElementOf0(sdtasdt0(xz,xk),xI) ),
inference(skolemisation,[status(esa)],[f29_nnf]) ).
cnf(c74,plain,
( ~ aElementOf0(sdtasdt0(xz,xl),xJ)
| ~ aElementOf0(sdtasdt0(xz,xk),xI) ),
inference(cnf_transformation,[status(esa)],[f29_sk]) ).
cnf(hi68,negated_conjecture,
ifeq(aElementOf0(sdtasdt0(xz,xk),xI),true,ifeq(aElementOf0(sdtasdt0(xz,xl),xJ),true,false,true),true) = true,
inference(equality_encoding,[status(esa)],[c74]) ).
cnf(t0,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi68,h162,h166]) ).
cnf(t1660,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,c74]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t1660]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG089+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/5.39 % Computer : n016.cluster.edu
% 0.10/5.39 % Model : x86_64 x86_64
% 0.10/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.39 % Memory : 8046.5625MB
% 0.10/5.39 % OS : Linux 6.8.0-71-generic
% 0.10/5.39 % CPULimit : 300
% 0.10/5.39 % WCLimit : 300
% 0.10/5.39 % DateTime : Thu Sep 24 08:15:03 UTC 2026
% 0.10/5.39 % CPUTime :
% 0.10/5.39 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 57.10/13.21 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 57.10/13.21 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------