%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : RNG087+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 : n015.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 8.73s 1.66s
% Output : Proof 8.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 24 ( 16 unt; 0 def)
% Number of atoms : 58 ( 24 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 50 ( 16 ~; 6 |; 28 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 13 con; 0-4 aty)
% Number of variables : 20 ( 0 sgn 4 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f27,conjecture,
? [W0,W1] :
( xy = sdtpldt0(W0,W1)
& aElementOf0(W1,xJ)
& aElementOf0(W0,xI) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f27_neg,negated_conjecture,
~ ? [W0,W1] :
( xy = sdtpldt0(W0,W1)
& aElementOf0(W1,xJ)
& aElementOf0(W0,xI) ),
inference(negated_conjecture,[status(cth)],[f27]) ).
fof(f27_nnf,plain,
! [W0,W1] :
( xy != sdtpldt0(W0,W1)
| ~ aElementOf0(W1,xJ)
| ~ aElementOf0(W0,xI) ),
inference(nnf_transformation,[status(thm)],[f27_neg]) ).
fof(f27_sk,plain,
! [W0,W1] :
( xy != sdtpldt0(W0,W1)
| ~ aElementOf0(W1,xJ)
| ~ aElementOf0(W0,xI) ),
inference(skolemisation,[status(esa)],[f27_nnf]) ).
cnf(c81,plain,
( xy != sdtpldt0(X0,X1)
| ~ aElementOf0(X1,xJ)
| ~ aElementOf0(X0,xI) ),
inference(cnf_transformation,[status(esa)],[f27_sk]) ).
cnf(hi75,negated_conjecture,
ifeq(aElementOf0(X0,xI),true,ifeq(aElementOf0(X1,xJ),true,ifeq(xy,sdtpldt0(X0,X1),false,true),true),true) = true,
inference(equality_encoding,[status(esa)],[c81]) ).
fof(f25,hypothesis,
( aElement0(xz)
& aElementOf0(xy,sdtpldt1(xI,xJ))
& ? [W0,W1] :
( sdtpldt0(W0,W1) = xy
& aElementOf0(W1,xJ)
& aElementOf0(W0,xI) )
& aElementOf0(xx,sdtpldt1(xI,xJ))
& ? [W0,W1] :
( sdtpldt0(W0,W1) = xx
& aElementOf0(W1,xJ)
& aElementOf0(W0,xI) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__901) ).
fof(f25_nnf,plain,
( aElement0(xz)
& aElementOf0(xy,sdtpldt1(xI,xJ))
& ? [W0,W1] :
( sdtpldt0(W0,W1) = xy
& aElementOf0(W1,xJ)
& aElementOf0(W0,xI) )
& aElementOf0(xx,sdtpldt1(xI,xJ))
& ? [W0,W1] :
( sdtpldt0(W0,W1) = xx
& aElementOf0(W1,xJ)
& aElementOf0(W0,xI) ) ),
inference(nnf_transformation,[status(thm)],[f25]) ).
fof(f25_sk,plain,
( aElement0(xz)
& aElementOf0(xy,sdtpldt1(xI,xJ))
& sdtpldt0(sk13,sk14) = xy
& aElementOf0(sk14,xJ)
& aElementOf0(sk13,xI)
& aElementOf0(xx,sdtpldt1(xI,xJ))
& sdtpldt0(sk11,sk12) = xx
& aElementOf0(sk12,xJ)
& aElementOf0(sk11,xI) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk11,sk12,sk13,sk14])],[f25_nnf]) ).
cnf(c73,plain,
aElementOf0(sk13,xI),
inference(cnf_transformation,[status(esa)],[f25_sk]) ).
cnf(hi66,axiom,
aElementOf0(sk13,xI) = true,
inference(equality_encoding,[status(esa)],[c73]) ).
cnf(c74,plain,
aElementOf0(sk14,xJ),
inference(cnf_transformation,[status(esa)],[f25_sk]) ).
cnf(hi67,axiom,
aElementOf0(sk14,xJ) = true,
inference(equality_encoding,[status(esa)],[c74]) ).
cnf(c75,plain,
sdtpldt0(sk13,sk14) = xy,
inference(cnf_transformation,[status(esa)],[f25_sk]) ).
cnf(hi68,axiom,
sdtpldt0(sk13,sk14) = xy,
inference(equality_encoding,[status(esa)],[c75]) ).
cnf(t0,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi75,hi66,hi67,hi68]) ).
cnf(t2163,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,c81]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t2163]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG087+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n015.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Thu Sep 24 08:12:42 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 8.73/1.66 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.73/1.66 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------