%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : RNG088+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 : n020.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 134.13s 17.39s
% Output : Proof 134.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 9
% Syntax : Number of formulae : 69 ( 53 unt; 0 def)
% Number of atoms : 129 ( 54 equ)
% Maximal formula atoms : 14 ( 1 avg)
% Number of connectives : 89 ( 29 ~; 19 |; 35 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 12 con; 0-4 aty)
% Number of variables : 39 ( 2 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f24,hypothesis,
( aIdeal0(xJ)
& ! [W0] :
( aElementOf0(W0,xJ)
=> ( ! [W1] :
( aElement0(W1)
=> aElementOf0(sdtasdt0(W1,W0),xJ) )
& ! [W1] :
( aElementOf0(W1,xJ)
=> aElementOf0(sdtpldt0(W0,W1),xJ) ) ) )
& aSet0(xJ)
& aIdeal0(xI)
& ! [W0] :
( aElementOf0(W0,xI)
=> ( ! [W1] :
( aElement0(W1)
=> aElementOf0(sdtasdt0(W1,W0),xI) )
& ! [W1] :
( aElementOf0(W1,xI)
=> aElementOf0(sdtpldt0(W0,W1),xI) ) ) )
& aSet0(xI) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__870) ).
fof(f24_nnf,plain,
( aIdeal0(xJ)
& ! [W0] :
( ( ! [W1] :
( aElementOf0(sdtasdt0(W1,W0),xJ)
| ~ aElement0(W1) )
& ! [W1] :
( aElementOf0(sdtpldt0(W0,W1),xJ)
| ~ aElementOf0(W1,xJ) ) )
| ~ aElementOf0(W0,xJ) )
& aSet0(xJ)
& aIdeal0(xI)
& ! [W0] :
( ( ! [W1] :
( aElementOf0(sdtasdt0(W1,W0),xI)
| ~ aElement0(W1) )
& ! [W1] :
( aElementOf0(sdtpldt0(W0,W1),xI)
| ~ aElementOf0(W1,xI) ) )
| ~ aElementOf0(W0,xI) )
& aSet0(xI) ),
inference(nnf_transformation,[status(thm)],[f24]) ).
fof(f24_sk,plain,
! [W0,W1] :
( aIdeal0(xJ)
& ( ( ( aElementOf0(sdtasdt0(W1,W0),xJ)
| ~ aElement0(W1) )
& ( aElementOf0(sdtpldt0(W0,W1),xJ)
| ~ aElementOf0(W1,xJ) ) )
| ~ aElementOf0(W0,xJ) )
& aSet0(xJ)
& aIdeal0(xI)
& ( ( ( aElementOf0(sdtasdt0(W1,W0),xI)
| ~ aElement0(W1) )
& ( aElementOf0(sdtpldt0(W0,W1),xI)
| ~ aElementOf0(W1,xI) ) )
| ~ aElementOf0(W0,xI) )
& aSet0(xI) ),
inference(skolemisation,[status(esa)],[f24_nnf]) ).
cnf(c66,plain,
( aElementOf0(sdtpldt0(X0,X1),xJ)
| ~ aElementOf0(X1,xJ)
| ~ aElementOf0(X0,xJ) ),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
cnf(t219,plain,
ifeq(aElementOf0(X1,xJ),true,ifeq(aElementOf0(X2,xJ),true,aElementOf0(sdtpldt0(X1,X2),xJ),true),true) = true,
inference(equality_encoding,[status(esa)],[c66]) ).
cnf(t265,plain,
ifeq(aElementOf0(X1,xJ),true,ifeq(aElementOf0(X2,xJ),true,aElementOf0(sdtpldt0(X1,X2),xJ),true),true) = true,
inference(orient,[status(thm)],[t219]) ).
cnf(t159,plain,
ifeq(not(X1),true,X1,false) = false,
introduced(definition) ).
cnf(t2382,plain,
ifeq(not(X1),true,X1,false) = false,
inference(orient,[status(thm)],[t159]) ).
fof(f28,conjecture,
( aElementOf0(sdtpldt0(xl,xn),xJ)
& aElementOf0(sdtpldt0(xk,xm),xI) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f28_neg,negated_conjecture,
~ ( aElementOf0(sdtpldt0(xl,xn),xJ)
& aElementOf0(sdtpldt0(xk,xm),xI) ),
inference(negated_conjecture,[status(cth)],[f28]) ).
fof(f28_nnf,plain,
( ~ aElementOf0(sdtpldt0(xl,xn),xJ)
| ~ aElementOf0(sdtpldt0(xk,xm),xI) ),
inference(nnf_transformation,[status(thm)],[f28_neg]) ).
fof(f28_sk,plain,
( ~ aElementOf0(sdtpldt0(xl,xn),xJ)
| ~ aElementOf0(sdtpldt0(xk,xm),xI) ),
inference(skolemisation,[status(esa)],[f28_nnf]) ).
cnf(c84,plain,
( ~ aElementOf0(sdtpldt0(xl,xn),xJ)
| ~ aElementOf0(sdtpldt0(xk,xm),xI) ),
inference(cnf_transformation,[status(esa)],[f28_sk]) ).
cnf(t212,plain,
or(not(aElementOf0(sdtpldt0(xk,xm),xI)),not(aElementOf0(sdtpldt0(xl,xn),xJ))) = true,
inference(equality_encoding,[status(esa)],[c84]) ).
cnf(t1410,plain,
or(not(aElementOf0(sdtpldt0(xk,xm),xI)),not(aElementOf0(sdtpldt0(xl,xn),xJ))) = true,
inference(orient,[status(thm)],[t212]) ).
cnf(c62,plain,
( aElementOf0(sdtpldt0(X0,X1),xI)
| ~ aElementOf0(X1,xI)
| ~ aElementOf0(X0,xI) ),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
cnf(t218,plain,
ifeq(aElementOf0(X1,xI),true,ifeq(aElementOf0(X2,xI),true,aElementOf0(sdtpldt0(X1,X2),xI),true),true) = true,
inference(equality_encoding,[status(esa)],[c62]) ).
cnf(t267,plain,
ifeq(aElementOf0(X1,xI),true,ifeq(aElementOf0(X2,xI),true,aElementOf0(sdtpldt0(X1,X2),xI),true),true) = true,
inference(orient,[status(thm)],[t218]) ).
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(c78,plain,
aElementOf0(xk,xI),
inference(cnf_transformation,[status(esa)],[f26_sk]) ).
cnf(t32,plain,
aElementOf0(xk,xI) = true,
inference(equality_encoding,[status(esa)],[c78]) ).
cnf(t340,plain,
aElementOf0(xk,xI) = true,
inference(orient,[status(thm)],[t32]) ).
cnf(t343,plain,
true = ifeq(true,true,ifeq(aElementOf0(X1,xI),true,aElementOf0(sdtpldt0(xk,X1),xI),true),true),
inference(cp,[status(thm)],[t267,t340]) ).
cnf(t120,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t256,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t120]) ).
cnf(t62182,plain,
true = ifeq(aElementOf0(X1,xI),true,aElementOf0(sdtpldt0(xk,X1),xI),true),
inference(step,[status(thm)],[t343,t256]) ).
cnf(t54244,plain,
ifeq(aElementOf0(X1,xI),true,aElementOf0(sdtpldt0(xk,X1),xI),true) = true,
inference(orient,[status(thm)],[t62182]) ).
fof(f27,hypothesis,
( xy = sdtpldt0(xm,xn)
& aElementOf0(xn,xJ)
& aElementOf0(xm,xI) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__967) ).
fof(f27_nnf,plain,
( xy = sdtpldt0(xm,xn)
& aElementOf0(xn,xJ)
& aElementOf0(xm,xI) ),
inference(nnf_transformation,[status(thm)],[f27]) ).
fof(f27_sk,plain,
( xy = sdtpldt0(xm,xn)
& aElementOf0(xn,xJ)
& aElementOf0(xm,xI) ),
inference(skolemisation,[status(esa)],[f27_nnf]) ).
cnf(c81,plain,
aElementOf0(xm,xI),
inference(cnf_transformation,[status(esa)],[f27_sk]) ).
cnf(t34,plain,
aElementOf0(xm,xI) = true,
inference(equality_encoding,[status(esa)],[c81]) ).
cnf(t442,plain,
aElementOf0(xm,xI) = true,
inference(orient,[status(thm)],[t34]) ).
cnf(t54273,plain,
true = ifeq(true,true,aElementOf0(sdtpldt0(xk,xm),xI),true),
inference(cp,[status(thm)],[t54244,t442]) ).
cnf(t62192,plain,
true = aElementOf0(sdtpldt0(xk,xm),xI),
inference(step,[status(thm)],[t54273,t256]) ).
cnf(t54627,plain,
aElementOf0(sdtpldt0(xk,xm),xI) = true,
inference(orient,[status(thm)],[t62192]) ).
cnf(t62193,plain,
or(not(true),not(aElementOf0(sdtpldt0(xl,xn),xJ))) = true,
inference(step,[status(thm)],[t1410,t54627]) ).
cnf(t16,plain,
not(true) = false,
introduced(definition) ).
cnf(t4313,plain,
not(true) = false,
inference(orient,[status(thm)],[t16]) ).
cnf(t62194,plain,
or(false,not(aElementOf0(sdtpldt0(xl,xn),xJ))) = true,
inference(step,[status(thm)],[t62193,t4313]) ).
cnf(t40,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t264,plain,
or(false,X1) = X1,
inference(orient,[status(thm)],[t40]) ).
cnf(t62195,plain,
not(aElementOf0(sdtpldt0(xl,xn),xJ)) = true,
inference(step,[status(thm)],[t62194,t264]) ).
cnf(t54679,plain,
not(aElementOf0(sdtpldt0(xl,xn),xJ)) = true,
inference(rw,[status(thm)],[t62195]) ).
cnf(t60200,plain,
not(aElementOf0(sdtpldt0(xl,xn),xJ)) = true,
inference(orient,[status(thm)],[t54679]) ).
cnf(t60201,plain,
false = ifeq(true,true,aElementOf0(sdtpldt0(xl,xn),xJ),false),
inference(cp,[status(thm)],[t2382,t60200]) ).
cnf(t62378,plain,
false = aElementOf0(sdtpldt0(xl,xn),xJ),
inference(step,[status(thm)],[t60201,t256]) ).
cnf(t60202,plain,
aElementOf0(sdtpldt0(xl,xn),xJ) = false,
inference(orient,[status(thm)],[t62378]) ).
cnf(t60207,plain,
true = ifeq(aElementOf0(xl,xJ),true,ifeq(aElementOf0(xn,xJ),true,false,true),true),
inference(cp,[status(thm)],[t265,t60202]) ).
cnf(c79,plain,
aElementOf0(xl,xJ),
inference(cnf_transformation,[status(esa)],[f26_sk]) ).
cnf(t33,plain,
aElementOf0(xl,xJ) = true,
inference(equality_encoding,[status(esa)],[c79]) ).
cnf(t391,plain,
aElementOf0(xl,xJ) = true,
inference(orient,[status(thm)],[t33]) ).
cnf(t62379,plain,
true = ifeq(true,true,ifeq(aElementOf0(xn,xJ),true,false,true),true),
inference(step,[status(thm)],[t60207,t391]) ).
cnf(t62380,plain,
true = ifeq(aElementOf0(xn,xJ),true,false,true),
inference(step,[status(thm)],[t62379,t256]) ).
cnf(c82,plain,
aElementOf0(xn,xJ),
inference(cnf_transformation,[status(esa)],[f27_sk]) ).
cnf(t35,plain,
aElementOf0(xn,xJ) = true,
inference(equality_encoding,[status(esa)],[c82]) ).
cnf(t493,plain,
aElementOf0(xn,xJ) = true,
inference(orient,[status(thm)],[t35]) ).
cnf(t62381,plain,
true = ifeq(true,true,false,true),
inference(step,[status(thm)],[t62380,t493]) ).
cnf(t62382,plain,
true = false,
inference(step,[status(thm)],[t62381,t256]) ).
cnf(t60255,plain,
false = true,
inference(orient,[status(thm)],[t62382]) ).
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,c84]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t60255]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG088+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.37 % Computer : n020.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 08:11:03 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 134.13/17.39 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 134.13/17.39 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------