%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : RNG100+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n005.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 02:38:56 PM UTC 2026
% Result : Theorem 128.00s 42.35s
% Output : CNFRefutation 128.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 15
% Syntax : Number of formulae : 173 ( 17 unt; 0 def)
% Number of atoms : 655 ( 231 equ)
% Maximal formula atoms : 17 ( 3 avg)
% Number of connectives : 855 ( 373 ~; 368 |; 85 &)
% ( 9 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-2 aty)
% Number of variables : 342 ( 0 sgn 312 !; 30 ?; 198 :)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0,X1] :
( ( aElement0(X1)
& aElement0(X0) )
=> aElement0(sdtpldt0(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB) ).
fof(f6,axiom,
! [X0,X1] :
( ( aElement0(X1)
& aElement0(X0) )
=> aElement0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB_02) ).
fof(f11,axiom,
! [X0,X1] :
( ( aElement0(X1)
& aElement0(X0) )
=> sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulComm) ).
fof(f12,axiom,
! [X0,X1,X2] :
( ( aElement0(X2)
& aElement0(X1)
& aElement0(X0) )
=> sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulAsso) ).
fof(f14,axiom,
! [X0,X1,X2] :
( ( aElement0(X2)
& aElement0(X1)
& aElement0(X0) )
=> ( sdtasdt0(sdtpldt0(X1,X2),X0) = sdtpldt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0))
& sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAMDistr) ).
fof(f20,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aElementOf0(X1,X0)
=> aElement0(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEOfElem) ).
fof(f37,axiom,
! [X0] :
( aElement0(X0)
=> ! [X1] :
( X1 = slsdtgt0(X0)
<=> ( ! [X2] :
( aElementOf0(X2,X1)
<=> ? [X3] :
( sdtasdt0(X0,X3) = X2
& aElement0(X3) ) )
& aSet0(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefPrIdeal) ).
fof(f38,axiom,
aElement0(xc),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1905) ).
fof(f39,conjecture,
( ( ! [X0] :
( aElementOf0(X0,slsdtgt0(xc))
<=> ? [X1] :
( sdtasdt0(xc,X1) = X0
& aElement0(X1) ) )
& aSet0(slsdtgt0(xc)) )
=> ( aIdeal0(slsdtgt0(xc))
| ! [X0] :
( aElementOf0(X0,slsdtgt0(xc))
=> ( ! [X1] :
( aElement0(X1)
=> aElementOf0(sdtasdt0(X1,X0),slsdtgt0(xc)) )
& ! [X1] :
( aElementOf0(X1,slsdtgt0(xc))
=> aElementOf0(sdtpldt0(X0,X1),slsdtgt0(xc)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f40,negated_conjecture,
~ ( ( ! [X0] :
( aElementOf0(X0,slsdtgt0(xc))
<=> ? [X1] :
( sdtasdt0(xc,X1) = X0
& aElement0(X1) ) )
& aSet0(slsdtgt0(xc)) )
=> ( aIdeal0(slsdtgt0(xc))
| ! [X0] :
( aElementOf0(X0,slsdtgt0(xc))
=> ( ! [X1] :
( aElement0(X1)
=> aElementOf0(sdtasdt0(X1,X0),slsdtgt0(xc)) )
& ! [X1] :
( aElementOf0(X1,slsdtgt0(xc))
=> aElementOf0(sdtpldt0(X0,X1),slsdtgt0(xc)) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f39]) ).
fof(f48,plain,
~ ( ( ! [X0] :
( aElementOf0(X0,slsdtgt0(xc))
<=> ? [X1] :
( sdtasdt0(xc,X1) = X0
& aElement0(X1) ) )
& aSet0(slsdtgt0(xc)) )
=> ( aIdeal0(slsdtgt0(xc))
| ! [X2] :
( aElementOf0(X2,slsdtgt0(xc))
=> ( ! [X4] :
( aElement0(X4)
=> aElementOf0(sdtasdt0(X4,X2),slsdtgt0(xc)) )
& ! [X3] :
( aElementOf0(X3,slsdtgt0(xc))
=> aElementOf0(sdtpldt0(X2,X3),slsdtgt0(xc)) ) ) ) ) ),
inference(rectify,[],[f40]) ).
fof(f52,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aElement0(X0)
| aElement0(sdtpldt0(X0,X1)) ),
inference(ennf_transformation,[],[f5]) ).
fof(f53,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aElement0(X0)
| aElement0(sdtpldt0(X0,X1)) ),
inference(flattening,[],[f52]) ).
fof(f54,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aElement0(X0)
| aElement0(sdtasdt0(X0,X1)) ),
inference(ennf_transformation,[],[f6]) ).
fof(f55,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aElement0(X0)
| aElement0(sdtasdt0(X0,X1)) ),
inference(flattening,[],[f54]) ).
fof(f62,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aElement0(X0)
| sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f63,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aElement0(X0)
| sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
inference(flattening,[],[f62]) ).
fof(f64,plain,
! [X0,X1,X2] :
( ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0)
| sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2)) ),
inference(ennf_transformation,[],[f12]) ).
fof(f65,plain,
! [X0,X1,X2] :
( ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0)
| sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2)) ),
inference(flattening,[],[f64]) ).
fof(f67,plain,
! [X0,X1,X2] :
( ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0)
| ( sdtasdt0(sdtpldt0(X1,X2),X0) = sdtpldt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0))
& sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2)) ) ),
inference(ennf_transformation,[],[f14]) ).
fof(f68,plain,
! [X0,X1,X2] :
( ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0)
| ( sdtasdt0(sdtpldt0(X1,X2),X0) = sdtpldt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0))
& sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2)) ) ),
inference(flattening,[],[f67]) ).
fof(f73,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( ~ aElementOf0(X1,X0)
| aElement0(X1) ) ),
inference(ennf_transformation,[],[f20]) ).
fof(f98,plain,
! [X0] :
( ~ aElement0(X0)
| ! [X1] :
( X1 = slsdtgt0(X0)
<=> ( ! [X2] :
( aElementOf0(X2,X1)
<=> ? [X3] :
( sdtasdt0(X0,X3) = X2
& aElement0(X3) ) )
& aSet0(X1) ) ) ),
inference(ennf_transformation,[],[f37]) ).
fof(f99,plain,
( ! [X0] :
( aElementOf0(X0,slsdtgt0(xc))
<=> ? [X1] :
( sdtasdt0(xc,X1) = X0
& aElement0(X1) ) )
& aSet0(slsdtgt0(xc))
& ~ aIdeal0(slsdtgt0(xc))
& ? [X2] :
( aElementOf0(X2,slsdtgt0(xc))
& ( ? [X4] :
( aElement0(X4)
& ~ aElementOf0(sdtasdt0(X4,X2),slsdtgt0(xc)) )
| ? [X3] :
( aElementOf0(X3,slsdtgt0(xc))
& ~ aElementOf0(sdtpldt0(X2,X3),slsdtgt0(xc)) ) ) ) ),
inference(ennf_transformation,[],[f48]) ).
fof(f100,plain,
( ! [X0] :
( aElementOf0(X0,slsdtgt0(xc))
<=> ? [X1] :
( sdtasdt0(xc,X1) = X0
& aElement0(X1) ) )
& aSet0(slsdtgt0(xc))
& ~ aIdeal0(slsdtgt0(xc))
& ? [X2] :
( aElementOf0(X2,slsdtgt0(xc))
& ( ? [X4] :
( aElement0(X4)
& ~ aElementOf0(sdtasdt0(X4,X2),slsdtgt0(xc)) )
| ? [X3] :
( aElementOf0(X3,slsdtgt0(xc))
& ~ aElementOf0(sdtpldt0(X2,X3),slsdtgt0(xc)) ) ) ) ),
inference(flattening,[],[f99]) ).
fof(f133,plain,
! [X0] :
( ~ aElement0(X0)
| ! [X1] :
( ( slsdtgt0(X0) != X1
| ( ! [X2] :
( ( ~ aElementOf0(X2,X1)
| ? [X3] :
( sdtasdt0(X0,X3) = X2
& aElement0(X3) ) )
& ( ! [X3] :
( sdtasdt0(X0,X3) != X2
| ~ aElement0(X3) )
| aElementOf0(X2,X1) ) )
& aSet0(X1) ) )
& ( ? [X2] :
( ( aElementOf0(X2,X1)
| ? [X3] :
( sdtasdt0(X0,X3) = X2
& aElement0(X3) ) )
& ( ~ aElementOf0(X2,X1)
| ! [X3] :
( sdtasdt0(X0,X3) != X2
| ~ aElement0(X3) ) ) )
| ~ aSet0(X1)
| X1 = slsdtgt0(X0) ) ) ),
inference(nnf_transformation,[],[f98]) ).
fof(f134,plain,
! [X0] :
( ~ aElement0(X0)
| ! [X1] :
( ( slsdtgt0(X0) != X1
| ( ! [X2] :
( ( ~ aElementOf0(X2,X1)
| ? [X3] :
( sdtasdt0(X0,X3) = X2
& aElement0(X3) ) )
& ( ! [X3] :
( sdtasdt0(X0,X3) != X2
| ~ aElement0(X3) )
| aElementOf0(X2,X1) ) )
& aSet0(X1) ) )
& ( ? [X2] :
( ( aElementOf0(X2,X1)
| ? [X3] :
( sdtasdt0(X0,X3) = X2
& aElement0(X3) ) )
& ( ~ aElementOf0(X2,X1)
| ! [X3] :
( sdtasdt0(X0,X3) != X2
| ~ aElement0(X3) ) ) )
| ~ aSet0(X1)
| X1 = slsdtgt0(X0) ) ) ),
inference(flattening,[],[f133]) ).
fof(f135,plain,
! [X0] :
( ~ aElement0(X0)
| ! [X1] :
( ( slsdtgt0(X0) != X1
| ( ! [X5] :
( ( ~ aElementOf0(X5,X1)
| ? [X7] :
( sdtasdt0(X0,X7) = X5
& aElement0(X7) ) )
& ( ! [X6] :
( sdtasdt0(X0,X6) != X5
| ~ aElement0(X6) )
| aElementOf0(X5,X1) ) )
& aSet0(X1) ) )
& ( ? [X2] :
( ( aElementOf0(X2,X1)
| ? [X4] :
( sdtasdt0(X0,X4) = X2
& aElement0(X4) ) )
& ( ~ aElementOf0(X2,X1)
| ! [X3] :
( sdtasdt0(X0,X3) != X2
| ~ aElement0(X3) ) ) )
| ~ aSet0(X1)
| X1 = slsdtgt0(X0) ) ) ),
inference(rectify,[],[f134]) ).
fof(f136,plain,
! [X0] :
( ~ aElement0(X0)
| ! [X1] :
( ( slsdtgt0(X0) != X1
| ( ! [X5] :
( ( ~ aElementOf0(X5,X1)
| ( sdtasdt0(X0,sK21(X0,X5)) = X5
& aElement0(sK21(X0,X5)) ) )
& ( ! [X6] :
( sdtasdt0(X0,X6) != X5
| ~ aElement0(X6) )
| aElementOf0(X5,X1) ) )
& aSet0(X1) ) )
& ( ( ( aElementOf0(sK19(X0,X1),X1)
| ( sK19(X0,X1) = sdtasdt0(X0,sK20(X0,X1))
& aElement0(sK20(X0,X1)) ) )
& ( ~ aElementOf0(sK19(X0,X1),X1)
| ! [X3] :
( sdtasdt0(X0,X3) != sK19(X0,X1)
| ~ aElement0(X3) ) ) )
| ~ aSet0(X1)
| X1 = slsdtgt0(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19,sK20,sK21]),skolemize(X2,sK19(X0,X1)),skolemize(X4,sK20(X0,X1)),skolemize(X7,sK21(X0,X5))],[f135]) ).
fof(f137,plain,
( ! [X0] :
( ( ~ aElementOf0(X0,slsdtgt0(xc))
| ? [X1] :
( sdtasdt0(xc,X1) = X0
& aElement0(X1) ) )
& ( ! [X1] :
( sdtasdt0(xc,X1) != X0
| ~ aElement0(X1) )
| aElementOf0(X0,slsdtgt0(xc)) ) )
& aSet0(slsdtgt0(xc))
& ~ aIdeal0(slsdtgt0(xc))
& ? [X2] :
( aElementOf0(X2,slsdtgt0(xc))
& ( ? [X4] :
( aElement0(X4)
& ~ aElementOf0(sdtasdt0(X4,X2),slsdtgt0(xc)) )
| ? [X3] :
( aElementOf0(X3,slsdtgt0(xc))
& ~ aElementOf0(sdtpldt0(X2,X3),slsdtgt0(xc)) ) ) ) ),
inference(nnf_transformation,[],[f100]) ).
fof(f138,plain,
( ! [X3] :
( ( ~ aElementOf0(X3,slsdtgt0(xc))
| ? [X5] :
( sdtasdt0(xc,X5) = X3
& aElement0(X5) ) )
& ( ! [X4] :
( sdtasdt0(xc,X4) != X3
| ~ aElement0(X4) )
| aElementOf0(X3,slsdtgt0(xc)) ) )
& aSet0(slsdtgt0(xc))
& ~ aIdeal0(slsdtgt0(xc))
& ? [X0] :
( aElementOf0(X0,slsdtgt0(xc))
& ( ? [X2] :
( aElement0(X2)
& ~ aElementOf0(sdtasdt0(X2,X0),slsdtgt0(xc)) )
| ? [X1] :
( aElementOf0(X1,slsdtgt0(xc))
& ~ aElementOf0(sdtpldt0(X0,X1),slsdtgt0(xc)) ) ) ) ),
inference(rectify,[],[f137]) ).
fof(f139,plain,
( ! [X3] :
( ( ~ aElementOf0(X3,slsdtgt0(xc))
| ( sdtasdt0(xc,sK25(X3)) = X3
& aElement0(sK25(X3)) ) )
& ( ! [X4] :
( sdtasdt0(xc,X4) != X3
| ~ aElement0(X4) )
| aElementOf0(X3,slsdtgt0(xc)) ) )
& aSet0(slsdtgt0(xc))
& ~ aIdeal0(slsdtgt0(xc))
& aElementOf0(sK22,slsdtgt0(xc))
& ( ( aElement0(sK24)
& ~ aElementOf0(sdtasdt0(sK24,sK22),slsdtgt0(xc)) )
| ( aElementOf0(sK23,slsdtgt0(xc))
& ~ aElementOf0(sdtpldt0(sK22,sK23),slsdtgt0(xc)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK22,sK23,sK24,sK25]),skolemize(X0,sK22),skolemize(X1,sK23),skolemize(X2,sK24),skolemize(X5,sK25(X3))],[f138]) ).
fof(f143,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aElement0(X0)
| aElement0(sdtpldt0(X0,X1)) ),
inference(cnf_transformation,[],[f53]) ).
fof(f144,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aElement0(X0)
| aElement0(sdtasdt0(X0,X1)) ),
inference(cnf_transformation,[],[f55]) ).
fof(f151,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aElement0(X0)
| sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
inference(cnf_transformation,[],[f63]) ).
fof(f152,plain,
! [X2,X0,X1] :
( ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0)
| sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2)) ),
inference(cnf_transformation,[],[f65]) ).
fof(f156,plain,
! [X2,X0,X1] :
( ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0)
| sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2)) ),
inference(cnf_transformation,[],[f68]) ).
fof(f163,plain,
! [X0,X1] :
( ~ aSet0(X0)
| ~ aElementOf0(X1,X0)
| aElement0(X1) ),
inference(cnf_transformation,[],[f73]) ).
fof(f224,plain,
! [X0,X1,X6,X5] :
( ~ aElement0(X0)
| slsdtgt0(X0) != X1
| sdtasdt0(X0,X6) != X5
| ~ aElement0(X6)
| aElementOf0(X5,X1) ),
inference(cnf_transformation,[],[f136]) ).
fof(f229,plain,
aElement0(xc),
inference(cnf_transformation,[],[f38]) ).
fof(f230,plain,
! [X3] :
( ~ aElementOf0(X3,slsdtgt0(xc))
| sdtasdt0(xc,sK25(X3)) = X3 ),
inference(cnf_transformation,[],[f139]) ).
fof(f231,plain,
! [X3] :
( ~ aElementOf0(X3,slsdtgt0(xc))
| aElement0(sK25(X3)) ),
inference(cnf_transformation,[],[f139]) ).
fof(f232,plain,
! [X3,X4] :
( sdtasdt0(xc,X4) != X3
| ~ aElement0(X4)
| aElementOf0(X3,slsdtgt0(xc)) ),
inference(cnf_transformation,[],[f139]) ).
fof(f233,plain,
aSet0(slsdtgt0(xc)),
inference(cnf_transformation,[],[f139]) ).
fof(f235,plain,
aElementOf0(sK22,slsdtgt0(xc)),
inference(cnf_transformation,[],[f139]) ).
fof(f236,plain,
( aElement0(sK24)
| aElementOf0(sK23,slsdtgt0(xc)) ),
inference(cnf_transformation,[],[f139]) ).
fof(f237,plain,
( ~ aElementOf0(sdtasdt0(sK24,sK22),slsdtgt0(xc))
| aElementOf0(sK23,slsdtgt0(xc)) ),
inference(cnf_transformation,[],[f139]) ).
fof(f238,plain,
( aElement0(sK24)
| ~ aElementOf0(sdtpldt0(sK22,sK23),slsdtgt0(xc)) ),
inference(cnf_transformation,[],[f139]) ).
fof(f239,plain,
( ~ aElementOf0(sdtasdt0(sK24,sK22),slsdtgt0(xc))
| ~ aElementOf0(sdtpldt0(sK22,sK23),slsdtgt0(xc)) ),
inference(cnf_transformation,[],[f139]) ).
fof(f248,plain,
! [X0,X1,X6] :
( ~ aElement0(X0)
| slsdtgt0(X0) != X1
| ~ aElement0(X6)
| aElementOf0(sdtasdt0(X0,X6),X1) ),
inference(equality_resolution,[],[f224]) ).
fof(f249,plain,
! [X0,X6] :
( ~ aElement0(X0)
| ~ aElement0(X6)
| aElementOf0(sdtasdt0(X0,X6),slsdtgt0(X0)) ),
inference(equality_resolution,[],[f248]) ).
fof(f252,plain,
! [X4] :
( ~ aElement0(X4)
| aElementOf0(sdtasdt0(xc,X4),slsdtgt0(xc)) ),
inference(equality_resolution,[],[f232]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] :
( aElement0(sdtpldt0(X0,X1))
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f143]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( aElement0(sdtasdt0(X0,X1))
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f144]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] :
( ( sdtasdt0(X0,X1) = sdtasdt0(X1,X0) )
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f151]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2)) )
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f152]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2)) = sdtasdt0(X0,sdtpldt0(X1,X2)) )
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f156]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i] :
( aElement0(X0)
| ~ aSet0(X1)
| ~ aElementOf0(X0,X1) ),
inference(cnf_transformation,[],[f163]) ).
tcf(c_135,plain,
! [X0: $i,X1: $i] :
( aElementOf0(sdtasdt0(X0,X1),slsdtgt0(X0))
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f249]) ).
tcf(c_138,plain,
aElement0(xc),
inference(cnf_transformation,[],[f229]) ).
tcf(c_139,negated_conjecture,
( ~ aElementOf0(sdtasdt0(sK24,sK22),slsdtgt0(xc))
| ~ aElementOf0(sdtpldt0(sK22,sK23),slsdtgt0(xc)) ),
inference(cnf_transformation,[],[f239]) ).
tcf(c_140,negated_conjecture,
( aElement0(sK24)
| ~ aElementOf0(sdtpldt0(sK22,sK23),slsdtgt0(xc)) ),
inference(cnf_transformation,[],[f238]) ).
tcf(c_141,negated_conjecture,
( aElementOf0(sK23,slsdtgt0(xc))
| ~ aElementOf0(sdtasdt0(sK24,sK22),slsdtgt0(xc)) ),
inference(cnf_transformation,[],[f237]) ).
tcf(c_142,negated_conjecture,
( aElement0(sK24)
| aElementOf0(sK23,slsdtgt0(xc)) ),
inference(cnf_transformation,[],[f236]) ).
tcf(c_143,negated_conjecture,
aElementOf0(sK22,slsdtgt0(xc)),
inference(cnf_transformation,[],[f235]) ).
tcf(c_145,negated_conjecture,
aSet0(slsdtgt0(xc)),
inference(cnf_transformation,[],[f233]) ).
tcf(c_146,negated_conjecture,
! [X0: $i] :
( aElementOf0(sdtasdt0(xc,X0),slsdtgt0(xc))
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f252]) ).
tcf(c_147,negated_conjecture,
! [X0: $i] :
( aElement0(sK25(X0))
| ~ aElementOf0(X0,slsdtgt0(xc)) ),
inference(cnf_transformation,[],[f231]) ).
tcf(c_148,negated_conjecture,
! [X0: $i] :
( ( sdtasdt0(xc,sK25(X0)) = X0 )
| ~ aElementOf0(X0,slsdtgt0(xc)) ),
inference(cnf_transformation,[],[f230]) ).
tcf(c_3841,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_3843,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_3844,plain,
! [X0: $i,X1: $i] :
( aElement0(X0)
| ~ aElement0(X1)
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_3846,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sdtpldt0(X0,X2) = sdtpldt0(X1,X3) )
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_3847,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sdtasdt0(X0,X2) = sdtasdt0(X1,X3) )
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_3848,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( aElementOf0(X0,X2)
| ~ aElementOf0(X1,X3)
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_5368,plain,
aElement0(sK25(sK22)),
inference(superposition,[status(thm)],[c_143,c_147]) ).
tcf(c_5373,plain,
! [X0: $i] :
( aElement0(sdtasdt0(xc,X0))
| ~ aElement0(X0)
| ~ aSet0(slsdtgt0(xc)) ),
inference(superposition,[status(thm)],[c_146,c_72]) ).
tcf(c_5378,plain,
sdtasdt0(xc,sK25(sK22)) = sK22,
inference(superposition,[status(thm)],[c_143,c_148]) ).
tcf(c_5408,plain,
( aElement0(sK25(sK23))
| ~ aElementOf0(sK23,slsdtgt0(xc)) ),
inference(instantiation,[status(thm)],[c_147]) ).
tcf(c_5438,plain,
( ( sdtasdt0(xc,sK25(sK23)) = sK23 )
| ~ aElementOf0(sK23,slsdtgt0(xc)) ),
inference(instantiation,[status(thm)],[c_148]) ).
tcf(c_5456,plain,
slsdtgt0(xc) = slsdtgt0(xc),
inference(instantiation,[status(thm)],[c_3841]) ).
tcf(c_5538,plain,
sK22 = sK22,
inference(instantiation,[status(thm)],[c_3841]) ).
tcf(c_5565,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X3 = sdtasdt0(X0,X1) )
| ( X3 != X2 )
| ( sdtasdt0(X0,X1) != X2 ) ),
inference(instantiation,[status(thm)],[c_3843]) ).
tcf(c_5572,plain,
! [X0: $i] :
( ( sdtasdt0(X0,xc) = sdtasdt0(xc,X0) )
| ~ aElement0(X0) ),
inference(superposition,[status(thm)],[c_138,c_60]) ).
tcf(c_5600,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( aElementOf0(X0,X2)
| ~ aElementOf0(X1,slsdtgt0(X3))
| ( X2 != slsdtgt0(X3) )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_3848]) ).
tcf(c_5647,plain,
! [X0: $i,X1: $i] :
( ( sK22 = X0 )
| ( sK22 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_3843]) ).
tcf(c_5731,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( aElementOf0(X2,slsdtgt0(X0))
| ~ aElementOf0(X3,slsdtgt0(X1))
| ( X2 != X3 )
| ( slsdtgt0(X0) != slsdtgt0(X1) ) ),
inference(instantiation,[status(thm)],[c_5600]) ).
tcf(c_5941,plain,
! [X0: $i] :
( aElement0(sdtasdt0(xc,X0))
| ~ aElement0(X0)
| ~ aSet0(slsdtgt0(xc)) ),
inference(resolution,[status(thm)],[c_72,c_146]) ).
tcf(c_5993,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = sdtasdt0(xc,X0) )
| ( X2 != X1 )
| ( sdtasdt0(xc,X0) != X1 ) ),
inference(instantiation,[status(thm)],[c_5565]) ).
tcf(c_6011,plain,
! [X0: $i] :
( ( sK22 = X0 )
| ( sK22 != sK22 )
| ( X0 != sK22 ) ),
inference(instantiation,[status(thm)],[c_5647]) ).
tcf(c_6046,plain,
! [X0: $i] :
( aElement0(sdtasdt0(xc,X0))
| ~ aElement0(X0) ),
inference(global_subsumption_just,[status(thm)],[c_5941,c_145,c_5373]) ).
tcf(c_6196,plain,
! [X0: $i,X1: $i] :
( aElementOf0(sdtasdt0(sK24,sK22),slsdtgt0(xc))
| ~ aElementOf0(X0,slsdtgt0(X1))
| ( slsdtgt0(xc) != slsdtgt0(X1) )
| ( sdtasdt0(sK24,sK22) != X0 ) ),
inference(instantiation,[status(thm)],[c_5731]) ).
tcf(c_6198,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElementOf0(X1,slsdtgt0(xc))
| ~ aElementOf0(X2,slsdtgt0(X0))
| ( X1 != X2 )
| ( slsdtgt0(xc) != slsdtgt0(X0) ) ),
inference(instantiation,[status(thm)],[c_5731]) ).
tcf(c_6317,plain,
! [X0: $i,X1: $i] :
( ( sdtasdt0(xc,sK25(X1)) = X0 )
| ~ aElementOf0(X1,slsdtgt0(xc))
| ( X0 != X1 ) ),
inference(resolution,[status(thm)],[c_3843,c_148]) ).
tcf(c_6318,plain,
! [X0: $i,X1: $i] :
( ( X1 = X0 )
| ( X0 != X1 ) ),
inference(resolution,[status(thm)],[c_3843,c_3841]) ).
tcf(c_6335,plain,
! [X0: $i] :
( aElementOf0(sdtasdt0(sK24,sK22),slsdtgt0(xc))
| ~ aElementOf0(X0,slsdtgt0(xc))
| ( slsdtgt0(xc) != slsdtgt0(xc) )
| ( sdtasdt0(sK24,sK22) != X0 ) ),
inference(instantiation,[status(thm)],[c_6196]) ).
tcf(c_6344,plain,
! [X0: $i,X1: $i] :
( aElementOf0(X0,slsdtgt0(xc))
| ~ aElementOf0(X1,slsdtgt0(xc))
| ( X0 != X1 )
| ( slsdtgt0(xc) != slsdtgt0(xc) ) ),
inference(instantiation,[status(thm)],[c_6198]) ).
tcf(c_6449,plain,
! [X0: $i] :
( ( X0 = sdtasdt0(xc,sK25(sK23)) )
| ( X0 != sK23 )
| ( sdtasdt0(xc,sK25(sK23)) != sK23 ) ),
inference(instantiation,[status(thm)],[c_5993]) ).
tcf(c_6488,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sdtasdt0(xc,sK25(X1)) = X2 )
| ~ aElementOf0(X1,slsdtgt0(xc))
| ( X2 != X0 )
| ( X0 != X1 ) ),
inference(resolution,[status(thm)],[c_6317,c_3843]) ).
tcf(c_6531,plain,
( ( sK22 = sdtasdt0(xc,sK25(sK22)) )
| ( sK22 != sK22 )
| ( sdtasdt0(xc,sK25(sK22)) != sK22 ) ),
inference(instantiation,[status(thm)],[c_6011]) ).
tcf(c_6796,plain,
! [X0: $i,X1: $i] :
( aElementOf0(sdtasdt0(sK24,sK22),slsdtgt0(xc))
| ~ aElementOf0(sdtasdt0(X0,X1),slsdtgt0(xc))
| ( slsdtgt0(xc) != slsdtgt0(xc) )
| ( sdtasdt0(sK24,sK22) != sdtasdt0(X0,X1) ) ),
inference(instantiation,[status(thm)],[c_6335]) ).
tcf(c_6797,plain,
! [X0: $i,X1: $i] :
( ( sdtasdt0(sK24,sK22) = sdtasdt0(X1,X0) )
| ( sK24 != X1 )
| ( sK22 != X0 ) ),
inference(instantiation,[status(thm)],[c_3847]) ).
tcf(c_6813,plain,
! [X0: $i,X1: $i] :
( ( sdtasdt0(xc,sK25(X1)) = sdtasdt0(xc,sK25(X0)) )
| ~ aElementOf0(X1,slsdtgt0(xc))
| ~ aElementOf0(X0,slsdtgt0(xc))
| ( X0 != X1 ) ),
inference(resolution,[status(thm)],[c_6488,c_148]) ).
tcf(c_6819,plain,
( ( sK23 = sdtasdt0(xc,sK25(sK23)) )
| ( sK23 != sK23 )
| ( sdtasdt0(xc,sK25(sK23)) != sK23 ) ),
inference(instantiation,[status(thm)],[c_6449]) ).
tcf(c_6820,plain,
sK23 = sK23,
inference(instantiation,[status(thm)],[c_3841]) ).
tcf(c_6837,plain,
sdtasdt0(sK25(sK22),xc) = sdtasdt0(xc,sK25(sK22)),
inference(superposition,[status(thm)],[c_5368,c_5572]) ).
tcf(c_6929,plain,
! [X0: $i,X1: $i] :
( ( sdtasdt0(xc,sK25(X1)) = sdtasdt0(xc,sK25(X0)) )
| ~ aElementOf0(X1,slsdtgt0(xc))
| ( X0 != X1 ) ),
inference(global_subsumption_just,[status(thm)],[c_6813,c_5456,c_6344,c_6813]) ).
tcf(c_6943,plain,
! [X0: $i,X1: $i] :
( aElement0(sdtasdt0(xc,sK25(X1)))
| ~ aElementOf0(X1,slsdtgt0(xc))
| ~ aElement0(sdtasdt0(xc,sK25(X0)))
| ( X0 != X1 ) ),
inference(resolution,[status(thm)],[c_6929,c_3844]) ).
tcf(c_7006,plain,
( aElement0(sdtasdt0(xc,sK25(sK22)))
| ~ aElement0(xc)
| ~ aElement0(sK25(sK22)) ),
inference(superposition,[status(thm)],[c_6837,c_53]) ).
tcf(c_7101,plain,
! [X0: $i,X1: $i] :
( aElement0(sdtasdt0(xc,sK25(X1)))
| ~ aElement0(xc)
| ~ aElement0(sK25(X0))
| ~ aElementOf0(X1,slsdtgt0(xc))
| ( X0 != X1 ) ),
inference(resolution,[status(thm)],[c_6943,c_53]) ).
tcf(c_7103,plain,
! [X0: $i,X1: $i] :
( aElement0(sdtasdt0(xc,sK25(X1)))
| ~ aElement0(sK25(X0))
| ~ aElementOf0(X1,slsdtgt0(xc))
| ( X0 != X1 ) ),
inference(resolution,[status(thm)],[c_6943,c_6046]) ).
tcf(c_7113,plain,
! [X0: $i,X1: $i] :
( aElement0(sdtasdt0(xc,sK25(X1)))
| ( X0 != X1 )
| ~ aElementOf0(X1,slsdtgt0(xc)) ),
inference(global_subsumption_just,[status(thm)],[c_7103,c_138,c_147,c_5456,c_6344,c_7101]) ).
tcf(c_7114,plain,
! [X0: $i,X1: $i] :
( aElement0(sdtasdt0(xc,sK25(X1)))
| ~ aElementOf0(X1,slsdtgt0(xc))
| ( X0 != X1 ) ),
inference(renaming,[status(thm)],[c_7113]) ).
tcf(c_7140,plain,
! [X0: $i] :
( aElement0(sdtasdt0(xc,sK25(X0)))
| ~ aElementOf0(X0,slsdtgt0(xc)) ),
inference(resolution,[status(thm)],[c_7114,c_148]) ).
tcf(c_7224,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElementOf0(X0,X2)
| ~ aElementOf0(X1,X2)
| ( X0 != X1 ) ),
inference(resolution,[status(thm)],[c_3848,c_3841]) ).
tcf(c_8421,plain,
! [X0: $i] :
( ( sdtasdt0(sK24,sK22) = sdtasdt0(sK24,X0) )
| ( sK24 != sK24 )
| ( sK22 != X0 ) ),
inference(instantiation,[status(thm)],[c_6797]) ).
tcf(c_8422,plain,
sK24 = sK24,
inference(instantiation,[status(thm)],[c_3841]) ).
tcf(c_10443,plain,
! [X0: $i] :
( ( X0 = sdtasdt0(xc,sK25(X0)) )
| ~ aElementOf0(X0,slsdtgt0(xc)) ),
inference(resolution,[status(thm)],[c_6318,c_148]) ).
tcf(c_12315,plain,
( ( sdtasdt0(sK24,sK22) = sdtasdt0(sK24,sdtasdt0(xc,sK25(sK22))) )
| ( sK24 != sK24 )
| ( sK22 != sdtasdt0(xc,sK25(sK22)) ) ),
inference(instantiation,[status(thm)],[c_8421]) ).
tcf(c_12383,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( aElementOf0(sdtasdt0(X0,X2),X4)
| ~ aElementOf0(sdtasdt0(X1,X3),X4)
| ( X2 != X3 )
| ( X0 != X1 ) ),
inference(resolution,[status(thm)],[c_7224,c_3847]) ).
tcf(c_22154,plain,
( aElementOf0(sdtasdt0(sK24,sK22),slsdtgt0(xc))
| ~ aElementOf0(sdtasdt0(sK24,sdtasdt0(xc,sK25(sK22))),slsdtgt0(xc))
| ( slsdtgt0(xc) != slsdtgt0(xc) )
| ( sdtasdt0(sK24,sK22) != sdtasdt0(sK24,sdtasdt0(xc,sK25(sK22))) ) ),
inference(instantiation,[status(thm)],[c_6796]) ).
tcf(c_47660,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElementOf0(sdtasdt0(X0,X1),slsdtgt0(xc))
| ~ aElement0(X2)
| ( X1 != X2 )
| ( X0 != xc ) ),
inference(resolution,[status(thm)],[c_12383,c_146]) ).
tcf(c_48443,plain,
! [X0: $i,X1: $i] :
( aElementOf0(sdtasdt0(X0,X1),slsdtgt0(xc))
| ~ aElementOf0(X1,slsdtgt0(xc))
| ~ aElement0(sdtasdt0(xc,sK25(X1)))
| ( X0 != xc ) ),
inference(resolution,[status(thm)],[c_47660,c_10443]) ).
tcf(c_100581,plain,
! [X0: $i,X1: $i] :
( aElementOf0(sdtasdt0(X0,X1),slsdtgt0(xc))
| ~ aElementOf0(X1,slsdtgt0(xc))
| ( X0 != xc ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_48443,c_7140]) ).
tcf(c_117226,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( aElementOf0(X0,X3)
| ~ aElementOf0(sdtasdt0(X1,X2),slsdtgt0(X1))
| ( X3 != slsdtgt0(X1) )
| ( X0 != sdtasdt0(X1,X2) ) ),
inference(instantiation,[status(thm)],[c_3848]) ).
tcf(c_117237,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElementOf0(X1,slsdtgt0(X0))
| ~ aElementOf0(sdtasdt0(X0,X2),slsdtgt0(X0))
| ( X1 != sdtasdt0(X0,X2) )
| ( slsdtgt0(X0) != slsdtgt0(X0) ) ),
inference(instantiation,[status(thm)],[c_117226]) ).
tcf(c_117269,plain,
! [X0: $i,X1: $i] :
( aElementOf0(X0,slsdtgt0(xc))
| ~ aElementOf0(sdtasdt0(xc,X1),slsdtgt0(xc))
| ( X0 != sdtasdt0(xc,X1) )
| ( slsdtgt0(xc) != slsdtgt0(xc) ) ),
inference(instantiation,[status(thm)],[c_117237]) ).
tcf(c_117270,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( aElementOf0(X0,X2)
| ~ aElementOf0(X1,slsdtgt0(X3))
| ( X2 != slsdtgt0(X3) )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_3848]) ).
tcf(c_117283,plain,
! [X0: $i,X1: $i] :
( aElementOf0(sdtasdt0(sdtasdt0(xc,X0),X1),slsdtgt0(xc))
| ~ aElementOf0(sdtasdt0(xc,sdtasdt0(X0,X1)),slsdtgt0(xc))
| ( slsdtgt0(xc) != slsdtgt0(xc) )
| ( sdtasdt0(sdtasdt0(xc,X0),X1) != sdtasdt0(xc,sdtasdt0(X0,X1)) ) ),
inference(instantiation,[status(thm)],[c_117269]) ).
tcf(c_117284,plain,
! [X0: $i,X1: $i] :
( ( sdtasdt0(sdtasdt0(xc,X0),X1) = sdtasdt0(xc,sdtasdt0(X0,X1)) )
| ~ aElement0(xc)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(instantiation,[status(thm)],[c_61]) ).
tcf(c_117348,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( aElementOf0(X2,slsdtgt0(X0))
| ~ aElementOf0(X3,slsdtgt0(X1))
| ( X2 != X3 )
| ( slsdtgt0(X0) != slsdtgt0(X1) ) ),
inference(instantiation,[status(thm)],[c_117270]) ).
tcf(c_117426,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElementOf0(X1,slsdtgt0(xc))
| ~ aElementOf0(X2,slsdtgt0(X0))
| ( X1 != X2 )
| ( slsdtgt0(xc) != slsdtgt0(X0) ) ),
inference(instantiation,[status(thm)],[c_117348]) ).
tcf(c_117448,plain,
! [X0: $i,X1: $i] :
( aElementOf0(X0,slsdtgt0(xc))
| ~ aElementOf0(X1,slsdtgt0(xc))
| ( X0 != X1 )
| ( slsdtgt0(xc) != slsdtgt0(xc) ) ),
inference(instantiation,[status(thm)],[c_117426]) ).
tcf(c_117617,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElementOf0(X0,slsdtgt0(xc))
| ~ aElementOf0(sdtasdt0(sdtasdt0(xc,X1),X2),slsdtgt0(xc))
| ( X0 != sdtasdt0(sdtasdt0(xc,X1),X2) )
| ( slsdtgt0(xc) != slsdtgt0(xc) ) ),
inference(instantiation,[status(thm)],[c_117448]) ).
tcf(c_117699,plain,
! [X0: $i,X1: $i] :
( ( sdtasdt0(X1,sdtasdt0(xc,X0)) = sdtasdt0(sdtasdt0(xc,X0),X1) )
| ~ aElement0(X1)
| ~ aElement0(sdtasdt0(xc,X0)) ),
inference(instantiation,[status(thm)],[c_60]) ).
tcf(c_118256,plain,
! [X0: $i,X1: $i] :
( aElementOf0(sdtasdt0(X0,sdtasdt0(xc,X1)),slsdtgt0(xc))
| ~ aElementOf0(sdtasdt0(sdtasdt0(xc,X1),X0),slsdtgt0(xc))
| ( slsdtgt0(xc) != slsdtgt0(xc) )
| ( sdtasdt0(X0,sdtasdt0(xc,X1)) != sdtasdt0(sdtasdt0(xc,X1),X0) ) ),
inference(instantiation,[status(thm)],[c_117617]) ).
tcf(c_125659,plain,
( aElementOf0(sdtasdt0(sK24,sdtasdt0(xc,sK25(sK22))),slsdtgt0(xc))
| ~ aElementOf0(sdtasdt0(sdtasdt0(xc,sK25(sK22)),sK24),slsdtgt0(xc))
| ( slsdtgt0(xc) != slsdtgt0(xc) )
| ( sdtasdt0(sK24,sdtasdt0(xc,sK25(sK22))) != sdtasdt0(sdtasdt0(xc,sK25(sK22)),sK24) ) ),
inference(instantiation,[status(thm)],[c_118256]) ).
tcf(c_130202,plain,
! [X0: $i] :
( aElementOf0(sdtasdt0(sdtasdt0(xc,sK25(sK22)),X0),slsdtgt0(xc))
| ~ aElementOf0(sdtasdt0(xc,sdtasdt0(sK25(sK22),X0)),slsdtgt0(xc))
| ( slsdtgt0(xc) != slsdtgt0(xc) )
| ( sdtasdt0(sdtasdt0(xc,sK25(sK22)),X0) != sdtasdt0(xc,sdtasdt0(sK25(sK22),X0)) ) ),
inference(instantiation,[status(thm)],[c_117283]) ).
tcf(c_152031,plain,
( ( sdtasdt0(sK24,sdtasdt0(xc,sK25(sK22))) = sdtasdt0(sdtasdt0(xc,sK25(sK22)),sK24) )
| ~ aElement0(sK24)
| ~ aElement0(sdtasdt0(xc,sK25(sK22))) ),
inference(instantiation,[status(thm)],[c_117699]) ).
tcf(c_156283,plain,
! [X0: $i] :
( ( sdtasdt0(sdtasdt0(xc,sK25(sK22)),X0) = sdtasdt0(xc,sdtasdt0(sK25(sK22),X0)) )
| ~ aElement0(xc)
| ~ aElement0(X0)
| ~ aElement0(sK25(sK22)) ),
inference(instantiation,[status(thm)],[c_117284]) ).
tcf(c_167841,plain,
( aElementOf0(sdtasdt0(sdtasdt0(xc,sK25(sK22)),sK24),slsdtgt0(xc))
| ~ aElementOf0(sdtasdt0(xc,sdtasdt0(sK25(sK22),sK24)),slsdtgt0(xc))
| ( slsdtgt0(xc) != slsdtgt0(xc) )
| ( sdtasdt0(sdtasdt0(xc,sK25(sK22)),sK24) != sdtasdt0(xc,sdtasdt0(sK25(sK22),sK24)) ) ),
inference(instantiation,[status(thm)],[c_130202]) ).
tcf(c_174320,plain,
( ( sdtasdt0(sdtasdt0(xc,sK25(sK22)),sK24) = sdtasdt0(xc,sdtasdt0(sK25(sK22),sK24)) )
| ~ aElement0(sK24)
| ~ aElement0(xc)
| ~ aElement0(sK25(sK22)) ),
inference(instantiation,[status(thm)],[c_156283]) ).
tcf(c_180368,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( aElementOf0(X0,X3)
| ~ aElementOf0(sdtasdt0(X1,X2),slsdtgt0(X1))
| ( X3 != slsdtgt0(X1) )
| ( X0 != sdtasdt0(X1,X2) ) ),
inference(instantiation,[status(thm)],[c_3848]) ).
tcf(c_180399,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElementOf0(X1,slsdtgt0(X0))
| ~ aElementOf0(sdtasdt0(X0,X2),slsdtgt0(X0))
| ( X1 != sdtasdt0(X0,X2) )
| ( slsdtgt0(X0) != slsdtgt0(X0) ) ),
inference(instantiation,[status(thm)],[c_180368]) ).
tcf(c_180467,plain,
! [X0: $i,X1: $i] :
( aElementOf0(X0,slsdtgt0(xc))
| ~ aElementOf0(sdtasdt0(xc,X1),slsdtgt0(xc))
| ( X0 != sdtasdt0(xc,X1) )
| ( slsdtgt0(xc) != slsdtgt0(xc) ) ),
inference(instantiation,[status(thm)],[c_180399]) ).
tcf(c_180468,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( aElementOf0(X0,X2)
| ~ aElementOf0(X1,slsdtgt0(X3))
| ( X2 != slsdtgt0(X3) )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_3848]) ).
tcf(c_180500,plain,
! [X0: $i,X1: $i] :
( aElementOf0(sdtpldt0(sdtasdt0(xc,X0),sdtasdt0(xc,X1)),slsdtgt0(xc))
| ~ aElementOf0(sdtasdt0(xc,sdtpldt0(X0,X1)),slsdtgt0(xc))
| ( slsdtgt0(xc) != slsdtgt0(xc) )
| ( sdtpldt0(sdtasdt0(xc,X0),sdtasdt0(xc,X1)) != sdtasdt0(xc,sdtpldt0(X0,X1)) ) ),
inference(instantiation,[status(thm)],[c_180467]) ).
tcf(c_180600,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( aElementOf0(X2,slsdtgt0(X0))
| ~ aElementOf0(X3,slsdtgt0(X1))
| ( X2 != X3 )
| ( slsdtgt0(X0) != slsdtgt0(X1) ) ),
inference(instantiation,[status(thm)],[c_180468]) ).
tcf(c_180615,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(sK22,sK23) = sdtpldt0(X0,X1) )
| ( sK23 != X1 )
| ( sK22 != X0 ) ),
inference(instantiation,[status(thm)],[c_3846]) ).
tcf(c_180905,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElementOf0(X1,slsdtgt0(xc))
| ~ aElementOf0(X2,slsdtgt0(X0))
| ( X1 != X2 )
| ( slsdtgt0(xc) != slsdtgt0(X0) ) ),
inference(instantiation,[status(thm)],[c_180600]) ).
tcf(c_180953,plain,
! [X0: $i,X1: $i] :
( aElementOf0(X0,slsdtgt0(xc))
| ~ aElementOf0(X1,slsdtgt0(xc))
| ( X0 != X1 )
| ( slsdtgt0(xc) != slsdtgt0(xc) ) ),
inference(instantiation,[status(thm)],[c_180905]) ).
tcf(c_181026,plain,
! [X0: $i,X1: $i] :
( ( X1 = X0 )
| ( X0 != X1 ) ),
inference(resolution,[status(thm)],[c_3843,c_3841]) ).
tcf(c_181304,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElementOf0(X0,slsdtgt0(xc))
| ~ aElementOf0(sdtpldt0(sdtasdt0(xc,X1),sdtasdt0(xc,X2)),slsdtgt0(xc))
| ( X0 != sdtpldt0(sdtasdt0(xc,X1),sdtasdt0(xc,X2)) )
| ( slsdtgt0(xc) != slsdtgt0(xc) ) ),
inference(instantiation,[status(thm)],[c_180953]) ).
tcf(c_181560,plain,
! [X0: $i] :
( ( sdtpldt0(sK22,sK23) = sdtpldt0(sdtasdt0(xc,sK25(sK22)),X0) )
| ( sK23 != X0 )
| ( sK22 != sdtasdt0(xc,sK25(sK22)) ) ),
inference(instantiation,[status(thm)],[c_180615]) ).
tcf(c_181618,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElementOf0(X0,X2)
| ~ aElementOf0(X1,X2)
| ( X0 != X1 ) ),
inference(resolution,[status(thm)],[c_3848,c_3841]) ).
tcf(c_183167,plain,
( ( sdtpldt0(sK22,sK23) = sdtpldt0(sdtasdt0(xc,sK25(sK22)),sdtasdt0(xc,sK25(sK23))) )
| ( sK23 != sdtasdt0(xc,sK25(sK23)) )
| ( sK22 != sdtasdt0(xc,sK25(sK22)) ) ),
inference(instantiation,[status(thm)],[c_181560]) ).
tcf(c_183670,plain,
! [X0: $i] :
( ( X0 = sdtasdt0(xc,sK25(X0)) )
| ~ aElementOf0(X0,slsdtgt0(xc)) ),
inference(resolution,[status(thm)],[c_181026,c_148]) ).
tcf(c_185605,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( aElementOf0(sdtasdt0(X0,X2),X4)
| ~ aElementOf0(sdtasdt0(X1,X3),X4)
| ( X2 != X3 )
| ( X0 != X1 ) ),
inference(resolution,[status(thm)],[c_181618,c_3847]) ).
tcf(c_193551,plain,
! [X0: $i,X1: $i] :
( aElementOf0(sdtpldt0(sK22,sK23),slsdtgt0(xc))
| ~ aElementOf0(sdtpldt0(sdtasdt0(xc,X0),sdtasdt0(xc,X1)),slsdtgt0(xc))
| ( slsdtgt0(xc) != slsdtgt0(xc) )
| ( sdtpldt0(sK22,sK23) != sdtpldt0(sdtasdt0(xc,X0),sdtasdt0(xc,X1)) ) ),
inference(instantiation,[status(thm)],[c_181304]) ).
tcf(c_208567,plain,
( aElementOf0(sdtasdt0(xc,sdtasdt0(sK25(sK22),sK24)),slsdtgt0(xc))
| ~ aElement0(sdtasdt0(sK25(sK22),sK24)) ),
inference(instantiation,[status(thm)],[c_146]) ).
tcf(c_211558,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElementOf0(sdtasdt0(X0,X1),slsdtgt0(xc))
| ~ aElement0(X2)
| ( X1 != X2 )
| ( X0 != xc ) ),
inference(resolution,[status(thm)],[c_185605,c_146]) ).
tcf(c_211603,plain,
! [X0: $i,X1: $i] :
( aElementOf0(sdtasdt0(X0,X1),slsdtgt0(xc))
| ~ aElementOf0(X1,slsdtgt0(xc))
| ~ aElement0(sdtasdt0(xc,sK25(X1)))
| ( X0 != xc ) ),
inference(resolution,[status(thm)],[c_211558,c_183670]) ).
tcf(c_215022,plain,
( aElement0(sdtasdt0(sK25(sK22),sK24))
| ~ aElement0(sK24)
| ~ aElement0(sK25(sK22)) ),
inference(instantiation,[status(thm)],[c_53]) ).
tcf(c_231824,plain,
! [X0: $i,X1: $i] :
( aElementOf0(sdtasdt0(X0,X1),slsdtgt0(xc))
| ~ aElementOf0(X1,slsdtgt0(xc))
| ( X0 != xc ) ),
inference(global_subsumption_just,[status(thm)],[c_211603,c_100581]) ).
tcf(c_231839,plain,
( aElementOf0(sK23,slsdtgt0(xc))
| ~ aElementOf0(sK22,slsdtgt0(xc))
| ( sK24 != xc ) ),
inference(resolution,[status(thm)],[c_231824,c_141]) ).
tcf(c_231921,plain,
aElementOf0(sK23,slsdtgt0(xc)),
inference(global_subsumption_just,[status(thm)],[c_231839,c_138,c_142,c_141,c_5368,c_5378,c_5456,c_5538,c_6531,c_7006,c_8422,c_12315,c_22154,c_125659,c_152031,c_167841,c_174320,c_208567,c_215022]) ).
tcf(c_250741,plain,
( aElementOf0(sdtpldt0(sK22,sK23),slsdtgt0(xc))
| ~ aElementOf0(sdtpldt0(sdtasdt0(xc,sK25(sK22)),sdtasdt0(xc,sK25(sK23))),slsdtgt0(xc))
| ( slsdtgt0(xc) != slsdtgt0(xc) )
| ( sdtpldt0(sK22,sK23) != sdtpldt0(sdtasdt0(xc,sK25(sK22)),sdtasdt0(xc,sK25(sK23))) ) ),
inference(instantiation,[status(thm)],[c_193551]) ).
tcf(c_252994,plain,
( aElementOf0(sdtpldt0(sdtasdt0(xc,sK25(sK22)),sdtasdt0(xc,sK25(sK23))),slsdtgt0(xc))
| ~ aElementOf0(sdtasdt0(xc,sdtpldt0(sK25(sK22),sK25(sK23))),slsdtgt0(xc))
| ( slsdtgt0(xc) != slsdtgt0(xc) )
| ( sdtpldt0(sdtasdt0(xc,sK25(sK22)),sdtasdt0(xc,sK25(sK23))) != sdtasdt0(xc,sdtpldt0(sK25(sK22),sK25(sK23))) ) ),
inference(instantiation,[status(thm)],[c_180500]) ).
tcf(c_266422,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(sdtasdt0(xc,X0),sdtasdt0(xc,X1)) = sdtasdt0(xc,sdtpldt0(X0,X1)) )
| ~ aElement0(xc)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(instantiation,[status(thm)],[c_64]) ).
tcf(c_280519,plain,
( ( sdtpldt0(sdtasdt0(xc,sK25(sK22)),sdtasdt0(xc,sK25(sK23))) = sdtasdt0(xc,sdtpldt0(sK25(sK22),sK25(sK23))) )
| ~ aElement0(xc)
| ~ aElement0(sK25(sK23))
| ~ aElement0(sK25(sK22)) ),
inference(instantiation,[status(thm)],[c_266422]) ).
tcf(c_287568,plain,
( aElementOf0(sdtasdt0(xc,sdtpldt0(sK25(sK22),sK25(sK23))),slsdtgt0(xc))
| ~ aElement0(xc)
| ~ aElement0(sdtpldt0(sK25(sK22),sK25(sK23))) ),
inference(instantiation,[status(thm)],[c_135]) ).
tcf(c_293263,plain,
( aElement0(sdtpldt0(sK25(sK22),sK25(sK23)))
| ~ aElement0(sK25(sK23))
| ~ aElement0(sK25(sK22)) ),
inference(instantiation,[status(thm)],[c_52]) ).
tcf(c_293264,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_293263,c_287568,c_280519,c_252994,c_250741,c_231921,c_215022,c_208567,c_183167,c_174320,c_167841,c_152031,c_125659,c_22154,c_12315,c_8422,c_7006,c_6820,c_6819,c_6531,c_5538,c_5456,c_5438,c_5408,c_5378,c_5368,c_139,c_140,c_138]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : RNG100+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.16/5.43 % Computer : n005.cluster.edu
% 0.16/5.43 % Model : x86_64 x86_64
% 0.16/5.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/5.43 % Memory : 8046.5625MB
% 0.16/5.43 % OS : Linux 6.8.0-71-generic
% 0.16/5.43 % CPULimit : 300
% 0.16/5.43 % WCLimit : 300
% 0.16/5.43 % DateTime : Thu Sep 24 08:13:54 UTC 2026
% 0.16/5.43 % CPUTime :
% 0.16/5.43 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.16/5.49 Running first-order theorem proving
% 0.16/5.49 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/5.50
% 0.20/5.50 % ======== iProver multi-core TPTP/SMT =========
% 0.20/5.50
% 0.20/5.50 % Detected problem language: tptp
% 0.20/5.52 % Proving...
% 128.00/42.35 % SZS status Started for theBenchmark.p
% 128.00/42.35 % SZS status Theorem for theBenchmark.p
% 128.00/42.35
% 128.00/42.35 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 128.00/42.35
% 128.00/42.35 % ------ iProver source info
% 128.00/42.35
% 128.00/42.35 % git: date: 2026-07-19 20:42:38 +0200
% 128.00/42.35 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 128.00/42.35 % git: non_committed_changes: false
% 128.00/42.35
% 128.00/42.35 % ------ Parsing...
% 128.00/42.35 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 128.00/42.35
% 128.00/42.35 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 128.00/42.35
% 128.00/42.35 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 128.00/42.35
% 128.00/42.35 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 128.00/42.35 % ------ Proving...
% 128.00/42.35 % ------ Problem Properties
% 128.00/42.35
% 128.00/42.35 %
% 128.00/42.35 % clauses 95
% 128.00/42.35 % conjectures 10
% 128.00/42.35 % EPR 13
% 128.00/42.35 % Horn 71
% 128.00/42.35 % unary 7
% 128.00/42.35 % binary 21
% 128.00/42.35 % lits 337
% 128.00/42.35 % lits eq 43
% 128.00/42.35 % fd_pure 0
% 128.00/42.35 % fd_pseudo 0
% 128.00/42.35 % fd_cond 3
% 128.00/42.35 % fd_pseudo_cond 11
% 128.00/42.35 % AC symbols 0
% 128.00/42.35
% 128.00/42.35 % ------ Input Options Time Limit: Unbounded
% 128.00/42.35
% 128.00/42.35
% 128.00/42.35 % ------
% 128.00/42.35 % Current options:
% 128.00/42.35 % ------
% 128.00/42.35
% 128.00/42.35
% 128.00/42.35 %
% 128.00/42.35
% 128.00/42.35 % ------ Proving...
% 128.00/42.35 %
% 128.00/42.35
% 128.00/42.35 % ------ Proving...
% 128.00/42.35 %
% 128.00/42.35
% 128.00/42.35 % SZS status Theorem for theBenchmark.p
% 128.00/42.35
% 128.00/42.35 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 128.00/42.36
% 128.00/42.36
%------------------------------------------------------------------------------