%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM555+1 : 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 : n007.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 02:26:00 PM UTC 2026
% Result : Theorem 3.40s 1.20s
% Output : CNFRefutation 3.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 42 ( 17 unt; 3 def)
% Number of atoms : 185 ( 33 equ)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 222 ( 84 ~; 78 |; 50 &)
% ( 9 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 2 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 72 ( 0 sgn 69 !; 3 ?; 15 :)
% Comments :
%------------------------------------------------------------------------------
fof(f16,axiom,
! [X0,X1] :
( ( aElement0(X1)
& aSet0(X0) )
=> ! [X2] :
( X2 = sdtmndt0(X0,X1)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( X3 != X1
& aElementOf0(X3,X0)
& aElement0(X3) ) )
& aSet0(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefDiff) ).
fof(f66,axiom,
( sbrdtbr0(xQ) = xk
& isFinite0(xQ)
& aSet0(xQ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2291) ).
fof(f67,axiom,
( aElementOf0(xy,xQ)
& aElement0(xy) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2304) ).
fof(f69,axiom,
~ aElementOf0(xx,xQ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2338) ).
fof(f71,conjecture,
~ aElementOf0(xx,sdtmndt0(xQ,xy)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f72,negated_conjecture,
~ ~ aElementOf0(xx,sdtmndt0(xQ,xy)),
inference(negated_conjecture,[status(cth)],[f71]) ).
fof(f79,plain,
aElementOf0(xx,sdtmndt0(xQ,xy)),
inference(flattening,[],[f72]) ).
fof(f97,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aSet0(X0)
| ! [X2] :
( X2 = sdtmndt0(X0,X1)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( X3 != X1
& aElementOf0(X3,X0)
& aElement0(X3) ) )
& aSet0(X2) ) ) ),
inference(ennf_transformation,[],[f16]) ).
fof(f98,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aSet0(X0)
| ! [X2] :
( X2 = sdtmndt0(X0,X1)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( X3 != X1
& aElementOf0(X3,X0)
& aElement0(X3) ) )
& aSet0(X2) ) ) ),
inference(flattening,[],[f97]) ).
fof(f182,plain,
! [X1,X0] :
( ~ sP3(X1,X0)
| ! [X2] :
( ( sdtmndt0(X0,X1) != X2
| sP2(X2,X0,X1) )
& ( ~ sP2(X2,X0,X1)
| X2 = sdtmndt0(X0,X1) ) ) ),
inference(nnf_transformation,[],[f166]) ).
fof(f183,plain,
! [X0,X1] :
( ~ sP3(X0,X1)
| ! [X2] :
( ( sdtmndt0(X1,X0) != X2
| sP2(X2,X1,X0) )
& ( ~ sP2(X2,X1,X0)
| sdtmndt0(X1,X0) = X2 ) ) ),
inference(rectify,[],[f182]) ).
fof(f240,plain,
! [X2,X0,X1] :
( ~ sP3(X0,X1)
| sdtmndt0(X1,X0) != X2
| sP2(X2,X1,X0) ),
inference(cnf_transformation,[],[f183]) ).
fof(f251,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aSet0(X0)
| sP3(X1,X0) ),
inference(cnf_transformation,[],[f167]) ).
fof(f332,plain,
aSet0(xQ),
inference(cnf_transformation,[],[f66]) ).
fof(f334,plain,
aElement0(xy),
inference(cnf_transformation,[],[f67]) ).
fof(f336,plain,
~ aElementOf0(xx,xQ),
inference(cnf_transformation,[],[f69]) ).
fof(f338,plain,
aElementOf0(xx,sdtmndt0(xQ,xy)),
inference(cnf_transformation,[],[f79]) ).
fof(f344,plain,
! [X0,X1] :
( ~ sP3(X0,X1)
| sP2(sdtmndt0(X1,X0),X1,X0) ),
inference(equality_resolution,[],[f240]) ).
tcf(c_77,plain,
! [X0: $i,X1: $i] :
( sP2(sdtmndt0(X1,X0),X1,X0)
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f344]) ).
tcf(c_87,plain,
! [X0: $i,X1: $i] :
( sP3(X0,X1)
| ~ aSet0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f251]) ).
tcf(c_166,plain,
aSet0(xQ),
inference(cnf_transformation,[],[f332]) ).
tcf(c_169,plain,
aElement0(xy),
inference(cnf_transformation,[],[f334]) ).
tcf(c_172,plain,
~ aElementOf0(xx,xQ),
inference(cnf_transformation,[],[f336]) ).
tcf(c_174,negated_conjecture,
aElementOf0(xx,sdtmndt0(xQ,xy)),
inference(cnf_transformation,[],[f338]) ).
tcf(c_1853,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sP2(sdtmndt0(X3,X1),X3,X1)
| ~ aSet0(X2)
| ~ aElement0(X0)
| ( X2 != X3 )
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_87,c_77]) ).
tcf(c_1854,plain,
! [X0: $i,X1: $i] :
( sP2(sdtmndt0(X1,X0),X1,X0)
| ~ aSet0(X1)
| ~ aElement0(X0) ),
inference(unflattening,[status(thm)],[c_1853]) ).
tcf(c_9147,definition,
iPr_def_10 = sdtmndt0(xQ,xy),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_9148,negated_conjecture,
aElementOf0(xx,iPr_def_10),
inference(demodulation,[status(thm)],[c_174,c_9147]) ).
tcf(c_11822,plain,
( sP2(iPr_def_10,xQ,xy)
| ~ aSet0(xQ)
| ~ aElement0(xy) ),
inference(superposition,[status(thm)],[c_9147,c_1854]) ).
tcf(c_11830,plain,
sP2(iPr_def_10,xQ,xy),
inference(forward_subsumption_resolution,[status(thm)],[c_11822,c_166,c_169]) ).
fof(f165,definition,
! [X2,X0,X1] :
( sP2(X2,X0,X1)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( X3 != X1
& aElementOf0(X3,X0)
& aElement0(X3) ) )
& aSet0(X2) ) ),
introduced(definition,[new_symbols(definition,[sP2])],[predicate_definition_introduction]) ).
fof(f166,definition,
! [X1,X0] :
( ~ sP3(X1,X0)
| ! [X2] :
( X2 = sdtmndt0(X0,X1)
<=> sP2(X2,X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sP3])],[predicate_definition_introduction]) ).
fof(f167,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aSet0(X0)
| sP3(X1,X0) ),
inference(definition_folding,[],[f98,f166,f165]) ).
fof(f184,plain,
! [X2,X0,X1] :
( ( ~ sP2(X2,X0,X1)
| ( ! [X3] :
( ( ~ aElementOf0(X3,X2)
| ( X3 != X1
& aElementOf0(X3,X0)
& aElement0(X3) ) )
& ( X1 = X3
| ~ aElementOf0(X3,X0)
| ~ aElement0(X3)
| aElementOf0(X3,X2) ) )
& aSet0(X2) ) )
& ( ? [X3] :
( ( aElementOf0(X3,X2)
| ( X3 != X1
& aElementOf0(X3,X0)
& aElement0(X3) ) )
& ( ~ aElementOf0(X3,X2)
| X1 = X3
| ~ aElementOf0(X3,X0)
| ~ aElement0(X3) ) )
| ~ aSet0(X2)
| sP2(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f165]) ).
fof(f185,plain,
! [X2,X0,X1] :
( ( ~ sP2(X2,X0,X1)
| ( ! [X3] :
( ( ~ aElementOf0(X3,X2)
| ( X3 != X1
& aElementOf0(X3,X0)
& aElement0(X3) ) )
& ( X1 = X3
| ~ aElementOf0(X3,X0)
| ~ aElement0(X3)
| aElementOf0(X3,X2) ) )
& aSet0(X2) ) )
& ( ? [X3] :
( ( aElementOf0(X3,X2)
| ( X3 != X1
& aElementOf0(X3,X0)
& aElement0(X3) ) )
& ( ~ aElementOf0(X3,X2)
| X1 = X3
| ~ aElementOf0(X3,X0)
| ~ aElement0(X3) ) )
| ~ aSet0(X2)
| sP2(X2,X0,X1) ) ),
inference(flattening,[],[f184]) ).
fof(f186,plain,
! [X0,X1,X2] :
( ( ~ sP2(X0,X1,X2)
| ( ! [X4] :
( ( ~ aElementOf0(X4,X0)
| ( X2 != X4
& aElementOf0(X4,X1)
& aElement0(X4) ) )
& ( X2 = X4
| ~ aElementOf0(X4,X1)
| ~ aElement0(X4)
| aElementOf0(X4,X0) ) )
& aSet0(X0) ) )
& ( ? [X3] :
( ( aElementOf0(X3,X0)
| ( X2 != X3
& aElementOf0(X3,X1)
& aElement0(X3) ) )
& ( ~ aElementOf0(X3,X0)
| X2 = X3
| ~ aElementOf0(X3,X1)
| ~ aElement0(X3) ) )
| ~ aSet0(X0)
| sP2(X0,X1,X2) ) ),
inference(rectify,[],[f185]) ).
fof(f187,plain,
! [X0,X1,X2] :
( ( ~ sP2(X0,X1,X2)
| ( ! [X4] :
( ( ~ aElementOf0(X4,X0)
| ( X2 != X4
& aElementOf0(X4,X1)
& aElement0(X4) ) )
& ( X2 = X4
| ~ aElementOf0(X4,X1)
| ~ aElement0(X4)
| aElementOf0(X4,X0) ) )
& aSet0(X0) ) )
& ( ( ( aElementOf0(sK7(X0,X1,X2),X0)
| ( sK7(X0,X1,X2) != X2
& aElementOf0(sK7(X0,X1,X2),X1)
& aElement0(sK7(X0,X1,X2)) ) )
& ( ~ aElementOf0(sK7(X0,X1,X2),X0)
| sK7(X0,X1,X2) = X2
| ~ aElementOf0(sK7(X0,X1,X2),X1)
| ~ aElement0(sK7(X0,X1,X2)) ) )
| ~ aSet0(X0)
| sP2(X0,X1,X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(X3,sK7(X0,X1,X2))],[f186]) ).
fof(f243,plain,
! [X2,X0,X1,X4] :
( ~ sP2(X0,X1,X2)
| ~ aElementOf0(X4,X0)
| aElementOf0(X4,X1) ),
inference(cnf_transformation,[],[f187]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( aElementOf0(X3,X1)
| ~ aElementOf0(X3,X0)
| ~ sP2(X0,X1,X2) ),
inference(cnf_transformation,[],[f243]) ).
tcf(c_11842,plain,
! [X0: $i] :
( aElementOf0(X0,xQ)
| ~ aElementOf0(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_11830,c_85]) ).
tcf(c_11874,plain,
aElementOf0(xx,xQ),
inference(superposition,[status(thm)],[c_9148,c_11842]) ).
tcf(c_11875,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_11874,c_172]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM555+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n007.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 04:34:07 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 0.10/0.41
% 0.10/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.41
% 0.10/0.41 % Detected problem language: tptp
% 0.10/0.42 % Proving...
% 3.40/1.20 % SZS status Started for theBenchmark.p
% 3.40/1.20 % SZS status Theorem for theBenchmark.p
% 3.40/1.20
% 3.40/1.20 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.40/1.20
% 3.40/1.20 % ------ iProver source info
% 3.40/1.20
% 3.40/1.20 % git: date: 2026-07-19 20:42:38 +0200
% 3.40/1.20 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.40/1.20 % git: non_committed_changes: false
% 3.40/1.20
% 3.40/1.20 % ------ Parsing...
% 3.40/1.20 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.40/1.20
% 3.40/1.20 % ------ 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: 1 0s sf_e pe_s pe_e %
% 3.40/1.20
% 3.40/1.20 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.40/1.20
% 3.40/1.20 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.40/1.20 % ------ Proving...
% 3.40/1.20 % ------ Problem Properties
% 3.40/1.20
% 3.40/1.20 %
% 3.40/1.20 % clauses 124
% 3.40/1.20 % conjectures 1
% 3.40/1.20 % EPR 40
% 3.40/1.20 % Horn 94
% 3.40/1.20 % unary 26
% 3.40/1.20 % binary 16
% 3.40/1.20 % lits 394
% 3.40/1.20 % lits eq 60
% 3.40/1.20 % fd_pure 0
% 3.40/1.20 % fd_pseudo 0
% 3.40/1.20 % fd_cond 9
% 3.40/1.20 % fd_pseudo_cond 18
% 3.40/1.20 % AC symbols 0
% 3.40/1.20
% 3.40/1.20 % ------ Schedule dynamic 5 is on
% 3.40/1.20
% 3.40/1.20 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.40/1.20
% 3.40/1.20
% 3.40/1.20 % ------
% 3.40/1.20 % Current options:
% 3.40/1.20 % ------
% 3.40/1.20
% 3.40/1.20
% 3.40/1.20 %
% 3.40/1.20
% 3.40/1.20 % ------ Proving...
% 3.40/1.20 %
% 3.40/1.20
% 3.40/1.20 % SZS status Theorem for theBenchmark.p
% 3.40/1.20
% 3.40/1.20 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.40/1.20
% 3.40/1.20
%------------------------------------------------------------------------------