%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM539+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 : 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 02:25:56 PM UTC 2026
% Result : Theorem 3.82s 1.27s
% Output : CNFRefutation 3.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 48 ( 19 unt; 2 def)
% Number of atoms : 214 ( 28 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 210 ( 67 ~; 47 |; 77 &)
% ( 0 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 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 : 8 ( 6 usr; 3 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 7 con; 0-1 aty)
% Number of variables : 55 ( 0 sgn 44 !; 11 ?; 7 :)
% Comments :
%------------------------------------------------------------------------------
fof(f35,axiom,
! [X0,X1] :
( ( aElementOf0(X1,szNzAzT0)
& aElementOf0(X0,szNzAzT0) )
=> ( ( sdtlseqdt0(X1,X0)
& sdtlseqdt0(X0,X1) )
=> X0 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLessASymm) ).
fof(f49,axiom,
( ~ ( xT = slcrc0
| ~ ? [X0] : aElementOf0(X0,xT) )
& ~ ( xS = slcrc0
| ~ ? [X0] : aElementOf0(X0,xS) )
& aSubsetOf0(xT,szNzAzT0)
& ! [X0] :
( aElementOf0(X0,xT)
=> aElementOf0(X0,szNzAzT0) )
& aSet0(xT)
& aSubsetOf0(xS,szNzAzT0)
& ! [X0] :
( aElementOf0(X0,xS)
=> aElementOf0(X0,szNzAzT0) )
& aSet0(xS) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1779) ).
fof(f50,axiom,
( aElementOf0(szmzizndt0(xT),xS)
& ! [X0] :
( aElementOf0(X0,xT)
=> sdtlseqdt0(szmzizndt0(xT),X0) )
& aElementOf0(szmzizndt0(xT),xT)
& aElementOf0(szmzizndt0(xS),xT)
& ! [X0] :
( aElementOf0(X0,xS)
=> sdtlseqdt0(szmzizndt0(xS),X0) )
& aElementOf0(szmzizndt0(xS),xS) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1802) ).
fof(f51,conjecture,
( ( ! [X0] :
( aElementOf0(X0,xS)
=> sdtlseqdt0(szmzizndt0(xS),X0) )
& aElementOf0(szmzizndt0(xS),xS) )
=> ( szmzizndt0(xS) = szmzizndt0(xT)
| ! [X0] :
( aElementOf0(X0,xT)
=> sdtlseqdt0(szmzizndt0(xS),X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f52,negated_conjecture,
~ ( ( ! [X0] :
( aElementOf0(X0,xS)
=> sdtlseqdt0(szmzizndt0(xS),X0) )
& aElementOf0(szmzizndt0(xS),xS) )
=> ( szmzizndt0(xS) = szmzizndt0(xT)
| ! [X0] :
( aElementOf0(X0,xT)
=> sdtlseqdt0(szmzizndt0(xS),X0) ) ) ),
inference(negated_conjecture,[status(cth)],[f51]) ).
fof(f59,plain,
( ~ ( xT = slcrc0
| ~ ? [X3] : aElementOf0(X3,xT) )
& ~ ( xS = slcrc0
| ~ ? [X2] : aElementOf0(X2,xS) )
& aSubsetOf0(xT,szNzAzT0)
& ! [X1] :
( aElementOf0(X1,xT)
=> aElementOf0(X1,szNzAzT0) )
& aSet0(xT)
& aSubsetOf0(xS,szNzAzT0)
& ! [X0] :
( aElementOf0(X0,xS)
=> aElementOf0(X0,szNzAzT0) )
& aSet0(xS) ),
inference(rectify,[],[f49]) ).
fof(f60,plain,
( aElementOf0(szmzizndt0(xT),xS)
& ! [X1] :
( aElementOf0(X1,xT)
=> sdtlseqdt0(szmzizndt0(xT),X1) )
& aElementOf0(szmzizndt0(xT),xT)
& aElementOf0(szmzizndt0(xS),xT)
& ! [X0] :
( aElementOf0(X0,xS)
=> sdtlseqdt0(szmzizndt0(xS),X0) )
& aElementOf0(szmzizndt0(xS),xS) ),
inference(rectify,[],[f50]) ).
fof(f61,plain,
~ ( ( ! [X0] :
( aElementOf0(X0,xS)
=> sdtlseqdt0(szmzizndt0(xS),X0) )
& aElementOf0(szmzizndt0(xS),xS) )
=> ( szmzizndt0(xS) = szmzizndt0(xT)
| ! [X1] :
( aElementOf0(X1,xT)
=> sdtlseqdt0(szmzizndt0(xS),X1) ) ) ),
inference(rectify,[],[f52]) ).
fof(f104,plain,
! [X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1 ),
inference(ennf_transformation,[],[f35]) ).
fof(f105,plain,
! [X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1 ),
inference(flattening,[],[f104]) ).
fof(f125,plain,
( slcrc0 != xT
& ? [X3] : aElementOf0(X3,xT)
& slcrc0 != xS
& ? [X2] : aElementOf0(X2,xS)
& aSubsetOf0(xT,szNzAzT0)
& ! [X1] :
( ~ aElementOf0(X1,xT)
| aElementOf0(X1,szNzAzT0) )
& aSet0(xT)
& aSubsetOf0(xS,szNzAzT0)
& ! [X0] :
( ~ aElementOf0(X0,xS)
| aElementOf0(X0,szNzAzT0) )
& aSet0(xS) ),
inference(ennf_transformation,[],[f59]) ).
fof(f126,plain,
( slcrc0 != xT
& ? [X3] : aElementOf0(X3,xT)
& slcrc0 != xS
& ? [X2] : aElementOf0(X2,xS)
& aSubsetOf0(xT,szNzAzT0)
& ! [X1] :
( ~ aElementOf0(X1,xT)
| aElementOf0(X1,szNzAzT0) )
& aSet0(xT)
& aSubsetOf0(xS,szNzAzT0)
& ! [X0] :
( ~ aElementOf0(X0,xS)
| aElementOf0(X0,szNzAzT0) )
& aSet0(xS) ),
inference(flattening,[],[f125]) ).
fof(f127,plain,
( aElementOf0(szmzizndt0(xT),xS)
& ! [X1] :
( ~ aElementOf0(X1,xT)
| sdtlseqdt0(szmzizndt0(xT),X1) )
& aElementOf0(szmzizndt0(xT),xT)
& aElementOf0(szmzizndt0(xS),xT)
& ! [X0] :
( ~ aElementOf0(X0,xS)
| sdtlseqdt0(szmzizndt0(xS),X0) )
& aElementOf0(szmzizndt0(xS),xS) ),
inference(ennf_transformation,[],[f60]) ).
fof(f128,plain,
( ! [X0] :
( ~ aElementOf0(X0,xS)
| sdtlseqdt0(szmzizndt0(xS),X0) )
& aElementOf0(szmzizndt0(xS),xS)
& szmzizndt0(xS) != szmzizndt0(xT)
& ? [X1] :
( aElementOf0(X1,xT)
& ~ sdtlseqdt0(szmzizndt0(xS),X1) ) ),
inference(ennf_transformation,[],[f61]) ).
fof(f129,plain,
( ! [X0] :
( ~ aElementOf0(X0,xS)
| sdtlseqdt0(szmzizndt0(xS),X0) )
& aElementOf0(szmzizndt0(xS),xS)
& szmzizndt0(xS) != szmzizndt0(xT)
& ? [X1] :
( aElementOf0(X1,xT)
& ~ sdtlseqdt0(szmzizndt0(xS),X1) ) ),
inference(flattening,[],[f128]) ).
fof(f169,plain,
( slcrc0 != xT
& aElementOf0(sK13,xT)
& slcrc0 != xS
& aElementOf0(sK12,xS)
& aSubsetOf0(xT,szNzAzT0)
& ! [X1] :
( ~ aElementOf0(X1,xT)
| aElementOf0(X1,szNzAzT0) )
& aSet0(xT)
& aSubsetOf0(xS,szNzAzT0)
& ! [X0] :
( ~ aElementOf0(X0,xS)
| aElementOf0(X0,szNzAzT0) )
& aSet0(xS) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12,sK13]),skolemize(X2,sK12),skolemize(X3,sK13)],[f126]) ).
fof(f170,plain,
( ! [X1] :
( ~ aElementOf0(X1,xS)
| sdtlseqdt0(szmzizndt0(xS),X1) )
& aElementOf0(szmzizndt0(xS),xS)
& szmzizndt0(xS) != szmzizndt0(xT)
& ? [X0] :
( aElementOf0(X0,xT)
& ~ sdtlseqdt0(szmzizndt0(xS),X0) ) ),
inference(rectify,[],[f129]) ).
fof(f171,plain,
( ! [X1] :
( ~ aElementOf0(X1,xS)
| sdtlseqdt0(szmzizndt0(xS),X1) )
& aElementOf0(szmzizndt0(xS),xS)
& szmzizndt0(xS) != szmzizndt0(xT)
& aElementOf0(sK14,xT)
& ~ sdtlseqdt0(szmzizndt0(xS),sK14) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(X0,sK14)],[f170]) ).
fof(f232,plain,
! [X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f105]) ).
fof(f261,plain,
! [X0] :
( ~ aElementOf0(X0,xS)
| aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f169]) ).
fof(f263,plain,
aElementOf0(szmzizndt0(xT),xS),
inference(cnf_transformation,[],[f127]) ).
fof(f264,plain,
! [X1] :
( ~ aElementOf0(X1,xT)
| sdtlseqdt0(szmzizndt0(xT),X1) ),
inference(cnf_transformation,[],[f127]) ).
fof(f266,plain,
aElementOf0(szmzizndt0(xS),xT),
inference(cnf_transformation,[],[f127]) ).
fof(f269,plain,
! [X1] :
( ~ aElementOf0(X1,xS)
| sdtlseqdt0(szmzizndt0(xS),X1) ),
inference(cnf_transformation,[],[f171]) ).
fof(f270,plain,
aElementOf0(szmzizndt0(xS),xS),
inference(cnf_transformation,[],[f171]) ).
fof(f271,plain,
szmzizndt0(xS) != szmzizndt0(xT),
inference(cnf_transformation,[],[f171]) ).
tcf(c_109,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f232]) ).
tcf(c_131,plain,
! [X0: $i] :
( aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X0,xS) ),
inference(cnf_transformation,[],[f261]) ).
tcf(c_142,plain,
aElementOf0(szmzizndt0(xS),xT),
inference(cnf_transformation,[],[f266]) ).
tcf(c_144,plain,
! [X0: $i] :
( sdtlseqdt0(szmzizndt0(xT),X0)
| ~ aElementOf0(X0,xT) ),
inference(cnf_transformation,[],[f264]) ).
tcf(c_145,plain,
aElementOf0(szmzizndt0(xT),xS),
inference(cnf_transformation,[],[f263]) ).
tcf(c_148,negated_conjecture,
szmzizndt0(xS) != szmzizndt0(xT),
inference(cnf_transformation,[],[f271]) ).
tcf(c_149,negated_conjecture,
aElementOf0(szmzizndt0(xS),xS),
inference(cnf_transformation,[],[f270]) ).
tcf(c_150,negated_conjecture,
! [X0: $i] :
( sdtlseqdt0(szmzizndt0(xS),X0)
| ~ aElementOf0(X0,xS) ),
inference(cnf_transformation,[],[f269]) ).
tcf(c_7910,definition,
iPr_def_10 = szmzizndt0(xS),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_7911,definition,
iPr_def_11 = szmzizndt0(xT),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_7912,negated_conjecture,
iPr_def_10 != iPr_def_11,
inference(demodulation,[status(thm)],[c_148,c_7911,c_7910]) ).
tcf(c_7915,negated_conjecture,
! [X0: $i] :
( sdtlseqdt0(iPr_def_10,X0)
| ~ aElementOf0(X0,xS) ),
inference(demodulation,[status(thm)],[c_150]) ).
tcf(c_7916,negated_conjecture,
aElementOf0(iPr_def_10,xS),
inference(demodulation,[status(thm)],[c_149]) ).
tcf(c_9288,plain,
aElementOf0(iPr_def_10,xT),
inference(light_normalisation,[status(thm)],[c_142,c_7910]) ).
tcf(c_9290,plain,
aElementOf0(iPr_def_11,xS),
inference(light_normalisation,[status(thm)],[c_145,c_7911]) ).
tcf(c_9291,plain,
sdtlseqdt0(iPr_def_10,iPr_def_11),
inference(superposition,[status(thm)],[c_9290,c_7915]) ).
tcf(c_9325,plain,
aElementOf0(iPr_def_10,szNzAzT0),
inference(superposition,[status(thm)],[c_7916,c_131]) ).
tcf(c_9326,plain,
aElementOf0(iPr_def_11,szNzAzT0),
inference(superposition,[status(thm)],[c_9290,c_131]) ).
tcf(c_9357,plain,
! [X0: $i] :
( sdtlseqdt0(iPr_def_11,X0)
| ~ aElementOf0(X0,xT) ),
inference(light_normalisation,[status(thm)],[c_144,c_7911]) ).
tcf(c_9366,plain,
sdtlseqdt0(iPr_def_11,iPr_def_10),
inference(superposition,[status(thm)],[c_9288,c_9357]) ).
tcf(c_11093,plain,
( ( iPr_def_10 = iPr_def_11 )
| ~ sdtlseqdt0(iPr_def_11,iPr_def_10)
| ~ sdtlseqdt0(iPr_def_10,iPr_def_11)
| ~ aElementOf0(iPr_def_11,szNzAzT0)
| ~ aElementOf0(iPr_def_10,szNzAzT0) ),
inference(instantiation,[status(thm)],[c_109]) ).
tcf(c_11094,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_11093,c_9366,c_9325,c_9326,c_9291,c_7912]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM539+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.36 % Computer : n016.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Thu Sep 24 04:36:12 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.39 Running first-order theorem proving
% 0.08/0.39 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
% 0.08/0.41
% 0.08/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.08/0.41
% 0.08/0.41 % Detected problem language: tptp
% 0.08/0.42 % Proving...
% 3.82/1.27 % SZS status Started for theBenchmark.p
% 3.82/1.27 % SZS status Theorem for theBenchmark.p
% 3.82/1.27
% 3.82/1.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.82/1.27
% 3.82/1.27 % ------ iProver source info
% 3.82/1.27
% 3.82/1.27 % git: date: 2026-07-19 20:42:38 +0200
% 3.82/1.27 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.82/1.27 % git: non_committed_changes: false
% 3.82/1.27
% 3.82/1.27 % ------ Parsing...
% 3.82/1.27 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.82/1.27
% 3.82/1.27 % ------ 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 %
% 3.82/1.27
% 3.82/1.27 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.82/1.27
% 3.82/1.27 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.82/1.27 % ------ Proving...
% 3.82/1.27 % ------ Problem Properties
% 3.82/1.27
% 3.82/1.27 %
% 3.82/1.27 % clauses 100
% 3.82/1.27 % conjectures 5
% 3.82/1.27 % EPR 44
% 3.82/1.27 % Horn 77
% 3.82/1.27 % unary 25
% 3.82/1.27 % binary 16
% 3.82/1.27 % lits 291
% 3.82/1.27 % lits eq 43
% 3.82/1.27 % fd_pure 0
% 3.82/1.27 % fd_pseudo 0
% 3.82/1.27 % fd_cond 7
% 3.82/1.27 % fd_pseudo_cond 11
% 3.82/1.27 % AC symbols 0
% 3.82/1.27
% 3.82/1.27 % ------ Schedule dynamic 5 is on
% 3.82/1.27
% 3.82/1.27 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.82/1.27
% 3.82/1.27
% 3.82/1.27 % ------
% 3.82/1.27 % Current options:
% 3.82/1.27 % ------
% 3.82/1.27
% 3.82/1.27
% 3.82/1.27 %
% 3.82/1.27
% 3.82/1.27 % ------ Proving...
% 3.82/1.27 %
% 3.82/1.27
% 3.82/1.27 % SZS status Theorem for theBenchmark.p
% 3.82/1.27
% 3.82/1.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.82/1.27
% 3.82/1.27
%------------------------------------------------------------------------------