%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : RNG047+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 : n001.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 02:38:18 PM UTC 2026
% Result : Theorem 2.56s 1.09s
% Output : CNFRefutation 2.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 10
% Syntax : Number of formulae : 61 ( 25 unt; 4 def)
% Number of atoms : 205 ( 95 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 186 ( 71 ~; 81 |; 25 &)
% ( 3 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 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 : 8 ( 6 usr; 5 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 48 ( 0 sgn 45 !; 3 ?; 7 :)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( szszuzczcdt0(X0) = szszuzczcdt0(X1)
=> X0 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSuccEqu) ).
fof(f30,axiom,
! [X0] :
( aVector0(X0)
=> aNaturalNumber0(aDimensionOf0(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDimNat) ).
fof(f32,axiom,
! [X0] :
( aVector0(X0)
=> ( aDimensionOf0(X0) != sz00
=> ! [X1] :
( X1 = sziznziztdt0(X0)
<=> ( ! [X2] :
( aNaturalNumber0(X2)
=> sdtlbdtrb0(X1,X2) = sdtlbdtrb0(X0,X2) )
& szszuzczcdt0(aDimensionOf0(X1)) = aDimensionOf0(X0)
& aVector0(X1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefInit) ).
fof(f33,axiom,
( aVector0(xt)
& aVector0(xs) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1329) ).
fof(f34,axiom,
( aDimensionOf0(xt) != sz00
& aDimensionOf0(xs) = aDimensionOf0(xt) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1329_01) ).
fof(f35,conjecture,
aDimensionOf0(sziznziztdt0(xs)) = aDimensionOf0(sziznziztdt0(xt)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f36,negated_conjecture,
aDimensionOf0(sziznziztdt0(xs)) != aDimensionOf0(sziznziztdt0(xt)),
inference(negated_conjecture,[status(cth)],[f35]) ).
fof(f42,plain,
aDimensionOf0(sziznziztdt0(xs)) != aDimensionOf0(sziznziztdt0(xt)),
inference(flattening,[],[f36]) ).
fof(f47,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| szszuzczcdt0(X0) != szszuzczcdt0(X1)
| X0 = X1 ),
inference(ennf_transformation,[],[f5]) ).
fof(f48,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| szszuzczcdt0(X0) != szszuzczcdt0(X1)
| X0 = X1 ),
inference(flattening,[],[f47]) ).
fof(f81,plain,
! [X0] :
( ~ aVector0(X0)
| aNaturalNumber0(aDimensionOf0(X0)) ),
inference(ennf_transformation,[],[f30]) ).
fof(f84,plain,
! [X0] :
( ~ aVector0(X0)
| sz00 = aDimensionOf0(X0)
| ! [X1] :
( X1 = sziznziztdt0(X0)
<=> ( ! [X2] :
( ~ aNaturalNumber0(X2)
| sdtlbdtrb0(X1,X2) = sdtlbdtrb0(X0,X2) )
& szszuzczcdt0(aDimensionOf0(X1)) = aDimensionOf0(X0)
& aVector0(X1) ) ) ),
inference(ennf_transformation,[],[f32]) ).
fof(f85,plain,
! [X0] :
( ~ aVector0(X0)
| sz00 = aDimensionOf0(X0)
| ! [X1] :
( X1 = sziznziztdt0(X0)
<=> ( ! [X2] :
( ~ aNaturalNumber0(X2)
| sdtlbdtrb0(X1,X2) = sdtlbdtrb0(X0,X2) )
& szszuzczcdt0(aDimensionOf0(X1)) = aDimensionOf0(X0)
& aVector0(X1) ) ) ),
inference(flattening,[],[f84]) ).
fof(f87,plain,
! [X0] :
( ~ aVector0(X0)
| sz00 = aDimensionOf0(X0)
| ! [X1] :
( ( sziznziztdt0(X0) != X1
| ( ! [X2] :
( ~ aNaturalNumber0(X2)
| sdtlbdtrb0(X1,X2) = sdtlbdtrb0(X0,X2) )
& szszuzczcdt0(aDimensionOf0(X1)) = aDimensionOf0(X0)
& aVector0(X1) ) )
& ( ? [X2] :
( aNaturalNumber0(X2)
& sdtlbdtrb0(X1,X2) != sdtlbdtrb0(X0,X2) )
| aDimensionOf0(X0) != szszuzczcdt0(aDimensionOf0(X1))
| ~ aVector0(X1)
| X1 = sziznziztdt0(X0) ) ) ),
inference(nnf_transformation,[],[f85]) ).
fof(f88,plain,
! [X0] :
( ~ aVector0(X0)
| sz00 = aDimensionOf0(X0)
| ! [X1] :
( ( sziznziztdt0(X0) != X1
| ( ! [X2] :
( ~ aNaturalNumber0(X2)
| sdtlbdtrb0(X1,X2) = sdtlbdtrb0(X0,X2) )
& szszuzczcdt0(aDimensionOf0(X1)) = aDimensionOf0(X0)
& aVector0(X1) ) )
& ( ? [X2] :
( aNaturalNumber0(X2)
& sdtlbdtrb0(X1,X2) != sdtlbdtrb0(X0,X2) )
| aDimensionOf0(X0) != szszuzczcdt0(aDimensionOf0(X1))
| ~ aVector0(X1)
| X1 = sziznziztdt0(X0) ) ) ),
inference(flattening,[],[f87]) ).
fof(f89,plain,
! [X0] :
( ~ aVector0(X0)
| sz00 = aDimensionOf0(X0)
| ! [X1] :
( ( sziznziztdt0(X0) != X1
| ( ! [X3] :
( ~ aNaturalNumber0(X3)
| sdtlbdtrb0(X1,X3) = sdtlbdtrb0(X0,X3) )
& szszuzczcdt0(aDimensionOf0(X1)) = aDimensionOf0(X0)
& aVector0(X1) ) )
& ( ? [X2] :
( aNaturalNumber0(X2)
& sdtlbdtrb0(X1,X2) != sdtlbdtrb0(X0,X2) )
| aDimensionOf0(X0) != szszuzczcdt0(aDimensionOf0(X1))
| ~ aVector0(X1)
| X1 = sziznziztdt0(X0) ) ) ),
inference(rectify,[],[f88]) ).
fof(f90,plain,
! [X0] :
( ~ aVector0(X0)
| sz00 = aDimensionOf0(X0)
| ! [X1] :
( ( sziznziztdt0(X0) != X1
| ( ! [X3] :
( ~ aNaturalNumber0(X3)
| sdtlbdtrb0(X1,X3) = sdtlbdtrb0(X0,X3) )
& szszuzczcdt0(aDimensionOf0(X1)) = aDimensionOf0(X0)
& aVector0(X1) ) )
& ( ( aNaturalNumber0(sK1(X0,X1))
& sdtlbdtrb0(X1,sK1(X0,X1)) != sdtlbdtrb0(X0,sK1(X0,X1)) )
| aDimensionOf0(X0) != szszuzczcdt0(aDimensionOf0(X1))
| ~ aVector0(X1)
| X1 = sziznziztdt0(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X2,sK1(X0,X1))],[f89]) ).
fof(f96,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| szszuzczcdt0(X0) != szszuzczcdt0(X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f48]) ).
fof(f129,plain,
! [X0] :
( ~ aVector0(X0)
| aNaturalNumber0(aDimensionOf0(X0)) ),
inference(cnf_transformation,[],[f81]) ).
fof(f132,plain,
! [X0,X1] :
( ~ aVector0(X0)
| sz00 = aDimensionOf0(X0)
| sziznziztdt0(X0) != X1
| aDimensionOf0(X0) = szszuzczcdt0(aDimensionOf0(X1)) ),
inference(cnf_transformation,[],[f90]) ).
fof(f133,plain,
! [X0,X1] :
( ~ aVector0(X0)
| sz00 = aDimensionOf0(X0)
| sziznziztdt0(X0) != X1
| aVector0(X1) ),
inference(cnf_transformation,[],[f90]) ).
fof(f136,plain,
aVector0(xt),
inference(cnf_transformation,[],[f33]) ).
fof(f137,plain,
aVector0(xs),
inference(cnf_transformation,[],[f33]) ).
fof(f138,plain,
sz00 != aDimensionOf0(xt),
inference(cnf_transformation,[],[f34]) ).
fof(f139,plain,
aDimensionOf0(xs) = aDimensionOf0(xt),
inference(cnf_transformation,[],[f34]) ).
fof(f140,plain,
aDimensionOf0(sziznziztdt0(xs)) != aDimensionOf0(sziznziztdt0(xt)),
inference(cnf_transformation,[],[f42]) ).
fof(f141,plain,
! [X0] :
( ~ aVector0(X0)
| sz00 = aDimensionOf0(X0)
| aVector0(sziznziztdt0(X0)) ),
inference(equality_resolution,[],[f133]) ).
fof(f142,plain,
! [X0] :
( ~ aVector0(X0)
| sz00 = aDimensionOf0(X0)
| aDimensionOf0(X0) = szszuzczcdt0(aDimensionOf0(sziznziztdt0(X0))) ),
inference(equality_resolution,[],[f132]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( szszuzczcdt0(X0) != szszuzczcdt0(X1) ) ),
inference(cnf_transformation,[],[f96]) ).
tcf(c_87,plain,
! [X0: $i] :
( aNaturalNumber0(aDimensionOf0(X0))
| ~ aVector0(X0) ),
inference(cnf_transformation,[],[f129]) ).
tcf(c_91,plain,
! [X0: $i] :
( aVector0(sziznziztdt0(X0))
| ( aDimensionOf0(X0) = sz00 )
| ~ aVector0(X0) ),
inference(cnf_transformation,[],[f141]) ).
tcf(c_92,plain,
! [X0: $i] :
( ( aDimensionOf0(X0) = sz00 )
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(X0))) = aDimensionOf0(X0) )
| ~ aVector0(X0) ),
inference(cnf_transformation,[],[f142]) ).
tcf(c_94,plain,
aVector0(xs),
inference(cnf_transformation,[],[f137]) ).
tcf(c_95,plain,
aVector0(xt),
inference(cnf_transformation,[],[f136]) ).
tcf(c_96,plain,
aDimensionOf0(xs) = aDimensionOf0(xt),
inference(cnf_transformation,[],[f139]) ).
tcf(c_97,plain,
aDimensionOf0(xt) != sz00,
inference(cnf_transformation,[],[f138]) ).
tcf(c_98,negated_conjecture,
aDimensionOf0(sziznziztdt0(xs)) != aDimensionOf0(sziznziztdt0(xt)),
inference(cnf_transformation,[],[f140]) ).
tcf(c_777,definition,
iPr_def_13 = sziznziztdt0(xs),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_778,definition,
iPr_def_14 = aDimensionOf0(iPr_def_13),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_779,definition,
iPr_def_15 = sziznziztdt0(xt),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_780,definition,
iPr_def_16 = aDimensionOf0(iPr_def_15),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_781,negated_conjecture,
iPr_def_14 != iPr_def_16,
inference(demodulation,[status(thm)],[c_98,c_779,c_780,c_777,c_778]) ).
tcf(c_1625,plain,
( aNaturalNumber0(iPr_def_14)
| ~ aVector0(iPr_def_13) ),
inference(superposition,[status(thm)],[c_778,c_87]) ).
tcf(c_1626,plain,
( aNaturalNumber0(iPr_def_16)
| ~ aVector0(iPr_def_15) ),
inference(superposition,[status(thm)],[c_780,c_87]) ).
tcf(c_1904,plain,
( aVector0(iPr_def_13)
| ( aDimensionOf0(xs) = sz00 )
| ~ aVector0(xs) ),
inference(superposition,[status(thm)],[c_777,c_91]) ).
tcf(c_1905,plain,
( aVector0(iPr_def_15)
| ( aDimensionOf0(xt) = sz00 )
| ~ aVector0(xt) ),
inference(superposition,[status(thm)],[c_779,c_91]) ).
tcf(c_1906,plain,
aVector0(iPr_def_15),
inference(forward_subsumption_resolution,[status(thm)],[c_1905,c_97,c_95]) ).
tcf(c_1907,plain,
( aVector0(iPr_def_13)
| ( aDimensionOf0(xt) = sz00 )
| ~ aVector0(xs) ),
inference(light_normalisation,[status(thm)],[c_1904,c_96]) ).
tcf(c_1908,plain,
aVector0(iPr_def_13),
inference(forward_subsumption_resolution,[status(thm)],[c_1907,c_97,c_94]) ).
tcf(c_1909,plain,
aNaturalNumber0(iPr_def_16),
inference(backward_subsumption_resolution,[status(thm)],[c_1626,c_1906]) ).
tcf(c_1910,plain,
aNaturalNumber0(iPr_def_14),
inference(backward_subsumption_resolution,[status(thm)],[c_1625,c_1908]) ).
tcf(c_2350,plain,
( ( aDimensionOf0(xs) = sz00 )
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) = aDimensionOf0(xs) ) ),
inference(superposition,[status(thm)],[c_94,c_92]) ).
tcf(c_2351,plain,
( ( aDimensionOf0(xt) = sz00 )
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) = aDimensionOf0(xt) ) ),
inference(superposition,[status(thm)],[c_95,c_92]) ).
tcf(c_2360,plain,
( ( aDimensionOf0(xt) = sz00 )
| ( szszuzczcdt0(iPr_def_16) = aDimensionOf0(xt) ) ),
inference(light_normalisation,[status(thm)],[c_2351,c_779,c_780]) ).
tcf(c_2361,plain,
szszuzczcdt0(iPr_def_16) = aDimensionOf0(xt),
inference(forward_subsumption_resolution,[status(thm)],[c_2360,c_97]) ).
tcf(c_2362,plain,
( ( aDimensionOf0(xt) = sz00 )
| ( szszuzczcdt0(iPr_def_14) = aDimensionOf0(xt) ) ),
inference(light_normalisation,[status(thm)],[c_2350,c_96,c_777,c_778]) ).
tcf(c_2363,plain,
szszuzczcdt0(iPr_def_14) = aDimensionOf0(xt),
inference(forward_subsumption_resolution,[status(thm)],[c_2362,c_97]) ).
tcf(c_2437,plain,
! [X0: $i] :
( ( X0 = iPr_def_16 )
| ~ aNaturalNumber0(iPr_def_16)
| ~ aNaturalNumber0(X0)
| ( szszuzczcdt0(X0) != aDimensionOf0(xt) ) ),
inference(superposition,[status(thm)],[c_2361,c_54]) ).
tcf(c_2438,plain,
! [X0: $i] :
( ( X0 = iPr_def_16 )
| ~ aNaturalNumber0(X0)
| ( szszuzczcdt0(X0) != aDimensionOf0(xt) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2437,c_1909]) ).
tcf(c_4979,plain,
( ( iPr_def_14 = iPr_def_16 )
| ~ aNaturalNumber0(iPr_def_14) ),
inference(superposition,[status(thm)],[c_2363,c_2438]) ).
tcf(c_4988,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_4979,c_781,c_1910]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG047+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.38 % Computer : n001.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Thu Sep 24 08:02:54 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 0.11/0.43
% 0.11/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.43
% 0.11/0.43 % Detected problem language: tptp
% 0.11/0.44 % Proving...
% 2.56/1.09 % SZS status Started for theBenchmark.p
% 2.56/1.09 % SZS status Theorem for theBenchmark.p
% 2.56/1.09
% 2.56/1.09 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.56/1.09
% 2.56/1.09 % ------ iProver source info
% 2.56/1.09
% 2.56/1.09 % git: date: 2026-07-19 20:42:38 +0200
% 2.56/1.09 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.56/1.09 % git: non_committed_changes: false
% 2.56/1.09
% 2.56/1.09 % ------ Parsing...
% 2.56/1.09 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.56/1.09
% 2.56/1.09 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 2.56/1.09
% 2.56/1.09 % ------ Preprocessing... gs_s sp: 4 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.56/1.09
% 2.56/1.09 % ------ Preprocessing... sf_s rm: 4 0s sf_e sf_s rm: 0 0s sf_e
% 2.56/1.09 % ------ Proving...
% 2.56/1.09 % ------ Problem Properties
% 2.56/1.09
% 2.56/1.09 %
% 2.56/1.09 % clauses 57
% 2.56/1.09 % conjectures 1
% 2.56/1.09 % EPR 12
% 2.56/1.09 % Horn 47
% 2.56/1.09 % unary 12
% 2.56/1.09 % binary 16
% 2.56/1.09 % lits 169
% 2.56/1.09 % lits eq 46
% 2.56/1.09 % fd_pure 0
% 2.56/1.09 % fd_pseudo 0
% 2.56/1.09 % fd_cond 1
% 2.56/1.09 % fd_pseudo_cond 5
% 2.56/1.09 % AC symbols 0
% 2.56/1.09
% 2.56/1.09 % ------ Schedule dynamic 5 is on
% 2.56/1.09
% 2.56/1.09 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.56/1.09
% 2.56/1.09
% 2.56/1.09 % ------
% 2.56/1.09 % Current options:
% 2.56/1.09 % ------
% 2.56/1.09
% 2.56/1.09
% 2.56/1.09 %
% 2.56/1.09
% 2.56/1.09 % ------ Proving...
% 2.56/1.09 %
% 2.56/1.09
% 2.56/1.09 % SZS status Theorem for theBenchmark.p
% 2.56/1.09
% 2.56/1.09 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.56/1.09
% 2.56/1.09
%------------------------------------------------------------------------------