%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : RNG108+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n013.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 02:39:09 PM UTC 2026
% Result : Theorem 4.25s 2.11s
% Output : CNFRefutation 4.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 9
% Syntax : Number of formulae : 55 ( 21 unt; 2 def)
% Number of atoms : 206 ( 49 equ)
% Maximal formula atoms : 17 ( 3 avg)
% Number of connectives : 224 ( 90 ~; 88 |; 39 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 56 ( 0 sgn 45 !; 11 ?; 4 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aElement0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC) ).
fof(f3,axiom,
aElement0(sz10),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC_01) ).
fof(f13,axiom,
! [X0] :
( aElement0(X0)
=> ( X0 = sdtasdt0(sz10,X0)
& sdtasdt0(X0,sz10) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulUnit) ).
fof(f16,axiom,
! [X0] :
( aElement0(X0)
=> ( sz00 = sdtasdt0(sz00,X0)
& sdtasdt0(X0,sz00) = sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulZero) ).
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/sandbox2/benchmark/theBenchmark.p',mDefPrIdeal) ).
fof(f39,axiom,
( aElement0(xb)
& aElement0(xa) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2091) ).
fof(f43,conjecture,
( aElementOf0(xb,slsdtgt0(xb))
& aElementOf0(sz00,slsdtgt0(xb))
& aElementOf0(xa,slsdtgt0(xa))
& aElementOf0(sz00,slsdtgt0(xa)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f44,negated_conjecture,
~ ( aElementOf0(xb,slsdtgt0(xb))
& aElementOf0(sz00,slsdtgt0(xb))
& aElementOf0(xa,slsdtgt0(xa))
& aElementOf0(sz00,slsdtgt0(xa)) ),
inference(negated_conjecture,[status(cth)],[f43]) ).
fof(f69,plain,
! [X0] :
( ~ aElement0(X0)
| ( X0 = sdtasdt0(sz10,X0)
& sdtasdt0(X0,sz10) = X0 ) ),
inference(ennf_transformation,[],[f13]) ).
fof(f73,plain,
! [X0] :
( ~ aElement0(X0)
| ( sz00 = sdtasdt0(sz00,X0)
& sdtasdt0(X0,sz00) = sz00 ) ),
inference(ennf_transformation,[],[f16]) ).
fof(f101,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(f103,plain,
( ~ aElementOf0(xb,slsdtgt0(xb))
| ~ aElementOf0(sz00,slsdtgt0(xb))
| ~ aElementOf0(xa,slsdtgt0(xa))
| ~ aElementOf0(sz00,slsdtgt0(xa)) ),
inference(ennf_transformation,[],[f44]) ).
fof(f136,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,[],[f101]) ).
fof(f137,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,[],[f136]) ).
fof(f138,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,[],[f137]) ).
fof(f139,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))],[f138]) ).
fof(f140,plain,
aElement0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f141,plain,
aElement0(sz10),
inference(cnf_transformation,[],[f3]) ).
fof(f154,plain,
! [X0] :
( ~ aElement0(X0)
| sdtasdt0(X0,sz10) = X0 ),
inference(cnf_transformation,[],[f69]) ).
fof(f160,plain,
! [X0] :
( ~ aElement0(X0)
| sz00 = sdtasdt0(X0,sz00) ),
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,[],[f139]) ).
fof(f230,plain,
aElement0(xb),
inference(cnf_transformation,[],[f39]) ).
fof(f231,plain,
aElement0(xa),
inference(cnf_transformation,[],[f39]) ).
fof(f236,plain,
( ~ aElementOf0(xb,slsdtgt0(xb))
| ~ aElementOf0(sz00,slsdtgt0(xb))
| ~ aElementOf0(xa,slsdtgt0(xa))
| ~ aElementOf0(sz00,slsdtgt0(xa)) ),
inference(cnf_transformation,[],[f103]) ).
fof(f245,plain,
! [X0,X1,X6] :
( ~ aElement0(X0)
| slsdtgt0(X0) != X1
| ~ aElement0(X6)
| aElementOf0(sdtasdt0(X0,X6),X1) ),
inference(equality_resolution,[],[f224]) ).
fof(f246,plain,
! [X0,X6] :
( ~ aElement0(X0)
| ~ aElement0(X6)
| aElementOf0(sdtasdt0(X0,X6),slsdtgt0(X0)) ),
inference(equality_resolution,[],[f245]) ).
tcf(c_49,plain,
aElement0(sz00),
inference(cnf_transformation,[],[f140]) ).
tcf(c_50,plain,
aElement0(sz10),
inference(cnf_transformation,[],[f141]) ).
tcf(c_62,plain,
! [X0: $i] :
( ( sdtasdt0(X0,sz10) = X0 )
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f154]) ).
tcf(c_68,plain,
! [X0: $i] :
( ( sdtasdt0(X0,sz00) = sz00 )
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f160]) ).
tcf(c_135,plain,
! [X0: $i,X1: $i] :
( aElementOf0(sdtasdt0(X0,X1),slsdtgt0(X0))
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f246]) ).
tcf(c_139,plain,
aElement0(xa),
inference(cnf_transformation,[],[f231]) ).
tcf(c_140,plain,
aElement0(xb),
inference(cnf_transformation,[],[f230]) ).
tcf(c_145,negated_conjecture,
( ~ aElementOf0(xb,slsdtgt0(xb))
| ~ aElementOf0(xa,slsdtgt0(xa))
| ~ aElementOf0(sz00,slsdtgt0(xb))
| ~ aElementOf0(sz00,slsdtgt0(xa)) ),
inference(cnf_transformation,[],[f236]) ).
tcf(c_5215,definition,
iPr_def_10 = slsdtgt0(xa),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_5216,definition,
iPr_def_11 = slsdtgt0(xb),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_5217,negated_conjecture,
( ~ aElementOf0(xb,iPr_def_11)
| ~ aElementOf0(xa,iPr_def_10)
| ~ aElementOf0(sz00,iPr_def_11)
| ~ aElementOf0(sz00,iPr_def_10) ),
inference(demodulation,[status(thm)],[c_145,c_5216,c_5215]) ).
tcf(c_6831,plain,
sdtasdt0(xa,sz10) = xa,
inference(superposition,[status(thm)],[c_139,c_62]) ).
tcf(c_6832,plain,
sdtasdt0(xb,sz10) = xb,
inference(superposition,[status(thm)],[c_140,c_62]) ).
tcf(c_6855,plain,
sdtasdt0(xa,sz00) = sz00,
inference(superposition,[status(thm)],[c_139,c_68]) ).
tcf(c_6856,plain,
sdtasdt0(xb,sz00) = sz00,
inference(superposition,[status(thm)],[c_140,c_68]) ).
tcf(c_7357,plain,
( aElementOf0(xa,slsdtgt0(xa))
| ~ aElement0(xa)
| ~ aElement0(sz10) ),
inference(superposition,[status(thm)],[c_6831,c_135]) ).
tcf(c_7358,plain,
( aElementOf0(xb,slsdtgt0(xb))
| ~ aElement0(xb)
| ~ aElement0(sz10) ),
inference(superposition,[status(thm)],[c_6832,c_135]) ).
tcf(c_7361,plain,
( aElementOf0(sz00,slsdtgt0(xa))
| ~ aElement0(xa)
| ~ aElement0(sz00) ),
inference(superposition,[status(thm)],[c_6855,c_135]) ).
tcf(c_7362,plain,
( aElementOf0(sz00,slsdtgt0(xb))
| ~ aElement0(xb)
| ~ aElement0(sz00) ),
inference(superposition,[status(thm)],[c_6856,c_135]) ).
tcf(c_7377,plain,
( aElementOf0(sz00,iPr_def_11)
| ~ aElement0(xb)
| ~ aElement0(sz00) ),
inference(light_normalisation,[status(thm)],[c_7362,c_5216]) ).
tcf(c_7378,plain,
aElementOf0(sz00,iPr_def_11),
inference(forward_subsumption_resolution,[status(thm)],[c_7377,c_140,c_49]) ).
tcf(c_7379,plain,
( aElementOf0(sz00,iPr_def_10)
| ~ aElement0(xa)
| ~ aElement0(sz00) ),
inference(light_normalisation,[status(thm)],[c_7361,c_5215]) ).
tcf(c_7380,plain,
aElementOf0(sz00,iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_7379,c_139,c_49]) ).
tcf(c_7383,plain,
( aElementOf0(xb,iPr_def_11)
| ~ aElement0(xb)
| ~ aElement0(sz10) ),
inference(light_normalisation,[status(thm)],[c_7358,c_5216]) ).
tcf(c_7384,plain,
aElementOf0(xb,iPr_def_11),
inference(forward_subsumption_resolution,[status(thm)],[c_7383,c_140,c_50]) ).
tcf(c_7385,plain,
( aElementOf0(xa,iPr_def_10)
| ~ aElement0(xa)
| ~ aElement0(sz10) ),
inference(light_normalisation,[status(thm)],[c_7357,c_5215]) ).
tcf(c_7386,plain,
aElementOf0(xa,iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_7385,c_139,c_50]) ).
tcf(c_7412,plain,
( ~ aElementOf0(xb,iPr_def_11)
| ~ aElementOf0(xa,iPr_def_10)
| ~ aElementOf0(sz00,iPr_def_10) ),
inference(backward_subsumption_resolution,[status(thm)],[c_5217,c_7378]) ).
tcf(c_7413,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_7412,c_7384,c_7386,c_7380]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG108+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/1.20 % Computer : n013.cluster.edu
% 0.10/1.20 % Model : x86_64 x86_64
% 0.10/1.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/1.20 % Memory : 8046.5625MB
% 0.10/1.20 % OS : Linux 6.8.0-71-generic
% 0.02/1.20 % CPULimit : 300
% 0.02/1.20 % WCLimit : 300
% 0.02/1.20 % DateTime : Thu Sep 24 08:16:29 UTC 2026
% 0.02/1.20 % CPUTime :
% 0.02/1.20 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.02/1.23 Running first-order theorem proving
% 0.02/1.23 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.02/1.24
% 0.02/1.24 % ======== iProver multi-core TPTP/SMT =========
% 0.02/1.24
% 0.02/1.24 % Detected problem language: tptp
% 0.02/1.26 % Proving...
% 4.25/2.11 % SZS status Started for theBenchmark.p
% 4.25/2.11 % SZS status Theorem for theBenchmark.p
% 4.25/2.11
% 4.25/2.11 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.25/2.11
% 4.25/2.11 % ------ iProver source info
% 4.25/2.11
% 4.25/2.11 % git: date: 2026-07-19 20:42:38 +0200
% 4.25/2.11 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.25/2.11 % git: non_committed_changes: false
% 4.25/2.11
% 4.25/2.11 % ------ Parsing...
% 4.25/2.11 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.25/2.11
% 4.25/2.11 % ------ 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 %
% 4.25/2.11
% 4.25/2.11 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.25/2.11
% 4.25/2.11 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.25/2.11 % ------ Proving...
% 4.25/2.11 % ------ Problem Properties
% 4.25/2.11
% 4.25/2.11 %
% 4.25/2.11 % clauses 94
% 4.25/2.11 % conjectures 1
% 4.25/2.11 % EPR 18
% 4.25/2.11 % Horn 71
% 4.25/2.11 % unary 10
% 4.25/2.11 % binary 16
% 4.25/2.11 % lits 334
% 4.25/2.11 % lits eq 47
% 4.25/2.11 % fd_pure 0
% 4.25/2.11 % fd_pseudo 0
% 4.25/2.11 % fd_cond 3
% 4.25/2.11 % fd_pseudo_cond 11
% 4.25/2.11 % AC symbols 0
% 4.25/2.11
% 4.25/2.11 % ------ Schedule dynamic 5 is on
% 4.25/2.11
% 4.25/2.11 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.25/2.11
% 4.25/2.11
% 4.25/2.11 % ------
% 4.25/2.11 % Current options:
% 4.25/2.11 % ------
% 4.25/2.11
% 4.25/2.11
% 4.25/2.11 %
% 4.25/2.11
% 4.25/2.11 % ------ Proving...
% 4.25/2.11 %
% 4.25/2.11
% 4.25/2.11 % SZS status Theorem for theBenchmark.p
% 4.25/2.11
% 4.25/2.11 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.25/2.12
% 4.25/2.12
%------------------------------------------------------------------------------