%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : RNG116+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 : 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 02:39:12 PM UTC 2026
% Result : Theorem 3.56s 1.19s
% Output : CNFRefutation 3.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 4
% Syntax : Number of formulae : 42 ( 16 unt; 0 def)
% Number of atoms : 151 ( 48 equ)
% Maximal formula atoms : 17 ( 3 avg)
% Number of connectives : 182 ( 73 ~; 69 |; 35 &)
% ( 4 <=>; 1 =>; 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 : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-2 aty)
% Number of variables : 63 ( 0 sgn 48 !; 15 ?; 8 :)
% Comments :
%------------------------------------------------------------------------------
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(f39,axiom,
( aElement0(xb)
& aElement0(xa) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2091) ).
fof(f47,axiom,
( xu = sdtpldt0(xk,xl)
& aElementOf0(xl,slsdtgt0(xb))
& aElementOf0(xk,slsdtgt0(xa)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2456) ).
fof(f48,conjecture,
? [X0,X1] :
( xu = sdtpldt0(sdtasdt0(xa,X0),sdtasdt0(xb,X1))
& aElement0(X1)
& aElement0(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f49,negated_conjecture,
~ ? [X0,X1] :
( xu = sdtpldt0(sdtasdt0(xa,X0),sdtasdt0(xb,X1))
& aElement0(X1)
& aElement0(X0) ),
inference(negated_conjecture,[status(cth)],[f48]) ).
fof(f60,plain,
! [X0,X1] :
( xu != sdtpldt0(sdtasdt0(xa,X0),sdtasdt0(xb,X1))
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f49]) ).
fof(f73,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(f114,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,[],[f73]) ).
fof(f115,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,[],[f114]) ).
fof(f116,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,[],[f115]) ).
fof(f117,plain,
! [X0] :
( ~ aElement0(X0)
| ! [X1] :
( ( slsdtgt0(X0) != X1
| ( ! [X5] :
( ( ~ aElementOf0(X5,X1)
| ( sdtasdt0(X0,sK14(X0,X5)) = X5
& aElement0(sK14(X0,X5)) ) )
& ( ! [X6] :
( sdtasdt0(X0,X6) != X5
| ~ aElement0(X6) )
| aElementOf0(X5,X1) ) )
& aSet0(X1) ) )
& ( ( ( aElementOf0(sK12(X0,X1),X1)
| ( sK12(X0,X1) = sdtasdt0(X0,sK13(X0,X1))
& aElement0(sK13(X0,X1)) ) )
& ( ~ aElementOf0(sK12(X0,X1),X1)
| ! [X3] :
( sdtasdt0(X0,X3) != sK12(X0,X1)
| ~ aElement0(X3) ) ) )
| ~ aSet0(X1)
| X1 = slsdtgt0(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12,sK13,sK14]),skolemize(X2,sK12(X0,X1)),skolemize(X4,sK13(X0,X1)),skolemize(X7,sK14(X0,X5))],[f116]) ).
fof(f125,plain,
aElement0(xb),
inference(cnf_transformation,[],[f39]) ).
fof(f126,plain,
aElement0(xa),
inference(cnf_transformation,[],[f39]) ).
fof(f141,plain,
xu = sdtpldt0(xk,xl),
inference(cnf_transformation,[],[f47]) ).
fof(f142,plain,
aElementOf0(xl,slsdtgt0(xb)),
inference(cnf_transformation,[],[f47]) ).
fof(f143,plain,
aElementOf0(xk,slsdtgt0(xa)),
inference(cnf_transformation,[],[f47]) ).
fof(f144,plain,
! [X0,X1] :
( xu != sdtpldt0(sdtasdt0(xa,X0),sdtasdt0(xb,X1))
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f60]) ).
fof(f179,plain,
! [X0,X1,X5] :
( ~ aElement0(X0)
| slsdtgt0(X0) != X1
| ~ aElementOf0(X5,X1)
| sdtasdt0(X0,sK14(X0,X5)) = X5 ),
inference(cnf_transformation,[],[f117]) ).
fof(f180,plain,
! [X0,X1,X5] :
( ~ aElement0(X0)
| slsdtgt0(X0) != X1
| ~ aElementOf0(X5,X1)
| aElement0(sK14(X0,X5)) ),
inference(cnf_transformation,[],[f117]) ).
fof(f214,plain,
! [X0,X5] :
( ~ aElement0(X0)
| ~ aElementOf0(X5,slsdtgt0(X0))
| aElement0(sK14(X0,X5)) ),
inference(equality_resolution,[],[f180]) ).
fof(f215,plain,
! [X0,X5] :
( ~ aElement0(X0)
| ~ aElementOf0(X5,slsdtgt0(X0))
| sdtasdt0(X0,sK14(X0,X5)) = X5 ),
inference(equality_resolution,[],[f179]) ).
tcf(c_49,plain,
aElement0(xa),
inference(cnf_transformation,[],[f126]) ).
tcf(c_50,plain,
aElement0(xb),
inference(cnf_transformation,[],[f125]) ).
tcf(c_65,plain,
aElementOf0(xk,slsdtgt0(xa)),
inference(cnf_transformation,[],[f143]) ).
tcf(c_66,plain,
aElementOf0(xl,slsdtgt0(xb)),
inference(cnf_transformation,[],[f142]) ).
tcf(c_67,plain,
sdtpldt0(xk,xl) = xu,
inference(cnf_transformation,[],[f141]) ).
tcf(c_68,negated_conjecture,
! [X0: $i,X1: $i] :
( ~ aElement0(X1)
| ~ aElement0(X0)
| ( sdtpldt0(sdtasdt0(xa,X0),sdtasdt0(xb,X1)) != xu ) ),
inference(cnf_transformation,[],[f144]) ).
tcf(c_108,plain,
! [X0: $i,X1: $i] :
( aElement0(sK14(X1,X0))
| ~ aElement0(X1)
| ~ aElementOf0(X0,slsdtgt0(X1)) ),
inference(cnf_transformation,[],[f214]) ).
tcf(c_109,plain,
! [X0: $i,X1: $i] :
( ( sdtasdt0(X1,sK14(X1,X0)) = X0 )
| ~ aElement0(X1)
| ~ aElementOf0(X0,slsdtgt0(X1)) ),
inference(cnf_transformation,[],[f215]) ).
tcf(c_6076,plain,
( aElement0(sK14(xa,xk))
| ~ aElement0(xa) ),
inference(superposition,[status(thm)],[c_65,c_108]) ).
tcf(c_6077,plain,
( aElement0(sK14(xb,xl))
| ~ aElement0(xb) ),
inference(superposition,[status(thm)],[c_66,c_108]) ).
tcf(c_6081,plain,
aElement0(sK14(xb,xl)),
inference(forward_subsumption_resolution,[status(thm)],[c_6077,c_50]) ).
tcf(c_6082,plain,
aElement0(sK14(xa,xk)),
inference(forward_subsumption_resolution,[status(thm)],[c_6076,c_49]) ).
tcf(c_7015,plain,
( ( sdtasdt0(xa,sK14(xa,xk)) = xk )
| ~ aElement0(xa) ),
inference(superposition,[status(thm)],[c_65,c_109]) ).
tcf(c_7016,plain,
( ( sdtasdt0(xb,sK14(xb,xl)) = xl )
| ~ aElement0(xb) ),
inference(superposition,[status(thm)],[c_66,c_109]) ).
tcf(c_7034,plain,
sdtasdt0(xb,sK14(xb,xl)) = xl,
inference(forward_subsumption_resolution,[status(thm)],[c_7016,c_50]) ).
tcf(c_7035,plain,
sdtasdt0(xa,sK14(xa,xk)) = xk,
inference(forward_subsumption_resolution,[status(thm)],[c_7015,c_49]) ).
tcf(c_10036,plain,
! [X0: $i] :
( ~ aElement0(X0)
| ~ aElement0(sK14(xb,xl))
| ( sdtpldt0(sdtasdt0(xa,X0),xl) != xu ) ),
inference(superposition,[status(thm)],[c_7034,c_68]) ).
tcf(c_10050,plain,
! [X0: $i] :
( ~ aElement0(X0)
| ( sdtpldt0(sdtasdt0(xa,X0),xl) != xu ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_10036,c_6081]) ).
tcf(c_10243,plain,
( ~ aElement0(sK14(xa,xk))
| ( sdtpldt0(xk,xl) != xu ) ),
inference(superposition,[status(thm)],[c_7035,c_10050]) ).
tcf(c_10255,plain,
~ aElement0(sK14(xa,xk)),
inference(ground_joinability,[status(thm)],[c_10243,c_67]) ).
tcf(c_10256,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_10255,c_6082]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG116+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n005.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Thu Sep 24 08:19:02 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.41 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
% 0.09/0.42
% 0.09/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.42
% 0.09/0.42 % Detected problem language: tptp
% 0.09/0.43 % Proving...
% 3.56/1.19 % SZS status Started for theBenchmark.p
% 3.56/1.19 % SZS status Theorem for theBenchmark.p
% 3.56/1.19
% 3.56/1.19 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.56/1.19
% 3.56/1.19 % ------ iProver source info
% 3.56/1.19
% 3.56/1.19 % git: date: 2026-07-19 20:42:38 +0200
% 3.56/1.19 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.56/1.19 % git: non_committed_changes: false
% 3.56/1.19
% 3.56/1.19 % ------ Parsing...
% 3.56/1.19 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.56/1.19
% 3.56/1.19 % ------ Preprocessing... sup_sim: 1 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 3.56/1.19
% 3.56/1.19 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.56/1.19
% 3.56/1.19 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.56/1.19 % ------ Proving...
% 3.56/1.19 % ------ Problem Properties
% 3.56/1.19
% 3.56/1.19 %
% 3.56/1.19 % clauses 83
% 3.56/1.19 % conjectures 1
% 3.56/1.19 % EPR 20
% 3.56/1.19 % Horn 64
% 3.56/1.19 % unary 17
% 3.56/1.19 % binary 10
% 3.56/1.19 % lits 262
% 3.56/1.19 % lits eq 42
% 3.56/1.19 % fd_pure 0
% 3.56/1.19 % fd_pseudo 0
% 3.56/1.19 % fd_cond 5
% 3.56/1.19 % fd_pseudo_cond 8
% 3.56/1.19 % AC symbols 0
% 3.56/1.19
% 3.56/1.19 % ------ Schedule dynamic 5 is on
% 3.56/1.19
% 3.56/1.19 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.56/1.19
% 3.56/1.19
% 3.56/1.19 % ------
% 3.56/1.19 % Current options:
% 3.56/1.19 % ------
% 3.56/1.19
% 3.56/1.19
% 3.56/1.19 %
% 3.56/1.19
% 3.56/1.19 % ------ Proving...
% 3.56/1.19 %
% 3.56/1.19
% 3.56/1.19 % SZS status Theorem for theBenchmark.p
% 3.56/1.19
% 3.56/1.19 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.56/1.19
%------------------------------------------------------------------------------