%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET095+4 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n012.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 02:46:34 PM UTC 2026
% Result : Theorem 0.70s 1.13s
% Output : CNFRefutation 0.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 29 ( 9 unt; 1 def)
% Number of atoms : 72 ( 9 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 60 ( 24 ~; 21 |; 9 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 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 : 5 ( 3 usr; 2 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 41 ( 0 sgn 37 !; 4 ?; 8 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',subset) ).
fof(f8,axiom,
! [X0,X1] :
( member(X0,singleton(X1))
<=> X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',singleton) ).
fof(f12,conjecture,
! [X0,X1] :
( member(X1,X0)
=> subset(singleton(X1),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thI44) ).
fof(f13,negated_conjecture,
~ ! [X0,X1] :
( member(X1,X0)
=> subset(singleton(X1),X0) ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ member(X2,X0)
| member(X2,X1) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f16,plain,
? [X0,X1] :
( member(X1,X0)
& ~ subset(singleton(X1),X0) ),
inference(ennf_transformation,[],[f13]) ).
fof(f17,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X2] :
( ~ member(X2,X0)
| member(X2,X1) ) )
& ( ? [X2] :
( member(X2,X0)
& ~ member(X2,X1) )
| subset(X0,X1) ) ),
inference(nnf_transformation,[],[f14]) ).
fof(f18,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ member(X3,X0)
| member(X3,X1) ) )
& ( ? [X2] :
( member(X2,X0)
& ~ member(X2,X1) )
| subset(X0,X1) ) ),
inference(rectify,[],[f17]) ).
fof(f19,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ member(X3,X0)
| member(X3,X1) ) )
& ( ( member(sK0(X0,X1),X0)
& ~ member(sK0(X0,X1),X1) )
| subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f18]) ).
fof(f27,plain,
! [X0,X1] :
( ( ~ member(X0,singleton(X1))
| X0 = X1 )
& ( X0 != X1
| member(X0,singleton(X1)) ) ),
inference(nnf_transformation,[],[f8]) ).
fof(f36,plain,
( member(sK4,sK3)
& ~ subset(singleton(sK4),sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4]),skolemize(X0,sK3),skolemize(X1,sK4)],[f16]) ).
fof(f38,plain,
! [X0,X1] :
( member(sK0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f19]) ).
fof(f39,plain,
! [X0,X1] :
( ~ member(sK0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f19]) ).
fof(f52,plain,
! [X0,X1] :
( ~ member(X0,singleton(X1))
| X0 = X1 ),
inference(cnf_transformation,[],[f27]) ).
fof(f63,plain,
member(sK4,sK3),
inference(cnf_transformation,[],[f36]) ).
fof(f64,plain,
~ subset(singleton(sK4),sK3),
inference(cnf_transformation,[],[f36]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ member(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f39]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f38]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ member(X0,singleton(X1)) ),
inference(cnf_transformation,[],[f52]) ).
tcf(c_75,negated_conjecture,
~ subset(singleton(sK4),sK3),
inference(cnf_transformation,[],[f64]) ).
tcf(c_76,negated_conjecture,
member(sK4,sK3),
inference(cnf_transformation,[],[f63]) ).
tcf(c_498,definition,
iPr_def_10 = singleton(sK4),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_499,negated_conjecture,
member(sK4,sK3),
inference(demodulation,[status(thm)],[c_76]) ).
tcf(c_500,negated_conjecture,
~ subset(iPr_def_10,sK3),
inference(demodulation,[status(thm)],[c_75,c_498]) ).
tcf(c_1095,plain,
! [X0: $i] :
( ( X0 = sK4 )
| ~ member(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_498,c_65]) ).
tcf(c_1106,plain,
! [X0: $i] :
( subset(iPr_def_10,X0)
| ( sK0(iPr_def_10,X0) = sK4 ) ),
inference(superposition,[status(thm)],[c_50,c_1095]) ).
tcf(c_1146,plain,
sK0(iPr_def_10,sK3) = sK4,
inference(superposition,[status(thm)],[c_1106,c_500]) ).
tcf(c_1229,plain,
( subset(iPr_def_10,sK3)
| ~ member(sK4,sK3) ),
inference(superposition,[status(thm)],[c_1146,c_49]) ).
tcf(c_1230,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_1229,c_500,c_499]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET095+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.02 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.05/0.32 % Computer : n012.cluster.edu
% 0.05/0.32 % Model : x86_64 x86_64
% 0.05/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/0.32 % Memory : 8046.5625MB
% 0.05/0.32 % OS : Linux 6.8.0-71-generic
% 0.05/0.32 % CPULimit : 300
% 0.05/0.32 % WCLimit : 300
% 0.05/0.32 % DateTime : Thu Sep 24 09:45:06 UTC 2026
% 0.05/0.32 % CPUTime :
% 0.05/0.32 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.36 Running first-order theorem proving
% 0.09/0.36 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
% 0.09/0.37
% 0.09/0.37 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.37
% 0.09/0.37 % Detected problem language: tptp
% 0.09/0.38 % Proving...
% 0.70/1.13 % SZS status Started for theBenchmark.p
% 0.70/1.13 % SZS status Theorem for theBenchmark.p
% 0.70/1.13
% 0.70/1.13 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.70/1.13
% 0.70/1.13 % ------ iProver source info
% 0.70/1.13
% 0.70/1.13 % git: date: 2026-07-19 20:42:38 +0200
% 0.70/1.13 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.70/1.13 % git: non_committed_changes: false
% 0.70/1.13
% 0.70/1.13 % ------ Parsing...
% 0.70/1.13 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.70/1.13
% 0.70/1.13 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 0.70/1.13
% 0.70/1.13 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.70/1.13
% 0.70/1.13 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.70/1.13 % ------ Proving...
% 0.70/1.13 % ------ Problem Properties
% 0.70/1.13
% 0.70/1.13 %
% 0.70/1.13 % clauses 29
% 0.70/1.13 % conjectures 2
% 0.70/1.13 % EPR 4
% 0.70/1.13 % Horn 24
% 0.70/1.13 % unary 7
% 0.70/1.13 % binary 15
% 0.70/1.13 % lits 58
% 0.70/1.13 % lits eq 4
% 0.70/1.13 % fd_pure 0
% 0.70/1.13 % fd_pseudo 0
% 0.70/1.13 % fd_cond 0
% 0.70/1.13 % fd_pseudo_cond 2
% 0.70/1.13 % AC symbols 0
% 0.70/1.13
% 0.70/1.13 % ------ Schedule dynamic 5 is on
% 0.70/1.13
% 0.70/1.13 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.70/1.13
% 0.70/1.13
% 0.70/1.13 % ------
% 0.70/1.13 % Current options:
% 0.70/1.13 % ------
% 0.70/1.13
% 0.70/1.13
% 0.70/1.13 %
% 0.70/1.13
% 0.70/1.13 % ------ Proving...
% 0.70/1.13 %
% 0.70/1.13
% 0.70/1.13 % SZS status Theorem for theBenchmark.p
% 0.70/1.13
% 0.70/1.13 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.70/1.13
% 0.70/1.13
%------------------------------------------------------------------------------