%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET082+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n019.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 02:46:30 PM UTC 2026
% Result : Theorem 3.97s 6.50s
% Output : CNFRefutation 3.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 34 ( 13 unt; 1 def)
% Number of atoms : 89 ( 37 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 73 ( 30 ~; 24 |; 15 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 35 ( 0 sgn 32 !; 3 ?; 9 :)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1,X2] :
( member(X0,unordered_pair(X1,X2))
<=> ( ( X0 = X2
| X0 = X1 )
& member(X0,universal_class) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',unordered_pair_defn) ).
fof(f6,axiom,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',singleton_set_defn) ).
fof(f41,axiom,
! [X0] :
( X0 != null_class
=> ? [X1] :
( disjoint(X1,X0)
& member(X1,X0)
& member(X1,universal_class) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',regularity) ).
fof(f44,conjecture,
! [X0] :
( ~ member(X0,universal_class)
=> singleton(X0) = null_class ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_is_null_class) ).
fof(f45,negated_conjecture,
~ ! [X0] :
( ~ member(X0,universal_class)
=> singleton(X0) = null_class ),
inference(negated_conjecture,[status(cth)],[f44]) ).
fof(f57,plain,
! [X0] :
( null_class = X0
| ? [X1] :
( disjoint(X1,X0)
& member(X1,X0)
& member(X1,universal_class) ) ),
inference(ennf_transformation,[],[f41]) ).
fof(f60,plain,
? [X0] :
( ~ member(X0,universal_class)
& singleton(X0) != null_class ),
inference(ennf_transformation,[],[f45]) ).
fof(f66,plain,
! [X0,X1,X2] :
( ( ~ member(X0,unordered_pair(X1,X2))
| ( ( X0 = X2
| X0 = X1 )
& member(X0,universal_class) ) )
& ( ( X0 != X2
& X0 != X1 )
| ~ member(X0,universal_class)
| member(X0,unordered_pair(X1,X2)) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f67,plain,
! [X0,X1,X2] :
( ( ~ member(X0,unordered_pair(X1,X2))
| ( ( X0 = X2
| X0 = X1 )
& member(X0,universal_class) ) )
& ( ( X0 != X2
& X0 != X1 )
| ~ member(X0,universal_class)
| member(X0,unordered_pair(X1,X2)) ) ),
inference(flattening,[],[f66]) ).
fof(f101,plain,
! [X0] :
( null_class = X0
| ( disjoint(sK4(X0),X0)
& member(sK4(X0),X0)
& member(sK4(X0),universal_class) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X1,sK4(X0))],[f57]) ).
fof(f103,plain,
( ~ member(sK6,universal_class)
& null_class != singleton(sK6) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X0,sK6)],[f60]) ).
fof(f111,plain,
! [X2,X0,X1] :
( ~ member(X0,unordered_pair(X1,X2))
| X0 = X2
| X0 = X1 ),
inference(cnf_transformation,[],[f67]) ).
fof(f112,plain,
! [X2,X0,X1] :
( ~ member(X0,unordered_pair(X1,X2))
| member(X0,universal_class) ),
inference(cnf_transformation,[],[f67]) ).
fof(f116,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f6]) ).
fof(f186,plain,
! [X0] :
( null_class = X0
| member(sK4(X0),X0) ),
inference(cnf_transformation,[],[f101]) ).
fof(f191,plain,
~ member(sK6,universal_class),
inference(cnf_transformation,[],[f103]) ).
fof(f192,plain,
null_class != singleton(sK6),
inference(cnf_transformation,[],[f103]) ).
fof(f230,plain,
null_class != unordered_pair(sK6,sK6),
inference(definition_unfolding,[],[f192,f116]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,universal_class)
| ~ member(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[],[f112]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ( X0 = X1 )
| ~ member(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[],[f111]) ).
tcf(c_124,plain,
! [X0: $i] :
( member(sK4(X0),X0)
| ( X0 = null_class ) ),
inference(cnf_transformation,[],[f186]) ).
tcf(c_128,negated_conjecture,
unordered_pair(sK6,sK6) != null_class,
inference(cnf_transformation,[],[f230]) ).
tcf(c_129,negated_conjecture,
~ member(sK6,universal_class),
inference(cnf_transformation,[],[f191]) ).
tcf(c_1557,definition,
iPr_def_10 = unordered_pair(sK6,sK6),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_1558,negated_conjecture,
~ member(sK6,universal_class),
inference(demodulation,[status(thm)],[c_129]) ).
tcf(c_1559,negated_conjecture,
iPr_def_10 != null_class,
inference(demodulation,[status(thm)],[c_128,c_1557]) ).
tcf(c_2482,plain,
! [X0: $i] :
( member(X0,universal_class)
| ~ member(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_1557,c_58]) ).
tcf(c_2497,plain,
( member(sK4(iPr_def_10),universal_class)
| ( null_class = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_124,c_2482]) ).
tcf(c_3205,plain,
! [X0: $i] :
( ( X0 = sK6 )
| ~ member(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_1557,c_59]) ).
tcf(c_3312,plain,
( ( null_class = iPr_def_10 )
| ( sK4(iPr_def_10) = sK6 ) ),
inference(superposition,[status(thm)],[c_124,c_3205]) ).
tcf(c_3476,plain,
( member(sK6,universal_class)
| ( null_class = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_3312,c_2497]) ).
tcf(c_3477,plain,
null_class = iPr_def_10,
inference(forward_subsumption_resolution,[status(thm)],[c_3476,c_1558]) ).
tcf(c_3495,plain,
iPr_def_10 != iPr_def_10,
inference(demodulation,[status(thm)],[c_1559,c_3477]) ).
tcf(c_3496,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_3495]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET082+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/5.58 % Computer : n019.cluster.edu
% 0.09/5.58 % Model : x86_64 x86_64
% 0.09/5.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.58 % Memory : 8046.5625MB
% 0.09/5.58 % OS : Linux 6.8.0-71-generic
% 0.09/5.58 % CPULimit : 300
% 0.09/5.58 % WCLimit : 300
% 0.09/5.58 % DateTime : Thu Sep 24 09:39:58 UTC 2026
% 0.09/5.59 % CPUTime :
% 0.09/5.59 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.15/5.62 Running first-order theorem proving
% 0.15/5.63 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
% 0.15/5.64
% 0.15/5.64 % ======== iProver multi-core TPTP/SMT =========
% 0.15/5.64
% 0.15/5.64 % Detected problem language: tptp
% 0.15/5.65 % Proving...
% 3.97/6.50 % SZS status Started for theBenchmark.p
% 3.97/6.50 % SZS status Theorem for theBenchmark.p
% 3.97/6.50
% 3.97/6.50 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.97/6.50
% 3.97/6.50 % ------ iProver source info
% 3.97/6.50
% 3.97/6.50 % git: date: 2026-07-19 20:42:38 +0200
% 3.97/6.50 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.97/6.50 % git: non_committed_changes: false
% 3.97/6.50
% 3.97/6.50 % ------ Parsing...
% 3.97/6.50 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.97/6.50
% 3.97/6.50 % ------ 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: 4 0s sf_e pe_s pe_e %
% 3.97/6.50
% 3.97/6.50 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.97/6.50
% 3.97/6.50 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.97/6.50 % ------ Proving...
% 3.97/6.50 % ------ Problem Properties
% 3.97/6.50
% 3.97/6.50 %
% 3.97/6.50 % clauses 77
% 3.97/6.50 % conjectures 2
% 3.97/6.50 % EPR 9
% 3.97/6.50 % Horn 69
% 3.97/6.50 % unary 17
% 3.97/6.50 % binary 39
% 3.97/6.50 % lits 159
% 3.97/6.50 % lits eq 16
% 3.97/6.50 % fd_pure 0
% 3.97/6.50 % fd_pseudo 0
% 3.97/6.50 % fd_cond 4
% 3.97/6.50 % fd_pseudo_cond 3
% 3.97/6.50 % AC symbols 0
% 3.97/6.50
% 3.97/6.50 % ------ Schedule dynamic 5 is on
% 3.97/6.50
% 3.97/6.50 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.97/6.50
% 3.97/6.50
% 3.97/6.50 % ------
% 3.97/6.50 % Current options:
% 3.97/6.50 % ------
% 3.97/6.50
% 3.97/6.50
% 3.97/6.50 %
% 3.97/6.50
% 3.97/6.50 % ------ Proving...
% 3.97/6.50 %
% 3.97/6.50
% 3.97/6.50 % SZS status Theorem for theBenchmark.p
% 3.97/6.50
% 3.97/6.50 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.97/6.50
% 3.97/6.50
%------------------------------------------------------------------------------