%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET096-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/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 02:46:34 PM UTC 2026
% Result : Unsatisfiable 8.52s 11.96s
% Output : CNFRefutation 8.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 12
% Syntax : Number of formulae : 48 ( 26 unt; 1 def)
% Number of atoms : 88 ( 27 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 61 ( 33 ~; 28 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 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 : 45 ( 0 sgn 45 !; 0 ?; 22 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',subclass_members) ).
fof(f7,axiom,
! [X0,X1] :
( X0 = X1
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',subclass_implies_equal) ).
fof(f12,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',singleton_set) ).
fof(f67,axiom,
! [X0] :
( member(regular(X0),X0)
| X0 = null_class ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',regularity1) ).
fof(f68,plain,
! [X0] :
( member(regular(X0),X0)
| null_class = X0 ),
inference(reorient_equations,[],[f67]) ).
fof(f106,axiom,
! [X2,X0,X1] :
( subclass(X0,X2)
| ~ subclass(X1,X2)
| ~ subclass(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity_of_subclass) ).
fof(f121,axiom,
! [X0,X1] : subclass(singleton(X0),unordered_pair(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_in_unordered_pair1) ).
fof(f137,axiom,
! [X0,X1] :
( X0 = X1
| ~ member(X0,singleton(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',only_member_in_singleton) ).
fof(f153,axiom,
! [X0,X1] :
( subclass(singleton(X0),X1)
| ~ member(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',property_of_singletons2) ).
fof(f154,negated_conjecture,
subclass(x,singleton(y)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_two_subsets_of_singleton_1) ).
fof(f155,negated_conjecture,
x != null_class,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_two_subsets_of_singleton_2) ).
fof(f156,plain,
null_class != x,
inference(reorient_equations,[],[f155]) ).
fof(f157,negated_conjecture,
singleton(y) != x,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_two_subsets_of_singleton_3) ).
fof(f158,plain,
x != singleton(y),
inference(reorient_equations,[],[f157]) ).
fof(f211,plain,
! [X0,X1] : subclass(unordered_pair(X0,X0),unordered_pair(X0,X1)),
inference(definition_unfolding,[],[f121,f12]) ).
fof(f223,plain,
! [X0,X1] :
( X0 = X1
| ~ member(X0,unordered_pair(X1,X1)) ),
inference(definition_unfolding,[],[f137,f12]) ).
fof(f235,plain,
! [X0,X1] :
( subclass(unordered_pair(X0,X0),X1)
| ~ member(X0,X1) ),
inference(definition_unfolding,[],[f153,f12]) ).
fof(f236,plain,
subclass(x,unordered_pair(y,y)),
inference(definition_unfolding,[],[f154,f12]) ).
fof(f237,plain,
x != unordered_pair(y,y),
inference(definition_unfolding,[],[f158,f12]) ).
tcf(c_191,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ subclass(X1,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f1]) ).
tcf(c_197,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_243,plain,
! [X0: $i] :
( member(regular(X0),X0)
| ( X0 = null_class ) ),
inference(cnf_transformation,[],[f68]) ).
tcf(c_271,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(X0,X2)
| ~ subclass(X1,X2)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[],[f106]) ).
tcf(c_283,plain,
! [X0: $i,X1: $i] : subclass(unordered_pair(X0,X0),unordered_pair(X0,X1)),
inference(cnf_transformation,[],[f211]) ).
tcf(c_299,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ member(X0,unordered_pair(X1,X1)) ),
inference(cnf_transformation,[],[f223]) ).
tcf(c_313,plain,
! [X0: $i,X1: $i] :
( subclass(unordered_pair(X0,X0),X1)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f235]) ).
tcf(c_314,negated_conjecture,
subclass(x,unordered_pair(y,y)),
inference(cnf_transformation,[],[f236]) ).
tcf(c_315,negated_conjecture,
null_class != x,
inference(cnf_transformation,[],[f156]) ).
tcf(c_316,negated_conjecture,
unordered_pair(y,y) != x,
inference(cnf_transformation,[],[f237]) ).
tcf(c_3602,definition,
iPr_def_10 = unordered_pair(y,y),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_3603,negated_conjecture,
iPr_def_10 != x,
inference(demodulation,[status(thm)],[c_316,c_3602]) ).
tcf(c_3604,negated_conjecture,
null_class != x,
inference(demodulation,[status(thm)],[c_315]) ).
tcf(c_3605,negated_conjecture,
subclass(x,iPr_def_10),
inference(demodulation,[status(thm)],[c_314]) ).
tcf(c_4752,plain,
! [X0: $i] : subclass(iPr_def_10,unordered_pair(y,X0)),
inference(superposition,[status(thm)],[c_3602,c_283]) ).
tcf(c_4920,plain,
! [X0: $i] :
( subclass(iPr_def_10,X0)
| ~ member(y,X0) ),
inference(superposition,[status(thm)],[c_3602,c_313]) ).
tcf(c_5199,plain,
! [X0: $i] :
( subclass(x,X0)
| ~ subclass(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_3605,c_271]) ).
tcf(c_5292,plain,
! [X0: $i] : subclass(x,unordered_pair(y,X0)),
inference(superposition,[status(thm)],[c_4752,c_5199]) ).
tcf(c_5302,plain,
! [X0: $i,X1: $i] :
( member(X0,unordered_pair(y,X1))
| ~ member(X0,x) ),
inference(superposition,[status(thm)],[c_5292,c_191]) ).
tcf(c_5362,plain,
! [X0: $i] :
( ( X0 = y )
| ~ member(X0,x) ),
inference(superposition,[status(thm)],[c_5302,c_299]) ).
tcf(c_5558,plain,
( ( x = iPr_def_10 )
| ~ subclass(iPr_def_10,x) ),
inference(superposition,[status(thm)],[c_3605,c_197]) ).
tcf(c_5699,plain,
( ( null_class = x )
| ( regular(x) = y ) ),
inference(superposition,[status(thm)],[c_243,c_5362]) ).
tcf(c_5700,plain,
regular(x) = y,
inference(forward_subsumption_resolution,[status(thm)],[c_5699,c_3604]) ).
tcf(c_5713,plain,
( member(y,x)
| ( null_class = x ) ),
inference(superposition,[status(thm)],[c_5700,c_243]) ).
tcf(c_5714,plain,
member(y,x),
inference(forward_subsumption_resolution,[status(thm)],[c_5713,c_3604]) ).
tcf(c_5802,plain,
subclass(iPr_def_10,x),
inference(superposition,[status(thm)],[c_5714,c_4920]) ).
tcf(c_5805,plain,
x = iPr_def_10,
inference(backward_subsumption_resolution,[status(thm)],[c_5558,c_5802]) ).
tcf(c_5827,plain,
iPr_def_10 != iPr_def_10,
inference(demodulation,[status(thm)],[c_3603,c_5805]) ).
tcf(c_5829,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_5827]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET096-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/10.42 % Computer : n005.cluster.edu
% 0.13/10.42 % Model : x86_64 x86_64
% 0.13/10.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/10.42 % Memory : 8046.5625MB
% 0.13/10.42 % OS : Linux 6.8.0-71-generic
% 0.13/10.42 % CPULimit : 300
% 0.13/10.42 % WCLimit : 300
% 0.13/10.42 % DateTime : Thu Sep 24 09:46:28 UTC 2026
% 0.13/10.43 % CPUTime :
% 0.13/10.43 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/10.48 Running first-order theorem proving
% 0.13/10.48 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
% 0.18/10.50
% 0.18/10.50 % ======== iProver multi-core TPTP/SMT =========
% 0.18/10.50
% 0.18/10.50 % Detected problem language: tptp
% 0.18/10.51 % Proving...
% 8.52/11.96 % SZS status Started for theBenchmark.p
% 8.52/11.96 % SZS status Unsatisfiable for theBenchmark.p
% 8.52/11.96
% 8.52/11.96 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 8.52/11.96
% 8.52/11.96 % ------ iProver source info
% 8.52/11.96
% 8.52/11.96 % git: date: 2026-07-19 20:42:38 +0200
% 8.52/11.96 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 8.52/11.96 % git: non_committed_changes: false
% 8.52/11.96
% 8.52/11.96 % ------ Parsing...% successful
% 8.52/11.96
% 8.52/11.96
% 8.52/11.96 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 8.52/11.96
% 8.52/11.96 % ------ 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 %
% 8.52/11.96
% 8.52/11.96 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 8.52/11.96
% 8.52/11.96 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 8.52/11.96 % ------ Proving...
% 8.52/11.96 % ------ Problem Properties
% 8.52/11.96
% 8.52/11.96 %
% 8.52/11.96 % clauses 114
% 8.52/11.96 % conjectures 3
% 8.52/11.96 % EPR 20
% 8.52/11.96 % Horn 94
% 8.52/11.96 % unary 28
% 8.52/11.96 % binary 54
% 8.52/11.96 % lits 239
% 8.52/11.96 % lits eq 59
% 8.52/11.96 % fd_pure 0
% 8.52/11.96 % fd_pseudo 0
% 8.52/11.96 % fd_cond 5
% 8.52/11.96 % fd_pseudo_cond 13
% 8.52/11.96 % AC symbols 0
% 8.52/11.96
% 8.52/11.96 % ------ Schedule dynamic 5 is on
% 8.52/11.96
% 8.52/11.96 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 8.52/11.96
% 8.52/11.96
% 8.52/11.96 % ------
% 8.52/11.96 % Current options:
% 8.52/11.96 % ------
% 8.52/11.96
% 8.52/11.96
% 8.52/11.96 %
% 8.52/11.96
% 8.52/11.96 % ------ Proving...
% 8.52/11.96 %
% 8.52/11.96
% 8.52/11.96 % SZS status Unsatisfiable for theBenchmark.p
% 8.52/11.96
% 8.52/11.96 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 8.52/11.97
% 8.52/11.97
%------------------------------------------------------------------------------