%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET084-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n017.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 02:46:31 PM UTC 2026
% Result : Unsatisfiable 0.98s 1.28s
% Output : CNFRefutation 0.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of formulae : 34 ( 20 unt; 2 def)
% Number of atoms : 63 ( 23 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 28 ( 14 ~; 14 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 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; 3 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 18 ( 0 sgn 18 !; 0 ?; 8 :)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
! [X0,X1] :
( member(X0,unordered_pair(X0,X1))
| ~ member(X0,universal_class) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',unordered_pair2) ).
fof(f12,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',singleton_set) ).
fof(f113,axiom,
! [X0] : ~ member(X0,null_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_null_class) ).
fof(f137,axiom,
! [X0,X1] :
( X0 = X1
| ~ member(X0,singleton(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',only_member_in_singleton) ).
fof(f138,axiom,
! [X0] :
( singleton(X0) = null_class
| member(X0,universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_is_null_class) ).
fof(f139,negated_conjecture,
singleton(x) = singleton(y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_singleton_identified_by_element2_1) ).
fof(f140,negated_conjecture,
member(y,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_singleton_identified_by_element2_2) ).
fof(f141,negated_conjecture,
x != y,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_singleton_identified_by_element2_3) ).
fof(f206,plain,
! [X0,X1] :
( X0 = X1
| ~ member(X0,unordered_pair(X1,X1)) ),
inference(definition_unfolding,[],[f137,f12]) ).
fof(f207,plain,
! [X0] :
( unordered_pair(X0,X0) = null_class
| member(X0,universal_class) ),
inference(definition_unfolding,[],[f138,f12]) ).
fof(f208,plain,
unordered_pair(x,x) = unordered_pair(y,y),
inference(definition_unfolding,[],[f139,f12,f12]) ).
tcf(c_186,plain,
! [X0: $i,X1: $i] :
( member(X0,unordered_pair(X0,X1))
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_264,plain,
! [X0: $i] : ~ member(X0,null_class),
inference(cnf_transformation,[],[f113]) ).
tcf(c_286,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ member(X0,unordered_pair(X1,X1)) ),
inference(cnf_transformation,[],[f206]) ).
tcf(c_287,plain,
! [X0: $i] :
( member(X0,universal_class)
| ( unordered_pair(X0,X0) = null_class ) ),
inference(cnf_transformation,[],[f207]) ).
tcf(c_288,negated_conjecture,
unordered_pair(x,x) = unordered_pair(y,y),
inference(cnf_transformation,[],[f208]) ).
tcf(c_289,negated_conjecture,
member(y,universal_class),
inference(cnf_transformation,[],[f140]) ).
tcf(c_290,negated_conjecture,
x != y,
inference(cnf_transformation,[],[f141]) ).
tcf(c_3266,definition,
iPr_def_10 = unordered_pair(x,x),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_3267,definition,
iPr_def_11 = unordered_pair(y,y),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_3268,negated_conjecture,
x != y,
inference(demodulation,[status(thm)],[c_290]) ).
tcf(c_3269,negated_conjecture,
member(y,universal_class),
inference(demodulation,[status(thm)],[c_289]) ).
tcf(c_3270,negated_conjecture,
iPr_def_10 = iPr_def_11,
inference(demodulation,[status(thm)],[c_288,c_3267,c_3266]) ).
tcf(c_4275,plain,
unordered_pair(y,y) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_3267,c_3270]) ).
tcf(c_4363,plain,
( member(x,iPr_def_10)
| ~ member(x,universal_class) ),
inference(superposition,[status(thm)],[c_3266,c_186]) ).
tcf(c_4364,plain,
( member(y,iPr_def_10)
| ~ member(y,universal_class) ),
inference(superposition,[status(thm)],[c_4275,c_186]) ).
tcf(c_4365,plain,
member(y,iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_4364,c_3269]) ).
tcf(c_4473,plain,
( member(x,iPr_def_10)
| ( unordered_pair(x,x) = null_class ) ),
inference(superposition,[status(thm)],[c_287,c_4363]) ).
tcf(c_4474,plain,
( member(x,iPr_def_10)
| ( null_class = iPr_def_10 ) ),
inference(light_normalisation,[status(thm)],[c_4473,c_3266]) ).
tcf(c_4525,plain,
! [X0: $i] :
( ( X0 = y )
| ~ member(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_4275,c_286]) ).
tcf(c_4671,plain,
( ( x = y )
| ( null_class = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_4474,c_4525]) ).
tcf(c_4673,plain,
null_class = iPr_def_10,
inference(forward_subsumption_resolution,[status(thm)],[c_4671,c_3268]) ).
tcf(c_4685,plain,
! [X0: $i] : ~ member(X0,iPr_def_10),
inference(demodulation,[status(thm)],[c_264,c_4673]) ).
tcf(c_4688,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_4365,c_4685]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET084-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.38 % Computer : n017.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Thu Sep 24 09:36:17 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 0.11/0.42
% 0.11/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.42
% 0.11/0.42 % Detected problem language: tptp
% 0.11/0.43 % Proving...
% 0.98/1.28 % SZS status Started for theBenchmark.p
% 0.98/1.28 % SZS status Unsatisfiable for theBenchmark.p
% 0.98/1.28
% 0.98/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.98/1.28
% 0.98/1.28 % ------ iProver source info
% 0.98/1.28
% 0.98/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 0.98/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.98/1.28 % git: non_committed_changes: false
% 0.98/1.28
% 0.98/1.28 % ------ Parsing...% successful
% 0.98/1.28
% 0.98/1.28
% 0.98/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.98/1.28
% 0.98/1.28 % ------ 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 %
% 0.98/1.28
% 0.98/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.98/1.28
% 0.98/1.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.98/1.28 % ------ Proving...
% 0.98/1.28 % ------ Problem Properties
% 0.98/1.28
% 0.98/1.28 %
% 0.98/1.28 % clauses 102
% 0.98/1.28 % conjectures 3
% 0.98/1.28 % EPR 20
% 0.98/1.28 % Horn 87
% 0.98/1.28 % unary 29
% 0.98/1.28 % binary 45
% 0.98/1.28 % lits 209
% 0.98/1.28 % lits eq 42
% 0.98/1.28 % fd_pure 0
% 0.98/1.28 % fd_pseudo 0
% 0.98/1.28 % fd_cond 5
% 0.98/1.28 % fd_pseudo_cond 9
% 0.98/1.28 % AC symbols 0
% 0.98/1.28
% 0.98/1.28 % ------ Schedule dynamic 5 is on
% 0.98/1.28
% 0.98/1.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.98/1.28
% 0.98/1.28
% 0.98/1.28 % ------
% 0.98/1.28 % Current options:
% 0.98/1.28 % ------
% 0.98/1.28
% 0.98/1.28
% 0.98/1.28 %
% 0.98/1.28
% 0.98/1.28 % ------ Proving...
% 0.98/1.28 %
% 0.98/1.28
% 0.98/1.28 % SZS status Unsatisfiable for theBenchmark.p
% 0.98/1.28
% 0.98/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.98/1.28
% 0.98/1.28
%------------------------------------------------------------------------------