%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET116-7 : TPTP v9.3.1. Bugfixed v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/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 02:46:39 PM UTC 2026
% Result : Unsatisfiable 3.51s 11.31s
% Output : CNFRefutation 3.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 12
% Syntax : Number of formulae : 34 ( 24 unt; 6 def)
% Number of atoms : 86 ( 43 equ)
% Maximal formula atoms : 2 ( 2 avg)
% Number of connectives : 21 ( 11 ~; 10 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 7 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-2 aty)
% Number of variables : 11 ( 0 sgn 11 !; 0 ?; 2 :)
% Comments :
%------------------------------------------------------------------------------
fof(f12,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',singleton_set) ).
fof(f13,axiom,
! [X0,X1] : unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))) = ordered_pair(X0,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',ordered_pair) ).
fof(f177,axiom,
! [X0] :
( first(X0) = X0
| ordered_pair(first(X0),second(X0)) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_1st_and_2nd_4) ).
fof(f178,axiom,
! [X0] :
( second(X0) = X0
| ordered_pair(first(X0),second(X0)) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_1st_and_2nd_5) ).
fof(f181,negated_conjecture,
ordered_pair(first(x),second(x)) != x,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_unique_1st_and_2nd_in_pair_of_non_sets4_1) ).
fof(f182,plain,
x != ordered_pair(first(x),second(x)),
inference(reorient_equations,[],[f181]) ).
fof(f183,negated_conjecture,
second(x) != x,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_unique_2nd_in_pair_of_non_sets) ).
fof(f184,plain,
x != second(x),
inference(reorient_equations,[],[f183]) ).
fof(f189,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),
inference(definition_unfolding,[],[f13,f12,f12]) ).
fof(f278,plain,
! [X0] :
( first(X0) = X0
| unordered_pair(unordered_pair(first(X0),first(X0)),unordered_pair(first(X0),unordered_pair(second(X0),second(X0)))) = X0 ),
inference(definition_unfolding,[],[f177,f189]) ).
fof(f279,plain,
! [X0] :
( second(X0) = X0
| unordered_pair(unordered_pair(first(X0),first(X0)),unordered_pair(first(X0),unordered_pair(second(X0),second(X0)))) = X0 ),
inference(definition_unfolding,[],[f178,f189]) ).
fof(f282,plain,
x != unordered_pair(unordered_pair(first(x),first(x)),unordered_pair(first(x),unordered_pair(second(x),second(x)))),
inference(definition_unfolding,[],[f182,f189]) ).
tcf(c_349,plain,
! [X0: $i] :
( ( first(X0) = X0 )
| ( unordered_pair(unordered_pair(first(X0),first(X0)),unordered_pair(first(X0),unordered_pair(second(X0),second(X0)))) = X0 ) ),
inference(cnf_transformation,[],[f278]) ).
tcf(c_350,plain,
! [X0: $i] :
( ( second(X0) = X0 )
| ( unordered_pair(unordered_pair(first(X0),first(X0)),unordered_pair(first(X0),unordered_pair(second(X0),second(X0)))) = X0 ) ),
inference(cnf_transformation,[],[f279]) ).
tcf(c_353,negated_conjecture,
unordered_pair(unordered_pair(first(x),first(x)),unordered_pair(first(x),unordered_pair(second(x),second(x)))) != x,
inference(cnf_transformation,[],[f282]) ).
tcf(c_354,negated_conjecture,
second(x) != x,
inference(cnf_transformation,[],[f184]) ).
tcf(c_4042,definition,
iPr_def_10 = first(x),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_4043,definition,
iPr_def_11 = unordered_pair(iPr_def_10,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_4044,definition,
iPr_def_12 = second(x),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_4045,definition,
iPr_def_13 = unordered_pair(iPr_def_12,iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_4046,definition,
iPr_def_14 = unordered_pair(iPr_def_10,iPr_def_13),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_4047,definition,
iPr_def_15 = unordered_pair(iPr_def_11,iPr_def_14),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_4048,negated_conjecture,
iPr_def_15 != x,
inference(demodulation,[status(thm)],[c_353,c_4044,c_4045,c_4046,c_4042,c_4043,c_4047]) ).
tcf(c_4049,negated_conjecture,
iPr_def_12 != x,
inference(demodulation,[status(thm)],[c_354]) ).
tcf(c_5403,plain,
( ( first(x) = x )
| ( unordered_pair(unordered_pair(iPr_def_10,iPr_def_10),unordered_pair(iPr_def_10,unordered_pair(second(x),second(x)))) = x ) ),
inference(superposition,[status(thm)],[c_4042,c_349]) ).
tcf(c_5411,plain,
( ( x = iPr_def_15 )
| ( x = iPr_def_10 ) ),
inference(light_normalisation,[status(thm)],[c_5403,c_4042,c_4043,c_4044,c_4045,c_4046,c_4047]) ).
tcf(c_5472,plain,
x = iPr_def_10,
inference(superposition,[status(thm)],[c_5411,c_4048]) ).
tcf(c_5473,plain,
second(iPr_def_10) = iPr_def_12,
inference(demodulation,[status(thm)],[c_4044,c_5472]) ).
tcf(c_5474,plain,
first(iPr_def_10) = iPr_def_10,
inference(demodulation,[status(thm)],[c_4042,c_5472]) ).
tcf(c_5475,plain,
iPr_def_10 != iPr_def_12,
inference(demodulation,[status(thm)],[c_4049,c_5472]) ).
tcf(c_5476,plain,
iPr_def_10 != iPr_def_15,
inference(demodulation,[status(thm)],[c_4048,c_5472]) ).
tcf(c_5548,plain,
( ( second(iPr_def_10) = iPr_def_10 )
| ( unordered_pair(unordered_pair(iPr_def_10,iPr_def_10),unordered_pair(iPr_def_10,unordered_pair(second(iPr_def_10),second(iPr_def_10)))) = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_5474,c_350]) ).
tcf(c_5561,plain,
( ( iPr_def_10 = iPr_def_15 )
| ( iPr_def_10 = iPr_def_12 ) ),
inference(light_normalisation,[status(thm)],[c_5548,c_4043,c_4045,c_4046,c_4047,c_5473]) ).
tcf(c_5562,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_5561,c_5476,c_5475]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET116-7 : TPTP v9.3.1. Bugfixed v7.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/10.39 % Computer : n017.cluster.edu
% 0.10/10.39 % Model : x86_64 x86_64
% 0.10/10.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/10.39 % Memory : 8046.5625MB
% 0.10/10.39 % OS : Linux 6.8.0-71-generic
% 0.10/10.39 % CPULimit : 300
% 0.10/10.39 % WCLimit : 300
% 0.10/10.39 % DateTime : Thu Sep 24 09:50:11 UTC 2026
% 0.15/10.40 % CPUTime :
% 0.15/10.40 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.15/10.44 Running first-order theorem proving
% 0.15/10.44 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
% 0.15/10.45
% 0.15/10.45 % ======== iProver multi-core TPTP/SMT =========
% 0.15/10.45
% 0.15/10.45 % Detected problem language: tptp
% 0.15/10.46 % Proving...
% 3.51/11.31 % SZS status Started for theBenchmark.p
% 3.51/11.31 % SZS status Unsatisfiable for theBenchmark.p
% 3.51/11.31
% 3.51/11.31 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.51/11.31
% 3.51/11.31 % ------ iProver source info
% 3.51/11.31
% 3.51/11.31 % git: date: 2026-07-19 20:42:38 +0200
% 3.51/11.31 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.51/11.31 % git: non_committed_changes: false
% 3.51/11.31
% 3.51/11.31 % ------ Parsing...% successful
% 3.51/11.31
% 3.51/11.31
% 3.51/11.31 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.51/11.31
% 3.51/11.31 % ------ 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 %
% 3.51/11.31
% 3.51/11.31 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.51/11.31
% 3.51/11.31 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.51/11.31 % ------ Proving...
% 3.51/11.31 % ------ Problem Properties
% 3.51/11.31
% 3.51/11.31 %
% 3.51/11.31 % clauses 137
% 3.51/11.31 % conjectures 2
% 3.51/11.31 % EPR 19
% 3.51/11.31 % Horn 106
% 3.51/11.31 % unary 35
% 3.51/11.31 % binary 62
% 3.51/11.31 % lits 286
% 3.51/11.31 % lits eq 89
% 3.51/11.31 % fd_pure 0
% 3.51/11.31 % fd_pseudo 0
% 3.51/11.31 % fd_cond 5
% 3.51/11.31 % fd_pseudo_cond 16
% 3.51/11.31 % AC symbols 0
% 3.51/11.31
% 3.51/11.31 % ------ Schedule dynamic 5 is on
% 3.51/11.31
% 3.51/11.31 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.51/11.31
% 3.51/11.31
% 3.51/11.31 % ------
% 3.51/11.31 % Current options:
% 3.51/11.31 % ------
% 3.51/11.31
% 3.51/11.31
% 3.51/11.31 %
% 3.51/11.31
% 3.51/11.31 % ------ Proving...
% 3.51/11.31 %
% 3.51/11.31
% 3.51/11.31 % SZS status Unsatisfiable for theBenchmark.p
% 3.51/11.31
% 3.51/11.31 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.51/11.31
% 3.51/11.31
%------------------------------------------------------------------------------