%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET105-7 : 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 : n003.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 02:46:37 PM UTC 2026
% Result : Unsatisfiable 2.41s 1.29s
% Output : CNFRefutation 2.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 14
% Syntax : Number of formulae : 46 ( 40 unt; 6 def)
% Number of atoms : 99 ( 39 equ)
% Maximal formula atoms : 2 ( 2 avg)
% Number of connectives : 16 ( 10 ~; 6 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 7 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 19 ( 0 sgn 19 !; 0 ?; 6 :)
% 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(f120,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_unordered_pair) ).
fof(f123,axiom,
! [X0,X1] :
( unordered_pair(X1,X0) = singleton(X1)
| member(X0,universal_class) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair_equals_singleton1) ).
fof(f138,axiom,
! [X0] :
( singleton(X0) = null_class
| member(X0,universal_class) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_is_null_class) ).
fof(f166,negated_conjecture,
unordered_pair(null_class,singleton(null_class)) != ordered_pair(x,y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_property_3_of_ordered_pair_1) ).
fof(f167,negated_conjecture,
~ member(x,universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_property_3_of_ordered_pair_2) ).
fof(f168,negated_conjecture,
~ member(y,universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_property_3_of_ordered_pair_3) ).
fof(f173,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(f224,plain,
! [X0,X1] :
( unordered_pair(X1,X0) = unordered_pair(X1,X1)
| member(X0,universal_class) ),
inference(definition_unfolding,[],[f123,f12]) ).
fof(f235,plain,
! [X0] :
( unordered_pair(X0,X0) = null_class
| member(X0,universal_class) ),
inference(definition_unfolding,[],[f138,f12]) ).
fof(f254,plain,
unordered_pair(null_class,unordered_pair(null_class,null_class)) != unordered_pair(unordered_pair(x,x),unordered_pair(x,unordered_pair(y,y))),
inference(definition_unfolding,[],[f166,f12,f173]) ).
tcf(c_291,plain,
! [X0: $i,X1: $i] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f120]) ).
tcf(c_294,plain,
! [X0: $i,X1: $i] :
( member(X1,universal_class)
| ( unordered_pair(X0,X0) = unordered_pair(X0,X1) ) ),
inference(cnf_transformation,[],[f224]) ).
tcf(c_309,plain,
! [X0: $i] :
( member(X0,universal_class)
| ( unordered_pair(X0,X0) = null_class ) ),
inference(cnf_transformation,[],[f235]) ).
tcf(c_330,negated_conjecture,
unordered_pair(unordered_pair(x,x),unordered_pair(x,unordered_pair(y,y))) != unordered_pair(null_class,unordered_pair(null_class,null_class)),
inference(cnf_transformation,[],[f254]) ).
tcf(c_331,negated_conjecture,
~ member(x,universal_class),
inference(cnf_transformation,[],[f167]) ).
tcf(c_332,negated_conjecture,
~ member(y,universal_class),
inference(cnf_transformation,[],[f168]) ).
tcf(c_3744,definition,
iPr_def_10 = unordered_pair(x,x),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_3745,definition,
iPr_def_11 = unordered_pair(y,y),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_3746,definition,
iPr_def_12 = unordered_pair(x,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_3747,definition,
iPr_def_13 = unordered_pair(iPr_def_10,iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_3748,definition,
iPr_def_14 = unordered_pair(null_class,null_class),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_3749,definition,
iPr_def_15 = unordered_pair(null_class,iPr_def_14),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_3750,negated_conjecture,
~ member(y,universal_class),
inference(demodulation,[status(thm)],[c_332]) ).
tcf(c_3751,negated_conjecture,
~ member(x,universal_class),
inference(demodulation,[status(thm)],[c_331]) ).
tcf(c_3752,negated_conjecture,
iPr_def_13 != iPr_def_15,
inference(demodulation,[status(thm)],[c_330,c_3748,c_3749,c_3745,c_3746,c_3744,c_3747]) ).
tcf(c_4973,plain,
unordered_pair(iPr_def_11,x) = iPr_def_12,
inference(demodulation,[status(thm)],[c_3746,c_291]) ).
tcf(c_4977,plain,
unordered_pair(iPr_def_14,null_class) = iPr_def_15,
inference(demodulation,[status(thm)],[c_3749,c_291]) ).
tcf(c_5216,plain,
unordered_pair(x,x) = null_class,
inference(superposition,[status(thm)],[c_309,c_3751]) ).
tcf(c_5217,plain,
unordered_pair(y,y) = null_class,
inference(superposition,[status(thm)],[c_309,c_3750]) ).
tcf(c_5218,plain,
null_class = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_5217,c_3745]) ).
tcf(c_5219,plain,
null_class = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_5216,c_3744]) ).
tcf(c_5230,plain,
unordered_pair(iPr_def_14,iPr_def_11) = iPr_def_15,
inference(demodulation,[status(thm)],[c_4977,c_5218]) ).
tcf(c_5231,plain,
unordered_pair(iPr_def_11,iPr_def_11) = iPr_def_14,
inference(demodulation,[status(thm)],[c_3748,c_5218]) ).
tcf(c_5277,plain,
iPr_def_10 = iPr_def_11,
inference(demodulation,[status(thm)],[c_5218,c_5219]) ).
tcf(c_5284,plain,
unordered_pair(iPr_def_10,x) = iPr_def_12,
inference(demodulation,[status(thm)],[c_4973,c_5277]) ).
tcf(c_5295,plain,
unordered_pair(iPr_def_14,iPr_def_10) = iPr_def_15,
inference(light_normalisation,[status(thm)],[c_5230,c_5277]) ).
tcf(c_5296,plain,
unordered_pair(iPr_def_10,iPr_def_14) = iPr_def_15,
inference(demodulation,[status(thm)],[c_5295,c_291]) ).
tcf(c_5304,plain,
unordered_pair(iPr_def_10,iPr_def_10) = iPr_def_14,
inference(light_normalisation,[status(thm)],[c_5231,c_5277]) ).
tcf(c_5608,plain,
! [X0: $i] : unordered_pair(X0,X0) = unordered_pair(X0,x),
inference(superposition,[status(thm)],[c_294,c_3751]) ).
tcf(c_5610,plain,
unordered_pair(iPr_def_10,iPr_def_10) = iPr_def_12,
inference(demodulation,[status(thm)],[c_5284,c_5608]) ).
tcf(c_5611,plain,
iPr_def_12 = iPr_def_14,
inference(demodulation,[status(thm)],[c_5304,c_5610]) ).
tcf(c_5614,plain,
unordered_pair(iPr_def_10,iPr_def_12) = iPr_def_15,
inference(demodulation,[status(thm)],[c_5296,c_5611]) ).
tcf(c_5622,plain,
iPr_def_13 = iPr_def_15,
inference(light_normalisation,[status(thm)],[c_5614,c_3747]) ).
tcf(c_5623,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_5622,c_3752]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET105-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.38 % Computer : n003.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Thu Sep 24 09:52:38 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 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
% 0.10/0.43
% 0.10/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.43
% 0.10/0.43 % Detected problem language: tptp
% 0.10/0.44 % Proving...
% 2.41/1.29 % SZS status Started for theBenchmark.p
% 2.41/1.29 % SZS status Unsatisfiable for theBenchmark.p
% 2.41/1.29
% 2.41/1.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.41/1.29
% 2.41/1.29 % ------ iProver source info
% 2.41/1.29
% 2.41/1.29 % git: date: 2026-07-19 20:42:38 +0200
% 2.41/1.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.41/1.29 % git: non_committed_changes: false
% 2.41/1.29
% 2.41/1.29 % ------ Parsing...% successful
% 2.41/1.29
% 2.41/1.29
% 2.41/1.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.41/1.29
% 2.41/1.29 % ------ 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 %
% 2.41/1.29
% 2.41/1.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.41/1.29
% 2.41/1.29 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.41/1.29 % ------ Proving...
% 2.41/1.29 % ------ Problem Properties
% 2.41/1.29
% 2.41/1.29 %
% 2.41/1.29 % clauses 126
% 2.41/1.29 % conjectures 3
% 2.41/1.29 % EPR 20
% 2.41/1.29 % Horn 102
% 2.41/1.29 % unary 36
% 2.41/1.29 % binary 54
% 2.41/1.29 % lits 259
% 2.41/1.29 % lits eq 73
% 2.41/1.29 % fd_pure 0
% 2.41/1.29 % fd_pseudo 0
% 2.41/1.29 % fd_cond 5
% 2.41/1.29 % fd_pseudo_cond 14
% 2.41/1.29 % AC symbols 0
% 2.41/1.29
% 2.41/1.29 % ------ Schedule dynamic 5 is on
% 2.41/1.29
% 2.41/1.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.41/1.29
% 2.41/1.29
% 2.41/1.29 % ------
% 2.41/1.29 % Current options:
% 2.41/1.29 % ------
% 2.41/1.29
% 2.41/1.29
% 2.41/1.29 %
% 2.41/1.29
% 2.41/1.29 % ------ Proving...
% 2.41/1.29 %
% 2.41/1.29
% 2.41/1.29 % SZS status Unsatisfiable for theBenchmark.p
% 2.41/1.29
% 2.41/1.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.41/1.29
% 2.41/1.29
%------------------------------------------------------------------------------