TSTP Solution File: SEU106+1 by iProver---3.8
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SEU106+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n021.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 17:03:44 EDT 2023
% Result : Theorem 3.72s 1.13s
% Output : CNFRefutation 3.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 10
% Syntax : Number of formulae : 66 ( 23 unt; 0 def)
% Number of atoms : 197 ( 17 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 223 ( 92 ~; 79 |; 37 &)
% ( 3 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 7 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 1 con; 0-2 aty)
% Number of variables : 116 ( 1 sgn; 74 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(f9,axiom,
! [X0,X1] : symmetric_difference(X0,X1) = set_union2(set_difference(X0,X1),set_difference(X1,X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_xboole_0) ).
fof(f20,axiom,
! [X0,X1] : set_union2(X0,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
fof(f32,axiom,
! [X0,X1] : set_difference(X0,X1) = symmetric_difference(X0,set_intersection2(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t100_xboole_1) ).
fof(f33,axiom,
! [X0] :
( preboolean(X0)
<=> ! [X1,X2] :
( ( in(X2,X0)
& in(X1,X0) )
=> ( in(set_difference(X1,X2),X0)
& in(set_union2(X1,X2),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_finsub_1) ).
fof(f34,conjecture,
! [X0] :
( ~ empty(X0)
=> ( ! [X1] :
( element(X1,X0)
=> ! [X2] :
( element(X2,X0)
=> ( in(set_union2(X1,X2),X0)
& in(symmetric_difference(X1,X2),X0) ) ) )
=> preboolean(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_finsub_1) ).
fof(f35,negated_conjecture,
~ ! [X0] :
( ~ empty(X0)
=> ( ! [X1] :
( element(X1,X0)
=> ! [X2] :
( element(X2,X0)
=> ( in(set_union2(X1,X2),X0)
& in(symmetric_difference(X1,X2),X0) ) ) )
=> preboolean(X0) ) ),
inference(negated_conjecture,[],[f34]) ).
fof(f37,axiom,
! [X0,X1] :
( in(X0,X1)
=> element(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
fof(f49,axiom,
! [X0,X1] : set_intersection2(X0,X1) = symmetric_difference(symmetric_difference(X0,X1),set_union2(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t95_xboole_1) ).
fof(f50,plain,
! [X0] : set_union2(X0,X0) = X0,
inference(rectify,[],[f20]) ).
fof(f80,plain,
! [X0] :
( preboolean(X0)
<=> ! [X1,X2] :
( ( in(set_difference(X1,X2),X0)
& in(set_union2(X1,X2),X0) )
| ~ in(X2,X0)
| ~ in(X1,X0) ) ),
inference(ennf_transformation,[],[f33]) ).
fof(f81,plain,
! [X0] :
( preboolean(X0)
<=> ! [X1,X2] :
( ( in(set_difference(X1,X2),X0)
& in(set_union2(X1,X2),X0) )
| ~ in(X2,X0)
| ~ in(X1,X0) ) ),
inference(flattening,[],[f80]) ).
fof(f82,plain,
? [X0] :
( ~ preboolean(X0)
& ! [X1] :
( ! [X2] :
( ( in(set_union2(X1,X2),X0)
& in(symmetric_difference(X1,X2),X0) )
| ~ element(X2,X0) )
| ~ element(X1,X0) )
& ~ empty(X0) ),
inference(ennf_transformation,[],[f35]) ).
fof(f83,plain,
? [X0] :
( ~ preboolean(X0)
& ! [X1] :
( ! [X2] :
( ( in(set_union2(X1,X2),X0)
& in(symmetric_difference(X1,X2),X0) )
| ~ element(X2,X0) )
| ~ element(X1,X0) )
& ~ empty(X0) ),
inference(flattening,[],[f82]) ).
fof(f84,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f37]) ).
fof(f114,plain,
! [X0] :
( ( preboolean(X0)
| ? [X1,X2] :
( ( ~ in(set_difference(X1,X2),X0)
| ~ in(set_union2(X1,X2),X0) )
& in(X2,X0)
& in(X1,X0) ) )
& ( ! [X1,X2] :
( ( in(set_difference(X1,X2),X0)
& in(set_union2(X1,X2),X0) )
| ~ in(X2,X0)
| ~ in(X1,X0) )
| ~ preboolean(X0) ) ),
inference(nnf_transformation,[],[f81]) ).
fof(f115,plain,
! [X0] :
( ( preboolean(X0)
| ? [X1,X2] :
( ( ~ in(set_difference(X1,X2),X0)
| ~ in(set_union2(X1,X2),X0) )
& in(X2,X0)
& in(X1,X0) ) )
& ( ! [X3,X4] :
( ( in(set_difference(X3,X4),X0)
& in(set_union2(X3,X4),X0) )
| ~ in(X4,X0)
| ~ in(X3,X0) )
| ~ preboolean(X0) ) ),
inference(rectify,[],[f114]) ).
fof(f116,plain,
! [X0] :
( ? [X1,X2] :
( ( ~ in(set_difference(X1,X2),X0)
| ~ in(set_union2(X1,X2),X0) )
& in(X2,X0)
& in(X1,X0) )
=> ( ( ~ in(set_difference(sK10(X0),sK11(X0)),X0)
| ~ in(set_union2(sK10(X0),sK11(X0)),X0) )
& in(sK11(X0),X0)
& in(sK10(X0),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f117,plain,
! [X0] :
( ( preboolean(X0)
| ( ( ~ in(set_difference(sK10(X0),sK11(X0)),X0)
| ~ in(set_union2(sK10(X0),sK11(X0)),X0) )
& in(sK11(X0),X0)
& in(sK10(X0),X0) ) )
& ( ! [X3,X4] :
( ( in(set_difference(X3,X4),X0)
& in(set_union2(X3,X4),X0) )
| ~ in(X4,X0)
| ~ in(X3,X0) )
| ~ preboolean(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10,sK11])],[f115,f116]) ).
fof(f118,plain,
( ? [X0] :
( ~ preboolean(X0)
& ! [X1] :
( ! [X2] :
( ( in(set_union2(X1,X2),X0)
& in(symmetric_difference(X1,X2),X0) )
| ~ element(X2,X0) )
| ~ element(X1,X0) )
& ~ empty(X0) )
=> ( ~ preboolean(sK12)
& ! [X1] :
( ! [X2] :
( ( in(set_union2(X1,X2),sK12)
& in(symmetric_difference(X1,X2),sK12) )
| ~ element(X2,sK12) )
| ~ element(X1,sK12) )
& ~ empty(sK12) ) ),
introduced(choice_axiom,[]) ).
fof(f119,plain,
( ~ preboolean(sK12)
& ! [X1] :
( ! [X2] :
( ( in(set_union2(X1,X2),sK12)
& in(symmetric_difference(X1,X2),sK12) )
| ~ element(X2,sK12) )
| ~ element(X1,sK12) )
& ~ empty(sK12) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f83,f118]) ).
fof(f126,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f6]) ).
fof(f129,plain,
! [X0,X1] : symmetric_difference(X0,X1) = set_union2(set_difference(X0,X1),set_difference(X1,X0)),
inference(cnf_transformation,[],[f9]) ).
fof(f140,plain,
! [X0] : set_union2(X0,X0) = X0,
inference(cnf_transformation,[],[f50]) ).
fof(f164,plain,
! [X0,X1] : set_difference(X0,X1) = symmetric_difference(X0,set_intersection2(X0,X1)),
inference(cnf_transformation,[],[f32]) ).
fof(f167,plain,
! [X0] :
( preboolean(X0)
| in(sK10(X0),X0) ),
inference(cnf_transformation,[],[f117]) ).
fof(f168,plain,
! [X0] :
( preboolean(X0)
| in(sK11(X0),X0) ),
inference(cnf_transformation,[],[f117]) ).
fof(f169,plain,
! [X0] :
( preboolean(X0)
| ~ in(set_difference(sK10(X0),sK11(X0)),X0)
| ~ in(set_union2(sK10(X0),sK11(X0)),X0) ),
inference(cnf_transformation,[],[f117]) ).
fof(f171,plain,
! [X2,X1] :
( in(symmetric_difference(X1,X2),sK12)
| ~ element(X2,sK12)
| ~ element(X1,sK12) ),
inference(cnf_transformation,[],[f119]) ).
fof(f172,plain,
! [X2,X1] :
( in(set_union2(X1,X2),sK12)
| ~ element(X2,sK12)
| ~ element(X1,sK12) ),
inference(cnf_transformation,[],[f119]) ).
fof(f173,plain,
~ preboolean(sK12),
inference(cnf_transformation,[],[f119]) ).
fof(f175,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f84]) ).
fof(f187,plain,
! [X0,X1] : set_intersection2(X0,X1) = symmetric_difference(symmetric_difference(X0,X1),set_union2(X0,X1)),
inference(cnf_transformation,[],[f49]) ).
fof(f188,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_union2(set_difference(set_union2(set_difference(X0,X1),set_difference(X1,X0)),set_union2(X0,X1)),set_difference(set_union2(X0,X1),set_union2(set_difference(X0,X1),set_difference(X1,X0)))),
inference(definition_unfolding,[],[f187,f129,f129]) ).
fof(f189,plain,
! [X0,X1] : set_difference(X0,X1) = set_union2(set_difference(X0,set_union2(set_difference(set_union2(set_difference(X0,X1),set_difference(X1,X0)),set_union2(X0,X1)),set_difference(set_union2(X0,X1),set_union2(set_difference(X0,X1),set_difference(X1,X0))))),set_difference(set_union2(set_difference(set_union2(set_difference(X0,X1),set_difference(X1,X0)),set_union2(X0,X1)),set_difference(set_union2(X0,X1),set_union2(set_difference(X0,X1),set_difference(X1,X0)))),X0)),
inference(definition_unfolding,[],[f164,f129,f188]) ).
fof(f196,plain,
! [X2,X1] :
( in(set_union2(set_difference(X1,X2),set_difference(X2,X1)),sK12)
| ~ element(X2,sK12)
| ~ element(X1,sK12) ),
inference(definition_unfolding,[],[f171,f129]) ).
cnf(c_49,plain,
set_union2(set_difference(X0,set_union2(set_difference(set_union2(set_difference(X0,X1),set_difference(X1,X0)),set_union2(X0,X1)),set_difference(set_union2(X0,X1),set_union2(set_difference(X0,X1),set_difference(X1,X0))))),set_difference(set_union2(set_difference(set_union2(set_difference(X0,X1),set_difference(X1,X0)),set_union2(X0,X1)),set_difference(set_union2(X0,X1),set_union2(set_difference(X0,X1),set_difference(X1,X0)))),X0)) = set_difference(X0,X1),
inference(cnf_transformation,[],[f189]) ).
cnf(c_56,plain,
set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f126]) ).
cnf(c_69,plain,
set_union2(X0,X0) = X0,
inference(cnf_transformation,[],[f140]) ).
cnf(c_93,plain,
( ~ in(set_difference(sK10(X0),sK11(X0)),X0)
| ~ in(set_union2(sK10(X0),sK11(X0)),X0)
| preboolean(X0) ),
inference(cnf_transformation,[],[f169]) ).
cnf(c_94,plain,
( in(sK11(X0),X0)
| preboolean(X0) ),
inference(cnf_transformation,[],[f168]) ).
cnf(c_95,plain,
( in(sK10(X0),X0)
| preboolean(X0) ),
inference(cnf_transformation,[],[f167]) ).
cnf(c_98,negated_conjecture,
~ preboolean(sK12),
inference(cnf_transformation,[],[f173]) ).
cnf(c_99,negated_conjecture,
( ~ element(X0,sK12)
| ~ element(X1,sK12)
| in(set_union2(X0,X1),sK12) ),
inference(cnf_transformation,[],[f172]) ).
cnf(c_100,negated_conjecture,
( ~ element(X0,sK12)
| ~ element(X1,sK12)
| in(set_union2(set_difference(X0,X1),set_difference(X1,X0)),sK12) ),
inference(cnf_transformation,[],[f196]) ).
cnf(c_103,plain,
( ~ in(X0,X1)
| element(X0,X1) ),
inference(cnf_transformation,[],[f175]) ).
cnf(c_561,plain,
set_union2(set_difference(X0,set_union2(set_difference(set_union2(X0,X1),set_union2(set_difference(X0,X1),set_difference(X1,X0))),set_difference(set_union2(set_difference(X0,X1),set_difference(X1,X0)),set_union2(X0,X1)))),set_difference(set_union2(set_difference(set_union2(X0,X1),set_union2(set_difference(X0,X1),set_difference(X1,X0))),set_difference(set_union2(set_difference(X0,X1),set_difference(X1,X0)),set_union2(X0,X1))),X0)) = set_difference(X0,X1),
inference(demodulation,[status(thm)],[c_49,c_56]) ).
cnf(c_1651,plain,
( ~ element(X0,sK12)
| in(X0,sK12) ),
inference(superposition,[status(thm)],[c_69,c_99]) ).
cnf(c_1823,plain,
( ~ element(set_union2(set_difference(set_union2(X0,X1),set_union2(set_difference(X0,X1),set_difference(X1,X0))),set_difference(set_union2(set_difference(X0,X1),set_difference(X1,X0)),set_union2(X0,X1))),sK12)
| ~ element(X0,sK12)
| in(set_difference(X0,X1),sK12) ),
inference(superposition,[status(thm)],[c_561,c_100]) ).
cnf(c_1892,plain,
( element(sK11(X0),X0)
| preboolean(X0) ),
inference(superposition,[status(thm)],[c_94,c_103]) ).
cnf(c_1893,plain,
( element(sK10(X0),X0)
| preboolean(X0) ),
inference(superposition,[status(thm)],[c_95,c_103]) ).
cnf(c_1894,plain,
( ~ element(X0,sK12)
| ~ element(X1,sK12)
| element(set_union2(X0,X1),sK12) ),
inference(superposition,[status(thm)],[c_99,c_103]) ).
cnf(c_1895,plain,
( ~ element(X0,sK12)
| ~ element(X1,sK12)
| element(set_union2(set_difference(X0,X1),set_difference(X1,X0)),sK12) ),
inference(superposition,[status(thm)],[c_100,c_103]) ).
cnf(c_2008,plain,
( ~ element(X0,sK12)
| ~ element(X1,sK12)
| element(set_union2(set_difference(X1,X0),set_difference(X0,X1)),sK12) ),
inference(superposition,[status(thm)],[c_56,c_1895]) ).
cnf(c_2370,plain,
( ~ element(set_union2(set_difference(X0,X1),set_difference(X1,X0)),sK12)
| ~ element(set_union2(X0,X1),sK12)
| ~ element(X0,sK12)
| in(set_difference(X0,X1),sK12) ),
inference(superposition,[status(thm)],[c_2008,c_1823]) ).
cnf(c_2397,plain,
( ~ element(set_union2(X0,X1),sK12)
| ~ element(X0,sK12)
| ~ element(X1,sK12)
| in(set_difference(X0,X1),sK12) ),
inference(superposition,[status(thm)],[c_2008,c_2370]) ).
cnf(c_3874,plain,
( ~ element(X0,sK12)
| ~ element(X1,sK12)
| in(set_difference(X0,X1),sK12) ),
inference(global_subsumption_just,[status(thm)],[c_2397,c_1894,c_2397]) ).
cnf(c_3889,plain,
( ~ in(set_union2(sK10(sK12),sK11(sK12)),sK12)
| ~ element(sK10(sK12),sK12)
| ~ element(sK11(sK12),sK12)
| preboolean(sK12) ),
inference(superposition,[status(thm)],[c_3874,c_93]) ).
cnf(c_3896,plain,
( ~ in(set_union2(sK10(sK12),sK11(sK12)),sK12)
| ~ element(sK10(sK12),sK12)
| ~ element(sK11(sK12),sK12) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3889,c_98]) ).
cnf(c_3915,plain,
( ~ element(sK10(sK12),sK12)
| ~ element(sK11(sK12),sK12) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3896,c_99]) ).
cnf(c_4090,plain,
( in(sK11(sK12),sK12)
| preboolean(sK12) ),
inference(superposition,[status(thm)],[c_1892,c_1651]) ).
cnf(c_4092,plain,
in(sK11(sK12),sK12),
inference(forward_subsumption_resolution,[status(thm)],[c_4090,c_98]) ).
cnf(c_4125,plain,
( ~ element(sK11(sK12),sK12)
| preboolean(sK12) ),
inference(superposition,[status(thm)],[c_1893,c_3915]) ).
cnf(c_4127,plain,
~ element(sK11(sK12),sK12),
inference(forward_subsumption_resolution,[status(thm)],[c_4125,c_98]) ).
cnf(c_4184,plain,
element(sK11(sK12),sK12),
inference(superposition,[status(thm)],[c_4092,c_103]) ).
cnf(c_4185,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_4184,c_4127]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU106+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : run_iprover %s %d THM
% 0.12/0.34 % Computer : n021.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Aug 24 01:05:25 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.46 Running first-order theorem proving
% 0.19/0.46 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 3.72/1.13 % SZS status Started for theBenchmark.p
% 3.72/1.13 % SZS status Theorem for theBenchmark.p
% 3.72/1.13
% 3.72/1.13 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 3.72/1.13
% 3.72/1.13 ------ iProver source info
% 3.72/1.13
% 3.72/1.13 git: date: 2023-05-31 18:12:56 +0000
% 3.72/1.13 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 3.72/1.13 git: non_committed_changes: false
% 3.72/1.13 git: last_make_outside_of_git: false
% 3.72/1.13
% 3.72/1.13 ------ Parsing...
% 3.72/1.13 ------ Clausification by vclausify_rel & Parsing by iProver...
% 3.72/1.13
% 3.72/1.13 ------ Preprocessing... sup_sim: 7 sf_s rm: 13 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
% 3.72/1.13
% 3.72/1.13 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 3.72/1.13
% 3.72/1.13 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.72/1.13 ------ Proving...
% 3.72/1.13 ------ Problem Properties
% 3.72/1.13
% 3.72/1.13
% 3.72/1.13 clauses 46
% 3.72/1.13 conjectures 4
% 3.72/1.13 EPR 14
% 3.72/1.13 Horn 40
% 3.72/1.13 unary 23
% 3.72/1.13 binary 14
% 3.72/1.13 lits 80
% 3.72/1.13 lits eq 10
% 3.72/1.13 fd_pure 0
% 3.72/1.13 fd_pseudo 0
% 3.72/1.13 fd_cond 1
% 3.72/1.13 fd_pseudo_cond 1
% 3.72/1.13 AC symbols 0
% 3.72/1.13
% 3.72/1.13 ------ Schedule dynamic 5 is on
% 3.72/1.13
% 3.72/1.13 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.72/1.13
% 3.72/1.13
% 3.72/1.13 ------
% 3.72/1.13 Current options:
% 3.72/1.13 ------
% 3.72/1.13
% 3.72/1.13
% 3.72/1.13
% 3.72/1.13
% 3.72/1.13 ------ Proving...
% 3.72/1.13
% 3.72/1.13
% 3.72/1.13 % SZS status Theorem for theBenchmark.p
% 3.72/1.13
% 3.72/1.13 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.72/1.13
% 3.72/1.13
%------------------------------------------------------------------------------