TSTP Solution File: NUM385+1 by iProver---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : NUM385+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n016.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 : Fri May 3 02:49:08 EDT 2024
% Result : Theorem 3.23s 1.17s
% Output : CNFRefutation 3.23s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named definition)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( in(X0,X1)
=> ~ in(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(f5,axiom,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(f6,axiom,
! [X0] : succ(X0) = set_union2(X0,singleton(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_ordinal1) ).
fof(f7,axiom,
! [X0,X1] :
( singleton(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> X0 = X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
fof(f8,axiom,
! [X0,X1,X2] :
( set_union2(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
| in(X3,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(f28,axiom,
! [X0] : in(X0,succ(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_ordinal1) ).
fof(f29,conjecture,
! [X0,X1] :
( succ(X0) = succ(X1)
=> X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_ordinal1) ).
fof(f30,negated_conjecture,
~ ! [X0,X1] :
( succ(X0) = succ(X1)
=> X0 = X1 ),
inference(negated_conjecture,[],[f29]) ).
fof(f44,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f1]) ).
fof(f53,plain,
? [X0,X1] :
( X0 != X1
& succ(X0) = succ(X1) ),
inference(ennf_transformation,[],[f30]) ).
fof(f60,plain,
! [X0,X1] :
( ( singleton(X0) = X1
| ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X0 = X2
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| X0 != X2 )
& ( X0 = X2
| ~ in(X2,X1) ) )
| singleton(X0) != X1 ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f61,plain,
! [X0,X1] :
( ( singleton(X0) = X1
| ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X0 = X2
| in(X2,X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| singleton(X0) != X1 ) ),
inference(rectify,[],[f60]) ).
fof(f62,plain,
! [X0,X1] :
( ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X0 = X2
| in(X2,X1) ) )
=> ( ( sK0(X0,X1) != X0
| ~ in(sK0(X0,X1),X1) )
& ( sK0(X0,X1) = X0
| in(sK0(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f63,plain,
! [X0,X1] :
( ( singleton(X0) = X1
| ( ( sK0(X0,X1) != X0
| ~ in(sK0(X0,X1),X1) )
& ( sK0(X0,X1) = X0
| in(sK0(X0,X1),X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| singleton(X0) != X1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f61,f62]) ).
fof(f64,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) = X2
| ? [X3] :
( ( ( ~ in(X3,X1)
& ~ in(X3,X0) )
| ~ in(X3,X2) )
& ( in(X3,X1)
| in(X3,X0)
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( ~ in(X3,X1)
& ~ in(X3,X0) ) )
& ( in(X3,X1)
| in(X3,X0)
| ~ in(X3,X2) ) )
| set_union2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f8]) ).
fof(f65,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) = X2
| ? [X3] :
( ( ( ~ in(X3,X1)
& ~ in(X3,X0) )
| ~ in(X3,X2) )
& ( in(X3,X1)
| in(X3,X0)
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( ~ in(X3,X1)
& ~ in(X3,X0) ) )
& ( in(X3,X1)
| in(X3,X0)
| ~ in(X3,X2) ) )
| set_union2(X0,X1) != X2 ) ),
inference(flattening,[],[f64]) ).
fof(f66,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) = X2
| ? [X3] :
( ( ( ~ in(X3,X1)
& ~ in(X3,X0) )
| ~ in(X3,X2) )
& ( in(X3,X1)
| in(X3,X0)
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( ~ in(X4,X1)
& ~ in(X4,X0) ) )
& ( in(X4,X1)
| in(X4,X0)
| ~ in(X4,X2) ) )
| set_union2(X0,X1) != X2 ) ),
inference(rectify,[],[f65]) ).
fof(f67,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ( ~ in(X3,X1)
& ~ in(X3,X0) )
| ~ in(X3,X2) )
& ( in(X3,X1)
| in(X3,X0)
| in(X3,X2) ) )
=> ( ( ( ~ in(sK1(X0,X1,X2),X1)
& ~ in(sK1(X0,X1,X2),X0) )
| ~ in(sK1(X0,X1,X2),X2) )
& ( in(sK1(X0,X1,X2),X1)
| in(sK1(X0,X1,X2),X0)
| in(sK1(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f68,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) = X2
| ( ( ( ~ in(sK1(X0,X1,X2),X1)
& ~ in(sK1(X0,X1,X2),X0) )
| ~ in(sK1(X0,X1,X2),X2) )
& ( in(sK1(X0,X1,X2),X1)
| in(sK1(X0,X1,X2),X0)
| in(sK1(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( ~ in(X4,X1)
& ~ in(X4,X0) ) )
& ( in(X4,X1)
| in(X4,X0)
| ~ in(X4,X2) ) )
| set_union2(X0,X1) != X2 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f66,f67]) ).
fof(f91,plain,
( ? [X0,X1] :
( X0 != X1
& succ(X0) = succ(X1) )
=> ( sK13 != sK14
& succ(sK13) = succ(sK14) ) ),
introduced(choice_axiom,[]) ).
fof(f92,plain,
( sK13 != sK14
& succ(sK13) = succ(sK14) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13,sK14])],[f53,f91]) ).
fof(f93,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f44]) ).
fof(f98,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f5]) ).
fof(f99,plain,
! [X0] : succ(X0) = set_union2(X0,singleton(X0)),
inference(cnf_transformation,[],[f6]) ).
fof(f100,plain,
! [X3,X0,X1] :
( X0 = X3
| ~ in(X3,X1)
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f63]) ).
fof(f104,plain,
! [X2,X0,X1,X4] :
( in(X4,X1)
| in(X4,X0)
| ~ in(X4,X2)
| set_union2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f68]) ).
fof(f139,plain,
! [X0] : in(X0,succ(X0)),
inference(cnf_transformation,[],[f28]) ).
fof(f140,plain,
succ(sK13) = succ(sK14),
inference(cnf_transformation,[],[f92]) ).
fof(f141,plain,
sK13 != sK14,
inference(cnf_transformation,[],[f92]) ).
fof(f149,plain,
! [X0] : in(X0,set_union2(X0,singleton(X0))),
inference(definition_unfolding,[],[f139,f99]) ).
fof(f150,plain,
set_union2(sK13,singleton(sK13)) = set_union2(sK14,singleton(sK14)),
inference(definition_unfolding,[],[f140,f99,f99]) ).
fof(f153,plain,
! [X3,X0] :
( X0 = X3
| ~ in(X3,singleton(X0)) ),
inference(equality_resolution,[],[f100]) ).
fof(f156,plain,
! [X0,X1,X4] :
( in(X4,X1)
| in(X4,X0)
| ~ in(X4,set_union2(X0,X1)) ),
inference(equality_resolution,[],[f104]) ).
cnf(c_49,plain,
( ~ in(X0,X1)
| ~ in(X1,X0) ),
inference(cnf_transformation,[],[f93]) ).
cnf(c_52,plain,
set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f98]) ).
cnf(c_56,plain,
( ~ in(X0,singleton(X1))
| X0 = X1 ),
inference(cnf_transformation,[],[f153]) ).
cnf(c_62,plain,
( ~ in(X0,set_union2(X1,X2))
| in(X0,X1)
| in(X0,X2) ),
inference(cnf_transformation,[],[f156]) ).
cnf(c_92,plain,
in(X0,set_union2(X0,singleton(X0))),
inference(cnf_transformation,[],[f149]) ).
cnf(c_93,negated_conjecture,
sK13 != sK14,
inference(cnf_transformation,[],[f141]) ).
cnf(c_94,negated_conjecture,
set_union2(sK13,singleton(sK13)) = set_union2(sK14,singleton(sK14)),
inference(cnf_transformation,[],[f150]) ).
cnf(c_588,plain,
singleton(sK13) = sP0_iProver_def,
definition ).
cnf(c_589,plain,
set_union2(sK13,sP0_iProver_def) = sP1_iProver_def,
definition ).
cnf(c_590,plain,
singleton(sK14) = sP2_iProver_def,
definition ).
cnf(c_591,plain,
set_union2(sK14,sP2_iProver_def) = sP3_iProver_def,
definition ).
cnf(c_592,negated_conjecture,
sP1_iProver_def = sP3_iProver_def,
inference(demodulation,[status(thm)],[c_94,c_590,c_591,c_588,c_589]) ).
cnf(c_593,negated_conjecture,
sK13 != sK14,
inference(demodulation,[status(thm)],[c_93]) ).
cnf(c_908,plain,
in(sK13,set_union2(sK13,sP0_iProver_def)),
inference(superposition,[status(thm)],[c_588,c_92]) ).
cnf(c_909,plain,
in(sK14,set_union2(sK14,sP2_iProver_def)),
inference(superposition,[status(thm)],[c_590,c_92]) ).
cnf(c_910,plain,
in(sK14,sP1_iProver_def),
inference(light_normalisation,[status(thm)],[c_909,c_591,c_592]) ).
cnf(c_911,plain,
in(sK13,sP1_iProver_def),
inference(light_normalisation,[status(thm)],[c_908,c_589]) ).
cnf(c_914,plain,
set_union2(sP0_iProver_def,sK13) = sP1_iProver_def,
inference(demodulation,[status(thm)],[c_589,c_52]) ).
cnf(c_915,plain,
set_union2(sK14,sP2_iProver_def) = sP1_iProver_def,
inference(light_normalisation,[status(thm)],[c_591,c_592]) ).
cnf(c_916,plain,
set_union2(sP2_iProver_def,sK14) = sP1_iProver_def,
inference(demodulation,[status(thm)],[c_915,c_52]) ).
cnf(c_985,plain,
( ~ in(X0,sP0_iProver_def)
| X0 = sK13 ),
inference(superposition,[status(thm)],[c_588,c_56]) ).
cnf(c_986,plain,
( ~ in(X0,sP2_iProver_def)
| X0 = sK14 ),
inference(superposition,[status(thm)],[c_590,c_56]) ).
cnf(c_1087,plain,
( ~ in(X0,sP1_iProver_def)
| in(X0,sK13)
| in(X0,sP0_iProver_def) ),
inference(superposition,[status(thm)],[c_914,c_62]) ).
cnf(c_1088,plain,
( ~ in(X0,sP1_iProver_def)
| in(X0,sK14)
| in(X0,sP2_iProver_def) ),
inference(superposition,[status(thm)],[c_916,c_62]) ).
cnf(c_1153,plain,
( in(sK13,sK14)
| in(sK13,sP2_iProver_def) ),
inference(superposition,[status(thm)],[c_911,c_1088]) ).
cnf(c_1566,plain,
( ~ in(sK14,sK13)
| in(sK13,sP2_iProver_def) ),
inference(superposition,[status(thm)],[c_1153,c_49]) ).
cnf(c_4282,plain,
( in(sK14,sK13)
| in(sK14,sP0_iProver_def) ),
inference(superposition,[status(thm)],[c_910,c_1087]) ).
cnf(c_4695,plain,
( in(sK13,sP2_iProver_def)
| in(sK14,sP0_iProver_def) ),
inference(superposition,[status(thm)],[c_4282,c_1566]) ).
cnf(c_4790,plain,
( sK13 = sK14
| in(sK13,sP2_iProver_def) ),
inference(superposition,[status(thm)],[c_4695,c_985]) ).
cnf(c_4792,plain,
in(sK13,sP2_iProver_def),
inference(forward_subsumption_resolution,[status(thm)],[c_4790,c_593]) ).
cnf(c_4811,plain,
sK13 = sK14,
inference(superposition,[status(thm)],[c_4792,c_986]) ).
cnf(c_4813,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_4811,c_593]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : NUM385+1 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.14 % Command : run_iprover %s %d THM
% 0.14/0.35 % Computer : n016.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu May 2 19:56:30 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.21/0.48 Running first-order theorem proving
% 0.21/0.48 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 3.23/1.17 % SZS status Started for theBenchmark.p
% 3.23/1.17 % SZS status Theorem for theBenchmark.p
% 3.23/1.17
% 3.23/1.17 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 3.23/1.17
% 3.23/1.17 ------ iProver source info
% 3.23/1.17
% 3.23/1.17 git: date: 2024-05-02 19:28:25 +0000
% 3.23/1.17 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 3.23/1.17 git: non_committed_changes: false
% 3.23/1.17
% 3.23/1.17 ------ Parsing...
% 3.23/1.17 ------ Clausification by vclausify_rel & Parsing by iProver...
% 3.23/1.17
% 3.23/1.17 ------ Preprocessing... sup_sim: 0 sf_s rm: 20 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 4 0s sf_e pe_s pe_e
% 3.23/1.17
% 3.23/1.17 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 3.23/1.17
% 3.23/1.17 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.23/1.17 ------ Proving...
% 3.23/1.17 ------ Problem Properties
% 3.23/1.17
% 3.23/1.17
% 3.23/1.17 clauses 34
% 3.23/1.17 conjectures 2
% 3.23/1.17 EPR 12
% 3.23/1.17 Horn 30
% 3.23/1.17 unary 18
% 3.23/1.17 binary 9
% 3.23/1.17 lits 58
% 3.23/1.17 lits eq 19
% 3.23/1.17 fd_pure 0
% 3.23/1.17 fd_pseudo 0
% 3.23/1.17 fd_cond 1
% 3.23/1.17 fd_pseudo_cond 6
% 3.23/1.17 AC symbols 0
% 3.23/1.17
% 3.23/1.17 ------ Schedule dynamic 5 is on
% 3.23/1.17
% 3.23/1.17 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.23/1.17
% 3.23/1.17
% 3.23/1.17 ------
% 3.23/1.17 Current options:
% 3.23/1.17 ------
% 3.23/1.17
% 3.23/1.17
% 3.23/1.17
% 3.23/1.17
% 3.23/1.17 ------ Proving...
% 3.23/1.17
% 3.23/1.17
% 3.23/1.17 % SZS status Theorem for theBenchmark.p
% 3.23/1.17
% 3.23/1.17 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.23/1.17
% 3.23/1.17
%------------------------------------------------------------------------------