TSTP Solution File: SET962+1 by iProver---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : SET962+1 : TPTP v8.1.2. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n010.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 03:02:07 EDT 2024
% Result : Theorem 0.45s 1.14s
% Output : CNFRefutation 0.45s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named definition)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f3,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
fof(f5,axiom,
! [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
<=> ( in(X1,X3)
& in(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l55_zfmisc_1) ).
fof(f8,conjecture,
! [X0,X1] :
( cartesian_product2(X0,X0) = cartesian_product2(X1,X1)
=> X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t115_zfmisc_1) ).
fof(f9,negated_conjecture,
~ ! [X0,X1] :
( cartesian_product2(X0,X0) = cartesian_product2(X1,X1)
=> X0 = X1 ),
inference(negated_conjecture,[],[f8]) ).
fof(f10,axiom,
! [X0,X1] :
( ! [X2] :
( in(X2,X0)
<=> in(X2,X1) )
=> X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_tarski) ).
fof(f12,plain,
? [X0,X1] :
( X0 != X1
& cartesian_product2(X0,X0) = cartesian_product2(X1,X1) ),
inference(ennf_transformation,[],[f9]) ).
fof(f13,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] :
( in(X2,X0)
<~> in(X2,X1) ) ),
inference(ennf_transformation,[],[f10]) ).
fof(f14,plain,
! [X0,X1,X2,X3] :
( ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X1,X3)
| ~ in(X0,X2) )
& ( ( in(X1,X3)
& in(X0,X2) )
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f15,plain,
! [X0,X1,X2,X3] :
( ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X1,X3)
| ~ in(X0,X2) )
& ( ( in(X1,X3)
& in(X0,X2) )
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(flattening,[],[f14]) ).
fof(f20,plain,
( ? [X0,X1] :
( X0 != X1
& cartesian_product2(X0,X0) = cartesian_product2(X1,X1) )
=> ( sK2 != sK3
& cartesian_product2(sK2,sK2) = cartesian_product2(sK3,sK3) ) ),
introduced(choice_axiom,[]) ).
fof(f21,plain,
( sK2 != sK3
& cartesian_product2(sK2,sK2) = cartesian_product2(sK3,sK3) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f12,f20]) ).
fof(f22,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] :
( ( ~ in(X2,X1)
| ~ in(X2,X0) )
& ( in(X2,X1)
| in(X2,X0) ) ) ),
inference(nnf_transformation,[],[f13]) ).
fof(f23,plain,
! [X0,X1] :
( ? [X2] :
( ( ~ in(X2,X1)
| ~ in(X2,X0) )
& ( in(X2,X1)
| in(X2,X0) ) )
=> ( ( ~ in(sK4(X0,X1),X1)
| ~ in(sK4(X0,X1),X0) )
& ( in(sK4(X0,X1),X1)
| in(sK4(X0,X1),X0) ) ) ),
introduced(choice_axiom,[]) ).
fof(f24,plain,
! [X0,X1] :
( X0 = X1
| ( ( ~ in(sK4(X0,X1),X1)
| ~ in(sK4(X0,X1),X0) )
& ( in(sK4(X0,X1),X1)
| in(sK4(X0,X1),X0) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f22,f23]) ).
fof(f26,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f27,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f3]) ).
fof(f30,plain,
! [X2,X3,X0,X1] :
( in(X1,X3)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f15]) ).
fof(f31,plain,
! [X2,X3,X0,X1] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X1,X3)
| ~ in(X0,X2) ),
inference(cnf_transformation,[],[f15]) ).
fof(f34,plain,
cartesian_product2(sK2,sK2) = cartesian_product2(sK3,sK3),
inference(cnf_transformation,[],[f21]) ).
fof(f35,plain,
sK2 != sK3,
inference(cnf_transformation,[],[f21]) ).
fof(f36,plain,
! [X0,X1] :
( X0 = X1
| in(sK4(X0,X1),X1)
| in(sK4(X0,X1),X0) ),
inference(cnf_transformation,[],[f24]) ).
fof(f37,plain,
! [X0,X1] :
( X0 = X1
| ~ in(sK4(X0,X1),X1)
| ~ in(sK4(X0,X1),X0) ),
inference(cnf_transformation,[],[f24]) ).
fof(f39,plain,
! [X2,X3,X0,X1] :
( in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3))
| ~ in(X1,X3)
| ~ in(X0,X2) ),
inference(definition_unfolding,[],[f31,f27]) ).
fof(f40,plain,
! [X2,X3,X0,X1] :
( in(X1,X3)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3)) ),
inference(definition_unfolding,[],[f30,f27]) ).
cnf(c_50,plain,
unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f26]) ).
cnf(c_52,plain,
( ~ in(X0,X1)
| ~ in(X2,X3)
| in(unordered_pair(unordered_pair(X2,X0),singleton(X2)),cartesian_product2(X3,X1)) ),
inference(cnf_transformation,[],[f39]) ).
cnf(c_53,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3))
| in(X1,X3) ),
inference(cnf_transformation,[],[f40]) ).
cnf(c_57,negated_conjecture,
sK2 != sK3,
inference(cnf_transformation,[],[f35]) ).
cnf(c_58,negated_conjecture,
cartesian_product2(sK2,sK2) = cartesian_product2(sK3,sK3),
inference(cnf_transformation,[],[f34]) ).
cnf(c_59,plain,
( ~ in(sK4(X0,X1),X0)
| ~ in(sK4(X0,X1),X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f37]) ).
cnf(c_60,plain,
( X0 = X1
| in(sK4(X0,X1),X0)
| in(sK4(X0,X1),X1) ),
inference(cnf_transformation,[],[f36]) ).
cnf(c_123,plain,
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),cartesian_product2(X2,X3))
| in(X1,X3) ),
inference(demodulation,[status(thm)],[c_53,c_50]) ).
cnf(c_134,plain,
( ~ in(X0,X1)
| ~ in(X2,X3)
| in(unordered_pair(singleton(X2),unordered_pair(X2,X0)),cartesian_product2(X3,X1)) ),
inference(demodulation,[status(thm)],[c_52,c_50]) ).
cnf(c_161,plain,
cartesian_product2(sK2,sK2) = sP0_iProver_def,
definition ).
cnf(c_162,plain,
cartesian_product2(sK3,sK3) = sP1_iProver_def,
definition ).
cnf(c_163,negated_conjecture,
sP0_iProver_def = sP1_iProver_def,
inference(demodulation,[status(thm)],[c_58,c_162,c_161]) ).
cnf(c_164,negated_conjecture,
sK2 != sK3,
inference(demodulation,[status(thm)],[c_57]) ).
cnf(c_337,plain,
cartesian_product2(sK3,sK3) = sP0_iProver_def,
inference(light_normalisation,[status(thm)],[c_162,c_163]) ).
cnf(c_380,plain,
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sP0_iProver_def)
| in(X1,sK2) ),
inference(superposition,[status(thm)],[c_161,c_123]) ).
cnf(c_381,plain,
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sP0_iProver_def)
| in(X1,sK3) ),
inference(superposition,[status(thm)],[c_337,c_123]) ).
cnf(c_418,plain,
( ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sP0_iProver_def)
| in(X1,sK2) ),
inference(superposition,[status(thm)],[c_50,c_380]) ).
cnf(c_426,plain,
( ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sP0_iProver_def)
| in(X1,sK3) ),
inference(superposition,[status(thm)],[c_50,c_381]) ).
cnf(c_484,plain,
( ~ in(X0,sK2)
| ~ in(X1,sK2)
| in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sP0_iProver_def) ),
inference(superposition,[status(thm)],[c_161,c_134]) ).
cnf(c_485,plain,
( ~ in(X0,sK3)
| ~ in(X1,sK3)
| in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sP0_iProver_def) ),
inference(superposition,[status(thm)],[c_337,c_134]) ).
cnf(c_525,plain,
( ~ in(X0,sK2)
| in(X0,sK3) ),
inference(superposition,[status(thm)],[c_484,c_426]) ).
cnf(c_543,plain,
( ~ in(sK4(sK2,sK3),sK2)
| ~ in(sK4(sK2,sK3),sK3)
| sK2 = sK3 ),
inference(instantiation,[status(thm)],[c_59]) ).
cnf(c_557,plain,
( ~ in(X0,sK3)
| in(X0,sK2) ),
inference(superposition,[status(thm)],[c_485,c_418]) ).
cnf(c_632,plain,
( X0 = sK3
| in(sK4(X0,sK3),X0)
| in(sK4(X0,sK3),sK2) ),
inference(superposition,[status(thm)],[c_60,c_557]) ).
cnf(c_641,plain,
( sK2 = sK3
| in(sK4(sK2,sK3),sK2) ),
inference(instantiation,[status(thm)],[c_632]) ).
cnf(c_692,plain,
( sK2 = sK3
| in(sK4(sK2,sK3),sK2) ),
inference(equality_factoring,[status(thm)],[c_632]) ).
cnf(c_694,plain,
in(sK4(sK2,sK3),sK2),
inference(forward_subsumption_resolution,[status(thm)],[c_692,c_164]) ).
cnf(c_712,plain,
in(sK4(sK2,sK3),sK3),
inference(superposition,[status(thm)],[c_694,c_525]) ).
cnf(c_713,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_712,c_641,c_543,c_57]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11 % Problem : SET962+1 : TPTP v8.1.2. Bugfixed v4.0.0.
% 0.09/0.12 % Command : run_iprover %s %d THM
% 0.11/0.32 % Computer : n010.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Thu May 2 20:03:49 EDT 2024
% 0.11/0.32 % CPUTime :
% 0.17/0.44 Running first-order theorem proving
% 0.17/0.44 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
% 0.45/1.14 % SZS status Started for theBenchmark.p
% 0.45/1.14 % SZS status Theorem for theBenchmark.p
% 0.45/1.14
% 0.45/1.14 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 0.45/1.14
% 0.45/1.14 ------ iProver source info
% 0.45/1.14
% 0.45/1.14 git: date: 2024-05-02 19:28:25 +0000
% 0.45/1.14 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 0.45/1.14 git: non_committed_changes: false
% 0.45/1.14
% 0.45/1.14 ------ Parsing...
% 0.45/1.14 ------ Clausification by vclausify_rel & Parsing by iProver...
% 0.45/1.14
% 0.45/1.14 ------ Preprocessing... sup_sim: 4 sf_s rm: 1 0s sf_e pe_s pe_e
% 0.45/1.14
% 0.45/1.14 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 0.45/1.14
% 0.45/1.14 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.45/1.14 ------ Proving...
% 0.45/1.14 ------ Problem Properties
% 0.45/1.14
% 0.45/1.14
% 0.45/1.14 clauses 14
% 0.45/1.14 conjectures 2
% 0.45/1.14 EPR 5
% 0.45/1.14 Horn 13
% 0.45/1.14 unary 8
% 0.45/1.14 binary 3
% 0.45/1.14 lits 23
% 0.45/1.14 lits eq 7
% 0.45/1.14 fd_pure 0
% 0.45/1.14 fd_pseudo 0
% 0.45/1.14 fd_cond 0
% 0.45/1.14 fd_pseudo_cond 2
% 0.45/1.14 AC symbols 0
% 0.45/1.14
% 0.45/1.14 ------ Schedule dynamic 5 is on
% 0.45/1.14
% 0.45/1.14 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.45/1.14
% 0.45/1.14
% 0.45/1.14 ------
% 0.45/1.14 Current options:
% 0.45/1.14 ------
% 0.45/1.14
% 0.45/1.14
% 0.45/1.14
% 0.45/1.14
% 0.45/1.14 ------ Proving...
% 0.45/1.14
% 0.45/1.14
% 0.45/1.14 % SZS status Theorem for theBenchmark.p
% 0.45/1.14
% 0.45/1.14 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.45/1.14
% 0.45/1.15
%------------------------------------------------------------------------------