%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : ALG211+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n026.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 12:53:48 PM UTC 2026
% Result : Theorem 1.76s 1.29s
% Output : CNFRefutation 1.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 53 ( 12 unt; 2 def)
% Number of atoms : 137 ( 2 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 141 ( 61 ~; 51 |; 19 &)
% ( 3 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 3 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-3 aty)
% Number of variables : 100 ( 0 sgn 87 !; 13 ?; 27 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( basis_of(X0,X1)
=> ( a_subset_of(X0,vec_to_class(X1))
& lin_ind_subset(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',basis_of) ).
fof(f2,axiom,
! [X0,X1,X2] :
( ( basis_of(X1,X2)
& lin_ind_subset(X0,X2) )
=> ? [X3] :
( basis_of(union(X0,X3),X2)
& a_subset_of(X3,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bg_2_2_5) ).
fof(f3,axiom,
! [X0] :
( a_vector_space(X0)
=> ? [X1] : basis_of(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bg_remark_63_a) ).
fof(f4,axiom,
! [X0,X1] :
( a_vector_subspace_of(X0,X1)
=> a_vector_space(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bg_2_4_a) ).
fof(f5,axiom,
! [X0,X1,X2] :
( ( a_subset_of(X2,vec_to_class(X0))
& a_vector_subspace_of(X0,X1) )
=> ( lin_ind_subset(X2,X0)
<=> lin_ind_subset(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bg_2_4_2) ).
fof(f6,conjecture,
! [X0,X1] :
( ( a_vector_space(X1)
& a_vector_subspace_of(X0,X1) )
=> ? [X2,X3] :
( basis_of(X2,X0)
& basis_of(union(X2,X3),X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bg_2_4_3) ).
fof(f7,negated_conjecture,
~ ! [X0,X1] :
( ( a_vector_space(X1)
& a_vector_subspace_of(X0,X1) )
=> ? [X2,X3] :
( basis_of(X2,X0)
& basis_of(union(X2,X3),X1) ) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
fof(f8,plain,
! [X0,X1] :
( ~ basis_of(X0,X1)
| ( a_subset_of(X0,vec_to_class(X1))
& lin_ind_subset(X0,X1) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f9,plain,
! [X0,X1,X2] :
( ~ basis_of(X1,X2)
| ~ lin_ind_subset(X0,X2)
| ? [X3] :
( basis_of(union(X0,X3),X2)
& a_subset_of(X3,X1) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f10,plain,
! [X0,X1,X2] :
( ~ basis_of(X1,X2)
| ~ lin_ind_subset(X0,X2)
| ? [X3] :
( basis_of(union(X0,X3),X2)
& a_subset_of(X3,X1) ) ),
inference(flattening,[],[f9]) ).
fof(f11,plain,
! [X0] :
( ~ a_vector_space(X0)
| ? [X1] : basis_of(X1,X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f12,plain,
! [X0,X1] :
( ~ a_vector_subspace_of(X0,X1)
| a_vector_space(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f13,plain,
! [X0,X1,X2] :
( ~ a_subset_of(X2,vec_to_class(X0))
| ~ a_vector_subspace_of(X0,X1)
| ( lin_ind_subset(X2,X0)
<=> lin_ind_subset(X2,X1) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f14,plain,
! [X0,X1,X2] :
( ~ a_subset_of(X2,vec_to_class(X0))
| ~ a_vector_subspace_of(X0,X1)
| ( lin_ind_subset(X2,X0)
<=> lin_ind_subset(X2,X1) ) ),
inference(flattening,[],[f13]) ).
fof(f15,plain,
? [X0,X1] :
( a_vector_space(X1)
& a_vector_subspace_of(X0,X1)
& ! [X2,X3] :
( ~ basis_of(X2,X0)
| ~ basis_of(union(X2,X3),X1) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f16,plain,
? [X0,X1] :
( a_vector_space(X1)
& a_vector_subspace_of(X0,X1)
& ! [X2,X3] :
( ~ basis_of(X2,X0)
| ~ basis_of(union(X2,X3),X1) ) ),
inference(flattening,[],[f15]) ).
fof(f17,plain,
! [X0,X1,X2] :
( ~ basis_of(X1,X2)
| ~ lin_ind_subset(X0,X2)
| ( basis_of(union(X0,sK0(X0,X1,X2)),X2)
& a_subset_of(sK0(X0,X1,X2),X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X3,sK0(X0,X1,X2))],[f10]) ).
fof(f18,plain,
! [X0] :
( ~ a_vector_space(X0)
| basis_of(sK1(X0),X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X1,sK1(X0))],[f11]) ).
fof(f19,plain,
! [X0,X1,X2] :
( ~ a_subset_of(X2,vec_to_class(X0))
| ~ a_vector_subspace_of(X0,X1)
| ( ( ~ lin_ind_subset(X2,X0)
| lin_ind_subset(X2,X1) )
& ( ~ lin_ind_subset(X2,X1)
| lin_ind_subset(X2,X0) ) ) ),
inference(nnf_transformation,[],[f14]) ).
fof(f20,plain,
( a_vector_space(sK3)
& a_vector_subspace_of(sK2,sK3)
& ! [X2,X3] :
( ~ basis_of(X2,sK2)
| ~ basis_of(union(X2,X3),sK3) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X0,sK2),skolemize(X1,sK3)],[f16]) ).
fof(f21,plain,
! [X0,X1] :
( ~ basis_of(X0,X1)
| a_subset_of(X0,vec_to_class(X1)) ),
inference(cnf_transformation,[],[f8]) ).
fof(f22,plain,
! [X0,X1] :
( ~ basis_of(X0,X1)
| lin_ind_subset(X0,X1) ),
inference(cnf_transformation,[],[f8]) ).
fof(f23,plain,
! [X2,X0,X1] :
( ~ basis_of(X1,X2)
| ~ lin_ind_subset(X0,X2)
| basis_of(union(X0,sK0(X0,X1,X2)),X2) ),
inference(cnf_transformation,[],[f17]) ).
fof(f25,plain,
! [X0] :
( ~ a_vector_space(X0)
| basis_of(sK1(X0),X0) ),
inference(cnf_transformation,[],[f18]) ).
fof(f26,plain,
! [X0,X1] :
( ~ a_vector_subspace_of(X0,X1)
| a_vector_space(X0) ),
inference(cnf_transformation,[],[f12]) ).
fof(f27,plain,
! [X2,X0,X1] :
( ~ a_subset_of(X2,vec_to_class(X0))
| ~ a_vector_subspace_of(X0,X1)
| ~ lin_ind_subset(X2,X0)
| lin_ind_subset(X2,X1) ),
inference(cnf_transformation,[],[f19]) ).
fof(f29,plain,
a_vector_space(sK3),
inference(cnf_transformation,[],[f20]) ).
fof(f30,plain,
a_vector_subspace_of(sK2,sK3),
inference(cnf_transformation,[],[f20]) ).
fof(f31,plain,
! [X2,X3] :
( ~ basis_of(X2,sK2)
| ~ basis_of(union(X2,X3),sK3) ),
inference(cnf_transformation,[],[f20]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] :
( lin_ind_subset(X0,X1)
| ~ basis_of(X0,X1) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] :
( a_subset_of(X0,vec_to_class(X1))
| ~ basis_of(X0,X1) ),
inference(cnf_transformation,[],[f21]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i,X2: $i] :
( basis_of(union(X0,sK0(X0,X2,X1)),X1)
| ~ basis_of(X2,X1)
| ~ lin_ind_subset(X0,X1) ),
inference(cnf_transformation,[],[f23]) ).
tcf(c_53,plain,
! [X0: $i] :
( basis_of(sK1(X0),X0)
| ~ a_vector_space(X0) ),
inference(cnf_transformation,[],[f25]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] :
( a_vector_space(X0)
| ~ a_vector_subspace_of(X0,X1) ),
inference(cnf_transformation,[],[f26]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] :
( lin_ind_subset(X0,X2)
| ~ a_vector_subspace_of(X1,X2)
| ~ lin_ind_subset(X0,X1)
| ~ a_subset_of(X0,vec_to_class(X1)) ),
inference(cnf_transformation,[],[f27]) ).
tcf(c_57,negated_conjecture,
! [X0: $i,X1: $i] :
( ~ basis_of(X0,sK2)
| ~ basis_of(union(X0,X1),sK3) ),
inference(cnf_transformation,[],[f31]) ).
tcf(c_58,negated_conjecture,
a_vector_subspace_of(sK2,sK3),
inference(cnf_transformation,[],[f30]) ).
tcf(c_59,negated_conjecture,
a_vector_space(sK3),
inference(cnf_transformation,[],[f29]) ).
tcf(c_118,plain,
! [X0: $i,X1: $i] :
( basis_of(sK1(X0),X0)
| ~ a_vector_subspace_of(X0,X1) ),
inference(resolution,[status(thm)],[c_54,c_53]) ).
tcf(c_126,plain,
basis_of(sK1(sK3),sK3),
inference(resolution,[status(thm)],[c_53,c_59]) ).
tcf(c_133,plain,
basis_of(sK1(sK2),sK2),
inference(resolution,[status(thm)],[c_118,c_58]) ).
tcf(c_137,plain,
! [X0: $i] :
( lin_ind_subset(X0,sK3)
| ~ lin_ind_subset(X0,sK2)
| ~ a_subset_of(X0,vec_to_class(sK2)) ),
inference(resolution,[status(thm)],[c_56,c_58]) ).
tcf(c_168,plain,
! [X0: $i] :
( lin_ind_subset(X0,sK3)
| ~ basis_of(X0,sK2)
| ~ lin_ind_subset(X0,sK2) ),
inference(resolution,[status(thm)],[c_50,c_137]) ).
tcf(c_176,plain,
! [X0: $i] :
( lin_ind_subset(X0,sK3)
| ~ basis_of(X0,sK2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_168,c_49]) ).
tcf(c_308,definition,
iPr_def_11 = sK1(sK2),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_309,definition,
iPr_def_12 = sK1(sK3),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_312,plain,
basis_of(iPr_def_11,sK2),
inference(demodulation,[status(thm)],[c_133,c_308]) ).
tcf(c_313,plain,
basis_of(iPr_def_12,sK3),
inference(demodulation,[status(thm)],[c_126,c_309]) ).
tcf(c_314,negated_conjecture,
! [X0: $i,X1: $i] :
( ~ basis_of(X0,sK2)
| ~ basis_of(union(X0,X1),sK3) ),
inference(demodulation,[status(thm)],[c_57]) ).
tcf(c_550,plain,
! [X0: $i,X1: $i] :
( ~ basis_of(X1,sK3)
| ~ basis_of(X0,sK2)
| ~ lin_ind_subset(X0,sK3) ),
inference(superposition,[status(thm)],[c_52,c_314]) ).
tcf(c_578,plain,
! [X0: $i,X1: $i] :
( ~ basis_of(X1,sK3)
| ~ basis_of(X0,sK2) ),
inference(global_subsumption_just,[status(thm)],[c_550,c_176,c_550]) ).
tcf(c_586,plain,
! [X0: $i] : ~ basis_of(X0,sK3),
inference(superposition,[status(thm)],[c_312,c_578]) ).
tcf(c_587,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_313,c_586]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG211+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.37 % Computer : n026.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Fri Sep 25 05:07:26 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 0.11/0.42
% 0.11/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.42
% 0.11/0.42 % Detected problem language: tptp
% 0.11/0.44 % Proving...
% 1.76/1.29 % SZS status Started for theBenchmark.p
% 1.76/1.29 % SZS status Theorem for theBenchmark.p
% 1.76/1.29
% 1.76/1.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.76/1.29
% 1.76/1.29 % ------ iProver source info
% 1.76/1.29
% 1.76/1.29 % git: date: 2026-07-19 20:42:38 +0200
% 1.76/1.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.76/1.29 % git: non_committed_changes: false
% 1.76/1.29
% 1.76/1.29 % ------ Parsing...
% 1.76/1.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.76/1.29
% 1.76/1.29 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sf_s rm: 0 0s sf_e pe_s pe_e %
% 1.76/1.29
% 1.76/1.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.76/1.29
% 1.76/1.29 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.76/1.29 % ------ Proving...
% 1.76/1.29 % ------ Problem Properties
% 1.76/1.29
% 1.76/1.29 %
% 1.76/1.29 % clauses 12
% 1.76/1.29 % conjectures 1
% 1.76/1.29 % EPR 5
% 1.76/1.29 % Horn 12
% 1.76/1.29 % unary 5
% 1.76/1.29 % binary 3
% 1.76/1.29 % lits 23
% 1.76/1.29 % lits eq 3
% 1.76/1.29 % fd_pure 0
% 1.76/1.29 % fd_pseudo 0
% 1.76/1.29 % fd_cond 0
% 1.76/1.29 % fd_pseudo_cond 0
% 1.76/1.29 % AC symbols 0
% 1.76/1.29
% 1.76/1.29 % ------ Schedule dynamic 5 is on
% 1.76/1.29
% 1.76/1.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.76/1.29
% 1.76/1.29
% 1.76/1.29 % ------
% 1.76/1.29 % Current options:
% 1.76/1.29 % ------
% 1.76/1.29
% 1.76/1.29
% 1.76/1.29 %
% 1.76/1.29
% 1.76/1.29 % ------ Proving...
% 1.76/1.29 %
% 1.76/1.29
% 1.76/1.29 % SZS status Theorem for theBenchmark.p
% 1.76/1.29
% 1.76/1.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.76/1.29
% 1.76/1.29
%------------------------------------------------------------------------------