%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU307+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n006.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 02:56:35 PM UTC 2026
% Result : Theorem 4.23s 6.30s
% Output : CNFRefutation 4.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 10
% Syntax : Number of formulae : 59 ( 28 unt; 3 def)
% Number of atoms : 124 ( 40 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 82 ( 38 ~; 30 |; 6 &)
% ( 1 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 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 : 8 ( 6 usr; 4 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 71 ( 1 sgn 69 !; 2 ?; 28 :)
% Comments :
%------------------------------------------------------------------------------
fof(f40,axiom,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(f44,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f47,axiom,
! [X0,X1,X2] :
( ( element(X2,powerset(X0))
& element(X1,powerset(X0)) )
=> subset_intersection2(X0,X1,X2) = set_intersection2(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k5_subset_1) ).
fof(f56,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
fof(f57,axiom,
! [X0] :
( one_sorted_str(X0)
=> cast_as_carrier_subset(X0) = the_carrier(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_pre_topc) ).
fof(f58,conjecture,
! [X0] :
( one_sorted_str(X0)
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> subset_intersection2(the_carrier(X0),X1,cast_as_carrier_subset(X0)) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_pre_topc) ).
fof(f59,negated_conjecture,
~ ! [X0] :
( one_sorted_str(X0)
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> subset_intersection2(the_carrier(X0),X1,cast_as_carrier_subset(X0)) = X1 ) ),
inference(negated_conjecture,[status(cth)],[f58]) ).
fof(f60,axiom,
! [X0,X1] :
( subset(X0,X1)
=> set_intersection2(X0,X1) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_xboole_1) ).
fof(f62,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f44]) ).
fof(f113,plain,
! [X0,X1,X2] :
( ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0))
| subset_intersection2(X0,X1,X2) = set_intersection2(X1,X2) ),
inference(ennf_transformation,[],[f47]) ).
fof(f114,plain,
! [X0,X1,X2] :
( ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0))
| subset_intersection2(X0,X1,X2) = set_intersection2(X1,X2) ),
inference(flattening,[],[f113]) ).
fof(f118,plain,
! [X0] :
( ~ one_sorted_str(X0)
| cast_as_carrier_subset(X0) = the_carrier(X0) ),
inference(ennf_transformation,[],[f57]) ).
fof(f119,plain,
? [X0] :
( one_sorted_str(X0)
& ? [X1] :
( element(X1,powerset(the_carrier(X0)))
& subset_intersection2(the_carrier(X0),X1,cast_as_carrier_subset(X0)) != X1 ) ),
inference(ennf_transformation,[],[f59]) ).
fof(f120,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| set_intersection2(X0,X1) = X0 ),
inference(ennf_transformation,[],[f60]) ).
fof(f126,plain,
! [X0,X1] :
( ( ~ element(X0,powerset(X1))
| subset(X0,X1) )
& ( ~ subset(X0,X1)
| element(X0,powerset(X1)) ) ),
inference(nnf_transformation,[],[f56]) ).
fof(f127,plain,
( one_sorted_str(sK5)
& element(sK6,powerset(the_carrier(sK5)))
& sK6 != subset_intersection2(the_carrier(sK5),sK6,cast_as_carrier_subset(sK5)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6]),skolemize(X0,sK5),skolemize(X1,sK6)],[f119]) ).
fof(f207,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[],[f40]) ).
fof(f211,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f62]) ).
fof(f214,plain,
! [X2,X0,X1] :
( ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0))
| subset_intersection2(X0,X1,X2) = set_intersection2(X1,X2) ),
inference(cnf_transformation,[],[f114]) ).
fof(f218,plain,
! [X0,X1] :
( ~ element(X0,powerset(X1))
| subset(X0,X1) ),
inference(cnf_transformation,[],[f126]) ).
fof(f219,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f126]) ).
fof(f220,plain,
! [X0] :
( ~ one_sorted_str(X0)
| cast_as_carrier_subset(X0) = the_carrier(X0) ),
inference(cnf_transformation,[],[f118]) ).
fof(f221,plain,
one_sorted_str(sK5),
inference(cnf_transformation,[],[f127]) ).
fof(f222,plain,
element(sK6,powerset(the_carrier(sK5))),
inference(cnf_transformation,[],[f127]) ).
fof(f223,plain,
sK6 != subset_intersection2(the_carrier(sK5),sK6,cast_as_carrier_subset(sK5)),
inference(cnf_transformation,[],[f127]) ).
fof(f224,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| set_intersection2(X0,X1) = X0 ),
inference(cnf_transformation,[],[f120]) ).
tcf(c_128,plain,
! [X0: $i,X1: $i] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[],[f207]) ).
tcf(c_132,plain,
! [X0: $i] : subset(X0,X0),
inference(cnf_transformation,[],[f211]) ).
tcf(c_135,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( subset_intersection2(X1,X0,X2) = set_intersection2(X0,X2) )
| ~ element(X2,powerset(X1))
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f214]) ).
tcf(c_139,plain,
! [X0: $i,X1: $i] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f219]) ).
tcf(c_140,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f218]) ).
tcf(c_141,plain,
! [X0: $i] :
( ( cast_as_carrier_subset(X0) = the_carrier(X0) )
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f220]) ).
tcf(c_142,negated_conjecture,
subset_intersection2(the_carrier(sK5),sK6,cast_as_carrier_subset(sK5)) != sK6,
inference(cnf_transformation,[],[f223]) ).
tcf(c_143,negated_conjecture,
element(sK6,powerset(the_carrier(sK5))),
inference(cnf_transformation,[],[f222]) ).
tcf(c_144,negated_conjecture,
one_sorted_str(sK5),
inference(cnf_transformation,[],[f221]) ).
tcf(c_145,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X0,X1) = X0 )
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f224]) ).
tcf(c_181,plain,
! [X0: $i,X1: $i] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_139]) ).
tcf(c_301,plain,
! [X0: $i] :
( ( cast_as_carrier_subset(X0) = the_carrier(X0) )
| ~ one_sorted_str(X0) ),
inference(prop_impl_just,[status(thm)],[c_141]) ).
tcf(c_473,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( subset_intersection2(X1,X2,X0) = set_intersection2(X2,X0) )
| ~ subset(X2,X1)
| ~ element(X0,powerset(X1)) ),
inference(bin_hyper_res,[status(thm)],[c_135,c_181]) ).
tcf(c_1223,plain,
! [X0: $i] :
( ( cast_as_carrier_subset(X0) = the_carrier(X0) )
| ( X0 != sK5 ) ),
inference(resolution_lifted,[status(thm)],[c_301,c_144]) ).
tcf(c_1224,plain,
cast_as_carrier_subset(sK5) = the_carrier(sK5),
inference(unflattening,[status(thm)],[c_1223]) ).
tcf(c_1388,plain,
! [X0: $i,X1: $i] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_139]) ).
tcf(c_1464,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( subset_intersection2(X1,X2,X0) = set_intersection2(X2,X0) )
| ~ subset(X2,X1)
| ~ subset(X0,X1) ),
inference(bin_hyper_res,[status(thm)],[c_473,c_1388]) ).
tcf(c_1628,plain,
subset_intersection2(the_carrier(sK5),sK6,the_carrier(sK5)) != sK6,
inference(light_normalisation,[status(thm)],[c_142,c_1224]) ).
tcf(c_1914,definition,
iPr_def_10 = the_carrier(sK5),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_1915,definition,
iPr_def_11 = subset_intersection2(iPr_def_10,sK6,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_1916,definition,
iPr_def_12 = powerset(iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_1918,plain,
iPr_def_11 != sK6,
inference(demodulation,[status(thm)],[c_1628,c_1914,c_1915]) ).
tcf(c_1921,negated_conjecture,
element(sK6,iPr_def_12),
inference(demodulation,[status(thm)],[c_143]) ).
tcf(c_2565,plain,
! [X0: $i] :
( subset(X0,iPr_def_10)
| ~ element(X0,iPr_def_12) ),
inference(superposition,[status(thm)],[c_1916,c_140]) ).
tcf(c_2587,plain,
subset(sK6,iPr_def_10),
inference(superposition,[status(thm)],[c_1921,c_2565]) ).
tcf(c_2641,plain,
set_intersection2(sK6,iPr_def_10) = sK6,
inference(superposition,[status(thm)],[c_2587,c_145]) ).
tcf(c_2659,plain,
set_intersection2(iPr_def_10,sK6) = sK6,
inference(demodulation,[status(thm)],[c_2641,c_128]) ).
tcf(c_5502,plain,
! [X0: $i,X1: $i] :
( ( subset_intersection2(X1,X0,X1) = set_intersection2(X0,X1) )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_132,c_1464]) ).
tcf(c_5798,plain,
subset_intersection2(iPr_def_10,sK6,iPr_def_10) = set_intersection2(sK6,iPr_def_10),
inference(superposition,[status(thm)],[c_2587,c_5502]) ).
tcf(c_5806,plain,
set_intersection2(sK6,iPr_def_10) = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_5798,c_1915]) ).
tcf(c_5888,plain,
sK6 = iPr_def_11,
inference(demodulation,[status(thm)],[c_5806,c_128,c_2659]) ).
tcf(c_5918,plain,
iPr_def_11 != iPr_def_11,
inference(demodulation,[status(thm)],[c_1918,c_5888]) ).
tcf(c_5920,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_5918]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU307+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/5.37 % Computer : n006.cluster.edu
% 0.12/5.37 % Model : x86_64 x86_64
% 0.12/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.37 % Memory : 8046.5625MB
% 0.12/5.37 % OS : Linux 6.8.0-71-generic
% 0.12/5.37 % CPULimit : 300
% 0.12/5.37 % WCLimit : 300
% 0.12/5.37 % DateTime : Thu Sep 24 13:37:16 UTC 2026
% 0.12/5.38 % CPUTime :
% 0.12/5.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.15/5.42 Running first-order theorem proving
% 0.15/5.42 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
% 0.15/5.43
% 0.15/5.43 % ======== iProver multi-core TPTP/SMT =========
% 0.15/5.43
% 0.15/5.43 % Detected problem language: tptp
% 0.15/5.44 % Proving...
% 4.23/6.30 % SZS status Started for theBenchmark.p
% 4.23/6.30 % SZS status Theorem for theBenchmark.p
% 4.23/6.30
% 4.23/6.30 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.23/6.30
% 4.23/6.30 % ------ iProver source info
% 4.23/6.30
% 4.23/6.30 % git: date: 2026-07-19 20:42:38 +0200
% 4.23/6.30 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.23/6.30 % git: non_committed_changes: false
% 4.23/6.30
% 4.23/6.30 % ------ Parsing...
% 4.23/6.30 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.23/6.30
% 4.23/6.30 % ------ Preprocessing... sup_sim: 0 sf_s rm: 70 0s sf_e pe_s pe:1:0s pe_e sup_sim: 3 sf_s rm: 7 0s sf_e pe_s pe_e %
% 4.23/6.30
% 4.23/6.30 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.23/6.30
% 4.23/6.30 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.23/6.30 % ------ Proving...
% 4.23/6.30 % ------ Problem Properties
% 4.23/6.30
% 4.23/6.30 %
% 4.23/6.30 % clauses 37
% 4.23/6.30 % conjectures 1
% 4.23/6.30 % EPR 15
% 4.23/6.30 % Horn 35
% 4.23/6.30 % unary 20
% 4.23/6.30 % binary 9
% 4.23/6.30 % lits 62
% 4.23/6.30 % lits eq 16
% 4.23/6.30 % fd_pure 0
% 4.23/6.30 % fd_pseudo 0
% 4.23/6.30 % fd_cond 1
% 4.23/6.30 % fd_pseudo_cond 1
% 4.23/6.30 % AC symbols 0
% 4.23/6.30
% 4.23/6.30 % ------ Schedule dynamic 5 is on
% 4.23/6.30
% 4.23/6.30 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.23/6.30
% 4.23/6.30
% 4.23/6.30 % ------
% 4.23/6.30 % Current options:
% 4.23/6.30 % ------
% 4.23/6.30
% 4.23/6.30
% 4.23/6.30 %
% 4.23/6.30
% 4.23/6.30 % ------ Proving...
% 4.23/6.30 %
% 4.23/6.30
% 4.23/6.30 % SZS status Theorem for theBenchmark.p
% 4.23/6.30
% 4.23/6.30 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.23/6.30
% 4.23/6.30
%------------------------------------------------------------------------------