%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU308+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n011.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 4.40s 16.55s
% Output : CNFRefutation 4.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 38 ( 13 unt; 0 def)
% Number of atoms : 74 ( 28 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 66 ( 30 ~; 23 |; 5 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-3 aty)
% Number of variables : 40 ( 0 sgn 38 !; 2 ?; 10 :)
% Comments :
%------------------------------------------------------------------------------
fof(f40,axiom,
! [X0,X1,X2] :
( ( element(X2,powerset(X0))
& element(X1,powerset(X0)) )
=> subset_difference(X0,X1,X2) = set_difference(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k6_subset_1) ).
fof(f42,axiom,
! [X0] :
( one_sorted_str(X0)
=> element(cast_as_carrier_subset(X0),powerset(the_carrier(X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_pre_topc) ).
fof(f51,axiom,
! [X0] :
( one_sorted_str(X0)
=> cast_as_carrier_subset(X0) = the_carrier(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_pre_topc) ).
fof(f52,conjecture,
! [X0] :
( one_sorted_str(X0)
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> subset_complement(the_carrier(X0),X1) = subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_pre_topc) ).
fof(f53,negated_conjecture,
~ ! [X0] :
( one_sorted_str(X0)
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> subset_complement(the_carrier(X0),X1) = subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1) ) ),
inference(negated_conjecture,[status(cth)],[f52]) ).
fof(f54,axiom,
! [X0,X1] :
( element(X1,powerset(X0))
=> subset_complement(X0,X1) = set_difference(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_subset_1) ).
fof(f55,plain,
? [X0] :
( one_sorted_str(X0)
& ? [X1] :
( element(X1,powerset(the_carrier(X0)))
& subset_complement(the_carrier(X0),X1) != subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1) ) ),
inference(ennf_transformation,[],[f53]) ).
fof(f60,plain,
! [X0,X1] :
( ~ element(X1,powerset(X0))
| subset_complement(X0,X1) = set_difference(X0,X1) ),
inference(ennf_transformation,[],[f54]) ).
fof(f65,plain,
! [X0,X1,X2] :
( ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0))
| subset_difference(X0,X1,X2) = set_difference(X1,X2) ),
inference(ennf_transformation,[],[f40]) ).
fof(f66,plain,
! [X0,X1,X2] :
( ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0))
| subset_difference(X0,X1,X2) = set_difference(X1,X2) ),
inference(flattening,[],[f65]) ).
fof(f67,plain,
! [X0] :
( ~ one_sorted_str(X0)
| cast_as_carrier_subset(X0) = the_carrier(X0) ),
inference(ennf_transformation,[],[f51]) ).
fof(f68,plain,
! [X0] :
( ~ one_sorted_str(X0)
| element(cast_as_carrier_subset(X0),powerset(the_carrier(X0))) ),
inference(ennf_transformation,[],[f42]) ).
fof(f82,plain,
( one_sorted_str(sK0)
& element(sK1,powerset(the_carrier(sK0)))
& subset_complement(the_carrier(sK0),sK1) != subset_difference(the_carrier(sK0),cast_as_carrier_subset(sK0),sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f55]) ).
fof(f88,plain,
one_sorted_str(sK0),
inference(cnf_transformation,[],[f82]) ).
fof(f89,plain,
element(sK1,powerset(the_carrier(sK0))),
inference(cnf_transformation,[],[f82]) ).
fof(f90,plain,
subset_complement(the_carrier(sK0),sK1) != subset_difference(the_carrier(sK0),cast_as_carrier_subset(sK0),sK1),
inference(cnf_transformation,[],[f82]) ).
fof(f98,plain,
! [X0,X1] :
( ~ element(X1,powerset(X0))
| set_difference(X0,X1) = subset_complement(X0,X1) ),
inference(cnf_transformation,[],[f60]) ).
fof(f102,plain,
! [X2,X0,X1] :
( ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0))
| subset_difference(X0,X1,X2) = set_difference(X1,X2) ),
inference(cnf_transformation,[],[f66]) ).
fof(f103,plain,
! [X0] :
( ~ one_sorted_str(X0)
| cast_as_carrier_subset(X0) = the_carrier(X0) ),
inference(cnf_transformation,[],[f67]) ).
fof(f104,plain,
! [X0] :
( ~ one_sorted_str(X0)
| element(cast_as_carrier_subset(X0),powerset(the_carrier(X0))) ),
inference(cnf_transformation,[],[f68]) ).
tcf(c_49,negated_conjecture,
subset_difference(the_carrier(sK0),cast_as_carrier_subset(sK0),sK1) != subset_complement(the_carrier(sK0),sK1),
inference(cnf_transformation,[],[f90]) ).
tcf(c_50,negated_conjecture,
element(sK1,powerset(the_carrier(sK0))),
inference(cnf_transformation,[],[f89]) ).
tcf(c_51,negated_conjecture,
one_sorted_str(sK0),
inference(cnf_transformation,[],[f88]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i] :
( ( subset_complement(X1,X0) = set_difference(X1,X0) )
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f98]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( subset_difference(X1,X0,X2) = set_difference(X0,X2) )
| ~ element(X2,powerset(X1))
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f102]) ).
tcf(c_64,plain,
! [X0: $i] :
( ( the_carrier(X0) = cast_as_carrier_subset(X0) )
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f103]) ).
tcf(c_65,plain,
! [X0: $i] :
( element(cast_as_carrier_subset(X0),powerset(the_carrier(X0)))
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f104]) ).
tcf(c_646,plain,
! [X0: $i] :
( element(cast_as_carrier_subset(X0),powerset(the_carrier(X0)))
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_51,c_65]) ).
tcf(c_647,plain,
element(cast_as_carrier_subset(sK0),powerset(the_carrier(sK0))),
inference(unflattening,[status(thm)],[c_646]) ).
tcf(c_651,plain,
! [X0: $i] :
( ( the_carrier(X0) = cast_as_carrier_subset(X0) )
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_51,c_64]) ).
tcf(c_652,plain,
the_carrier(sK0) = cast_as_carrier_subset(sK0),
inference(unflattening,[status(thm)],[c_651]) ).
tcf(c_731,plain,
element(the_carrier(sK0),powerset(the_carrier(sK0))),
inference(light_normalisation,[status(thm)],[c_647,c_652]) ).
tcf(c_756,plain,
subset_difference(the_carrier(sK0),the_carrier(sK0),sK1) != subset_complement(the_carrier(sK0),sK1),
inference(light_normalisation,[status(thm)],[c_49,c_652]) ).
tcf(c_1057,plain,
subset_complement(the_carrier(sK0),sK1) = set_difference(the_carrier(sK0),sK1),
inference(superposition,[status(thm)],[c_50,c_59]) ).
tcf(c_1068,plain,
subset_difference(the_carrier(sK0),the_carrier(sK0),sK1) != set_difference(the_carrier(sK0),sK1),
inference(demodulation,[status(thm)],[c_756,c_1057]) ).
tcf(c_1423,plain,
! [X0: $i] :
( ( subset_difference(the_carrier(sK0),the_carrier(sK0),X0) = set_difference(the_carrier(sK0),X0) )
| ~ element(X0,powerset(the_carrier(sK0)))
| ~ element(the_carrier(sK0),powerset(the_carrier(sK0))) ),
inference(instantiation,[status(thm)],[c_63]) ).
tcf(c_2032,plain,
( ( subset_difference(the_carrier(sK0),the_carrier(sK0),sK1) = set_difference(the_carrier(sK0),sK1) )
| ~ element(sK1,powerset(the_carrier(sK0)))
| ~ element(the_carrier(sK0),powerset(the_carrier(sK0))) ),
inference(instantiation,[status(thm)],[c_1423]) ).
tcf(c_2033,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_2032,c_1068,c_731,c_50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU308+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.34 % Computer : n011.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.11/15.59 % CPULimit : 300
% 0.11/15.59 % WCLimit : 300
% 0.11/15.59 % DateTime : Thu Sep 24 13:38:44 UTC 2026
% 0.11/15.59 % CPUTime :
% 0.11/15.59 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.50/15.64 Running first-order theorem proving
% 0.50/15.64 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.50/15.65
% 0.50/15.65 % ======== iProver multi-core TPTP/SMT =========
% 0.50/15.65
% 0.50/15.65 % Detected problem language: tptp
% 0.50/15.66 % Proving...
% 4.40/16.55 % SZS status Started for theBenchmark.p
% 4.40/16.55 % SZS status Theorem for theBenchmark.p
% 4.40/16.55
% 4.40/16.55 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.40/16.55
% 4.40/16.55 % ------ iProver source info
% 4.40/16.55
% 4.40/16.55 % git: date: 2026-07-19 20:42:38 +0200
% 4.40/16.55 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.40/16.55 % git: non_committed_changes: false
% 4.40/16.55
% 4.40/16.55 % ------ Parsing...
% 4.40/16.55 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.40/16.55
% 4.40/16.55 % ------ Preprocessing... sup_sim: 0 sf_s rm: 50 0s sf_e pe_s pe:1:0s pe_e sup_sim: 3 sf_s rm: 7 0s sf_e pe_s pe_e %
% 4.40/16.55
% 4.40/16.55 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.40/16.55
% 4.40/16.55 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.40/16.55 % ------ Proving...
% 4.40/16.55 % ------ Problem Properties
% 4.40/16.55
% 4.40/16.55 %
% 4.40/16.55 % clauses 19
% 4.40/16.55 % conjectures 1
% 4.40/16.55 % EPR 2
% 4.40/16.55 % Horn 18
% 4.40/16.55 % unary 11
% 4.40/16.55 % binary 5
% 4.40/16.55 % lits 30
% 4.40/16.55 % lits eq 7
% 4.40/16.55 % fd_pure 0
% 4.40/16.55 % fd_pseudo 0
% 4.40/16.55 % fd_cond 0
% 4.40/16.55 % fd_pseudo_cond 1
% 4.40/16.55 % AC symbols 0
% 4.40/16.55
% 4.40/16.55 % ------ Schedule dynamic 5 is on
% 4.40/16.55
% 4.40/16.55 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.40/16.55
% 4.40/16.55
% 4.40/16.55 % ------
% 4.40/16.55 % Current options:
% 4.40/16.55 % ------
% 4.40/16.55
% 4.40/16.55
% 4.40/16.55 %
% 4.40/16.55
% 4.40/16.55 % ------ Proving...
% 4.40/16.55 %
% 4.40/16.55
% 4.40/16.55 % SZS status Theorem for theBenchmark.p
% 4.40/16.55
% 4.40/16.55 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.40/16.55
% 4.40/16.55
%------------------------------------------------------------------------------