%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET015-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n001.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 02:46:03 PM UTC 2026
% Result : Unsatisfiable 2.24s 6.20s
% Output : CNFRefutation 2.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 12
% Syntax : Number of formulae : 61 ( 15 unt; 0 def)
% Number of atoms : 140 ( 17 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 148 ( 69 ~; 79 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 4 ( 1 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; 4 con; 0-2 aty)
% Number of variables : 66 ( 0 sgn 66 !; 0 ?; 45 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( little_set(X0)
| ~ member(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a2) ).
fof(f3,axiom,
! [X0,X1] :
( X0 = X1
| member(f1(X0,X1),X1)
| member(f1(X0,X1),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',extensionality2) ).
fof(f4,axiom,
! [X0,X1] :
( X0 = X1
| ~ member(f1(X0,X1),X1)
| ~ member(f1(X0,X1),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',extensionality3) ).
fof(f5,axiom,
! [X2,X0,X1] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection1) ).
fof(f6,axiom,
! [X2,X0,X1] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection2) ).
fof(f7,axiom,
! [X2,X0,X1] :
( ~ member(X0,X2)
| ~ member(X0,X1)
| member(X0,intersection(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection3) ).
fof(f8,axiom,
! [X0,X1] :
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement1) ).
fof(f9,axiom,
! [X0,X1] :
( member(X0,X1)
| ~ little_set(X0)
| member(X0,complement(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement2) ).
fof(f10,axiom,
! [X0,X1] : union(X0,X1) = complement(intersection(complement(X0),complement(X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union) ).
fof(f13,axiom,
union(as,bs) = cs,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_union_b_is_c) ).
fof(f14,axiom,
union(bs,as) = ds,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_union_a_is_d) ).
fof(f15,negated_conjecture,
cs != ds,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_c_equals_d) ).
fof(f16,plain,
cs = complement(intersection(complement(as),complement(bs))),
inference(definition_unfolding,[],[f13,f10]) ).
fof(f17,plain,
ds = complement(intersection(complement(bs),complement(as))),
inference(definition_unfolding,[],[f14,f10]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i] :
( little_set(X0)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f1]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i] :
( member(f1(X0,X1),X1)
| member(f1(X0,X1),X0)
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ member(f1(X0,X1),X1)
| ~ member(f1(X0,X1),X0) ),
inference(cnf_transformation,[],[f4]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f5]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i] :
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i] :
( member(X0,X1)
| member(X0,complement(X1))
| ~ little_set(X0) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_75,plain,
complement(intersection(complement(as),complement(bs))) = cs,
inference(cnf_transformation,[],[f16]) ).
tcf(c_76,plain,
complement(intersection(complement(bs),complement(as))) = ds,
inference(cnf_transformation,[],[f17]) ).
tcf(c_77,negated_conjecture,
cs != ds,
inference(cnf_transformation,[],[f15]) ).
tcf(c_247,negated_conjecture,
cs != ds,
inference(demodulation,[status(thm)],[c_77]) ).
tcf(c_460,plain,
! [X0: $i] :
( ~ member(X0,cs)
| ~ member(X0,intersection(complement(as),complement(bs))) ),
inference(superposition,[status(thm)],[c_75,c_71]) ).
tcf(c_464,plain,
! [X0: $i] :
( ~ member(X0,ds)
| ~ member(X0,intersection(complement(bs),complement(as))) ),
inference(superposition,[status(thm)],[c_76,c_71]) ).
tcf(c_474,plain,
! [X0: $i] :
( member(X0,cs)
| member(X0,intersection(complement(as),complement(bs)))
| ~ little_set(X0) ),
inference(superposition,[status(thm)],[c_75,c_72]) ).
tcf(c_475,plain,
! [X0: $i] :
( member(X0,ds)
| member(X0,intersection(complement(bs),complement(as)))
| ~ little_set(X0) ),
inference(superposition,[status(thm)],[c_76,c_72]) ).
tcf(c_604,plain,
! [X0: $i] :
( ~ member(X0,cs)
| ~ member(X0,complement(bs))
| ~ member(X0,complement(as)) ),
inference(superposition,[status(thm)],[c_70,c_460]) ).
tcf(c_635,plain,
! [X0: $i] :
( ~ member(X0,ds)
| ~ member(X0,complement(bs))
| ~ member(X0,complement(as)) ),
inference(superposition,[status(thm)],[c_70,c_464]) ).
tcf(c_738,plain,
! [X0: $i] :
( member(X0,cs)
| member(X0,complement(bs))
| ~ little_set(X0) ),
inference(superposition,[status(thm)],[c_474,c_69]) ).
tcf(c_739,plain,
! [X0: $i] :
( member(X0,cs)
| member(X0,complement(as))
| ~ little_set(X0) ),
inference(superposition,[status(thm)],[c_474,c_68]) ).
tcf(c_834,plain,
! [X0: $i] :
( member(X0,cs)
| ~ little_set(X0)
| ~ member(X0,bs) ),
inference(superposition,[status(thm)],[c_738,c_71]) ).
tcf(c_883,plain,
! [X0: $i] :
( member(X0,cs)
| ~ little_set(X0)
| ~ member(X0,as) ),
inference(superposition,[status(thm)],[c_739,c_71]) ).
tcf(c_912,plain,
! [X0: $i] :
( member(X0,cs)
| ~ member(X0,bs) ),
inference(forward_subsumption_resolution,[status(thm)],[c_834,c_64]) ).
tcf(c_1014,plain,
! [X0: $i] :
( member(X0,cs)
| ~ member(X0,as) ),
inference(forward_subsumption_resolution,[status(thm)],[c_883,c_64]) ).
tcf(c_1070,plain,
! [X0: $i] :
( member(X0,ds)
| member(X0,complement(as))
| ~ little_set(X0) ),
inference(superposition,[status(thm)],[c_475,c_69]) ).
tcf(c_1071,plain,
! [X0: $i] :
( member(X0,ds)
| member(X0,complement(bs))
| ~ little_set(X0) ),
inference(superposition,[status(thm)],[c_475,c_68]) ).
tcf(c_1561,plain,
! [X0: $i] :
( member(X0,as)
| ~ little_set(X0)
| ~ member(X0,cs)
| ~ member(X0,complement(bs)) ),
inference(superposition,[status(thm)],[c_72,c_604]) ).
tcf(c_1568,plain,
! [X0: $i] :
( member(X0,ds)
| ~ little_set(X0)
| ~ member(X0,cs)
| ~ member(X0,complement(bs)) ),
inference(superposition,[status(thm)],[c_1070,c_604]) ).
tcf(c_1648,plain,
! [X0: $i] :
( member(X0,as)
| ~ little_set(X0)
| ~ member(X0,ds)
| ~ member(X0,complement(bs)) ),
inference(superposition,[status(thm)],[c_72,c_635]) ).
tcf(c_2322,plain,
! [X0: $i] :
( little_set(X0)
| ~ member(X0,cs) ),
inference(instantiation,[status(thm)],[c_64]) ).
tcf(c_2930,plain,
! [X0: $i] :
( member(X0,as)
| ~ member(X0,complement(bs))
| ~ member(X0,cs) ),
inference(global_subsumption_just,[status(thm)],[c_1561,c_1561,c_2322]) ).
tcf(c_2931,plain,
! [X0: $i] :
( member(X0,as)
| ~ member(X0,cs)
| ~ member(X0,complement(bs)) ),
inference(renaming,[status(thm)],[c_2930]) ).
tcf(c_2948,plain,
! [X0: $i] :
( member(X0,ds)
| member(X0,as)
| ~ little_set(X0)
| ~ member(X0,cs) ),
inference(superposition,[status(thm)],[c_1071,c_2931]) ).
tcf(c_3290,plain,
! [X0: $i] :
( member(X0,ds)
| ~ member(X0,cs) ),
inference(global_subsumption_just,[status(thm)],[c_2948,c_1071,c_1568,c_2322]) ).
tcf(c_3298,plain,
! [X0: $i] :
( member(f1(X0,cs),ds)
| member(f1(X0,cs),X0)
| ( X0 = cs ) ),
inference(superposition,[status(thm)],[c_66,c_3290]) ).
tcf(c_3647,plain,
( member(f1(ds,cs),ds)
| ( cs = ds ) ),
inference(equality_factoring,[status(thm)],[c_3298]) ).
tcf(c_3649,plain,
member(f1(ds,cs),ds),
inference(forward_subsumption_resolution,[status(thm)],[c_3647,c_247]) ).
tcf(c_3745,plain,
( ( cs = ds )
| ~ member(f1(ds,cs),cs) ),
inference(superposition,[status(thm)],[c_3649,c_67]) ).
tcf(c_3746,plain,
~ member(f1(ds,cs),cs),
inference(forward_subsumption_resolution,[status(thm)],[c_3745,c_247]) ).
tcf(c_3877,plain,
! [X0: $i] :
( member(X0,as)
| ~ member(X0,ds)
| ~ member(X0,complement(bs)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1648,c_64]) ).
tcf(c_3889,plain,
! [X0: $i] :
( member(X0,bs)
| member(X0,as)
| ~ little_set(X0)
| ~ member(X0,ds) ),
inference(superposition,[status(thm)],[c_72,c_3877]) ).
tcf(c_3999,plain,
! [X0: $i] :
( member(X0,bs)
| member(X0,as)
| ~ member(X0,ds) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3889,c_64]) ).
tcf(c_4019,plain,
( member(f1(ds,cs),bs)
| member(f1(ds,cs),as) ),
inference(superposition,[status(thm)],[c_3649,c_3999]) ).
tcf(c_4159,plain,
( member(f1(ds,cs),cs)
| member(f1(ds,cs),as) ),
inference(superposition,[status(thm)],[c_4019,c_912]) ).
tcf(c_4160,plain,
member(f1(ds,cs),as),
inference(forward_subsumption_resolution,[status(thm)],[c_4159,c_3746]) ).
tcf(c_4163,plain,
member(f1(ds,cs),cs),
inference(superposition,[status(thm)],[c_4160,c_1014]) ).
tcf(c_4164,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_4163,c_3746]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET015-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/5.38 % Computer : n001.cluster.edu
% 0.10/5.38 % Model : x86_64 x86_64
% 0.10/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.38 % Memory : 8046.5625MB
% 0.10/5.38 % OS : Linux 6.8.0-71-generic
% 0.10/5.38 % CPULimit : 300
% 0.10/5.38 % WCLimit : 300
% 0.10/5.38 % DateTime : Thu Sep 24 09:14:28 UTC 2026
% 0.10/5.38 % CPUTime :
% 0.10/5.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/5.42 Running first-order theorem proving
% 0.14/5.42 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
% 0.14/5.43
% 0.14/5.43 % ======== iProver multi-core TPTP/SMT =========
% 0.14/5.43
% 0.14/5.43 % Detected problem language: tptp
% 0.14/5.44 % Proving...
% 2.24/6.20 % SZS status Started for theBenchmark.p
% 2.24/6.20 % SZS status Unsatisfiable for theBenchmark.p
% 2.24/6.20
% 2.24/6.20 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.24/6.20
% 2.24/6.20 % ------ iProver source info
% 2.24/6.20
% 2.24/6.20 % git: date: 2026-07-19 20:42:38 +0200
% 2.24/6.20 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.24/6.20 % git: non_committed_changes: false
% 2.24/6.20
% 2.24/6.20 % ------ Parsing...% successful
% 2.24/6.20
% 2.24/6.20
% 2.24/6.20 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.24/6.20
% 2.24/6.20 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 2.24/6.20
% 2.24/6.20 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.24/6.20
% 2.24/6.20 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.24/6.20 % ------ Proving...
% 2.24/6.20 % ------ Problem Properties
% 2.24/6.20
% 2.24/6.20 %
% 2.24/6.20 % clauses 14
% 2.24/6.20 % conjectures 1
% 2.24/6.20 % EPR 4
% 2.24/6.20 % Horn 11
% 2.24/6.20 % unary 4
% 2.24/6.20 % binary 6
% 2.24/6.20 % lits 28
% 2.24/6.20 % lits eq 6
% 2.24/6.20 % fd_pure 0
% 2.24/6.20 % fd_pseudo 0
% 2.24/6.20 % fd_cond 0
% 2.24/6.20 % fd_pseudo_cond 3
% 2.24/6.20 % AC symbols 0
% 2.24/6.20
% 2.24/6.20 % ------ Schedule dynamic 5 is on
% 2.24/6.20
% 2.24/6.20 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.24/6.20
% 2.24/6.20
% 2.24/6.20 % ------
% 2.24/6.20 % Current options:
% 2.24/6.20 % ------
% 2.24/6.20
% 2.24/6.20
% 2.24/6.20 %
% 2.24/6.20
% 2.24/6.20 % ------ Proving...
% 2.24/6.20 %
% 2.24/6.20
% 2.24/6.20 % SZS status Unsatisfiable for theBenchmark.p
% 2.24/6.20
% 2.24/6.20 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.24/6.20
%------------------------------------------------------------------------------