%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET012-4 : 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 : n020.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 02:46:01 PM UTC 2026
% Result : Unsatisfiable 2.48s 6.28s
% Output : CNFRefutation 2.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 8
% Syntax : Number of formulae : 33 ( 13 unt; 0 def)
% Number of atoms : 63 ( 14 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 58 ( 28 ~; 30 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 2 ( 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 : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 27 ( 0 sgn 27 !; 0 ?; 17 :)
% 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,
! [X0,X1] :
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement1) ).
fof(f6,axiom,
! [X0,X1] :
( member(X0,X1)
| ~ little_set(X0)
| member(X0,complement(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement2) ).
fof(f9,axiom,
complement(as) = bs,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement_of_a_is_b) ).
fof(f10,axiom,
complement(bs) = cs,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement_of_b_is_c) ).
fof(f11,negated_conjecture,
as != cs,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_a_equals_c) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] :
( little_set(X0)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f1]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i] :
( member(f1(X0,X1),X1)
| member(f1(X0,X1),X0)
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ member(f1(X0,X1),X1)
| ~ member(f1(X0,X1),X0) ),
inference(cnf_transformation,[],[f4]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i] :
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
inference(cnf_transformation,[],[f5]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i] :
( member(X0,X1)
| member(X0,complement(X1))
| ~ little_set(X0) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_68,plain,
complement(as) = bs,
inference(cnf_transformation,[],[f9]) ).
tcf(c_69,plain,
complement(bs) = cs,
inference(cnf_transformation,[],[f10]) ).
tcf(c_70,negated_conjecture,
as != cs,
inference(cnf_transformation,[],[f11]) ).
tcf(c_209,negated_conjecture,
as != cs,
inference(demodulation,[status(thm)],[c_70]) ).
tcf(c_372,plain,
! [X0: $i] :
( ~ member(X0,bs)
| ~ member(X0,as) ),
inference(superposition,[status(thm)],[c_68,c_64]) ).
tcf(c_373,plain,
! [X0: $i] :
( ~ member(X0,cs)
| ~ member(X0,bs) ),
inference(superposition,[status(thm)],[c_69,c_64]) ).
tcf(c_390,plain,
! [X0: $i] :
( member(X0,bs)
| member(X0,as)
| ~ little_set(X0) ),
inference(superposition,[status(thm)],[c_68,c_65]) ).
tcf(c_391,plain,
! [X0: $i] :
( member(X0,cs)
| member(X0,bs)
| ~ little_set(X0) ),
inference(superposition,[status(thm)],[c_69,c_65]) ).
tcf(c_483,plain,
! [X0: $i] :
( member(X0,as)
| ~ little_set(X0)
| ~ member(X0,cs) ),
inference(superposition,[status(thm)],[c_390,c_373]) ).
tcf(c_566,plain,
! [X0: $i] :
( member(X0,as)
| ~ member(X0,cs) ),
inference(forward_subsumption_resolution,[status(thm)],[c_483,c_60]) ).
tcf(c_574,plain,
! [X0: $i] :
( member(f1(X0,cs),as)
| member(f1(X0,cs),X0)
| ( X0 = cs ) ),
inference(superposition,[status(thm)],[c_62,c_566]) ).
tcf(c_849,plain,
( member(f1(as,cs),as)
| ( as = cs ) ),
inference(equality_factoring,[status(thm)],[c_574]) ).
tcf(c_851,plain,
member(f1(as,cs),as),
inference(forward_subsumption_resolution,[status(thm)],[c_849,c_209]) ).
tcf(c_908,plain,
little_set(f1(as,cs)),
inference(superposition,[status(thm)],[c_851,c_60]) ).
tcf(c_909,plain,
( ( as = cs )
| ~ member(f1(as,cs),cs) ),
inference(superposition,[status(thm)],[c_851,c_63]) ).
tcf(c_910,plain,
~ member(f1(as,cs),cs),
inference(forward_subsumption_resolution,[status(thm)],[c_909,c_209]) ).
tcf(c_912,plain,
( member(f1(as,cs),bs)
| ~ little_set(f1(as,cs)) ),
inference(superposition,[status(thm)],[c_391,c_910]) ).
tcf(c_913,plain,
member(f1(as,cs),bs),
inference(forward_subsumption_resolution,[status(thm)],[c_912,c_908]) ).
tcf(c_916,plain,
~ member(f1(as,cs),as),
inference(superposition,[status(thm)],[c_913,c_372]) ).
tcf(c_917,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_916,c_851]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET012-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/5.37 % Computer : n020.cluster.edu
% 0.10/5.37 % Model : x86_64 x86_64
% 0.10/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.37 % Memory : 8046.5625MB
% 0.10/5.37 % OS : Linux 6.8.0-71-generic
% 0.10/5.37 % CPULimit : 300
% 0.10/5.37 % WCLimit : 300
% 0.10/5.37 % DateTime : Thu Sep 24 09:06:25 UTC 2026
% 0.10/5.37 % CPUTime :
% 0.10/5.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/5.41 Running first-order theorem proving
% 0.14/5.41 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
% 0.14/5.42
% 0.14/5.42 % ======== iProver multi-core TPTP/SMT =========
% 0.14/5.42
% 0.14/5.42 % Detected problem language: tptp
% 0.14/5.44 % Proving...
% 2.48/6.28 % SZS status Started for theBenchmark.p
% 2.48/6.28 % SZS status Unsatisfiable for theBenchmark.p
% 2.48/6.28
% 2.48/6.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.48/6.28
% 2.48/6.28 % ------ iProver source info
% 2.48/6.28
% 2.48/6.28 % git: date: 2026-07-19 20:42:38 +0200
% 2.48/6.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.48/6.28 % git: non_committed_changes: false
% 2.48/6.28
% 2.48/6.28 % ------ Parsing...% successful
% 2.48/6.28
% 2.48/6.28
% 2.48/6.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.48/6.28
% 2.48/6.28 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 2.48/6.28
% 2.48/6.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.48/6.28
% 2.48/6.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.48/6.28 % ------ Proving...
% 2.48/6.28 % ------ Problem Properties
% 2.48/6.28
% 2.48/6.28 %
% 2.48/6.28 % clauses 11
% 2.48/6.28 % conjectures 1
% 2.48/6.28 % EPR 4
% 2.48/6.28 % Horn 8
% 2.48/6.28 % unary 4
% 2.48/6.28 % binary 4
% 2.48/6.28 % lits 21
% 2.48/6.28 % lits eq 6
% 2.48/6.28 % fd_pure 0
% 2.48/6.28 % fd_pseudo 0
% 2.48/6.28 % fd_cond 0
% 2.48/6.28 % fd_pseudo_cond 3
% 2.48/6.28 % AC symbols 0
% 2.48/6.28
% 2.48/6.28 % ------ Schedule dynamic 5 is on
% 2.48/6.28
% 2.48/6.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.48/6.28
% 2.48/6.28
% 2.48/6.28 % ------
% 2.48/6.28 % Current options:
% 2.48/6.28 % ------
% 2.48/6.28
% 2.48/6.28
% 2.48/6.28 %
% 2.48/6.28
% 2.48/6.28 % ------ Proving...
% 2.48/6.28 %
% 2.48/6.28
% 2.48/6.28 % SZS status Unsatisfiable for theBenchmark.p
% 2.48/6.28
% 2.48/6.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.48/6.28
% 2.48/6.28
%------------------------------------------------------------------------------