%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET012-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n016.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 02:46:00 PM UTC 2026
% Result : Unsatisfiable 46.57s 7.83s
% Output : CNFRefutation 46.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of formulae : 31 ( 10 unt; 0 def)
% Number of atoms : 65 ( 17 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 60 ( 26 ~; 34 |; 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 : 30 ( 0 sgn 30 !; 0 ?; 18 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( little_set(X0)
| ~ member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',a2) ).
fof(f2,axiom,
! [X0,X1] :
( X0 = X1
| little_set(f1(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',extensionality1) ).
fof(f3,axiom,
! [X0,X1] :
( X0 = X1
| member(f1(X0,X1),X1)
| member(f1(X0,X1),X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',extensionality2) ).
fof(f4,axiom,
! [X0,X1] :
( X0 = X1
| ~ member(f1(X0,X1),X1)
| ~ member(f1(X0,X1),X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',extensionality3) ).
fof(f37,axiom,
! [X0,X1] :
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',complement1) ).
fof(f38,axiom,
! [X0,X1] :
( member(X0,X1)
| ~ little_set(X0)
| member(X0,complement(X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',complement2) ).
fof(f162,axiom,
complement(as) = bs,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement_of_a_is_b) ).
fof(f163,axiom,
complement(bs) = cs,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement_of_b_is_c) ).
fof(f164,negated_conjecture,
as != cs,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_a_equals_c) ).
tcf(c_193,plain,
! [X0: $i,X1: $i] :
( little_set(X0)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f1]) ).
tcf(c_194,plain,
! [X0: $i,X1: $i] :
( little_set(f1(X0,X1))
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f2]) ).
tcf(c_195,plain,
! [X0: $i,X1: $i] :
( member(f1(X0,X1),X1)
| member(f1(X0,X1),X0)
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_196,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ member(f1(X0,X1),X1)
| ~ member(f1(X0,X1),X0) ),
inference(cnf_transformation,[],[f4]) ).
tcf(c_221,plain,
! [X0: $i,X1: $i] :
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
inference(cnf_transformation,[],[f37]) ).
tcf(c_222,plain,
! [X0: $i,X1: $i] :
( member(X0,X1)
| member(X0,complement(X1))
| ~ little_set(X0) ),
inference(cnf_transformation,[],[f38]) ).
tcf(c_328,plain,
complement(as) = bs,
inference(cnf_transformation,[],[f162]) ).
tcf(c_329,plain,
complement(bs) = cs,
inference(cnf_transformation,[],[f163]) ).
tcf(c_330,negated_conjecture,
as != cs,
inference(cnf_transformation,[],[f164]) ).
tcf(c_487,plain,
( little_set(f1(as,cs))
| ( as = cs ) ),
inference(instantiation,[status(thm)],[c_194]) ).
tcf(c_495,plain,
( member(f1(as,cs),cs)
| member(f1(as,cs),as)
| ( as = cs ) ),
inference(instantiation,[status(thm)],[c_195]) ).
tcf(c_576,plain,
! [X0: $i] :
( ~ member(X0,bs)
| ~ member(X0,as) ),
inference(superposition,[status(thm)],[c_328,c_221]) ).
tcf(c_577,plain,
! [X0: $i] :
( ~ member(X0,cs)
| ~ member(X0,bs) ),
inference(superposition,[status(thm)],[c_329,c_221]) ).
tcf(c_706,plain,
! [X0: $i] :
( member(X0,bs)
| member(X0,as)
| ~ little_set(X0) ),
inference(superposition,[status(thm)],[c_328,c_222]) ).
tcf(c_707,plain,
! [X0: $i] :
( member(X0,cs)
| member(X0,bs)
| ~ little_set(X0) ),
inference(superposition,[status(thm)],[c_329,c_222]) ).
tcf(c_922,plain,
! [X0: $i] :
( member(f1(as,X0),bs)
| ( X0 = as )
| ~ little_set(f1(as,X0))
| ~ member(f1(as,X0),X0) ),
inference(superposition,[status(thm)],[c_706,c_196]) ).
tcf(c_928,plain,
! [X0: $i] :
( member(f1(as,X0),bs)
| ( X0 = as )
| ~ member(f1(as,X0),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_922,c_193]) ).
tcf(c_990,plain,
( member(f1(as,cs),bs)
| ( as = cs )
| ~ little_set(f1(as,cs)) ),
inference(superposition,[status(thm)],[c_707,c_928]) ).
tcf(c_991,plain,
member(f1(as,cs),bs),
inference(global_subsumption_just,[status(thm)],[c_990,c_330,c_487,c_990]) ).
tcf(c_1190,plain,
~ member(f1(as,cs),cs),
inference(superposition,[status(thm)],[c_991,c_577]) ).
tcf(c_1191,plain,
~ member(f1(as,cs),as),
inference(superposition,[status(thm)],[c_991,c_576]) ).
tcf(c_1192,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_1190,c_1191,c_495,c_330]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET012-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.37 % Computer : n016.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Thu Sep 24 09:10:29 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 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
% 0.09/0.42
% 0.09/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.42
% 0.09/0.42 % Detected problem language: tptp
% 0.09/0.43 % Proving...
% 46.57/7.83 % SZS status Started for theBenchmark.p
% 46.57/7.83 % SZS status Unsatisfiable for theBenchmark.p
% 46.57/7.83
% 46.57/7.83 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 46.57/7.83
% 46.57/7.83 % ------ iProver source info
% 46.57/7.83
% 46.57/7.83 % git: date: 2026-07-19 20:42:38 +0200
% 46.57/7.83 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 46.57/7.83 % git: non_committed_changes: false
% 46.57/7.83
% 46.57/7.83 % ------ Parsing...% successful
% 46.57/7.83
% 46.57/7.83
% 46.57/7.83 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 46.57/7.83
% 46.57/7.83 % ------ Preprocessing... sf_s rm: 1 0s sf_e %
% 46.57/7.83
% 46.57/7.83 % ------ Preprocessing...%
% 46.57/7.83
% 46.57/7.83 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 46.57/7.83 % ------ Proving...
% 46.57/7.83 % ------ Problem Properties
% 46.57/7.83
% 46.57/7.83 %
% 46.57/7.83 % clauses 138
% 46.57/7.83 % conjectures 1
% 46.57/7.83 % EPR 25
% 46.57/7.83 % Horn 118
% 46.57/7.83 % unary 9
% 46.57/7.83 % binary 92
% 46.57/7.83 % lits 338
% 46.57/7.83 % lits eq 30
% 46.57/7.83 % fd_pure 0
% 46.57/7.83 % fd_pseudo 0
% 46.57/7.83 % fd_cond 4
% 46.57/7.83 % fd_pseudo_cond 7
% 46.57/7.83 % AC symbols 0
% 46.57/7.83
% 46.57/7.83 % ------ Input Options Time Limit: Unbounded
% 46.57/7.83
% 46.57/7.83
% 46.57/7.83 % ------
% 46.57/7.83 % Current options:
% 46.57/7.83 % ------
% 46.57/7.83
% 46.57/7.83
% 46.57/7.83 %
% 46.57/7.83
% 46.57/7.83 % ------ Proving...
% 46.57/7.83 %
% 46.57/7.83
% 46.57/7.83 % SZS status Unsatisfiable for theBenchmark.p
% 46.57/7.83
% 46.57/7.83 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 46.57/7.83
% 46.57/7.83
%------------------------------------------------------------------------------