%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET016-3 : 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 : n018.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 02:46:04 PM UTC 2026
% Result : Unsatisfiable 3.85s 1.26s
% Output : CNFRefutation 3.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 10
% Syntax : Number of formulae : 37 ( 19 unt; 0 def)
% Number of atoms : 64 ( 30 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 46 ( 19 ~; 27 |; 0 &)
% ( 0 <=>; 0 =>; 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 : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 31 ( 0 sgn 31 !; 0 ?; 11 :)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X2,X0,X1] :
( X0 = X2
| X0 = X1
| ~ member(X0,non_ordered_pair(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',non_ordered_pair1) ).
fof(f6,axiom,
! [X2,X0,X1] :
( X0 != X1
| ~ little_set(X0)
| member(X0,non_ordered_pair(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',non_ordered_pair2) ).
fof(f7,axiom,
! [X2,X0,X1] :
( X0 != X2
| ~ little_set(X0)
| member(X0,non_ordered_pair(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',non_ordered_pair3) ).
fof(f8,axiom,
! [X0,X1] : little_set(non_ordered_pair(X0,X1)),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',non_ordered_pair4) ).
fof(f9,axiom,
! [X0] : singleton_set(X0) = non_ordered_pair(X0,X0),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',singleton_set) ).
fof(f10,axiom,
! [X0,X1] : ordered_pair(X0,X1) = non_ordered_pair(singleton_set(X0),non_ordered_pair(X0,X1)),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',ordered_pair) ).
fof(f162,axiom,
little_set(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',little_set_a) ).
fof(f163,axiom,
little_set(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',little_set_b) ).
fof(f164,axiom,
ordered_pair(a,c) = ordered_pair(b,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_ordered_pairs) ).
fof(f165,negated_conjecture,
a != b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_first_components_equal) ).
fof(f167,plain,
! [X0,X1] : ordered_pair(X0,X1) = non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)),
inference(definition_unfolding,[],[f10,f9]) ).
fof(f194,plain,
non_ordered_pair(non_ordered_pair(a,a),non_ordered_pair(a,c)) = non_ordered_pair(non_ordered_pair(b,b),non_ordered_pair(b,d)),
inference(definition_unfolding,[],[f164,f167,f167]) ).
fof(f195,plain,
! [X2,X1] :
( ~ little_set(X1)
| member(X1,non_ordered_pair(X1,X2)) ),
inference(equality_resolution,[],[f6]) ).
fof(f196,plain,
! [X2,X1] :
( ~ little_set(X2)
| member(X2,non_ordered_pair(X1,X2)) ),
inference(equality_resolution,[],[f7]) ).
tcf(c_198,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ( X0 = X1 )
| ~ member(X0,non_ordered_pair(X1,X2)) ),
inference(cnf_transformation,[],[f5]) ).
tcf(c_199,plain,
! [X0: $i,X1: $i] :
( member(X0,non_ordered_pair(X0,X1))
| ~ little_set(X0) ),
inference(cnf_transformation,[],[f195]) ).
tcf(c_200,plain,
! [X0: $i,X1: $i] :
( member(X0,non_ordered_pair(X1,X0))
| ~ little_set(X0) ),
inference(cnf_transformation,[],[f196]) ).
tcf(c_201,plain,
! [X0: $i,X1: $i] : little_set(non_ordered_pair(X0,X1)),
inference(cnf_transformation,[],[f8]) ).
tcf(c_329,plain,
little_set(a),
inference(cnf_transformation,[],[f162]) ).
tcf(c_330,plain,
little_set(b),
inference(cnf_transformation,[],[f163]) ).
tcf(c_331,plain,
non_ordered_pair(non_ordered_pair(a,a),non_ordered_pair(a,c)) = non_ordered_pair(non_ordered_pair(b,b),non_ordered_pair(b,d)),
inference(cnf_transformation,[],[f194]) ).
tcf(c_332,negated_conjecture,
a != b,
inference(cnf_transformation,[],[f165]) ).
tcf(c_406,plain,
( member(non_ordered_pair(b,b),non_ordered_pair(non_ordered_pair(a,a),non_ordered_pair(a,c)))
| ~ little_set(non_ordered_pair(b,b)) ),
inference(superposition,[status(thm)],[c_331,c_199]) ).
tcf(c_408,plain,
! [X0: $i] :
( ( non_ordered_pair(b,d) = X0 )
| ( non_ordered_pair(b,b) = X0 )
| ~ member(X0,non_ordered_pair(non_ordered_pair(a,a),non_ordered_pair(a,c))) ),
inference(superposition,[status(thm)],[c_331,c_198]) ).
tcf(c_418,plain,
member(non_ordered_pair(b,b),non_ordered_pair(non_ordered_pair(a,a),non_ordered_pair(a,c))),
inference(forward_subsumption_resolution,[status(thm)],[c_406,c_201]) ).
tcf(c_420,plain,
( ( non_ordered_pair(a,c) = non_ordered_pair(b,b) )
| ( non_ordered_pair(a,a) = non_ordered_pair(b,b) ) ),
inference(superposition,[status(thm)],[c_418,c_198]) ).
tcf(c_427,plain,
( ( non_ordered_pair(a,a) = non_ordered_pair(b,d) )
| ( non_ordered_pair(a,a) = non_ordered_pair(b,b) )
| ~ little_set(non_ordered_pair(a,a)) ),
inference(superposition,[status(thm)],[c_199,c_408]) ).
tcf(c_477,plain,
! [X0: $i] :
( ( X0 = b )
| ( non_ordered_pair(a,a) = non_ordered_pair(b,b) )
| ~ member(X0,non_ordered_pair(a,c)) ),
inference(superposition,[status(thm)],[c_420,c_198]) ).
tcf(c_479,plain,
( member(non_ordered_pair(a,c),non_ordered_pair(non_ordered_pair(a,a),non_ordered_pair(a,c)))
| ( non_ordered_pair(a,a) = non_ordered_pair(b,b) ) ),
inference(superposition,[status(thm)],[c_420,c_418]) ).
tcf(c_508,plain,
( ( non_ordered_pair(a,a) = non_ordered_pair(b,d) )
| ( non_ordered_pair(a,a) = non_ordered_pair(b,b) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_427,c_201]) ).
tcf(c_515,plain,
( member(b,non_ordered_pair(a,a))
| ( non_ordered_pair(a,a) = non_ordered_pair(b,b) )
| ~ little_set(b) ),
inference(superposition,[status(thm)],[c_508,c_199]) ).
tcf(c_608,plain,
( ( a = b )
| ( non_ordered_pair(a,a) = non_ordered_pair(b,b) )
| ~ little_set(a) ),
inference(superposition,[status(thm)],[c_199,c_477]) ).
tcf(c_613,plain,
non_ordered_pair(a,a) = non_ordered_pair(b,b),
inference(global_subsumption_just,[status(thm)],[c_479,c_329,c_332,c_608]) ).
tcf(c_618,plain,
( member(b,non_ordered_pair(a,a))
| ~ little_set(b) ),
inference(superposition,[status(thm)],[c_613,c_200]) ).
tcf(c_695,plain,
member(b,non_ordered_pair(a,a)),
inference(global_subsumption_just,[status(thm)],[c_515,c_330,c_618]) ).
tcf(c_698,plain,
a = b,
inference(superposition,[status(thm)],[c_695,c_198]) ).
tcf(c_699,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_332,c_698]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET016-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.35 % Computer : n018.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Thu Sep 24 09:09:48 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/0.39 Running first-order theorem proving
% 0.14/0.39 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
% 0.14/0.40
% 0.14/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.40
% 0.14/0.40 % Detected problem language: tptp
% 0.14/0.41 % Proving...
% 3.85/1.26 % SZS status Started for theBenchmark.p
% 3.85/1.26 % SZS status Unsatisfiable for theBenchmark.p
% 3.85/1.26
% 3.85/1.26 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.85/1.26
% 3.85/1.26 % ------ iProver source info
% 3.85/1.26
% 3.85/1.26 % git: date: 2026-07-19 20:42:38 +0200
% 3.85/1.26 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.85/1.26 % git: non_committed_changes: false
% 3.85/1.26
% 3.85/1.26 % ------ Parsing...% successful
% 3.85/1.26
% 3.85/1.26
% 3.85/1.26 % ------ Clausification by vclausify_rel & Parsing by iProver...
% 3.85/1.26 % ------ Proving...
% 3.85/1.26 % ------ Problem Properties
% 3.85/1.26
% 3.85/1.26 %
% 3.85/1.26 % clauses 139
% 3.85/1.26 % conjectures 1
% 3.85/1.26 % EPR 27
% 3.85/1.26 % Horn 119
% 3.85/1.26 % unary 10
% 3.85/1.26 % binary 92
% 3.85/1.26 % lits 339
% 3.85/1.26 % lits eq 29
% 3.85/1.26 % fd_pure 0
% 3.85/1.26 % fd_pseudo 0
% 3.85/1.26 % fd_cond 4
% 3.85/1.26 % fd_pseudo_cond 7
% 3.85/1.26 % AC symbols 0
% 3.85/1.26
% 3.85/1.26 % ------ Input Options Time Limit: Unbounded
% 3.85/1.26
% 3.85/1.26
% 3.85/1.26 % ------
% 3.85/1.26 % Current options:
% 3.85/1.26 % ------
% 3.85/1.26
% 3.85/1.26
% 3.85/1.26 %
% 3.85/1.26
% 3.85/1.26 % ------ Proving...
% 3.85/1.26 %
% 3.85/1.26
% 3.85/1.26 % ------ Proving...
% 3.85/1.26 %
% 3.85/1.26
% 3.85/1.26 % ------ Proving...
% 3.85/1.26 %
% 3.85/1.26
% 3.85/1.26 % SZS status Unsatisfiable for theBenchmark.p
% 3.85/1.26
% 3.85/1.26 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.85/1.26
% 3.85/1.26
%------------------------------------------------------------------------------