%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET018-4 : 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 : 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 02:46:05 PM UTC 2026
% Result : Unsatisfiable 2.99s 1.30s
% Output : CNFRefutation 2.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 11
% Syntax : Number of formulae : 61 ( 23 unt; 0 def)
% Number of atoms : 118 ( 65 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 84 ( 27 ~; 57 |; 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 : 32 ( 0 sgn 32 !; 0 ?; 12 :)
% 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(f163,axiom,
little_set(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_little_set) ).
fof(f164,axiom,
little_set(c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_little_set) ).
fof(f165,axiom,
little_set(d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d_little_set) ).
fof(f166,axiom,
ordered_pair(a,b) = ordered_pair(c,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_ordered_pair) ).
fof(f167,negated_conjecture,
b != d,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_second_components_equal) ).
fof(f169,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(f196,plain,
non_ordered_pair(non_ordered_pair(a,a),non_ordered_pair(a,b)) = non_ordered_pair(non_ordered_pair(c,c),non_ordered_pair(c,d)),
inference(definition_unfolding,[],[f166,f169,f169]) ).
fof(f197,plain,
! [X2,X1] :
( ~ little_set(X1)
| member(X1,non_ordered_pair(X1,X2)) ),
inference(equality_resolution,[],[f6]) ).
fof(f198,plain,
! [X2,X1] :
( ~ little_set(X2)
| member(X2,non_ordered_pair(X1,X2)) ),
inference(equality_resolution,[],[f7]) ).
tcf(c_200,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ( X0 = X1 )
| ~ member(X0,non_ordered_pair(X1,X2)) ),
inference(cnf_transformation,[],[f5]) ).
tcf(c_201,plain,
! [X0: $i,X1: $i] :
( member(X0,non_ordered_pair(X0,X1))
| ~ little_set(X0) ),
inference(cnf_transformation,[],[f197]) ).
tcf(c_202,plain,
! [X0: $i,X1: $i] :
( member(X0,non_ordered_pair(X1,X0))
| ~ little_set(X0) ),
inference(cnf_transformation,[],[f198]) ).
tcf(c_203,plain,
! [X0: $i,X1: $i] : little_set(non_ordered_pair(X0,X1)),
inference(cnf_transformation,[],[f8]) ).
tcf(c_332,plain,
little_set(b),
inference(cnf_transformation,[],[f163]) ).
tcf(c_333,plain,
little_set(c),
inference(cnf_transformation,[],[f164]) ).
tcf(c_334,plain,
little_set(d),
inference(cnf_transformation,[],[f165]) ).
tcf(c_335,plain,
non_ordered_pair(non_ordered_pair(a,a),non_ordered_pair(a,b)) = non_ordered_pair(non_ordered_pair(c,c),non_ordered_pair(c,d)),
inference(cnf_transformation,[],[f196]) ).
tcf(c_336,negated_conjecture,
b != d,
inference(cnf_transformation,[],[f167]) ).
tcf(c_410,plain,
( member(non_ordered_pair(c,c),non_ordered_pair(non_ordered_pair(a,a),non_ordered_pair(a,b)))
| ~ little_set(non_ordered_pair(c,c)) ),
inference(superposition,[status(thm)],[c_335,c_201]) ).
tcf(c_412,plain,
! [X0: $i] :
( ( non_ordered_pair(c,d) = X0 )
| ( non_ordered_pair(c,c) = X0 )
| ~ member(X0,non_ordered_pair(non_ordered_pair(a,a),non_ordered_pair(a,b))) ),
inference(superposition,[status(thm)],[c_335,c_200]) ).
tcf(c_413,plain,
( member(non_ordered_pair(c,d),non_ordered_pair(non_ordered_pair(a,a),non_ordered_pair(a,b)))
| ~ little_set(non_ordered_pair(c,d)) ),
inference(superposition,[status(thm)],[c_335,c_202]) ).
tcf(c_417,plain,
member(non_ordered_pair(c,d),non_ordered_pair(non_ordered_pair(a,a),non_ordered_pair(a,b))),
inference(forward_subsumption_resolution,[status(thm)],[c_413,c_203]) ).
tcf(c_419,plain,
( ( non_ordered_pair(a,b) = non_ordered_pair(c,d) )
| ( non_ordered_pair(a,a) = non_ordered_pair(c,d) ) ),
inference(superposition,[status(thm)],[c_417,c_200]) ).
tcf(c_422,plain,
member(non_ordered_pair(c,c),non_ordered_pair(non_ordered_pair(a,a),non_ordered_pair(a,b))),
inference(forward_subsumption_resolution,[status(thm)],[c_410,c_203]) ).
tcf(c_431,plain,
( ( non_ordered_pair(a,a) = non_ordered_pair(c,d) )
| ( non_ordered_pair(a,a) = non_ordered_pair(c,c) )
| ~ little_set(non_ordered_pair(a,a)) ),
inference(superposition,[status(thm)],[c_201,c_412]) ).
tcf(c_432,plain,
( ( non_ordered_pair(a,b) = non_ordered_pair(c,d) )
| ( non_ordered_pair(a,b) = non_ordered_pair(c,c) )
| ~ little_set(non_ordered_pair(a,b)) ),
inference(superposition,[status(thm)],[c_202,c_412]) ).
tcf(c_442,plain,
( member(d,non_ordered_pair(a,b))
| ( non_ordered_pair(a,a) = non_ordered_pair(c,d) )
| ~ little_set(d) ),
inference(superposition,[status(thm)],[c_419,c_202]) ).
tcf(c_489,plain,
( ( non_ordered_pair(a,b) = non_ordered_pair(c,d) )
| ( non_ordered_pair(a,b) = non_ordered_pair(c,c) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_432,c_203]) ).
tcf(c_494,plain,
( member(c,non_ordered_pair(a,b))
| ( non_ordered_pair(a,b) = non_ordered_pair(c,c) )
| ~ little_set(c) ),
inference(superposition,[status(thm)],[c_489,c_201]) ).
tcf(c_496,plain,
! [X0: $i] :
( ( X0 = d )
| ( X0 = c )
| ( non_ordered_pair(a,b) = non_ordered_pair(c,c) )
| ~ member(X0,non_ordered_pair(a,b)) ),
inference(superposition,[status(thm)],[c_489,c_200]) ).
tcf(c_512,plain,
( ( non_ordered_pair(a,a) = non_ordered_pair(c,d) )
| ( non_ordered_pair(a,a) = non_ordered_pair(c,c) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_431,c_203]) ).
tcf(c_519,plain,
( member(c,non_ordered_pair(a,a))
| ( non_ordered_pair(a,a) = non_ordered_pair(c,c) )
| ~ little_set(c) ),
inference(superposition,[status(thm)],[c_512,c_201]) ).
tcf(c_540,plain,
( member(d,non_ordered_pair(a,b))
| ( non_ordered_pair(a,a) = non_ordered_pair(c,d) ) ),
inference(global_subsumption_just,[status(thm)],[c_442,c_334,c_442]) ).
tcf(c_547,plain,
( ( b = d )
| ( a = d )
| ( non_ordered_pair(a,a) = non_ordered_pair(c,d) ) ),
inference(superposition,[status(thm)],[c_540,c_200]) ).
tcf(c_658,plain,
( member(c,non_ordered_pair(a,b))
| ( non_ordered_pair(a,b) = non_ordered_pair(c,c) ) ),
inference(global_subsumption_just,[status(thm)],[c_494,c_333,c_494]) ).
tcf(c_665,plain,
( ( b = c )
| ( a = c )
| ( non_ordered_pair(a,b) = non_ordered_pair(c,c) ) ),
inference(superposition,[status(thm)],[c_658,c_200]) ).
tcf(c_684,plain,
( ( b = d )
| ( b = c )
| ( non_ordered_pair(a,b) = non_ordered_pair(c,c) )
| ~ little_set(b) ),
inference(superposition,[status(thm)],[c_202,c_496]) ).
tcf(c_710,plain,
( member(c,non_ordered_pair(a,a))
| ( non_ordered_pair(a,a) = non_ordered_pair(c,c) ) ),
inference(global_subsumption_just,[status(thm)],[c_519,c_333,c_519]) ).
tcf(c_717,plain,
( ( a = c )
| ( non_ordered_pair(a,a) = non_ordered_pair(c,c) ) ),
inference(superposition,[status(thm)],[c_710,c_200]) ).
tcf(c_759,plain,
( ( non_ordered_pair(a,a) = non_ordered_pair(c,d) )
| ( a = d ) ),
inference(global_subsumption_just,[status(thm)],[c_547,c_336,c_547]) ).
tcf(c_760,plain,
( ( a = d )
| ( non_ordered_pair(a,a) = non_ordered_pair(c,d) ) ),
inference(renaming,[status(thm)],[c_759]) ).
tcf(c_770,plain,
( member(d,non_ordered_pair(a,a))
| ( a = d )
| ~ little_set(d) ),
inference(superposition,[status(thm)],[c_760,c_202]) ).
tcf(c_896,plain,
( ( b = c )
| ( non_ordered_pair(a,b) = non_ordered_pair(c,c) ) ),
inference(global_subsumption_just,[status(thm)],[c_665,c_332,c_336,c_684]) ).
tcf(c_905,plain,
! [X0: $i] :
( ( b = c )
| ( X0 = c )
| ~ member(X0,non_ordered_pair(a,b)) ),
inference(superposition,[status(thm)],[c_896,c_200]) ).
tcf(c_911,plain,
( member(non_ordered_pair(a,b),non_ordered_pair(non_ordered_pair(a,a),non_ordered_pair(a,b)))
| ( b = c ) ),
inference(superposition,[status(thm)],[c_896,c_422]) ).
tcf(c_1001,plain,
( member(c,non_ordered_pair(a,a))
| ( a = c )
| ~ little_set(c) ),
inference(superposition,[status(thm)],[c_717,c_202]) ).
tcf(c_1047,plain,
( member(d,non_ordered_pair(a,a))
| ( a = d ) ),
inference(global_subsumption_just,[status(thm)],[c_770,c_334,c_770]) ).
tcf(c_1054,plain,
a = d,
inference(superposition,[status(thm)],[c_1047,c_200]) ).
tcf(c_1075,plain,
a != b,
inference(demodulation,[status(thm)],[c_336,c_1054]) ).
tcf(c_1256,plain,
( ( b = c )
| ~ little_set(b) ),
inference(superposition,[status(thm)],[c_202,c_905]) ).
tcf(c_1261,plain,
b = c,
inference(global_subsumption_just,[status(thm)],[c_911,c_332,c_1256]) ).
tcf(c_1286,plain,
( member(c,non_ordered_pair(a,a))
| ( a = c ) ),
inference(global_subsumption_just,[status(thm)],[c_1001,c_333,c_1001]) ).
tcf(c_1290,plain,
( member(b,non_ordered_pair(a,a))
| ( a = b ) ),
inference(light_normalisation,[status(thm)],[c_1286,c_1261]) ).
tcf(c_1296,plain,
a = b,
inference(superposition,[status(thm)],[c_1290,c_200]) ).
tcf(c_1322,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_1296,c_1075]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET018-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.18/0.44 % Computer : n011.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Thu Sep 24 09:11:58 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.45 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.27/0.50 Running first-order theorem proving
% 0.27/0.50 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
% 0.27/0.52
% 0.27/0.52 % ======== iProver multi-core TPTP/SMT =========
% 0.27/0.52
% 0.27/0.52 % Detected problem language: tptp
% 0.27/0.54 % Proving...
% 2.99/1.30 % SZS status Started for theBenchmark.p
% 2.99/1.30 % SZS status Unsatisfiable for theBenchmark.p
% 2.99/1.30
% 2.99/1.30 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.99/1.30
% 2.99/1.30 % ------ iProver source info
% 2.99/1.30
% 2.99/1.30 % git: date: 2026-07-19 20:42:38 +0200
% 2.99/1.30 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.99/1.30 % git: non_committed_changes: false
% 2.99/1.30
% 2.99/1.30 % ------ Parsing...% successful
% 2.99/1.30
% 2.99/1.30
% 2.99/1.30 % ------ Clausification by vclausify_rel & Parsing by iProver...
% 2.99/1.30 % ------ Proving...
% 2.99/1.30 % ------ Problem Properties
% 2.99/1.30
% 2.99/1.30 %
% 2.99/1.30 % clauses 141
% 2.99/1.30 % conjectures 1
% 2.99/1.30 % EPR 29
% 2.99/1.30 % Horn 121
% 2.99/1.30 % unary 12
% 2.99/1.30 % binary 92
% 2.99/1.30 % lits 341
% 2.99/1.30 % lits eq 29
% 2.99/1.30 % fd_pure 0
% 2.99/1.30 % fd_pseudo 0
% 2.99/1.30 % fd_cond 4
% 2.99/1.30 % fd_pseudo_cond 7
% 2.99/1.30 % AC symbols 0
% 2.99/1.30
% 2.99/1.30 % ------ Input Options Time Limit: Unbounded
% 2.99/1.30
% 2.99/1.30
% 2.99/1.30 % ------
% 2.99/1.30 % Current options:
% 2.99/1.30 % ------
% 2.99/1.30
% 2.99/1.30
% 2.99/1.30 %
% 2.99/1.30
% 2.99/1.30 % ------ Proving...
% 2.99/1.30 %
% 2.99/1.30
% 2.99/1.30 % ------ Proving...
% 2.99/1.30 %
% 2.99/1.30
% 2.99/1.30 % ------ Proving...
% 2.99/1.30 %
% 2.99/1.30
% 2.99/1.30 % SZS status Unsatisfiable for theBenchmark.p
% 2.99/1.30
% 2.99/1.30 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.99/1.30
% 2.99/1.30
%------------------------------------------------------------------------------