%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET018-3 : 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 : n003.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 0.74s 1.28s
% Output : CNFRefutation 0.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 14
% Syntax : Number of formulae : 67 ( 24 unt; 0 def)
% Number of atoms : 157 ( 89 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 161 ( 71 ~; 90 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 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 : 69 ( 0 sgn 69 !; 0 ?; 34 :)
% 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,
! [X2,X3,X0,X1] :
( X0 = X1
| ordered_pair(X0,X2) != ordered_pair(X1,X3)
| ~ little_set(X1)
| ~ little_set(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',first_components_are_equal) ).
fof(f163,plain,
! [X2,X3,X0,X1] :
( X0 = X1
| ordered_pair(X1,X3) != ordered_pair(X0,X2)
| ~ little_set(X1)
| ~ little_set(X0) ),
inference(reorient_equations,[],[f162]) ).
fof(f164,axiom,
! [X2,X0,X1] :
( X0 = X1
| non_ordered_pair(X2,X0) != non_ordered_pair(X2,X1)
| ~ little_set(X1)
| ~ little_set(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_cancellation) ).
fof(f165,axiom,
little_set(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_little_set) ).
fof(f166,axiom,
little_set(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_little_set) ).
fof(f167,axiom,
little_set(c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_little_set) ).
fof(f168,axiom,
little_set(d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d_little_set) ).
fof(f169,axiom,
ordered_pair(a,b) = ordered_pair(c,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_ordered_pair) ).
fof(f170,negated_conjecture,
b != d,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_second_components_equal) ).
fof(f172,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(f199,plain,
! [X2,X3,X0,X1] :
( X0 = X1
| non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X3)) != non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X2))
| ~ little_set(X1)
| ~ little_set(X0) ),
inference(definition_unfolding,[],[f163,f172,f172]) ).
fof(f200,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,[],[f169,f172,f172]) ).
fof(f201,plain,
! [X2,X1] :
( ~ little_set(X1)
| member(X1,non_ordered_pair(X1,X2)) ),
inference(equality_resolution,[],[f6]) ).
fof(f202,plain,
! [X2,X1] :
( ~ little_set(X2)
| member(X2,non_ordered_pair(X1,X2)) ),
inference(equality_resolution,[],[f7]) ).
tcf(c_202,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ( X0 = X1 )
| ~ member(X0,non_ordered_pair(X1,X2)) ),
inference(cnf_transformation,[],[f5]) ).
tcf(c_203,plain,
! [X0: $i,X1: $i] :
( member(X0,non_ordered_pair(X0,X1))
| ~ little_set(X0) ),
inference(cnf_transformation,[],[f201]) ).
tcf(c_204,plain,
! [X0: $i,X1: $i] :
( member(X0,non_ordered_pair(X1,X0))
| ~ little_set(X0) ),
inference(cnf_transformation,[],[f202]) ).
tcf(c_205,plain,
! [X0: $i,X1: $i] : little_set(non_ordered_pair(X0,X1)),
inference(cnf_transformation,[],[f8]) ).
tcf(c_333,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X0 = X2 )
| ~ little_set(X2)
| ~ little_set(X0)
| ( non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)) != non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X3)) ) ),
inference(cnf_transformation,[],[f199]) ).
tcf(c_334,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ~ little_set(X2)
| ~ little_set(X1)
| ( non_ordered_pair(X0,X1) != non_ordered_pair(X0,X2) ) ),
inference(cnf_transformation,[],[f164]) ).
tcf(c_335,plain,
little_set(a),
inference(cnf_transformation,[],[f165]) ).
tcf(c_336,plain,
little_set(b),
inference(cnf_transformation,[],[f166]) ).
tcf(c_337,plain,
little_set(c),
inference(cnf_transformation,[],[f167]) ).
tcf(c_338,plain,
little_set(d),
inference(cnf_transformation,[],[f168]) ).
tcf(c_339,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,[],[f200]) ).
tcf(c_340,negated_conjecture,
b != d,
inference(cnf_transformation,[],[f170]) ).
tcf(c_416,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_339,c_203]) ).
tcf(c_418,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_339,c_202]) ).
tcf(c_419,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_339,c_204]) ).
tcf(c_443,plain,
! [X0: $i,X1: $i] :
( ( X0 = c )
| ~ little_set(c)
| ~ little_set(X0)
| ( non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)) != non_ordered_pair(non_ordered_pair(a,a),non_ordered_pair(a,b)) ) ),
inference(superposition,[status(thm)],[c_339,c_333]) ).
tcf(c_450,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_419,c_205]) ).
tcf(c_452,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_450,c_202]) ).
tcf(c_455,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_416,c_205]) ).
tcf(c_457,plain,
( ( non_ordered_pair(a,b) = non_ordered_pair(c,c) )
| ( non_ordered_pair(a,a) = non_ordered_pair(c,c) ) ),
inference(superposition,[status(thm)],[c_455,c_202]) ).
tcf(c_464,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_203,c_418]) ).
tcf(c_465,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_204,c_418]) ).
tcf(c_478,plain,
! [X0: $i,X1: $i] :
( ( X0 = c )
| ( non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)) != non_ordered_pair(non_ordered_pair(a,a),non_ordered_pair(a,b)) )
| ~ little_set(X0) ),
inference(global_subsumption_just,[status(thm)],[c_443,c_337,c_443]) ).
tcf(c_479,plain,
! [X0: $i,X1: $i] :
( ( X0 = c )
| ~ little_set(X0)
| ( non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)) != non_ordered_pair(non_ordered_pair(a,a),non_ordered_pair(a,b)) ) ),
inference(renaming,[status(thm)],[c_478]) ).
tcf(c_489,plain,
( ( a = c )
| ~ little_set(a) ),
inference(equality_resolution,[status(thm)],[c_479]) ).
tcf(c_538,plain,
! [X0: $i] :
( ( X0 = d )
| ( non_ordered_pair(a,a) = non_ordered_pair(c,d) )
| ~ little_set(d)
| ~ little_set(X0)
| ( non_ordered_pair(c,X0) != non_ordered_pair(a,b) ) ),
inference(superposition,[status(thm)],[c_452,c_334]) ).
tcf(c_610,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_465,c_205]) ).
tcf(c_620,plain,
! [X0: $i] :
( ( X0 = d )
| ( non_ordered_pair(a,b) = non_ordered_pair(c,c) )
| ~ little_set(d)
| ~ little_set(X0)
| ( non_ordered_pair(c,X0) != non_ordered_pair(a,b) ) ),
inference(superposition,[status(thm)],[c_610,c_334]) ).
tcf(c_651,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_464,c_205]) ).
tcf(c_694,plain,
a = c,
inference(global_subsumption_just,[status(thm)],[c_489,c_335,c_489]) ).
tcf(c_696,plain,
( ( non_ordered_pair(a,a) = non_ordered_pair(c,c) )
| ( non_ordered_pair(a,a) = non_ordered_pair(a,d) ) ),
inference(superposition,[status(thm)],[c_694,c_651]) ).
tcf(c_698,plain,
( ( non_ordered_pair(a,a) = non_ordered_pair(c,c) )
| ( non_ordered_pair(a,a) = non_ordered_pair(a,b) ) ),
inference(superposition,[status(thm)],[c_694,c_457]) ).
tcf(c_786,plain,
! [X0: $i] :
( ( X0 = d )
| ( non_ordered_pair(a,a) = non_ordered_pair(c,d) )
| ( non_ordered_pair(c,X0) != non_ordered_pair(a,b) )
| ~ little_set(X0) ),
inference(global_subsumption_just,[status(thm)],[c_538,c_338,c_538]) ).
tcf(c_787,plain,
! [X0: $i] :
( ( X0 = d )
| ( non_ordered_pair(a,a) = non_ordered_pair(c,d) )
| ~ little_set(X0)
| ( non_ordered_pair(c,X0) != non_ordered_pair(a,b) ) ),
inference(renaming,[status(thm)],[c_786]) ).
tcf(c_793,plain,
! [X0: $i] :
( ( X0 = d )
| ( non_ordered_pair(a,a) = non_ordered_pair(a,d) )
| ~ little_set(X0)
| ( non_ordered_pair(a,X0) != non_ordered_pair(a,b) ) ),
inference(light_normalisation,[status(thm)],[c_787,c_694]) ).
tcf(c_802,plain,
( ( b = d )
| ( non_ordered_pair(a,a) = non_ordered_pair(a,d) )
| ~ little_set(b) ),
inference(equality_resolution,[status(thm)],[c_793]) ).
tcf(c_964,plain,
! [X0: $i] :
( ( X0 = d )
| ( non_ordered_pair(a,b) = non_ordered_pair(c,c) )
| ( non_ordered_pair(c,X0) != non_ordered_pair(a,b) )
| ~ little_set(X0) ),
inference(global_subsumption_just,[status(thm)],[c_620,c_338,c_620]) ).
tcf(c_965,plain,
! [X0: $i] :
( ( X0 = d )
| ( non_ordered_pair(a,b) = non_ordered_pair(c,c) )
| ~ little_set(X0)
| ( non_ordered_pair(c,X0) != non_ordered_pair(a,b) ) ),
inference(renaming,[status(thm)],[c_964]) ).
tcf(c_971,plain,
! [X0: $i] :
( ( X0 = d )
| ( non_ordered_pair(a,a) = non_ordered_pair(a,b) )
| ~ little_set(X0)
| ( non_ordered_pair(a,X0) != non_ordered_pair(a,b) ) ),
inference(light_normalisation,[status(thm)],[c_965,c_694]) ).
tcf(c_980,plain,
( ( b = d )
| ( non_ordered_pair(a,a) = non_ordered_pair(a,b) )
| ~ little_set(b) ),
inference(equality_resolution,[status(thm)],[c_971]) ).
tcf(c_1074,plain,
non_ordered_pair(a,a) = non_ordered_pair(a,b),
inference(global_subsumption_just,[status(thm)],[c_698,c_336,c_340,c_980]) ).
tcf(c_1080,plain,
! [X0: $i] :
( ( X0 = b )
| ~ little_set(b)
| ~ little_set(X0)
| ( non_ordered_pair(a,X0) != non_ordered_pair(a,a) ) ),
inference(superposition,[status(thm)],[c_1074,c_334]) ).
tcf(c_1132,plain,
non_ordered_pair(a,a) = non_ordered_pair(a,d),
inference(global_subsumption_just,[status(thm)],[c_696,c_336,c_340,c_802]) ).
tcf(c_1296,plain,
! [X0: $i] :
( ( X0 = b )
| ( non_ordered_pair(a,X0) != non_ordered_pair(a,a) )
| ~ little_set(X0) ),
inference(global_subsumption_just,[status(thm)],[c_1080,c_336,c_1080]) ).
tcf(c_1297,plain,
! [X0: $i] :
( ( X0 = b )
| ~ little_set(X0)
| ( non_ordered_pair(a,X0) != non_ordered_pair(a,a) ) ),
inference(renaming,[status(thm)],[c_1296]) ).
tcf(c_1305,plain,
( ( b = d )
| ~ little_set(d) ),
inference(superposition,[status(thm)],[c_1132,c_1297]) ).
tcf(c_1307,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_1305,c_340,c_338]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET018-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.37 % Computer : n003.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Thu Sep 24 09:13:05 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 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
% 0.12/0.42
% 0.12/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.42
% 0.12/0.42 % Detected problem language: tptp
% 0.12/0.44 % Proving...
% 0.74/1.28 % SZS status Started for theBenchmark.p
% 0.74/1.28 % SZS status Unsatisfiable for theBenchmark.p
% 0.74/1.28
% 0.74/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.74/1.28
% 0.74/1.28 % ------ iProver source info
% 0.74/1.28
% 0.74/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 0.74/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.74/1.28 % git: non_committed_changes: false
% 0.74/1.28
% 0.74/1.28 % ------ Parsing...% successful
% 0.74/1.28
% 0.74/1.28
% 0.74/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...
% 0.74/1.28 % ------ Proving...
% 0.74/1.28 % ------ Problem Properties
% 0.74/1.28
% 0.74/1.28 %
% 0.74/1.28 % clauses 143
% 0.74/1.28 % conjectures 1
% 0.74/1.28 % EPR 29
% 0.74/1.28 % Horn 123
% 0.74/1.28 % unary 12
% 0.74/1.28 % binary 92
% 0.74/1.28 % lits 349
% 0.74/1.28 % lits eq 33
% 0.74/1.28 % fd_pure 0
% 0.74/1.28 % fd_pseudo 0
% 0.74/1.28 % fd_cond 4
% 0.74/1.28 % fd_pseudo_cond 9
% 0.74/1.28 % AC symbols 0
% 0.74/1.28
% 0.74/1.28 % ------ Input Options Time Limit: Unbounded
% 0.74/1.28
% 0.74/1.28
% 0.74/1.28 % ------
% 0.74/1.28 % Current options:
% 0.74/1.28 % ------
% 0.74/1.28
% 0.74/1.28
% 0.74/1.28 %
% 0.74/1.28
% 0.74/1.28 % ------ Proving...
% 0.74/1.28 %
% 0.74/1.28
% 0.74/1.28 % ------ Proving...
% 0.74/1.28 %
% 0.74/1.28
% 0.74/1.28 % ------ Proving...
% 0.74/1.28 %
% 0.74/1.28
% 0.74/1.28 % SZS status Unsatisfiable for theBenchmark.p
% 0.74/1.28
% 0.74/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.74/1.28
% 0.74/1.28
%------------------------------------------------------------------------------