%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET031-4 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n013.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 02:46:11 PM UTC 2026
% Result : Unsatisfiable 10.58s 13.33s
% Output : CNFRefutation 10.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 10
% Syntax : Number of formulae : 39 ( 11 unt; 1 def)
% Number of atoms : 110 ( 15 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 76 ( 39 ~; 37 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 2 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-3 aty)
% Number of variables : 50 ( 0 sgn 50 !; 0 ?; 17 :)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
! [X0] : singleton_set(X0) = non_ordered_pair(X0,X0),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/SET003-0.ax',ordered_pair) ).
fof(f15,axiom,
! [X2,X0,X1] :
( X0 != ordered_pair(X1,X2)
| ~ little_set(X2)
| ~ little_set(X1)
| ordered_pair_predicate(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',ordered_pair_predicate4) ).
fof(f16,plain,
! [X2,X0,X1] :
( ordered_pair(X1,X2) != X0
| ~ little_set(X2)
| ~ little_set(X1)
| ordered_pair_predicate(X0) ),
inference(reorient_equations,[],[f15]) ).
fof(f89,axiom,
! [X0] :
( member(f18(X0),X0)
| relation(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',relation2) ).
fof(f90,axiom,
! [X0] :
( ~ ordered_pair_predicate(f18(X0))
| relation(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',relation3) ).
fof(f146,axiom,
! [X2,X0,X1] :
( little_set(f29(X0,X1,X2))
| ~ member(X0,compose(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',compose1) ).
fof(f147,axiom,
! [X2,X0,X1] :
( little_set(f30(X0,X1,X2))
| ~ member(X0,compose(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',compose2) ).
fof(f149,axiom,
! [X2,X0,X1] :
( X0 = ordered_pair(f29(X0,X1,X2),f30(X0,X1,X2))
| ~ member(X0,compose(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',compose4) ).
fof(f150,plain,
! [X2,X0,X1] :
( ordered_pair(f29(X0,X1,X2),f30(X0,X1,X2)) = X0
| ~ member(X0,compose(X1,X2)) ),
inference(reorient_equations,[],[f149]) ).
fof(f162,negated_conjecture,
~ relation(compose(a,b)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_composition_is_a_relation) ).
fof(f164,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(f167,plain,
! [X2,X0,X1] :
( non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2)) != X0
| ~ little_set(X2)
| ~ little_set(X1)
| ordered_pair_predicate(X0) ),
inference(definition_unfolding,[],[f16,f164]) ).
fof(f185,plain,
! [X2,X0,X1] :
( non_ordered_pair(non_ordered_pair(f29(X0,X1,X2),f29(X0,X1,X2)),non_ordered_pair(f29(X0,X1,X2),f30(X0,X1,X2))) = X0
| ~ member(X0,compose(X1,X2)) ),
inference(definition_unfolding,[],[f150,f164]) ).
fof(f193,plain,
! [X2,X1] :
( ~ little_set(X2)
| ~ little_set(X1)
| ordered_pair_predicate(non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2))) ),
inference(equality_resolution,[],[f167]) ).
tcf(c_202,plain,
! [X0: $i,X1: $i] :
( ordered_pair_predicate(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)))
| ~ little_set(X1)
| ~ little_set(X0) ),
inference(cnf_transformation,[],[f193]) ).
tcf(c_263,plain,
! [X0: $i] :
( relation(X0)
| member(f18(X0),X0) ),
inference(cnf_transformation,[],[f89]) ).
tcf(c_264,plain,
! [X0: $i] :
( relation(X0)
| ~ ordered_pair_predicate(f18(X0)) ),
inference(cnf_transformation,[],[f90]) ).
tcf(c_312,plain,
! [X0: $i,X1: $i,X2: $i] :
( little_set(f29(X0,X1,X2))
| ~ member(X0,compose(X1,X2)) ),
inference(cnf_transformation,[],[f146]) ).
tcf(c_313,plain,
! [X0: $i,X1: $i,X2: $i] :
( little_set(f30(X0,X1,X2))
| ~ member(X0,compose(X1,X2)) ),
inference(cnf_transformation,[],[f147]) ).
tcf(c_315,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( non_ordered_pair(non_ordered_pair(f29(X0,X1,X2),f29(X0,X1,X2)),non_ordered_pair(f29(X0,X1,X2),f30(X0,X1,X2))) = X0 )
| ~ member(X0,compose(X1,X2)) ),
inference(cnf_transformation,[],[f185]) ).
tcf(c_326,negated_conjecture,
~ relation(compose(a,b)),
inference(cnf_transformation,[],[f162]) ).
tcf(c_9426,definition,
iPr_def_10 = compose(a,b),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_9427,negated_conjecture,
~ relation(iPr_def_10),
inference(demodulation,[status(thm)],[c_326,c_9426]) ).
tcf(c_11115,plain,
! [X0: $i] :
( little_set(f29(X0,a,b))
| ~ member(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_9426,c_312]) ).
tcf(c_11294,plain,
! [X0: $i] :
( little_set(f30(X0,a,b))
| ~ member(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_9426,c_313]) ).
tcf(c_11695,plain,
( relation(iPr_def_10)
| ~ ordered_pair_predicate(f18(iPr_def_10)) ),
inference(instantiation,[status(thm)],[c_264]) ).
tcf(c_11729,plain,
( relation(iPr_def_10)
| member(f18(iPr_def_10),iPr_def_10) ),
inference(instantiation,[status(thm)],[c_263]) ).
tcf(c_11925,plain,
! [X0: $i,X1: $i] :
( relation(compose(X0,X1))
| ( non_ordered_pair(non_ordered_pair(f29(f18(compose(X0,X1)),X0,X1),f29(f18(compose(X0,X1)),X0,X1)),non_ordered_pair(f29(f18(compose(X0,X1)),X0,X1),f30(f18(compose(X0,X1)),X0,X1))) = f18(compose(X0,X1)) ) ),
inference(superposition,[status(thm)],[c_263,c_315]) ).
tcf(c_12666,plain,
( relation(iPr_def_10)
| ( non_ordered_pair(non_ordered_pair(f29(f18(compose(a,b)),a,b),f29(f18(compose(a,b)),a,b)),non_ordered_pair(f29(f18(compose(a,b)),a,b),f30(f18(compose(a,b)),a,b))) = f18(compose(a,b)) ) ),
inference(superposition,[status(thm)],[c_9426,c_11925]) ).
tcf(c_12667,plain,
( relation(iPr_def_10)
| ( non_ordered_pair(non_ordered_pair(f29(f18(iPr_def_10),a,b),f29(f18(iPr_def_10),a,b)),non_ordered_pair(f29(f18(iPr_def_10),a,b),f30(f18(iPr_def_10),a,b))) = f18(iPr_def_10) ) ),
inference(light_normalisation,[status(thm)],[c_12666,c_9426]) ).
tcf(c_12668,plain,
non_ordered_pair(non_ordered_pair(f29(f18(iPr_def_10),a,b),f29(f18(iPr_def_10),a,b)),non_ordered_pair(f29(f18(iPr_def_10),a,b),f30(f18(iPr_def_10),a,b))) = f18(iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_12667,c_9427]) ).
tcf(c_16786,plain,
( ordered_pair_predicate(f18(iPr_def_10))
| ~ little_set(f30(f18(iPr_def_10),a,b))
| ~ little_set(f29(f18(iPr_def_10),a,b)) ),
inference(superposition,[status(thm)],[c_12668,c_202]) ).
tcf(c_16983,plain,
( ~ little_set(f29(f18(iPr_def_10),a,b))
| ~ little_set(f30(f18(iPr_def_10),a,b)) ),
inference(global_subsumption_just,[status(thm)],[c_16786,c_9427,c_11695,c_16786]) ).
tcf(c_16984,plain,
( ~ little_set(f30(f18(iPr_def_10),a,b))
| ~ little_set(f29(f18(iPr_def_10),a,b)) ),
inference(renaming,[status(thm)],[c_16983]) ).
tcf(c_16989,plain,
( ~ member(f18(iPr_def_10),iPr_def_10)
| ~ little_set(f30(f18(iPr_def_10),a,b)) ),
inference(superposition,[status(thm)],[c_11115,c_16984]) ).
tcf(c_17121,plain,
~ little_set(f30(f18(iPr_def_10),a,b)),
inference(global_subsumption_just,[status(thm)],[c_16989,c_9427,c_11729,c_16989]) ).
tcf(c_17123,plain,
~ member(f18(iPr_def_10),iPr_def_10),
inference(superposition,[status(thm)],[c_11294,c_17121]) ).
tcf(c_17124,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_17123,c_11729,c_9427]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET031-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.17/11.26 % Computer : n013.cluster.edu
% 0.17/11.26 % Model : x86_64 x86_64
% 0.17/11.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/11.26 % Memory : 8046.5625MB
% 0.17/11.26 % OS : Linux 6.8.0-71-generic
% 0.17/11.26 % CPULimit : 300
% 0.17/11.26 % WCLimit : 300
% 0.17/11.26 % DateTime : Thu Sep 24 09:19:29 UTC 2026
% 0.17/11.26 % CPUTime :
% 0.17/11.26 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.20/11.32 Running first-order theorem proving
% 0.20/11.33 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
% 0.20/11.34
% 0.20/11.34 % ======== iProver multi-core TPTP/SMT =========
% 0.20/11.34
% 0.20/11.34 % Detected problem language: tptp
% 0.20/11.36 % Proving...
% 10.58/13.33 % SZS status Started for theBenchmark.p
% 10.58/13.33 % SZS status Unsatisfiable for theBenchmark.p
% 10.58/13.33
% 10.58/13.33 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 10.58/13.33
% 10.58/13.33 % ------ iProver source info
% 10.58/13.33
% 10.58/13.33 % git: date: 2026-07-19 20:42:38 +0200
% 10.58/13.33 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 10.58/13.33 % git: non_committed_changes: false
% 10.58/13.33
% 10.58/13.33 % ------ Parsing...% successful
% 10.58/13.33
% 10.58/13.33
% 10.58/13.33 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 10.58/13.33
% 10.58/13.33 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 10.58/13.33
% 10.58/13.33 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 10.58/13.33
% 10.58/13.33 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 10.58/13.33 % ------ Proving...
% 10.58/13.33 % ------ Problem Properties
% 10.58/13.33
% 10.58/13.33 %
% 10.58/13.33 % clauses 131
% 10.58/13.33 % conjectures 1
% 10.58/13.33 % EPR 21
% 10.58/13.33 % Horn 112
% 10.58/13.33 % unary 7
% 10.58/13.33 % binary 89
% 10.58/13.33 % lits 321
% 10.58/13.33 % lits eq 27
% 10.58/13.33 % fd_pure 0
% 10.58/13.33 % fd_pseudo 0
% 10.58/13.33 % fd_cond 4
% 10.58/13.33 % fd_pseudo_cond 6
% 10.58/13.33 % AC symbols 0
% 10.58/13.33
% 10.58/13.33 % ------ Schedule dynamic 5 is on
% 10.58/13.33
% 10.58/13.33 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 10.58/13.33
% 10.58/13.33
% 10.58/13.33 % ------
% 10.58/13.33 % Current options:
% 10.58/13.33 % ------
% 10.58/13.33
% 10.58/13.33
% 10.58/13.33 %
% 10.58/13.33
% 10.58/13.33 % ------ Proving...
% 10.58/13.33 %
% 10.58/13.33
% 10.58/13.33 % SZS status Unsatisfiable for theBenchmark.p
% 10.58/13.33
% 10.58/13.33 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 10.58/13.34
% 10.58/13.34
%------------------------------------------------------------------------------