%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU220+3 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n015.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 02:56:10 PM UTC 2026
% Result : Theorem 3.16s 1.19s
% Output : CNFRefutation 3.16s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f83ERROR: Could not build tree for root c_5401ERROR: MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ( function(function_inverse(X0))
& relation(function_inverse(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_funct_1) ).
fof(f31,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ! [X2] :
( ( function(X2)
& relation(X2) )
=> ( in(X0,relation_dom(X1))
=> apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_funct_1) ).
fof(f36,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ( one_to_one(X0)
=> ( relation_dom(X0) = relation_rng(function_inverse(X0))
& relation_rng(X0) = relation_dom(function_inverse(X0)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t55_funct_1) ).
fof(f37,conjecture,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ( ( in(X0,relation_rng(X1))
& one_to_one(X1) )
=> ( X0 = apply(relation_composition(function_inverse(X1),X1),X0)
& X0 = apply(X1,apply(function_inverse(X1),X0)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t57_funct_1) ).
fof(f38,negated_conjecture,
~ ! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ( ( in(X0,relation_rng(X1))
& one_to_one(X1) )
=> ( X0 = apply(relation_composition(function_inverse(X1),X1),X0)
& X0 = apply(X1,apply(function_inverse(X1),X0)) ) ) ),
inference(negated_conjecture,[status(cth)],[f37]) ).
fof(f43,plain,
? [X0,X1] :
( function(X1)
& relation(X1)
& in(X0,relation_rng(X1))
& one_to_one(X1)
& ( apply(relation_composition(function_inverse(X1),X1),X0) != X0
| apply(X1,apply(function_inverse(X1),X0)) != X0 ) ),
inference(ennf_transformation,[],[f38]) ).
fof(f44,plain,
? [X0,X1] :
( function(X1)
& relation(X1)
& in(X0,relation_rng(X1))
& one_to_one(X1)
& ( apply(relation_composition(function_inverse(X1),X1),X0) != X0
| apply(X1,apply(function_inverse(X1),X0)) != X0 ) ),
inference(flattening,[],[f43]) ).
fof(f47,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| ( relation_dom(X0) = relation_rng(function_inverse(X0))
& relation_rng(X0) = relation_dom(function_inverse(X0)) ) ),
inference(ennf_transformation,[],[f36]) ).
fof(f48,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| ( relation_dom(X0) = relation_rng(function_inverse(X0))
& relation_rng(X0) = relation_dom(function_inverse(X0)) ) ),
inference(flattening,[],[f47]) ).
fof(f51,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ( function(function_inverse(X0))
& relation(function_inverse(X0)) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f52,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ( function(function_inverse(X0))
& relation(function_inverse(X0)) ) ),
inference(flattening,[],[f51]) ).
fof(f76,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ! [X2] :
( ~ function(X2)
| ~ relation(X2)
| ~ in(X0,relation_dom(X1))
| apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0)) ) ),
inference(ennf_transformation,[],[f31]) ).
fof(f77,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ! [X2] :
( ~ function(X2)
| ~ relation(X2)
| ~ in(X0,relation_dom(X1))
| apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0)) ) ),
inference(flattening,[],[f76]) ).
fof(f84,plain,
( function(sK2)
& relation(sK2)
& in(sK1,relation_rng(sK2))
& one_to_one(sK2)
& ( sK1 != apply(relation_composition(function_inverse(sK2),sK2),sK1)
| sK1 != apply(sK2,apply(function_inverse(sK2),sK1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(X0,sK1),skolemize(X1,sK2)],[f44]) ).
fof(f88,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| ! [X1] :
( ~ function(X1)
| ~ relation(X1)
| ( ( function_inverse(X0) != X1
| ( ! [X2,X3] :
( sP0(X0,X2,X3,X1)
& ( apply(X1,X2) != X3
| ~ in(X2,relation_rng(X0))
| ( X2 = apply(X0,X3)
& in(X3,relation_dom(X0)) ) ) )
& relation_dom(X1) = relation_rng(X0) ) )
& ( ? [X2,X3] :
( ~ sP0(X0,X2,X3,X1)
| ( apply(X1,X2) = X3
& in(X2,relation_rng(X0))
& ( apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) ) ) )
| relation_rng(X0) != relation_dom(X1)
| X1 = function_inverse(X0) ) ) ) ),
inference(nnf_transformation,[],[f83]) ).
fof(f89,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| ! [X1] :
( ~ function(X1)
| ~ relation(X1)
| ( ( function_inverse(X0) != X1
| ( ! [X2,X3] :
( sP0(X0,X2,X3,X1)
& ( apply(X1,X2) != X3
| ~ in(X2,relation_rng(X0))
| ( X2 = apply(X0,X3)
& in(X3,relation_dom(X0)) ) ) )
& relation_dom(X1) = relation_rng(X0) ) )
& ( ? [X2,X3] :
( ~ sP0(X0,X2,X3,X1)
| ( apply(X1,X2) = X3
& in(X2,relation_rng(X0))
& ( apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) ) ) )
| relation_rng(X0) != relation_dom(X1)
| X1 = function_inverse(X0) ) ) ) ),
inference(flattening,[],[f88]) ).
fof(f90,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| ! [X1] :
( ~ function(X1)
| ~ relation(X1)
| ( ( function_inverse(X0) != X1
| ( ! [X4,X5] :
( sP0(X0,X4,X5,X1)
& ( apply(X1,X4) != X5
| ~ in(X4,relation_rng(X0))
| ( apply(X0,X5) = X4
& in(X5,relation_dom(X0)) ) ) )
& relation_dom(X1) = relation_rng(X0) ) )
& ( ? [X2,X3] :
( ~ sP0(X0,X2,X3,X1)
| ( apply(X1,X2) = X3
& in(X2,relation_rng(X0))
& ( apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) ) ) )
| relation_rng(X0) != relation_dom(X1)
| X1 = function_inverse(X0) ) ) ) ),
inference(rectify,[],[f89]) ).
fof(f91,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| ! [X1] :
( ~ function(X1)
| ~ relation(X1)
| ( ( function_inverse(X0) != X1
| ( ! [X4,X5] :
( sP0(X0,X4,X5,X1)
& ( apply(X1,X4) != X5
| ~ in(X4,relation_rng(X0))
| ( apply(X0,X5) = X4
& in(X5,relation_dom(X0)) ) ) )
& relation_dom(X1) = relation_rng(X0) ) )
& ( ~ sP0(X0,sK3(X0,X1),sK4(X0,X1),X1)
| ( sK4(X0,X1) = apply(X1,sK3(X0,X1))
& in(sK3(X0,X1),relation_rng(X0))
& ( sK3(X0,X1) != apply(X0,sK4(X0,X1))
| ~ in(sK4(X0,X1),relation_dom(X0)) ) )
| relation_rng(X0) != relation_dom(X1)
| X1 = function_inverse(X0) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4]),skolemize(X2,sK3(X0,X1)),skolemize(X3,sK4(X0,X1))],[f90]) ).
fof(f102,plain,
function(sK2),
inference(cnf_transformation,[],[f84]) ).
fof(f103,plain,
relation(sK2),
inference(cnf_transformation,[],[f84]) ).
fof(f104,plain,
in(sK1,relation_rng(sK2)),
inference(cnf_transformation,[],[f84]) ).
fof(f105,plain,
one_to_one(sK2),
inference(cnf_transformation,[],[f84]) ).
fof(f106,plain,
( sK1 != apply(relation_composition(function_inverse(sK2),sK2),sK1)
| sK1 != apply(sK2,apply(function_inverse(sK2),sK1)) ),
inference(cnf_transformation,[],[f84]) ).
fof(f110,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| relation_rng(X0) = relation_dom(function_inverse(X0)) ),
inference(cnf_transformation,[],[f48]) ).
fof(f117,plain,
! [X0,X1,X4,X5] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| ~ function(X1)
| ~ relation(X1)
| function_inverse(X0) != X1
| apply(X1,X4) != X5
| ~ in(X4,relation_rng(X0))
| apply(X0,X5) = X4 ),
inference(cnf_transformation,[],[f91]) ).
fof(f123,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| function(function_inverse(X0)) ),
inference(cnf_transformation,[],[f52]) ).
fof(f124,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| relation(function_inverse(X0)) ),
inference(cnf_transformation,[],[f52]) ).
fof(f158,plain,
! [X2,X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ in(X0,relation_dom(X1))
| apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0)) ),
inference(cnf_transformation,[],[f77]) ).
fof(f179,plain,
! [X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| ~ function(X1)
| ~ relation(X1)
| function_inverse(X0) != X1
| ~ in(X4,relation_rng(X0))
| apply(X0,apply(X1,X4)) = X4 ),
inference(equality_resolution,[],[f117]) ).
fof(f180,plain,
! [X0,X4] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| ~ function(function_inverse(X0))
| ~ relation(function_inverse(X0))
| ~ in(X4,relation_rng(X0))
| apply(X0,apply(function_inverse(X0),X4)) = X4 ),
inference(equality_resolution,[],[f179]) ).
tcf(c_49,negated_conjecture,
( ( apply(sK2,apply(function_inverse(sK2),sK1)) != sK1 )
| ( apply(relation_composition(function_inverse(sK2),sK2),sK1) != sK1 ) ),
inference(cnf_transformation,[],[f106]) ).
tcf(c_50,negated_conjecture,
one_to_one(sK2),
inference(cnf_transformation,[],[f105]) ).
tcf(c_51,negated_conjecture,
in(sK1,relation_rng(sK2)),
inference(cnf_transformation,[],[f104]) ).
tcf(c_52,negated_conjecture,
relation(sK2),
inference(cnf_transformation,[],[f103]) ).
tcf(c_53,negated_conjecture,
function(sK2),
inference(cnf_transformation,[],[f102]) ).
tcf(c_56,plain,
! [X0: $i] :
( ( relation_dom(function_inverse(X0)) = relation_rng(X0) )
| ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0) ),
inference(cnf_transformation,[],[f110]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i] :
( ( apply(X1,apply(function_inverse(X1),X0)) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1)
| ~ function(function_inverse(X1))
| ~ relation(function_inverse(X1))
| ~ in(X0,relation_rng(X1)) ),
inference(cnf_transformation,[],[f180]) ).
tcf(c_70,plain,
! [X0: $i] :
( relation(function_inverse(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f124]) ).
tcf(c_71,plain,
! [X0: $i] :
( function(function_inverse(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f123]) ).
tcf(c_103,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0)) )
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(X0,relation_dom(X1)) ),
inference(cnf_transformation,[],[f158]) ).
tcf(c_135,plain,
( function(function_inverse(sK2))
| ~ function(sK2)
| ~ relation(sK2) ),
inference(instantiation,[status(thm)],[c_71]) ).
tcf(c_136,plain,
( relation(function_inverse(sK2))
| ~ function(sK2)
| ~ relation(sK2) ),
inference(instantiation,[status(thm)],[c_70]) ).
tcf(c_289,plain,
! [X0: $i,X1: $i] :
( ( apply(X1,apply(function_inverse(X1),X0)) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1)
| ~ function(function_inverse(X1))
| ~ in(X0,relation_rng(X1)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_68,c_70]) ).
tcf(c_300,plain,
! [X0: $i,X1: $i] :
( ( apply(X1,apply(function_inverse(X1),X0)) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1)
| ~ in(X0,relation_rng(X1)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_289,c_71]) ).
tcf(c_3786,plain,
( ( apply(sK2,apply(function_inverse(sK2),sK1)) = sK1 )
| ~ function(sK2)
| ~ relation(sK2)
| ~ one_to_one(sK2) ),
inference(superposition,[status(thm)],[c_51,c_300]) ).
tcf(c_3787,plain,
apply(sK2,apply(function_inverse(sK2),sK1)) = sK1,
inference(forward_subsumption_resolution,[status(thm)],[c_3786,c_53,c_52,c_50]) ).
tcf(c_3788,plain,
apply(relation_composition(function_inverse(sK2),sK2),sK1) != sK1,
inference(backward_subsumption_resolution,[status(thm)],[c_49,c_3787]) ).
tcf(c_3929,plain,
( ( relation_dom(function_inverse(sK2)) = relation_rng(sK2) )
| ~ function(sK2)
| ~ relation(sK2) ),
inference(superposition,[status(thm)],[c_50,c_56]) ).
tcf(c_3936,plain,
relation_dom(function_inverse(sK2)) = relation_rng(sK2),
inference(forward_subsumption_resolution,[status(thm)],[c_3929,c_53,c_52]) ).
tcf(c_5044,plain,
! [X0: $i,X1: $i] :
( ( apply(relation_composition(function_inverse(sK2),X1),X0) = apply(X1,apply(function_inverse(sK2),X0)) )
| ~ function(X1)
| ~ relation(X1)
| ~ function(function_inverse(sK2))
| ~ relation(function_inverse(sK2))
| ~ in(X0,relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_3936,c_103]) ).
tcf(c_5353,plain,
! [X0: $i,X1: $i] :
( ( apply(relation_composition(function_inverse(sK2),X1),X0) = apply(X1,apply(function_inverse(sK2),X0)) )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_rng(sK2)) ),
inference(global_subsumption_just,[status(thm)],[c_5044,c_53,c_52,c_135,c_136,c_5044]) ).
tcf(c_5364,plain,
! [X0: $i] :
( ( apply(relation_composition(function_inverse(sK2),X0),sK1) = apply(X0,apply(function_inverse(sK2),sK1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_51,c_5353]) ).
tcf(c_5388,plain,
( ( apply(relation_composition(function_inverse(sK2),sK2),sK1) = apply(sK2,apply(function_inverse(sK2),sK1)) )
| ~ relation(sK2) ),
inference(superposition,[status(thm)],[c_53,c_5364]) ).
tcf(c_5400,plain,
( ( apply(relation_composition(function_inverse(sK2),sK2),sK1) = sK1 )
| ~ relation(sK2) ),
inference(light_normalisation,[status(thm)],[c_5388,c_3787]) ).
tcf(c_5401,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_5400,c_3788,c_52]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU220+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n015.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 13:18:11 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 3.16/1.19 % SZS status Started for theBenchmark.p
% 3.16/1.19 % SZS status Theorem for theBenchmark.p
% 3.16/1.19
% 3.16/1.19 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.16/1.19
% 3.16/1.19 % ------ iProver source info
% 3.16/1.19
% 3.16/1.19 % git: date: 2026-07-19 20:42:38 +0200
% 3.16/1.19 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.16/1.19 % git: non_committed_changes: false
% 3.16/1.19
% 3.16/1.19 % ------ Parsing...
% 3.16/1.19 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.16/1.19
% 3.16/1.19 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 3.16/1.19
% 3.16/1.19 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.16/1.19
% 3.16/1.19 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.16/1.19 % ------ Proving...
% 3.16/1.19 % ------ Problem Properties
% 3.16/1.19
% 3.16/1.19 %
% 3.16/1.19 % clauses 66
% 3.16/1.19 % conjectures 5
% 3.16/1.19 % EPR 28
% 3.16/1.19 % Horn 60
% 3.16/1.19 % unary 24
% 3.16/1.19 % binary 17
% 3.16/1.19 % lits 164
% 3.16/1.19 % lits eq 18
% 3.16/1.19 % fd_pure 0
% 3.16/1.19 % fd_pseudo 0
% 3.16/1.19 % fd_cond 1
% 3.16/1.19 % fd_pseudo_cond 5
% 3.16/1.19 % AC symbols 0
% 3.16/1.19
% 3.16/1.19 % ------ Schedule dynamic 5 is on
% 3.16/1.19
% 3.16/1.19 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.16/1.19
% 3.16/1.19
% 3.16/1.19 % ------
% 3.16/1.19 % Current options:
% 3.16/1.19 % ------
% 3.16/1.19
% 3.16/1.19
% 3.16/1.19 %
% 3.16/1.19
% 3.16/1.19 % ------ Proving...
% 3.16/1.19 %
% 3.16/1.19
% 3.16/1.19 % SZS status Theorem for theBenchmark.p
% 3.16/1.19
% 3.16/1.19 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.16/1.19
% 3.16/1.19
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