%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU220+1 : TPTP v9.3.1. Released v3.3.0.
% 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 02:56:10 PM UTC 2026
% Result : Theorem 4.62s 1.51s
% Output : CNFRefutation 4.62s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f74ERROR: Could not build tree for root c_4808ERROR: MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ( function(function_inverse(X0))
& relation(function_inverse(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_funct_1) ).
fof(f32,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/sandbox2/benchmark/theBenchmark.p',t23_funct_1) ).
fof(f35,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/sandbox2/benchmark/theBenchmark.p',t55_funct_1) ).
fof(f36,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/sandbox2/benchmark/theBenchmark.p',t57_funct_1) ).
fof(f37,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)],[f36]) ).
fof(f41,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,[],[f37]) ).
fof(f42,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,[],[f41]) ).
fof(f45,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,[],[f35]) ).
fof(f46,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,[],[f45]) ).
fof(f49,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ( function(function_inverse(X0))
& relation(function_inverse(X0)) ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f50,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ( function(function_inverse(X0))
& relation(function_inverse(X0)) ) ),
inference(flattening,[],[f49]) ).
fof(f68,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,[],[f32]) ).
fof(f69,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,[],[f68]) ).
fof(f75,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)],[f42]) ).
fof(f79,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,[],[f74]) ).
fof(f80,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,[],[f79]) ).
fof(f81,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,[],[f80]) ).
fof(f82,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))],[f81]) ).
fof(f90,plain,
function(sK2),
inference(cnf_transformation,[],[f75]) ).
fof(f91,plain,
relation(sK2),
inference(cnf_transformation,[],[f75]) ).
fof(f92,plain,
in(sK1,relation_rng(sK2)),
inference(cnf_transformation,[],[f75]) ).
fof(f93,plain,
one_to_one(sK2),
inference(cnf_transformation,[],[f75]) ).
fof(f94,plain,
( sK1 != apply(relation_composition(function_inverse(sK2),sK2),sK1)
| sK1 != apply(sK2,apply(function_inverse(sK2),sK1)) ),
inference(cnf_transformation,[],[f75]) ).
fof(f98,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| relation_rng(X0) = relation_dom(function_inverse(X0)) ),
inference(cnf_transformation,[],[f46]) ).
fof(f105,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,[],[f82]) ).
fof(f111,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| function(function_inverse(X0)) ),
inference(cnf_transformation,[],[f50]) ).
fof(f112,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| relation(function_inverse(X0)) ),
inference(cnf_transformation,[],[f50]) ).
fof(f142,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,[],[f69]) ).
fof(f157,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,[],[f105]) ).
fof(f158,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,[],[f157]) ).
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,[],[f94]) ).
tcf(c_50,negated_conjecture,
one_to_one(sK2),
inference(cnf_transformation,[],[f93]) ).
tcf(c_51,negated_conjecture,
in(sK1,relation_rng(sK2)),
inference(cnf_transformation,[],[f92]) ).
tcf(c_52,negated_conjecture,
relation(sK2),
inference(cnf_transformation,[],[f91]) ).
tcf(c_53,negated_conjecture,
function(sK2),
inference(cnf_transformation,[],[f90]) ).
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,[],[f98]) ).
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,[],[f158]) ).
tcf(c_70,plain,
! [X0: $i] :
( relation(function_inverse(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f112]) ).
tcf(c_71,plain,
! [X0: $i] :
( function(function_inverse(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f111]) ).
tcf(c_99,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,[],[f142]) ).
tcf(c_117,plain,
( function(function_inverse(sK2))
| ~ function(sK2)
| ~ relation(sK2) ),
inference(instantiation,[status(thm)],[c_71]) ).
tcf(c_118,plain,
( relation(function_inverse(sK2))
| ~ function(sK2)
| ~ relation(sK2) ),
inference(instantiation,[status(thm)],[c_70]) ).
tcf(c_251,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_262,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_251,c_71]) ).
tcf(c_3545,plain,
( ( apply(sK2,apply(function_inverse(sK2),sK1)) = sK1 )
| ~ function(sK2)
| ~ relation(sK2)
| ~ one_to_one(sK2) ),
inference(superposition,[status(thm)],[c_51,c_262]) ).
tcf(c_3546,plain,
apply(sK2,apply(function_inverse(sK2),sK1)) = sK1,
inference(forward_subsumption_resolution,[status(thm)],[c_3545,c_53,c_52,c_50]) ).
tcf(c_3547,plain,
apply(relation_composition(function_inverse(sK2),sK2),sK1) != sK1,
inference(backward_subsumption_resolution,[status(thm)],[c_49,c_3546]) ).
tcf(c_3614,plain,
( ( relation_dom(function_inverse(sK2)) = relation_rng(sK2) )
| ~ function(sK2)
| ~ relation(sK2) ),
inference(superposition,[status(thm)],[c_50,c_56]) ).
tcf(c_3626,plain,
relation_dom(function_inverse(sK2)) = relation_rng(sK2),
inference(forward_subsumption_resolution,[status(thm)],[c_3614,c_53,c_52]) ).
tcf(c_4528,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_3626,c_99]) ).
tcf(c_4760,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_4528,c_53,c_52,c_117,c_118,c_4528]) ).
tcf(c_4771,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_4760]) ).
tcf(c_4795,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_4771]) ).
tcf(c_4807,plain,
( ( apply(relation_composition(function_inverse(sK2),sK2),sK1) = sK1 )
| ~ relation(sK2) ),
inference(light_normalisation,[status(thm)],[c_4795,c_3546]) ).
tcf(c_4808,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_4807,c_3547,c_52]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU220+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.07 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.17/0.43 % Computer : n013.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Thu Sep 24 13:14:06 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.43 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.23/0.50 Running first-order theorem proving
% 0.23/0.50 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
% 0.23/0.51
% 0.23/0.51 % ======== iProver multi-core TPTP/SMT =========
% 0.23/0.51
% 0.23/0.51 % Detected problem language: tptp
% 0.23/0.53 % Proving...
% 4.62/1.51 % SZS status Started for theBenchmark.p
% 4.62/1.51 % SZS status Theorem for theBenchmark.p
% 4.62/1.51
% 4.62/1.51 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.62/1.51
% 4.62/1.51 % ------ iProver source info
% 4.62/1.51
% 4.62/1.51 % git: date: 2026-07-19 20:42:38 +0200
% 4.62/1.51 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.62/1.51 % git: non_committed_changes: false
% 4.62/1.51
% 4.62/1.51 % ------ Parsing...
% 4.62/1.51 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.62/1.51
% 4.62/1.51 % ------ 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 %
% 4.62/1.51
% 4.62/1.51 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.62/1.51
% 4.62/1.51 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.62/1.51 % ------ Proving...
% 4.62/1.51 % ------ Problem Properties
% 4.62/1.51
% 4.62/1.51 %
% 4.62/1.51 % clauses 56
% 4.62/1.51 % conjectures 5
% 4.62/1.51 % EPR 26
% 4.62/1.51 % Horn 52
% 4.62/1.51 % unary 20
% 4.62/1.51 % binary 14
% 4.62/1.51 % lits 145
% 4.62/1.51 % lits eq 18
% 4.62/1.51 % fd_pure 0
% 4.62/1.51 % fd_pseudo 0
% 4.62/1.51 % fd_cond 1
% 4.62/1.51 % fd_pseudo_cond 5
% 4.62/1.51 % AC symbols 0
% 4.62/1.51
% 4.62/1.51 % ------ Schedule dynamic 5 is on
% 4.62/1.51
% 4.62/1.51 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.62/1.51
% 4.62/1.51
% 4.62/1.51 % ------
% 4.62/1.51 % Current options:
% 4.62/1.51 % ------
% 4.62/1.51
% 4.62/1.51
% 4.62/1.51 %
% 4.62/1.51
% 4.62/1.51 % ------ Proving...
% 4.62/1.51 %
% 4.62/1.51
% 4.62/1.51 % SZS status Theorem for theBenchmark.p
% 4.62/1.51
% 4.62/1.51 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.62/1.51
% 4.62/1.51
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