%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU034+1 : 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 : n020.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 02:55:06 PM UTC 2026
% Result : Theorem 3.66s 1.17s
% Output : CNFRefutation 3.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 10
% Syntax : Number of formulae : 69 ( 36 unt; 2 def)
% Number of atoms : 229 ( 67 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 206 ( 94 ~; 87 |; 17 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-2 aty)
% Number of variables : 53 ( 0 sgn 52 !; 1 ?; 21 :)
% 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(f14,axiom,
! [X0] :
( function(identity_relation(X0))
& relation(identity_relation(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_funct_1) ).
fof(f35,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ! [X1] :
( ( function(X1)
& relation(X1) )
=> ( ( relation_composition(X0,X1) = X0
& relation_rng(X0) = relation_dom(X1) )
=> X1 = identity_relation(relation_dom(X1)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_funct_1) ).
fof(f37,axiom,
! [X0] : one_to_one(identity_relation(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t52_funct_1) ).
fof(f38,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(f40,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ( one_to_one(X0)
=> ( relation_composition(function_inverse(X0),X0) = identity_relation(relation_rng(X0))
& relation_composition(X0,function_inverse(X0)) = identity_relation(relation_dom(X0)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t61_funct_1) ).
fof(f41,conjecture,
! [X0] : function_inverse(identity_relation(X0)) = identity_relation(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t67_funct_1) ).
fof(f42,negated_conjecture,
~ ! [X0] : function_inverse(identity_relation(X0)) = identity_relation(X0),
inference(negated_conjecture,[status(cth)],[f41]) ).
fof(f44,axiom,
! [X0] :
( relation_rng(identity_relation(X0)) = X0
& relation_dom(identity_relation(X0)) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t71_relat_1) ).
fof(f56,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ( function(function_inverse(X0))
& relation(function_inverse(X0)) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f57,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ( function(function_inverse(X0))
& relation(function_inverse(X0)) ) ),
inference(flattening,[],[f56]) ).
fof(f77,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1] :
( ~ function(X1)
| ~ relation(X1)
| relation_composition(X0,X1) != X0
| relation_rng(X0) != relation_dom(X1)
| X1 = identity_relation(relation_dom(X1)) ) ),
inference(ennf_transformation,[],[f35]) ).
fof(f78,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1] :
( ~ function(X1)
| ~ relation(X1)
| relation_composition(X0,X1) != X0
| relation_rng(X0) != relation_dom(X1)
| X1 = identity_relation(relation_dom(X1)) ) ),
inference(flattening,[],[f77]) ).
fof(f81,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,[],[f38]) ).
fof(f82,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,[],[f81]) ).
fof(f84,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| ( relation_composition(function_inverse(X0),X0) = identity_relation(relation_rng(X0))
& relation_composition(X0,function_inverse(X0)) = identity_relation(relation_dom(X0)) ) ),
inference(ennf_transformation,[],[f40]) ).
fof(f85,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| ( relation_composition(function_inverse(X0),X0) = identity_relation(relation_rng(X0))
& relation_composition(X0,function_inverse(X0)) = identity_relation(relation_dom(X0)) ) ),
inference(flattening,[],[f84]) ).
fof(f86,plain,
? [X0] : identity_relation(X0) != function_inverse(identity_relation(X0)),
inference(ennf_transformation,[],[f42]) ).
fof(f101,plain,
identity_relation(sK11) != function_inverse(identity_relation(sK11)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(X0,sK11)],[f86]) ).
fof(f108,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| function(function_inverse(X0)) ),
inference(cnf_transformation,[],[f57]) ).
fof(f109,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| relation(function_inverse(X0)) ),
inference(cnf_transformation,[],[f57]) ).
fof(f121,plain,
! [X0] : function(identity_relation(X0)),
inference(cnf_transformation,[],[f14]) ).
fof(f122,plain,
! [X0] : relation(identity_relation(X0)),
inference(cnf_transformation,[],[f14]) ).
fof(f156,plain,
! [X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(X1)
| ~ relation(X1)
| relation_composition(X0,X1) != X0
| relation_rng(X0) != relation_dom(X1)
| identity_relation(relation_dom(X1)) = X1 ),
inference(cnf_transformation,[],[f78]) ).
fof(f158,plain,
! [X0] : one_to_one(identity_relation(X0)),
inference(cnf_transformation,[],[f37]) ).
fof(f160,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| relation_rng(X0) = relation_dom(function_inverse(X0)) ),
inference(cnf_transformation,[],[f82]) ).
fof(f163,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| relation_composition(X0,function_inverse(X0)) = identity_relation(relation_dom(X0)) ),
inference(cnf_transformation,[],[f85]) ).
fof(f164,plain,
identity_relation(sK11) != function_inverse(identity_relation(sK11)),
inference(cnf_transformation,[],[f101]) ).
fof(f166,plain,
! [X0] : relation_rng(identity_relation(X0)) = X0,
inference(cnf_transformation,[],[f44]) ).
fof(f167,plain,
! [X0] : relation_dom(identity_relation(X0)) = X0,
inference(cnf_transformation,[],[f44]) ).
tcf(c_53,plain,
! [X0: $i] :
( relation(function_inverse(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f109]) ).
tcf(c_54,plain,
! [X0: $i] :
( function(function_inverse(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f108]) ).
tcf(c_66,plain,
! [X0: $i] : relation(identity_relation(X0)),
inference(cnf_transformation,[],[f122]) ).
tcf(c_67,plain,
! [X0: $i] : function(identity_relation(X0)),
inference(cnf_transformation,[],[f121]) ).
tcf(c_101,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(X1)) = X1 )
| ~ relation(X1)
| ~ relation(X0)
| ~ function(X1)
| ~ function(X0)
| ( relation_dom(X1) != relation_rng(X0) )
| ( relation_composition(X0,X1) != X0 ) ),
inference(cnf_transformation,[],[f156]) ).
tcf(c_103,plain,
! [X0: $i] : one_to_one(identity_relation(X0)),
inference(cnf_transformation,[],[f158]) ).
tcf(c_104,plain,
! [X0: $i] :
( ( relation_dom(function_inverse(X0)) = relation_rng(X0) )
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f160]) ).
tcf(c_107,plain,
! [X0: $i] :
( ( relation_composition(X0,function_inverse(X0)) = identity_relation(relation_dom(X0)) )
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f163]) ).
tcf(c_109,negated_conjecture,
function_inverse(identity_relation(sK11)) != identity_relation(sK11),
inference(cnf_transformation,[],[f164]) ).
tcf(c_111,plain,
! [X0: $i] : relation_dom(identity_relation(X0)) = X0,
inference(cnf_transformation,[],[f167]) ).
tcf(c_112,plain,
! [X0: $i] : relation_rng(identity_relation(X0)) = X0,
inference(cnf_transformation,[],[f166]) ).
tcf(c_692,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(X1,function_inverse(X1)) = identity_relation(relation_dom(X1)) )
| ~ relation(X1)
| ~ function(X1)
| ( identity_relation(X0) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_107,c_103]) ).
tcf(c_693,plain,
! [X0: $i] :
( ( relation_composition(identity_relation(X0),function_inverse(identity_relation(X0))) = identity_relation(relation_dom(identity_relation(X0))) )
| ~ relation(identity_relation(X0))
| ~ function(identity_relation(X0)) ),
inference(unflattening,[status(thm)],[c_692]) ).
tcf(c_695,plain,
! [X0: $i] : relation_composition(identity_relation(X0),function_inverse(identity_relation(X0))) = identity_relation(relation_dom(identity_relation(X0))),
inference(global_subsumption_just,[status(thm)],[c_693,c_67,c_66,c_693]) ).
tcf(c_710,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(function_inverse(X1)) = relation_rng(X1) )
| ~ relation(X1)
| ~ function(X1)
| ( identity_relation(X0) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_104,c_103]) ).
tcf(c_711,plain,
! [X0: $i] :
( ( relation_dom(function_inverse(identity_relation(X0))) = relation_rng(identity_relation(X0)) )
| ~ relation(identity_relation(X0))
| ~ function(identity_relation(X0)) ),
inference(unflattening,[status(thm)],[c_710]) ).
tcf(c_713,plain,
! [X0: $i] : relation_dom(function_inverse(identity_relation(X0))) = relation_rng(identity_relation(X0)),
inference(global_subsumption_just,[status(thm)],[c_711,c_67,c_66,c_711]) ).
tcf(c_1015,plain,
! [X0: $i] : relation_dom(function_inverse(identity_relation(X0))) = X0,
inference(light_normalisation,[status(thm)],[c_713,c_112]) ).
tcf(c_1091,plain,
! [X0: $i] : relation_composition(identity_relation(X0),function_inverse(identity_relation(X0))) = identity_relation(X0),
inference(light_normalisation,[status(thm)],[c_695,c_111]) ).
tcf(c_1153,definition,
iPr_def_10 = identity_relation(sK11),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_1154,definition,
iPr_def_11 = function_inverse(iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_1155,negated_conjecture,
iPr_def_11 != iPr_def_10,
inference(demodulation,[status(thm)],[c_109,c_1153,c_1154]) ).
tcf(c_1783,plain,
function(iPr_def_10),
inference(superposition,[status(thm)],[c_1153,c_67]) ).
tcf(c_1784,plain,
relation(iPr_def_10),
inference(superposition,[status(thm)],[c_1153,c_66]) ).
tcf(c_1828,plain,
relation_rng(iPr_def_10) = sK11,
inference(superposition,[status(thm)],[c_1153,c_112]) ).
tcf(c_1947,plain,
( relation(iPr_def_11)
| ~ relation(iPr_def_10)
| ~ function(iPr_def_10) ),
inference(superposition,[status(thm)],[c_1154,c_53]) ).
tcf(c_1948,plain,
relation(iPr_def_11),
inference(forward_subsumption_resolution,[status(thm)],[c_1947,c_1784,c_1783]) ).
tcf(c_1955,plain,
( function(iPr_def_11)
| ~ relation(iPr_def_10)
| ~ function(iPr_def_10) ),
inference(superposition,[status(thm)],[c_1154,c_54]) ).
tcf(c_1956,plain,
function(iPr_def_11),
inference(forward_subsumption_resolution,[status(thm)],[c_1955,c_1784,c_1783]) ).
tcf(c_1957,plain,
relation_dom(function_inverse(iPr_def_10)) = sK11,
inference(superposition,[status(thm)],[c_1153,c_1015]) ).
tcf(c_1961,plain,
relation_dom(iPr_def_11) = sK11,
inference(light_normalisation,[status(thm)],[c_1957,c_1154]) ).
tcf(c_2117,plain,
relation_composition(iPr_def_10,function_inverse(iPr_def_10)) = iPr_def_10,
inference(superposition,[status(thm)],[c_1153,c_1091]) ).
tcf(c_2120,plain,
relation_composition(iPr_def_10,iPr_def_11) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_2117,c_1154]) ).
tcf(c_2534,plain,
( ( identity_relation(relation_dom(iPr_def_11)) = iPr_def_11 )
| ~ relation(iPr_def_11)
| ~ relation(iPr_def_10)
| ~ function(iPr_def_11)
| ~ function(iPr_def_10)
| ( relation_dom(iPr_def_11) != relation_rng(iPr_def_10) ) ),
inference(superposition,[status(thm)],[c_2120,c_101]) ).
tcf(c_2536,plain,
( ( identity_relation(relation_dom(iPr_def_11)) = iPr_def_11 )
| ~ relation(iPr_def_11)
| ~ relation(iPr_def_10)
| ~ function(iPr_def_11)
| ~ function(iPr_def_10) ),
inference(ground_joinability,[status(thm)],[c_2534,c_1828,c_1961]) ).
tcf(c_2537,plain,
( ( iPr_def_10 = iPr_def_11 )
| ~ relation(iPr_def_11)
| ~ relation(iPr_def_10)
| ~ function(iPr_def_11)
| ~ function(iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_2536,c_1153,c_1961]) ).
tcf(c_2538,plain,
iPr_def_10 = iPr_def_11,
inference(forward_subsumption_resolution,[status(thm)],[c_2537,c_1948,c_1784,c_1956,c_1783]) ).
tcf(c_2575,plain,
iPr_def_10 != iPr_def_10,
inference(demodulation,[status(thm)],[c_1155,c_2538]) ).
tcf(c_2576,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_2575]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU034+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n020.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Thu Sep 24 12:37:48 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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...
% 3.66/1.17 % SZS status Started for theBenchmark.p
% 3.66/1.17 % SZS status Theorem for theBenchmark.p
% 3.66/1.17
% 3.66/1.17 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.66/1.17
% 3.66/1.17 % ------ iProver source info
% 3.66/1.17
% 3.66/1.17 % git: date: 2026-07-19 20:42:38 +0200
% 3.66/1.17 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.66/1.17 % git: non_committed_changes: false
% 3.66/1.17
% 3.66/1.17 % ------ Parsing...
% 3.66/1.17 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.66/1.17
% 3.66/1.17 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 4 sf_s rm: 2 0s sf_e pe_s pe_e %
% 3.66/1.17
% 3.66/1.17 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.66/1.17
% 3.66/1.17 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.66/1.17 % ------ Proving...
% 3.66/1.17 % ------ Problem Properties
% 3.66/1.17
% 3.66/1.17 %
% 3.66/1.17 % clauses 67
% 3.66/1.17 % conjectures 1
% 3.66/1.17 % EPR 25
% 3.66/1.17 % Horn 65
% 3.66/1.17 % unary 36
% 3.66/1.17 % binary 16
% 3.66/1.17 % lits 119
% 3.66/1.17 % lits eq 22
% 3.66/1.17 % fd_pure 0
% 3.66/1.17 % fd_pseudo 0
% 3.66/1.17 % fd_cond 1
% 3.66/1.17 % fd_pseudo_cond 1
% 3.66/1.17 % AC symbols 0
% 3.66/1.17
% 3.66/1.17 % ------ Schedule dynamic 5 is on
% 3.66/1.17
% 3.66/1.17 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.66/1.17
% 3.66/1.17
% 3.66/1.17 % ------
% 3.66/1.17 % Current options:
% 3.66/1.17 % ------
% 3.66/1.17
% 3.66/1.17
% 3.66/1.17 %
% 3.66/1.17
% 3.66/1.17 % ------ Proving...
% 3.66/1.17 %
% 3.66/1.17
% 3.66/1.17 % SZS status Theorem for theBenchmark.p
% 3.66/1.17
% 3.66/1.17 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.66/1.17
% 3.66/1.17
%------------------------------------------------------------------------------