%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU080+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n002.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 02:55:20 PM UTC 2026
% Result : Theorem 2.33s 1.26s
% Output : CNFRefutation 2.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 7
% Syntax : Number of formulae : 54 ( 30 unt; 3 def)
% Number of atoms : 156 ( 28 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 137 ( 55 ~; 47 |; 28 &)
% ( 1 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 4 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 48 ( 1 sgn 42 !; 6 ?; 12 :)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X1,X0)
& subset(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_xboole_0) ).
fof(f23,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f24,axiom,
! [X0,X1,X2] :
( ( function(X2)
& relation(X2) )
=> ( ( subset(X0,relation_rng(X2))
& subset(relation_inverse_image(X2,X0),relation_inverse_image(X2,X1)) )
=> subset(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t158_funct_1) ).
fof(f25,conjecture,
! [X0,X1,X2] :
( ( function(X2)
& relation(X2) )
=> ( ( subset(X1,relation_rng(X2))
& subset(X0,relation_rng(X2))
& relation_inverse_image(X2,X0) = relation_inverse_image(X2,X1) )
=> X0 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t161_funct_1) ).
fof(f26,negated_conjecture,
~ ! [X0,X1,X2] :
( ( function(X2)
& relation(X2) )
=> ( ( subset(X1,relation_rng(X2))
& subset(X0,relation_rng(X2))
& relation_inverse_image(X2,X0) = relation_inverse_image(X2,X1) )
=> X0 = X1 ) ),
inference(negated_conjecture,[status(cth)],[f25]) ).
fof(f35,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f23]) ).
fof(f49,plain,
! [X0,X1,X2] :
( ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,relation_rng(X2))
| ~ subset(relation_inverse_image(X2,X0),relation_inverse_image(X2,X1))
| subset(X0,X1) ),
inference(ennf_transformation,[],[f24]) ).
fof(f50,plain,
! [X0,X1,X2] :
( ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,relation_rng(X2))
| ~ subset(relation_inverse_image(X2,X0),relation_inverse_image(X2,X1))
| subset(X0,X1) ),
inference(flattening,[],[f49]) ).
fof(f51,plain,
? [X0,X1,X2] :
( function(X2)
& relation(X2)
& subset(X1,relation_rng(X2))
& subset(X0,relation_rng(X2))
& relation_inverse_image(X2,X0) = relation_inverse_image(X2,X1)
& X0 != X1 ),
inference(ennf_transformation,[],[f26]) ).
fof(f52,plain,
? [X0,X1,X2] :
( function(X2)
& relation(X2)
& subset(X1,relation_rng(X2))
& subset(X0,relation_rng(X2))
& relation_inverse_image(X2,X0) = relation_inverse_image(X2,X1)
& X0 != X1 ),
inference(flattening,[],[f51]) ).
fof(f62,plain,
! [X0,X1] :
( ( X0 != X1
| ( subset(X1,X0)
& subset(X0,X1) ) )
& ( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f63,plain,
! [X0,X1] :
( ( X0 != X1
| ( subset(X1,X0)
& subset(X0,X1) ) )
& ( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ) ),
inference(flattening,[],[f62]) ).
fof(f75,plain,
( function(sK13)
& relation(sK13)
& subset(sK12,relation_rng(sK13))
& subset(sK11,relation_rng(sK13))
& relation_inverse_image(sK13,sK11) = relation_inverse_image(sK13,sK12)
& sK11 != sK12 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11,sK12,sK13]),skolemize(X0,sK11),skolemize(X1,sK12),skolemize(X2,sK13)],[f52]) ).
fof(f84,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f63]) ).
fof(f113,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f35]) ).
fof(f114,plain,
! [X2,X0,X1] :
( ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,relation_rng(X2))
| ~ subset(relation_inverse_image(X2,X0),relation_inverse_image(X2,X1))
| subset(X0,X1) ),
inference(cnf_transformation,[],[f50]) ).
fof(f115,plain,
function(sK13),
inference(cnf_transformation,[],[f75]) ).
fof(f116,plain,
relation(sK13),
inference(cnf_transformation,[],[f75]) ).
fof(f117,plain,
subset(sK12,relation_rng(sK13)),
inference(cnf_transformation,[],[f75]) ).
fof(f118,plain,
subset(sK11,relation_rng(sK13)),
inference(cnf_transformation,[],[f75]) ).
fof(f119,plain,
relation_inverse_image(sK13,sK11) = relation_inverse_image(sK13,sK12),
inference(cnf_transformation,[],[f75]) ).
fof(f120,plain,
sK11 != sK12,
inference(cnf_transformation,[],[f75]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f84]) ).
tcf(c_83,plain,
! [X0: $i] : subset(X0,X0),
inference(cnf_transformation,[],[f113]) ).
tcf(c_84,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X1,X2)
| ~ relation(X0)
| ~ function(X0)
| ~ subset(X1,relation_rng(X0))
| ~ subset(relation_inverse_image(X0,X1),relation_inverse_image(X0,X2)) ),
inference(cnf_transformation,[],[f114]) ).
tcf(c_85,negated_conjecture,
sK11 != sK12,
inference(cnf_transformation,[],[f120]) ).
tcf(c_86,negated_conjecture,
relation_inverse_image(sK13,sK11) = relation_inverse_image(sK13,sK12),
inference(cnf_transformation,[],[f119]) ).
tcf(c_87,negated_conjecture,
subset(sK11,relation_rng(sK13)),
inference(cnf_transformation,[],[f118]) ).
tcf(c_88,negated_conjecture,
subset(sK12,relation_rng(sK13)),
inference(cnf_transformation,[],[f117]) ).
tcf(c_89,negated_conjecture,
relation(sK13),
inference(cnf_transformation,[],[f116]) ).
tcf(c_90,negated_conjecture,
function(sK13),
inference(cnf_transformation,[],[f115]) ).
tcf(c_1722,definition,
iPr_def_10 = relation_rng(sK13),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_1723,definition,
iPr_def_11 = relation_inverse_image(sK13,sK11),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_1724,definition,
iPr_def_12 = relation_inverse_image(sK13,sK12),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_1725,negated_conjecture,
function(sK13),
inference(demodulation,[status(thm)],[c_90]) ).
tcf(c_1726,negated_conjecture,
relation(sK13),
inference(demodulation,[status(thm)],[c_89]) ).
tcf(c_1727,negated_conjecture,
subset(sK12,iPr_def_10),
inference(demodulation,[status(thm)],[c_88,c_1722]) ).
tcf(c_1728,negated_conjecture,
subset(sK11,iPr_def_10),
inference(demodulation,[status(thm)],[c_87]) ).
tcf(c_1729,negated_conjecture,
iPr_def_11 = iPr_def_12,
inference(demodulation,[status(thm)],[c_86,c_1724,c_1723]) ).
tcf(c_1730,negated_conjecture,
sK11 != sK12,
inference(demodulation,[status(thm)],[c_85]) ).
tcf(c_2455,plain,
relation_inverse_image(sK13,sK12) = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_1724,c_1729]) ).
tcf(c_2598,plain,
! [X0: $i] :
( subset(sK11,X0)
| ~ relation(sK13)
| ~ function(sK13)
| ~ subset(sK11,relation_rng(sK13))
| ~ subset(iPr_def_11,relation_inverse_image(sK13,X0)) ),
inference(superposition,[status(thm)],[c_1723,c_84]) ).
tcf(c_2599,plain,
! [X0: $i] :
( subset(sK12,X0)
| ~ relation(sK13)
| ~ function(sK13)
| ~ subset(sK12,relation_rng(sK13))
| ~ subset(iPr_def_11,relation_inverse_image(sK13,X0)) ),
inference(superposition,[status(thm)],[c_2455,c_84]) ).
tcf(c_2612,plain,
! [X0: $i] :
( subset(sK12,X0)
| ~ relation(sK13)
| ~ function(sK13)
| ~ subset(sK12,iPr_def_10)
| ~ subset(iPr_def_11,relation_inverse_image(sK13,X0)) ),
inference(light_normalisation,[status(thm)],[c_2599,c_1722]) ).
tcf(c_2613,plain,
! [X0: $i] :
( subset(sK12,X0)
| ~ subset(iPr_def_11,relation_inverse_image(sK13,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2612,c_1726,c_1725,c_1727]) ).
tcf(c_2616,plain,
! [X0: $i] :
( subset(sK11,X0)
| ~ relation(sK13)
| ~ function(sK13)
| ~ subset(sK11,iPr_def_10)
| ~ subset(iPr_def_11,relation_inverse_image(sK13,X0)) ),
inference(light_normalisation,[status(thm)],[c_2598,c_1722]) ).
tcf(c_2617,plain,
! [X0: $i] :
( subset(sK11,X0)
| ~ subset(iPr_def_11,relation_inverse_image(sK13,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2616,c_1726,c_1725,c_1728]) ).
tcf(c_2652,plain,
( subset(sK12,sK11)
| ~ subset(iPr_def_11,iPr_def_11) ),
inference(superposition,[status(thm)],[c_1723,c_2613]) ).
tcf(c_2654,plain,
subset(sK12,sK11),
inference(forward_subsumption_resolution,[status(thm)],[c_2652,c_83]) ).
tcf(c_2660,plain,
( subset(sK11,sK12)
| ~ subset(iPr_def_11,iPr_def_11) ),
inference(superposition,[status(thm)],[c_2455,c_2617]) ).
tcf(c_2661,plain,
subset(sK11,sK12),
inference(forward_subsumption_resolution,[status(thm)],[c_2660,c_83]) ).
tcf(c_2678,plain,
( ( sK11 = sK12 )
| ~ subset(sK11,sK12) ),
inference(superposition,[status(thm)],[c_2654,c_52]) ).
tcf(c_2679,plain,
~ subset(sK11,sK12),
inference(forward_subsumption_resolution,[status(thm)],[c_2678,c_1730]) ).
tcf(c_2680,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_2679,c_2661]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU080+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.34 % Computer : n002.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.34 % CPULimit : 300
% 0.09/0.34 % WCLimit : 300
% 0.09/0.34 % DateTime : Thu Sep 24 12:45:34 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/0.38 Running first-order theorem proving
% 0.13/0.38 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
% 0.13/0.39
% 0.13/0.39 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.39
% 0.13/0.40 % Detected problem language: tptp
% 0.13/0.41 % Proving...
% 2.33/1.26 % SZS status Started for theBenchmark.p
% 2.33/1.26 % SZS status Theorem for theBenchmark.p
% 2.33/1.26
% 2.33/1.26 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.33/1.26
% 2.33/1.26 % ------ iProver source info
% 2.33/1.26
% 2.33/1.26 % git: date: 2026-07-19 20:42:38 +0200
% 2.33/1.26 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.33/1.26 % git: non_committed_changes: false
% 2.33/1.26
% 2.33/1.26 % ------ Parsing...
% 2.33/1.26 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.33/1.26
% 2.33/1.26 % ------ 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 %
% 2.33/1.26
% 2.33/1.26 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.33/1.26
% 2.33/1.26 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.33/1.26 % ------ Proving...
% 2.33/1.26 % ------ Problem Properties
% 2.33/1.26
% 2.33/1.26 %
% 2.33/1.26 % clauses 49
% 2.33/1.26 % conjectures 6
% 2.33/1.26 % EPR 34
% 2.33/1.26 % Horn 47
% 2.33/1.26 % unary 30
% 2.33/1.26 % binary 12
% 2.33/1.26 % lits 77
% 2.33/1.26 % lits eq 8
% 2.33/1.26 % fd_pure 0
% 2.33/1.26 % fd_pseudo 0
% 2.33/1.26 % fd_cond 1
% 2.33/1.26 % fd_pseudo_cond 2
% 2.33/1.26 % AC symbols 0
% 2.33/1.26
% 2.33/1.26 % ------ Schedule dynamic 5 is on
% 2.33/1.26
% 2.33/1.26 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.33/1.26
% 2.33/1.26
% 2.33/1.26 % ------
% 2.33/1.26 % Current options:
% 2.33/1.26 % ------
% 2.33/1.26
% 2.33/1.26
% 2.33/1.26 %
% 2.33/1.26
% 2.33/1.26 % ------ Proving...
% 2.33/1.26 %
% 2.33/1.26
% 2.33/1.26 % SZS status Theorem for theBenchmark.p
% 2.33/1.26
% 2.33/1.26 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.33/1.26
% 2.33/1.26
%------------------------------------------------------------------------------