%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : COL042-2 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n026.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 01:02:37 PM UTC 2026
% Result : Unsatisfiable 4.12s 1.31s
% Output : CNFRefutation 4.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 11
% Syntax : Number of formulae : 33 ( 30 unt; 7 def)
% Number of atoms : 71 ( 31 equ)
% Maximal formula atoms : 2 ( 2 avg)
% Number of connectives : 13 ( 10 ~; 3 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 8 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 30 ( 0 sgn 30 !; 0 ?; 24 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : apply(apply(apply(b,X0),X1),X2) = apply(X0,apply(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_definition) ).
fof(f2,axiom,
! [X0,X1] : apply(apply(w1,X0),X1) = apply(apply(X1,X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',w1_definition) ).
fof(f3,axiom,
! [X0] :
( fixed_point(X0)
| apply(X0,fixed_pt) != apply(fixed_pt,apply(X0,fixed_pt)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',strong_fixed_point) ).
fof(f4,negated_conjecture,
~ fixed_point(apply(apply(b,apply(apply(b,apply(apply(b,apply(w1,w1)),apply(b,w1))),b)),b)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_strong_fixed_point) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i] : apply(apply(apply(b,X0),X1),X2) = apply(X0,apply(X1,X2)),
inference(cnf_transformation,[],[f1]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] : apply(apply(X0,X1),X1) = apply(apply(w1,X1),X0),
inference(cnf_transformation,[],[f2]) ).
tcf(c_55,plain,
! [X0: $i] :
( fixed_point(X0)
| ( apply(fixed_pt,apply(X0,fixed_pt)) != apply(X0,fixed_pt) ) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_56,negated_conjecture,
~ fixed_point(apply(apply(b,apply(apply(b,apply(apply(b,apply(w1,w1)),apply(b,w1))),b)),b)),
inference(cnf_transformation,[],[f4]) ).
tcf(c_77,plain,
! [X0: $i] :
( ( apply(fixed_pt,apply(X0,fixed_pt)) != apply(X0,fixed_pt) )
| ( apply(apply(b,apply(apply(b,apply(apply(b,apply(w1,w1)),apply(b,w1))),b)),b) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_55,c_56]) ).
tcf(c_78,plain,
apply(fixed_pt,apply(apply(apply(b,apply(apply(b,apply(apply(b,apply(w1,w1)),apply(b,w1))),b)),b),fixed_pt)) != apply(apply(apply(b,apply(apply(b,apply(apply(b,apply(w1,w1)),apply(b,w1))),b)),b),fixed_pt),
inference(unflattening,[status(thm)],[c_77]) ).
tcf(c_89,plain,
apply(fixed_pt,apply(apply(w1,w1),apply(apply(b,w1),apply(b,apply(b,fixed_pt))))) != apply(apply(w1,w1),apply(apply(b,w1),apply(b,apply(b,fixed_pt)))),
inference(demodulation,[status(thm)],[c_78,c_53]) ).
tcf(c_93,definition,
iPr_def_10 = apply(w1,w1),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_94,definition,
iPr_def_11 = apply(b,w1),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_95,definition,
iPr_def_12 = apply(b,fixed_pt),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_96,definition,
iPr_def_13 = apply(b,iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_97,definition,
iPr_def_14 = apply(iPr_def_11,iPr_def_13),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_98,definition,
iPr_def_15 = apply(iPr_def_10,iPr_def_14),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_99,definition,
iPr_def_16 = apply(fixed_pt,iPr_def_15),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_100,plain,
iPr_def_16 != iPr_def_15,
inference(demodulation,[status(thm)],[c_89,c_95,c_96,c_94,c_97,c_93,c_98,c_99]) ).
tcf(c_140,plain,
! [X0: $i,X1: $i] : apply(apply(iPr_def_11,X0),X1) = apply(w1,apply(X0,X1)),
inference(superposition,[status(thm)],[c_94,c_53]) ).
tcf(c_141,plain,
! [X0: $i,X1: $i] : apply(apply(iPr_def_12,X0),X1) = apply(fixed_pt,apply(X0,X1)),
inference(superposition,[status(thm)],[c_95,c_53]) ).
tcf(c_145,plain,
! [X0: $i,X1: $i,X2: $i] : apply(apply(w1,X0),apply(apply(b,X1),X2)) = apply(apply(X1,apply(X2,X0)),X0),
inference(superposition,[status(thm)],[c_53,c_54]) ).
tcf(c_150,plain,
! [X0: $i] : apply(apply(X0,w1),w1) = apply(iPr_def_10,X0),
inference(superposition,[status(thm)],[c_93,c_54]) ).
tcf(c_187,plain,
! [X0: $i] : apply(w1,apply(iPr_def_13,X0)) = apply(iPr_def_14,X0),
inference(superposition,[status(thm)],[c_97,c_140]) ).
tcf(c_290,plain,
! [X0: $i,X1: $i] : apply(apply(w1,X0),apply(apply(b,iPr_def_12),X1)) = apply(fixed_pt,apply(apply(X1,X0),X0)),
inference(superposition,[status(thm)],[c_145,c_141]) ).
tcf(c_296,plain,
! [X0: $i,X1: $i] : apply(fixed_pt,apply(apply(X0,X1),X1)) = apply(apply(w1,X1),apply(iPr_def_13,X0)),
inference(light_normalisation,[status(thm)],[c_290,c_96]) ).
tcf(c_1974,plain,
! [X0: $i,X1: $i] : apply(apply(w1,X0),apply(iPr_def_13,X1)) = apply(fixed_pt,apply(apply(w1,X0),X1)),
inference(superposition,[status(thm)],[c_54,c_296]) ).
tcf(c_2968,plain,
! [X0: $i] : apply(fixed_pt,apply(apply(w1,apply(iPr_def_13,X0)),X0)) = apply(apply(w1,apply(iPr_def_13,X0)),w1),
inference(superposition,[status(thm)],[c_1974,c_54]) ).
tcf(c_2979,plain,
! [X0: $i] : apply(fixed_pt,apply(apply(iPr_def_14,X0),X0)) = apply(apply(iPr_def_14,X0),w1),
inference(light_normalisation,[status(thm)],[c_2968,c_187]) ).
tcf(c_2998,plain,
apply(fixed_pt,apply(iPr_def_10,iPr_def_14)) = apply(iPr_def_10,iPr_def_14),
inference(superposition,[status(thm)],[c_150,c_2979]) ).
tcf(c_3011,plain,
iPr_def_15 = iPr_def_16,
inference(light_normalisation,[status(thm)],[c_2998,c_98,c_99]) ).
tcf(c_3024,plain,
iPr_def_15 != iPr_def_15,
inference(demodulation,[status(thm)],[c_100,c_3011]) ).
tcf(c_3025,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_3024]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL042-2 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.38 % Computer : n026.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Fri Sep 25 07:19:54 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 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
% 0.10/0.43
% 0.10/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.43
% 0.10/0.43 % Detected problem language: tptp
% 0.10/0.45 % Proving...
% 4.12/1.31 % SZS status Started for theBenchmark.p
% 4.12/1.31 % SZS status Unsatisfiable for theBenchmark.p
% 4.12/1.31
% 4.12/1.31 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.12/1.31
% 4.12/1.31 % ------ iProver source info
% 4.12/1.31
% 4.12/1.31 % git: date: 2026-07-19 20:42:38 +0200
% 4.12/1.31 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.12/1.31 % git: non_committed_changes: false
% 4.12/1.31
% 4.12/1.31 % ------ Parsing...% successful
% 4.12/1.31
% 4.12/1.31
% 4.12/1.31 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.12/1.31
% 4.12/1.31 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 1 sf_s rm: 2 0s sf_e pe_s pe_e %
% 4.12/1.31
% 4.12/1.31 % ------ Preprocessing...% ------ preprocesses with Option_UEQ
% 4.12/1.31 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.12/1.31
% 4.12/1.31 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 4.12/1.31 % ------ Proving...
% 4.12/1.31 % ------ Problem Properties
% 4.12/1.31
% 4.12/1.31 %
% 4.12/1.31 % clauses 10
% 4.12/1.31 % conjectures 0
% 4.12/1.31 % EPR 1
% 4.12/1.31 % Horn 10
% 4.12/1.31 % unary 10
% 4.12/1.31 % binary 0
% 4.12/1.31 % lits 10
% 4.12/1.31 % lits eq 10
% 4.12/1.31 % fd_pure 0
% 4.12/1.31 % fd_pseudo 0
% 4.12/1.31 % fd_cond 0
% 4.12/1.31 % fd_pseudo_cond 0
% 4.12/1.31 % AC symbols 0
% 4.12/1.31
% 4.12/1.31 % ------ Schedule UEQ
% 4.12/1.31
% 4.12/1.31 % ------ Option_UEQ Time Limit: 10.
% 4.12/1.31
% 4.12/1.31
% 4.12/1.31 % ------
% 4.12/1.31 % Current options:
% 4.12/1.31 % ------
% 4.12/1.31
% 4.12/1.31
% 4.12/1.31 %
% 4.12/1.31
% 4.12/1.31 % ------ Proving...
% 4.12/1.31 %
% 4.12/1.31
% 4.12/1.31 % SZS status Unsatisfiable for theBenchmark.p
% 4.12/1.31
% 4.12/1.31 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.12/1.31
% 4.12/1.31
%------------------------------------------------------------------------------