%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : COL003-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n005.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 01:02:30 PM UTC 2026
% Result : Unsatisfiable 2.30s 1.28s
% Output : CNFRefutation 2.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of formulae : 30 ( 27 unt; 6 def)
% Number of atoms : 65 ( 28 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 : 7 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 7 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 24 ( 0 sgn 24 !; 0 ?; 18 :)
% 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(w,X0),X1) = apply(apply(X0,X1),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',w_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(w,w)),apply(apply(b,w),apply(apply(b,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(w,X0),X1),
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(w,w)),apply(apply(b,w),apply(apply(b,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(w,w)),apply(apply(b,w),apply(apply(b,b),b))) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_55,c_56]) ).
tcf(c_78,plain,
apply(fixed_pt,apply(apply(apply(b,apply(w,w)),apply(apply(b,w),apply(apply(b,b),b))),fixed_pt)) != apply(apply(apply(b,apply(w,w)),apply(apply(b,w),apply(apply(b,b),b))),fixed_pt),
inference(unflattening,[status(thm)],[c_77]) ).
tcf(c_89,plain,
apply(fixed_pt,apply(apply(w,w),apply(w,apply(b,apply(b,fixed_pt))))) != apply(apply(w,w),apply(w,apply(b,apply(b,fixed_pt)))),
inference(demodulation,[status(thm)],[c_78,c_53]) ).
tcf(c_93,definition,
iPr_def_10 = apply(w,w),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_94,definition,
iPr_def_11 = apply(b,fixed_pt),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_95,definition,
iPr_def_12 = apply(b,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_96,definition,
iPr_def_13 = apply(w,iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_97,definition,
iPr_def_14 = apply(iPr_def_10,iPr_def_13),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_98,definition,
iPr_def_15 = apply(fixed_pt,iPr_def_14),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_99,plain,
iPr_def_15 != iPr_def_14,
inference(demodulation,[status(thm)],[c_89,c_94,c_95,c_96,c_93,c_97,c_98]) ).
tcf(c_143,plain,
! [X0: $i] : apply(apply(iPr_def_12,X0),X0) = apply(iPr_def_13,X0),
inference(superposition,[status(thm)],[c_96,c_54]) ).
tcf(c_147,plain,
! [X0: $i] : apply(apply(X0,X0),X0) = apply(apply(w,w),X0),
inference(superposition,[status(thm)],[c_54,c_54]) ).
tcf(c_148,plain,
! [X0: $i] : apply(apply(X0,X0),X0) = apply(iPr_def_10,X0),
inference(light_normalisation,[status(thm)],[c_147,c_93]) ).
tcf(c_151,plain,
! [X0: $i,X1: $i] : apply(apply(iPr_def_11,X0),X1) = apply(fixed_pt,apply(X0,X1)),
inference(superposition,[status(thm)],[c_94,c_53]) ).
tcf(c_152,plain,
! [X0: $i,X1: $i] : apply(apply(iPr_def_12,X0),X1) = apply(iPr_def_11,apply(X0,X1)),
inference(superposition,[status(thm)],[c_95,c_53]) ).
tcf(c_165,plain,
! [X0: $i] : apply(iPr_def_11,apply(X0,X0)) = apply(iPr_def_13,X0),
inference(demodulation,[status(thm)],[c_143,c_152]) ).
tcf(c_180,plain,
! [X0: $i,X1: $i] : apply(fixed_pt,apply(apply(X0,X0),X1)) = apply(apply(iPr_def_13,X0),X1),
inference(superposition,[status(thm)],[c_165,c_151]) ).
tcf(c_400,plain,
! [X0: $i] : apply(apply(iPr_def_13,X0),X0) = apply(fixed_pt,apply(iPr_def_10,X0)),
inference(superposition,[status(thm)],[c_148,c_180]) ).
tcf(c_443,plain,
apply(fixed_pt,apply(iPr_def_10,iPr_def_13)) = apply(iPr_def_10,iPr_def_13),
inference(superposition,[status(thm)],[c_400,c_148]) ).
tcf(c_446,plain,
iPr_def_14 = iPr_def_15,
inference(light_normalisation,[status(thm)],[c_443,c_97,c_98]) ).
tcf(c_451,plain,
iPr_def_14 != iPr_def_14,
inference(demodulation,[status(thm)],[c_99,c_446]) ).
tcf(c_452,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_451]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL003-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n005.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 07:09:03 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 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
% 0.09/0.42
% 0.09/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.42
% 0.09/0.42 % Detected problem language: tptp
% 0.09/0.43 % Proving...
% 2.30/1.28 % SZS status Started for theBenchmark.p
% 2.30/1.28 % SZS status Unsatisfiable for theBenchmark.p
% 2.30/1.28
% 2.30/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.30/1.28
% 2.30/1.28 % ------ iProver source info
% 2.30/1.28
% 2.30/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 2.30/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.30/1.28 % git: non_committed_changes: false
% 2.30/1.28
% 2.30/1.28 % ------ Parsing...% successful
% 2.30/1.28
% 2.30/1.28
% 2.30/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.30/1.28
% 2.30/1.28 % ------ 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 %
% 2.30/1.28
% 2.30/1.28 % ------ Preprocessing...% ------ preprocesses with Option_UEQ
% 2.30/1.28 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.30/1.28
% 2.30/1.28 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 2.30/1.28 % ------ Proving...
% 2.30/1.28 % ------ Problem Properties
% 2.30/1.28
% 2.30/1.28 %
% 2.30/1.28 % clauses 9
% 2.30/1.28 % conjectures 0
% 2.30/1.28 % EPR 1
% 2.30/1.28 % Horn 9
% 2.30/1.28 % unary 9
% 2.30/1.28 % binary 0
% 2.30/1.28 % lits 9
% 2.30/1.28 % lits eq 9
% 2.30/1.28 % fd_pure 0
% 2.30/1.28 % fd_pseudo 0
% 2.30/1.28 % fd_cond 0
% 2.30/1.28 % fd_pseudo_cond 0
% 2.30/1.28 % AC symbols 0
% 2.30/1.28
% 2.30/1.28 % ------ Schedule UEQ
% 2.30/1.28
% 2.30/1.28 % ------ Option_UEQ Time Limit: 10.
% 2.30/1.28
% 2.30/1.28
% 2.30/1.28 % ------
% 2.30/1.28 % Current options:
% 2.30/1.28 % ------
% 2.30/1.28
% 2.30/1.28
% 2.30/1.28 %
% 2.30/1.28
% 2.30/1.28 % ------ Proving...
% 2.30/1.28 %
% 2.30/1.28
% 2.30/1.28 % SZS status Unsatisfiable for theBenchmark.p
% 2.30/1.28
% 2.30/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.30/1.28
% 2.30/1.28
%------------------------------------------------------------------------------