%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : COL044-3 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n011.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 01:02:38 PM UTC 2026
% Result : Unsatisfiable 21.49s 19.53s
% Output : CNFRefutation 21.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 15
% Syntax : Number of formulae : 44 ( 41 unt; 11 def)
% Number of atoms : 112 ( 42 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 : 14 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 14 ( 12 usr; 12 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 47 ( 0 sgn 47 !; 0 ?; 40 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : apply(apply(apply(b,X0),X1),X2) = apply(X0,apply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_definition) ).
fof(f2,axiom,
! [X2,X0,X1] : apply(apply(apply(n,X0),X1),X2) = apply(apply(apply(X0,X2),X1),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',n_definition) ).
fof(f3,axiom,
! [X0] :
( fixed_point(X0)
| apply(X0,fixed_pt) != apply(fixed_pt,apply(X0,fixed_pt)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',strong_fixed_point) ).
fof(f4,negated_conjecture,
~ fixed_point(apply(apply(b,apply(apply(b,apply(apply(n,apply(apply(b,b),apply(apply(n,apply(n,apply(b,b))),n))),n)),b)),b)),
file('/export/starexec/sandbox2/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,X2: $i] : apply(apply(apply(X0,X1),X2),X1) = apply(apply(apply(n,X0),X2),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(apply(b,apply(apply(n,apply(apply(b,b),apply(apply(n,apply(n,apply(b,b))),n))),n)),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(n,apply(apply(b,b),apply(apply(n,apply(n,apply(b,b))),n))),n)),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(n,apply(apply(b,b),apply(apply(n,apply(n,apply(b,b))),n))),n)),b)),b),fixed_pt)) != apply(apply(apply(b,apply(apply(b,apply(apply(n,apply(apply(b,b),apply(apply(n,apply(n,apply(b,b))),n))),n)),b)),b),fixed_pt),
inference(unflattening,[status(thm)],[c_77]) ).
tcf(c_89,plain,
apply(fixed_pt,apply(apply(apply(n,apply(apply(b,b),apply(apply(n,apply(n,apply(b,b))),n))),n),apply(b,apply(b,fixed_pt)))) != apply(apply(apply(n,apply(apply(b,b),apply(apply(n,apply(n,apply(b,b))),n))),n),apply(b,apply(b,fixed_pt))),
inference(demodulation,[status(thm)],[c_78,c_53]) ).
tcf(c_93,definition,
iPr_def_10 = apply(b,b),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_94,definition,
iPr_def_11 = apply(n,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_95,definition,
iPr_def_12 = apply(n,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_96,definition,
iPr_def_13 = apply(iPr_def_12,n),
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(n,iPr_def_14),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_99,definition,
iPr_def_16 = apply(iPr_def_15,n),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_100,definition,
iPr_def_17 = apply(b,fixed_pt),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_101,definition,
iPr_def_18 = apply(b,iPr_def_17),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_102,definition,
iPr_def_19 = apply(iPr_def_16,iPr_def_18),
introduced(definition,[new_symbols(definition,[iPr_def_19])],[]) ).
tcf(c_103,definition,
iPr_def_20 = apply(fixed_pt,iPr_def_19),
introduced(definition,[new_symbols(definition,[iPr_def_20])],[]) ).
tcf(c_104,plain,
iPr_def_20 != iPr_def_19,
inference(demodulation,[status(thm)],[c_89,c_100,c_101,c_94,c_95,c_96,c_93,c_97,c_98,c_99,c_102,c_103]) ).
tcf(c_152,plain,
! [X0: $i,X1: $i] : apply(apply(iPr_def_10,X0),X1) = apply(b,apply(X0,X1)),
inference(superposition,[status(thm)],[c_93,c_53]) ).
tcf(c_153,plain,
! [X0: $i,X1: $i] : apply(apply(iPr_def_17,X0),X1) = apply(fixed_pt,apply(X0,X1)),
inference(superposition,[status(thm)],[c_100,c_53]) ).
tcf(c_156,plain,
! [X0: $i] : apply(b,apply(iPr_def_13,X0)) = apply(iPr_def_14,X0),
inference(superposition,[status(thm)],[c_97,c_152]) ).
tcf(c_158,plain,
! [X0: $i,X1: $i,X2: $i] : apply(apply(apply(iPr_def_14,X0),X1),X2) = apply(apply(iPr_def_13,X0),apply(X1,X2)),
inference(superposition,[status(thm)],[c_156,c_53]) ).
tcf(c_163,plain,
! [X0: $i,X1: $i,X2: $i] : apply(apply(apply(n,apply(b,X0)),X1),X2) = apply(apply(X0,apply(X2,X1)),X2),
inference(superposition,[status(thm)],[c_53,c_54]) ).
tcf(c_178,plain,
! [X0: $i,X1: $i] : apply(apply(apply(iPr_def_10,X0),X1),X0) = apply(apply(iPr_def_11,X1),X0),
inference(superposition,[status(thm)],[c_94,c_54]) ).
tcf(c_179,plain,
! [X0: $i,X1: $i] : apply(apply(apply(iPr_def_11,X0),X1),X0) = apply(apply(iPr_def_12,X1),X0),
inference(superposition,[status(thm)],[c_95,c_54]) ).
tcf(c_180,plain,
! [X0: $i,X1: $i] : apply(apply(apply(iPr_def_14,X0),X1),X0) = apply(apply(iPr_def_15,X1),X0),
inference(superposition,[status(thm)],[c_98,c_54]) ).
tcf(c_188,plain,
! [X0: $i,X1: $i] : apply(apply(b,apply(X0,X1)),X0) = apply(apply(iPr_def_11,X1),X0),
inference(light_normalisation,[status(thm)],[c_178,c_152]) ).
tcf(c_200,plain,
! [X0: $i,X1: $i] : apply(apply(iPr_def_13,X0),apply(X1,X0)) = apply(apply(iPr_def_15,X1),X0),
inference(demodulation,[status(thm)],[c_180,c_158]) ).
tcf(c_332,plain,
! [X0: $i,X1: $i,X2: $i] : apply(apply(X0,X1),apply(X0,X2)) = apply(apply(apply(iPr_def_11,X1),X0),X2),
inference(superposition,[status(thm)],[c_188,c_53]) ).
tcf(c_446,plain,
! [X0: $i,X1: $i] : apply(apply(apply(n,apply(b,iPr_def_17)),X0),X1) = apply(fixed_pt,apply(apply(X1,X0),X1)),
inference(superposition,[status(thm)],[c_163,c_153]) ).
tcf(c_459,plain,
! [X0: $i,X1: $i] : apply(fixed_pt,apply(apply(X0,X1),X0)) = apply(apply(apply(n,iPr_def_18),X1),X0),
inference(light_normalisation,[status(thm)],[c_446,c_101]) ).
tcf(c_790,plain,
! [X0: $i,X1: $i] : apply(apply(X0,X1),apply(X0,X1)) = apply(apply(iPr_def_12,X0),X1),
inference(superposition,[status(thm)],[c_332,c_179]) ).
tcf(c_2875,plain,
! [X0: $i] : apply(fixed_pt,apply(apply(X0,apply(n,iPr_def_18)),X0)) = apply(apply(apply(iPr_def_12,n),iPr_def_18),X0),
inference(superposition,[status(thm)],[c_790,c_459]) ).
tcf(c_2911,plain,
! [X0: $i] : apply(fixed_pt,apply(apply(X0,apply(n,iPr_def_18)),X0)) = apply(apply(iPr_def_13,iPr_def_18),X0),
inference(light_normalisation,[status(thm)],[c_2875,c_96]) ).
tcf(c_5969,plain,
apply(fixed_pt,apply(apply(apply(iPr_def_12,n),iPr_def_18),apply(n,iPr_def_18))) = apply(apply(iPr_def_13,iPr_def_18),apply(n,iPr_def_18)),
inference(superposition,[status(thm)],[c_790,c_2911]) ).
tcf(c_5996,plain,
apply(fixed_pt,apply(apply(iPr_def_13,iPr_def_18),apply(n,iPr_def_18))) = apply(apply(iPr_def_13,iPr_def_18),apply(n,iPr_def_18)),
inference(light_normalisation,[status(thm)],[c_5969,c_96]) ).
tcf(c_27144,plain,
iPr_def_19 = iPr_def_20,
inference(demodulation,[status(thm)],[c_5996,c_99,c_102,c_103,c_200]) ).
tcf(c_27167,plain,
iPr_def_19 != iPr_def_19,
inference(demodulation,[status(thm)],[c_104,c_27144]) ).
tcf(c_27168,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_27167]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL044-3 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.34 % Computer : n011.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/15.62 % CPULimit : 300
% 0.09/15.62 % WCLimit : 300
% 0.09/15.62 % DateTime : Fri Sep 25 07:19:00 UTC 2026
% 0.09/15.62 % CPUTime :
% 0.09/15.62 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/15.66 Running first-order theorem proving
% 0.09/15.66 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
% 0.09/15.67
% 0.09/15.67 % ======== iProver multi-core TPTP/SMT =========
% 0.09/15.67
% 0.09/15.67 % Detected problem language: tptp
% 0.09/15.68 % Proving...
% 21.49/19.53 % SZS status Started for theBenchmark.p
% 21.49/19.53 % SZS status Unsatisfiable for theBenchmark.p
% 21.49/19.53
% 21.49/19.53 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 21.49/19.53
% 21.49/19.53 % ------ iProver source info
% 21.49/19.53
% 21.49/19.53 % git: date: 2026-07-19 20:42:38 +0200
% 21.49/19.53 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 21.49/19.53 % git: non_committed_changes: false
% 21.49/19.53
% 21.49/19.53 % ------ Parsing...% successful
% 21.49/19.53
% 21.49/19.53
% 21.49/19.53 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 21.49/19.53
% 21.49/19.53 % ------ 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 %
% 21.49/19.53
% 21.49/19.53 % ------ Preprocessing...% ------ preprocesses with Option_UEQ
% 21.49/19.53 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 21.49/19.53
% 21.49/19.53 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 21.49/19.53 % ------ Proving...
% 21.49/19.53 % ------ Problem Properties
% 21.49/19.53
% 21.49/19.53 %
% 21.49/19.53 % clauses 14
% 21.49/19.53 % conjectures 0
% 21.49/19.53 % EPR 1
% 21.49/19.53 % Horn 14
% 21.49/19.53 % unary 14
% 21.49/19.53 % binary 0
% 21.49/19.53 % lits 14
% 21.49/19.53 % lits eq 14
% 21.49/19.53 % fd_pure 0
% 21.49/19.53 % fd_pseudo 0
% 21.49/19.53 % fd_cond 0
% 21.49/19.53 % fd_pseudo_cond 0
% 21.49/19.53 % AC symbols 0
% 21.49/19.53
% 21.49/19.53 % ------ Schedule UEQ
% 21.49/19.53
% 21.49/19.53 % ------ Option_UEQ Time Limit: 10.
% 21.49/19.53
% 21.49/19.53
% 21.49/19.53 % ------
% 21.49/19.53 % Current options:
% 21.49/19.53 % ------
% 21.49/19.53
% 21.49/19.53
% 21.49/19.53 %
% 21.49/19.53
% 21.49/19.53 % ------ Proving...
% 21.49/19.53 %
% 21.49/19.53
% 21.49/19.53 % SZS status Unsatisfiable for theBenchmark.p
% 21.49/19.53
% 21.49/19.53 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 21.49/19.53
% 21.49/19.53
%------------------------------------------------------------------------------