%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : COL044-9 : TPTP v9.3.1. Released v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n017.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 01:02:39 PM UTC 2026
% Result : Unsatisfiable 13.66s 2.95s
% Output : CNFRefutation 13.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 25 ( 25 unt; 0 def)
% Number of atoms : 25 ( 24 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 12 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 48 ( 0 sgn 48 !; 0 ?; 42 :)
% 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,
! [X2,X0,X1] : apply(apply(apply(n,X0),X1),X2) = apply(apply(apply(X0,X2),X1),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',n_definition) ).
fof(f3,axiom,
strong_fixed_point = apply(apply(b,apply(apply(b,apply(apply(n,apply(n,apply(apply(b,apply(b,b)),apply(n,apply(n,apply(b,b)))))),n)),b)),b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',strong_fixed_point) ).
fof(f4,negated_conjecture,
apply(strong_fixed_point,fixed_pt) != apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),
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,X2: $i] : apply(apply(apply(X0,X1),X2),X1) = apply(apply(apply(n,X0),X2),X1),
inference(cnf_transformation,[],[f2]) ).
tcf(c_55,plain,
apply(apply(b,apply(apply(b,apply(apply(n,apply(n,apply(apply(b,apply(b,b)),apply(n,apply(n,apply(b,b)))))),n)),b)),b) = strong_fixed_point,
inference(cnf_transformation,[],[f3]) ).
tcf(c_56,negated_conjecture,
apply(fixed_pt,apply(strong_fixed_point,fixed_pt)) != apply(strong_fixed_point,fixed_pt),
inference(cnf_transformation,[],[f4]) ).
tcf(c_97,plain,
! [X0: $i] : apply(apply(apply(b,apply(apply(n,apply(n,apply(apply(b,apply(b,b)),apply(n,apply(n,apply(b,b)))))),n)),b),apply(b,X0)) = apply(strong_fixed_point,X0),
inference(superposition,[status(thm)],[c_55,c_53]) ).
tcf(c_99,plain,
! [X0: $i] : apply(apply(apply(n,apply(n,apply(apply(b,apply(b,b)),apply(n,apply(n,apply(b,b)))))),n),apply(b,apply(b,X0))) = apply(strong_fixed_point,X0),
inference(demodulation,[status(thm)],[c_97,c_53]) ).
tcf(c_102,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_107,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : apply(apply(apply(n,apply(apply(b,X0),X1)),X2),X3) = apply(apply(apply(X0,apply(X1,X3)),X2),X3),
inference(superposition,[status(thm)],[c_53,c_54]) ).
tcf(c_115,plain,
! [X0: $i,X1: $i,X2: $i] : apply(apply(apply(apply(n,X0),X1),X2),X1) = apply(apply(apply(n,apply(X0,X2)),X2),X1),
inference(superposition,[status(thm)],[c_54,c_54]) ).
tcf(c_310,plain,
! [X0: $i,X1: $i,X2: $i] : apply(apply(apply(apply(n,apply(b,b)),X0),X1),X2) = apply(apply(X1,X0),apply(X1,X2)),
inference(superposition,[status(thm)],[c_102,c_53]) ).
tcf(c_311,plain,
! [X0: $i,X1: $i,X2: $i] : apply(apply(apply(n,apply(b,apply(b,X0))),X1),X2) = apply(X0,apply(apply(X2,X1),X2)),
inference(superposition,[status(thm)],[c_102,c_53]) ).
tcf(c_520,plain,
! [X0: $i,X1: $i,X2: $i] : apply(apply(apply(n,apply(X0,X1)),X1),X2) = apply(apply(apply(n,apply(n,X0)),X1),X2),
inference(demodulation,[status(thm)],[c_115,c_54]) ).
tcf(c_529,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : apply(apply(apply(n,apply(n,apply(apply(b,X0),X1))),X2),X3) = apply(apply(apply(n,apply(X0,apply(X1,X2))),X2),X3),
inference(superposition,[status(thm)],[c_53,c_520]) ).
tcf(c_583,plain,
! [X0: $i] : apply(apply(apply(n,apply(apply(b,b),apply(apply(n,apply(n,apply(b,b))),n))),n),apply(b,apply(b,X0))) = apply(strong_fixed_point,X0),
inference(demodulation,[status(thm)],[c_99,c_529]) ).
tcf(c_2070,plain,
! [X0: $i,X1: $i,X2: $i] : apply(apply(apply(n,apply(apply(b,b),X0)),X1),X2) = apply(apply(X0,X2),apply(X1,X2)),
inference(superposition,[status(thm)],[c_107,c_53]) ).
tcf(c_3423,plain,
! [X0: $i,X1: $i] : apply(apply(apply(n,apply(n,apply(b,b))),X0),X1) = apply(apply(X0,X1),apply(X0,X1)),
inference(superposition,[status(thm)],[c_310,c_54]) ).
tcf(c_9404,plain,
! [X0: $i] : apply(apply(apply(apply(n,apply(n,apply(b,b))),n),apply(b,apply(b,X0))),apply(n,apply(b,apply(b,X0)))) = apply(strong_fixed_point,X0),
inference(superposition,[status(thm)],[c_2070,c_583]) ).
tcf(c_11521,plain,
! [X0: $i] : apply(apply(apply(n,apply(b,apply(b,X0))),apply(n,apply(b,apply(b,X0)))),apply(n,apply(b,apply(b,X0)))) = apply(strong_fixed_point,X0),
inference(superposition,[status(thm)],[c_3423,c_9404]) ).
tcf(c_11614,plain,
! [X0: $i,X1: $i] : apply(apply(apply(n,apply(b,apply(b,X0))),apply(n,apply(b,apply(b,X1)))),apply(n,apply(b,apply(b,X1)))) = apply(X0,apply(strong_fixed_point,X1)),
inference(superposition,[status(thm)],[c_11521,c_311]) ).
tcf(c_11616,plain,
! [X0: $i] : apply(X0,apply(strong_fixed_point,X0)) = apply(strong_fixed_point,X0),
inference(demodulation,[status(thm)],[c_11521,c_11614]) ).
tcf(c_11617,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_56,c_11616]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : COL044-9 : TPTP v9.3.1. Released v2.1.0.
% 0.00/0.07 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.20/0.45 % Computer : n017.cluster.edu
% 0.20/0.45 % Model : x86_64 x86_64
% 0.20/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.45 % Memory : 8046.5625MB
% 0.20/0.45 % OS : Linux 6.8.0-71-generic
% 0.20/0.46 % CPULimit : 300
% 0.20/0.46 % WCLimit : 300
% 0.20/0.46 % DateTime : Fri Sep 25 07:16:02 UTC 2026
% 0.20/0.46 % CPUTime :
% 0.20/0.46 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.24/0.50 Running UEQ theorem proving
% 0.24/0.51 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s ueq_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.24/0.52
% 0.24/0.52 % ======== iProver multi-core TPTP/SMT =========
% 0.24/0.52
% 0.24/0.52 % Detected problem language: tptp
% 0.24/0.54 % Proving...
% 13.66/2.95 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 13.66/2.95 % SZS status Started for theBenchmark.p
% 13.66/2.95 % SZS status Unsatisfiable for theBenchmark.p
% 13.66/2.95
% 13.66/2.95 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 13.66/2.95
% 13.66/2.95 % ------ iProver source info
% 13.66/2.95
% 13.66/2.95 % git: date: 2026-07-19 20:42:38 +0200
% 13.66/2.95 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 13.66/2.95 % git: non_committed_changes: false
% 13.66/2.95
% 13.66/2.95 % ------ Parsing...% successful
% 13.66/2.95
% 13.66/2.95
% 13.66/2.95 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 13.66/2.95
% 13.66/2.95 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 13.66/2.95
% 13.66/2.95 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 13.66/2.95
% 13.66/2.95 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 13.66/2.95 % ------ Proving...
% 13.66/2.95 % ------ Problem Properties
% 13.66/2.95
% 13.66/2.95 %
% 13.66/2.95 % clauses 4
% 13.66/2.95 % conjectures 1
% 13.66/2.95 % EPR 0
% 13.66/2.95 % Horn 4
% 13.66/2.95 % unary 4
% 13.66/2.95 % binary 0
% 13.66/2.95 % lits 4
% 13.66/2.95 % lits eq 4
% 13.66/2.95 % fd_pure 0
% 13.66/2.95 % fd_pseudo 0
% 13.66/2.95 % fd_cond 0
% 13.66/2.95 % fd_pseudo_cond 0
% 13.66/2.95 % AC symbols 0
% 13.66/2.95
% 13.66/2.95 % ------ Input Options Time Limit: Unbounded
% 13.66/2.95
% 13.66/2.95
% 13.66/2.95 % ------
% 13.66/2.95 % Current options:
% 13.66/2.95 % ------
% 13.66/2.95
% 13.66/2.95
% 13.66/2.95 %
% 13.66/2.95
% 13.66/2.95 % ------ Proving...
% 13.66/2.95 %
% 13.66/2.95
% 13.66/2.95 % SZS status Unsatisfiable for theBenchmark.p
% 13.66/2.95
% 13.66/2.95 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 13.66/2.95
% 13.66/2.95
%------------------------------------------------------------------------------