%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : COL030-1 : 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 : n009.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 01:02:35 PM UTC 2026
% Result : Unsatisfiable 3.92s 6.52s
% Output : CNFRefutation 3.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 3
% Syntax : Number of formulae : 12 ( 12 unt; 0 def)
% Number of atoms : 12 ( 11 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 6 ( 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 : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 18 ( 0 sgn 18 !; 0 ?; 12 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : apply(apply(apply(s,X0),X1),X2) = apply(apply(X0,X2),apply(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s_definition) ).
fof(f2,axiom,
! [X0,X1] : apply(apply(l,X0),X1) = apply(X0,apply(X1,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l_definition) ).
fof(f3,negated_conjecture,
! [X0] : apply(X0,f(X0)) != apply(f(X0),apply(X0,f(X0))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_fixed_point) ).
tcf(c_52,plain,
! [X0: $i,X1: $i,X2: $i] : apply(apply(X0,X1),apply(X2,X1)) = apply(apply(apply(s,X0),X2),X1),
inference(cnf_transformation,[],[f1]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] : apply(X0,apply(X1,X1)) = apply(apply(l,X0),X1),
inference(cnf_transformation,[],[f2]) ).
tcf(c_54,negated_conjecture,
! [X0: $i] : apply(f(X0),apply(X0,f(X0))) != apply(X0,f(X0)),
inference(cnf_transformation,[],[f3]) ).
tcf(c_113,plain,
! [X0: $i,X1: $i,X2: $i] : apply(X0,apply(apply(apply(s,X1),X1),X2)) = apply(apply(l,X0),apply(X1,X2)),
inference(superposition,[status(thm)],[c_52,c_53]) ).
tcf(c_246,plain,
! [X0: $i,X1: $i] : apply(apply(X0,f(apply(apply(s,X0),X1))),apply(X1,f(apply(apply(s,X0),X1)))) = apply(apply(apply(s,X0),X1),f(apply(apply(s,X0),X1))),
inference(instantiation,[status(thm)],[c_52]) ).
tcf(c_248,plain,
apply(apply(l,f(apply(apply(s,l),l))),apply(l,f(apply(apply(s,l),l)))) = apply(apply(apply(s,l),l),f(apply(apply(s,l),l))),
inference(instantiation,[status(thm)],[c_246]) ).
tcf(c_637,plain,
! [X0: $i] : apply(apply(l,f(apply(apply(s,X0),X0))),apply(X0,f(apply(apply(s,X0),X0)))) != apply(apply(apply(s,X0),X0),f(apply(apply(s,X0),X0))),
inference(superposition,[status(thm)],[c_113,c_54]) ).
tcf(c_677,plain,
apply(apply(l,f(apply(apply(s,l),l))),apply(l,f(apply(apply(s,l),l)))) != apply(apply(apply(s,l),l),f(apply(apply(s,l),l))),
inference(instantiation,[status(thm)],[c_637]) ).
tcf(c_678,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_677,c_248]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL030-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/5.59 % Computer : n009.cluster.edu
% 0.11/5.59 % Model : x86_64 x86_64
% 0.11/5.59 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.59 % Memory : 8046.5625MB
% 0.11/5.59 % OS : Linux 6.8.0-71-generic
% 0.11/5.59 % CPULimit : 300
% 0.11/5.59 % WCLimit : 300
% 0.11/5.60 % DateTime : Fri Sep 25 07:15:19 UTC 2026
% 0.11/5.60 % CPUTime :
% 0.17/5.60 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.17/5.64 Running UEQ theorem proving
% 0.17/5.64 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
% 0.17/5.65
% 0.17/5.65 % ======== iProver multi-core TPTP/SMT =========
% 0.17/5.65
% 0.17/5.65 % Detected problem language: tptp
% 0.17/5.66 % Proving...
% 3.92/6.52 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 3.92/6.52 % SZS status Started for theBenchmark.p
% 3.92/6.52 % SZS status Unsatisfiable for theBenchmark.p
% 3.92/6.52
% 3.92/6.52 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.92/6.52
% 3.92/6.52 % ------ iProver source info
% 3.92/6.52
% 3.92/6.52 % git: date: 2026-07-19 20:42:38 +0200
% 3.92/6.52 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.92/6.52 % git: non_committed_changes: false
% 3.92/6.52
% 3.92/6.52 % ------ Parsing...% successful
% 3.92/6.52
% 3.92/6.52
% 3.92/6.52 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.92/6.52
% 3.92/6.52 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 3.92/6.52
% 3.92/6.52 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.92/6.52
% 3.92/6.52 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 3.92/6.52 % ------ Proving...
% 3.92/6.52 % ------ Problem Properties
% 3.92/6.52
% 3.92/6.52 %
% 3.92/6.52 % clauses 3
% 3.92/6.52 % conjectures 1
% 3.92/6.52 % EPR 0
% 3.92/6.52 % Horn 3
% 3.92/6.52 % unary 3
% 3.92/6.52 % binary 0
% 3.92/6.53 % lits 3
% 3.92/6.53 % lits eq 3
% 3.92/6.53 % fd_pure 0
% 3.92/6.53 % fd_pseudo 0
% 3.92/6.53 % fd_cond 0
% 3.92/6.53 % fd_pseudo_cond 0
% 3.92/6.53 % AC symbols 0
% 3.92/6.53
% 3.92/6.53 % ------ Input Options Time Limit: Unbounded
% 3.92/6.53
% 3.92/6.53
% 3.92/6.53 % ------
% 3.92/6.53 % Current options:
% 3.92/6.53 % ------
% 3.92/6.53
% 3.92/6.53
% 3.92/6.53 %
% 3.92/6.53
% 3.92/6.53 % ------ Proving...
% 3.92/6.53 %
% 3.92/6.53
% 3.92/6.53 % SZS status Unsatisfiable for theBenchmark.p
% 3.92/6.53
% 3.92/6.53 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.92/6.53
% 3.92/6.53
%------------------------------------------------------------------------------