%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET041-3 : 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 : n018.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 02:46:13 PM UTC 2026
% Result : Unsatisfiable 4.50s 1.31s
% Output : CNFRefutation 4.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 6
% Syntax : Number of formulae : 17 ( 7 unt; 0 def)
% Number of atoms : 34 ( 5 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 36 ( 19 ~; 17 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 17 ( 0 sgn 17 !; 0 ?; 9 :)
% Comments :
%------------------------------------------------------------------------------
fof(f166,axiom,
! [X0,X1] :
( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',two_sets_equal) ).
fof(f186,axiom,
! [X2,X0,X1] :
( subset(apply(X2,apply(X0,X1)),apply(compose(X2,X0),X1))
| ~ member(X1,domain_of(X0))
| ~ function(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apply_for_composition1) ).
fof(f187,axiom,
! [X2,X0,X1] :
( subset(apply(compose(X1,X0),X2),apply(X1,apply(X0,X2)))
| ~ function(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apply_for_composition2) ).
fof(f188,axiom,
function(a_function),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_function) ).
fof(f189,axiom,
member(a,domain_of(a_function)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',member_of_domain) ).
fof(f190,negated_conjecture,
apply(another_function,apply(a_function,a)) != apply(compose(another_function,a_function),a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_apply_for_composition3) ).
tcf(c_218,plain,
function(a_function),
inference(cnf_transformation,[],[f188]) ).
tcf(c_219,plain,
member(a,domain_of(a_function)),
inference(cnf_transformation,[],[f189]) ).
tcf(c_220,negated_conjecture,
apply(compose(another_function,a_function),a) != apply(another_function,apply(a_function,a)),
inference(cnf_transformation,[],[f190]) ).
tcf(c_221,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(apply(compose(X1,X0),X2),apply(X1,apply(X0,X2)))
| ~ function(X0) ),
inference(cnf_transformation,[],[f187]) ).
tcf(c_226,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(apply(X2,apply(X1,X0)),apply(compose(X2,X1),X0))
| ~ function(X1)
| ~ member(X0,domain_of(X1)) ),
inference(cnf_transformation,[],[f186]) ).
tcf(c_237,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f166]) ).
tcf(c_1814,plain,
( ( apply(compose(another_function,a_function),a) = apply(another_function,apply(a_function,a)) )
| ~ subset(apply(another_function,apply(a_function,a)),apply(compose(another_function,a_function),a))
| ~ subset(apply(compose(another_function,a_function),a),apply(another_function,apply(a_function,a))) ),
inference(instantiation,[status(thm)],[c_237]) ).
tcf(c_1936,plain,
! [X0: $i] :
( subset(apply(X0,apply(a_function,a)),apply(compose(X0,a_function),a))
| ~ function(a_function)
| ~ member(a,domain_of(a_function)) ),
inference(instantiation,[status(thm)],[c_226]) ).
tcf(c_2238,plain,
( subset(apply(compose(another_function,a_function),a),apply(another_function,apply(a_function,a)))
| ~ function(a_function) ),
inference(instantiation,[status(thm)],[c_221]) ).
tcf(c_3883,plain,
( subset(apply(another_function,apply(a_function,a)),apply(compose(another_function,a_function),a))
| ~ function(a_function)
| ~ member(a,domain_of(a_function)) ),
inference(instantiation,[status(thm)],[c_1936]) ).
tcf(c_3884,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_3883,c_2238,c_1814,c_220,c_219,c_218]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET041-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.37 % Computer : n018.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Thu Sep 24 09:25:48 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 0.11/0.43
% 0.11/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.43
% 0.11/0.43 % Detected problem language: tptp
% 0.11/0.44 % Proving...
% 4.50/1.31 % SZS status Started for theBenchmark.p
% 4.50/1.31 % SZS status Unsatisfiable for theBenchmark.p
% 4.50/1.31
% 4.50/1.31 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.50/1.31
% 4.50/1.31 % ------ iProver source info
% 4.50/1.31
% 4.50/1.31 % git: date: 2026-07-19 20:42:38 +0200
% 4.50/1.31 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.50/1.31 % git: non_committed_changes: false
% 4.50/1.31
% 4.50/1.31 % ------ Parsing...% successful
% 4.50/1.31
% 4.50/1.31
% 4.50/1.31 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.50/1.31
% 4.50/1.31 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 4.50/1.31
% 4.50/1.31 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.50/1.31
% 4.50/1.31 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.50/1.31 % ------ Proving...
% 4.50/1.31 % ------ Problem Properties
% 4.50/1.31
% 4.50/1.31 %
% 4.50/1.31 % clauses 36
% 4.50/1.31 % conjectures 1
% 4.50/1.31 % EPR 7
% 4.50/1.31 % Horn 36
% 4.50/1.31 % unary 5
% 4.50/1.31 % binary 10
% 4.50/1.31 % lits 100
% 4.50/1.31 % lits eq 11
% 4.50/1.31 % fd_pure 0
% 4.50/1.31 % fd_pseudo 0
% 4.50/1.31 % fd_cond 0
% 4.50/1.31 % fd_pseudo_cond 5
% 4.50/1.31 % AC symbols 0
% 4.50/1.31
% 4.50/1.31 % ------ Schedule dynamic 5 is on
% 4.50/1.31
% 4.50/1.31 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.50/1.31
% 4.50/1.31
% 4.50/1.31 % ------
% 4.50/1.31 % Current options:
% 4.50/1.31 % ------
% 4.50/1.31
% 4.50/1.31
% 4.50/1.31 %
% 4.50/1.31
% 4.50/1.31 % ------ Proving...
% 4.50/1.31 %
% 4.50/1.31
% 4.50/1.31 % SZS status Unsatisfiable for theBenchmark.p
% 4.50/1.31
% 4.50/1.31 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.50/1.31
% 4.50/1.31
%------------------------------------------------------------------------------