%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : MGT036-2 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n002.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 02:12:31 PM UTC 2026
% Result : Unsatisfiable 1.77s 1.27s
% Output : CNFRefutation 1.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 14
% Syntax : Number of formulae : 57 ( 21 unt; 2 def)
% Number of atoms : 134 ( 2 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 140 ( 74 ~; 66 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 12 ( 10 usr; 5 prp; 0-4 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 88 ( 0 sgn 88 !; 0 ?; 61 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X3,X0,X1] :
( subpopulations(X2,X1,X0,X3)
| ~ subpopulations(X1,X2,X0,X3)
| ~ environment(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_symmetry_of_subpopulations_1) ).
fof(f2,axiom,
! [X0,X1] :
( in_environment(X0,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_time_point_occur_2) ).
fof(f3,axiom,
! [X2,X0,X1] :
( ~ greater(zero,growth_rate(X1,X2))
| environment(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_growth_rate_relationships_3) ).
fof(f4,axiom,
! [X2,X3,X0,X1] :
( ~ greater(zero,growth_rate(X0,X3))
| subpopulations(X0,X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_growth_rate_relationships_4) ).
fof(f5,axiom,
! [X0,X1] :
( ~ greater(zero,growth_rate(X0,X1))
| ~ greater_or_equal(growth_rate(X0,X1),zero) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_growth_rate_relationships_5) ).
fof(f8,axiom,
! [X2,X3,X0,X1] :
( greater_or_equal(growth_rate(X2,X3),zero)
| ~ outcompetes(X2,X1,X3)
| ~ subpopulations(X1,X2,X0,X3)
| ~ environment(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_8) ).
fof(f9,axiom,
! [X2,X3,X0,X1] :
( greater(zero,growth_rate(X1,X3))
| ~ outcompetes(X2,X1,X3)
| ~ subpopulations(X1,X2,X0,X3)
| ~ environment(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_9) ).
fof(f10,axiom,
greater(resilience(efficient_producers),resilience(first_movers)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a2_10) ).
fof(f11,axiom,
! [X2,X3,X0,X1] :
( ~ greater(zero,growth_rate(X3,X1))
| ~ greater(resilience(X3),resilience(X2))
| greater(zero,growth_rate(X2,X1))
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a13_11) ).
fof(f12,negated_conjecture,
environment(sk1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_t5_12) ).
fof(f13,negated_conjecture,
subpopulations(first_movers,efficient_producers,sk1,sk2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_t5_13) ).
fof(f14,negated_conjecture,
outcompetes(first_movers,efficient_producers,sk2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_t5_14) ).
tcf(c_63,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subpopulations(X1,X0,X2,X3)
| ~ environment(X2)
| ~ subpopulations(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f1]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i] :
( in_environment(X0,X1)
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(cnf_transformation,[],[f2]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i,X2: $i] :
( environment(X2)
| ~ greater(zero,growth_rate(X0,X1)) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subpopulations(X0,X2,X3,X1)
| ~ greater(zero,growth_rate(X0,X1)) ),
inference(cnf_transformation,[],[f4]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i] :
( ~ greater_or_equal(growth_rate(X0,X1),zero)
| ~ greater(zero,growth_rate(X0,X1)) ),
inference(cnf_transformation,[],[f5]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( greater_or_equal(growth_rate(X1,X3),zero)
| ~ environment(X2)
| ~ outcompetes(X1,X0,X3)
| ~ subpopulations(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( greater(zero,growth_rate(X0,X3))
| ~ environment(X2)
| ~ outcompetes(X1,X0,X3)
| ~ subpopulations(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_72,plain,
greater(resilience(efficient_producers),resilience(first_movers)),
inference(cnf_transformation,[],[f10]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( greater(zero,growth_rate(X1,X2))
| ~ environment(X3)
| ~ in_environment(X3,X2)
| ~ greater(zero,growth_rate(X0,X2))
| ~ greater(resilience(X0),resilience(X1)) ),
inference(cnf_transformation,[],[f11]) ).
tcf(c_74,negated_conjecture,
environment(sk1),
inference(cnf_transformation,[],[f12]) ).
tcf(c_75,negated_conjecture,
subpopulations(first_movers,efficient_producers,sk1,sk2),
inference(cnf_transformation,[],[f13]) ).
tcf(c_76,negated_conjecture,
outcompetes(first_movers,efficient_producers,sk2),
inference(cnf_transformation,[],[f14]) ).
tcf(c_97,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( greater(zero,growth_rate(X1,X2))
| ~ in_environment(X3,X2)
| ~ greater(zero,growth_rate(X0,X2))
| ~ greater(resilience(X0),resilience(X1)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_73,c_65]) ).
tcf(c_159,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( greater(zero,growth_rate(X3,X1))
| ~ environment(X0)
| ~ greater(zero,growth_rate(X2,X1))
| ~ greater(resilience(X2),resilience(X3))
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(resolution,[status(thm)],[c_64,c_97]) ).
tcf(c_170,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( greater(zero,growth_rate(X3,X1))
| ~ greater(zero,growth_rate(X2,X1))
| ~ greater(resilience(X2),resilience(X3))
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_159,c_65]) ).
tcf(c_179,plain,
! [X0: $i] :
( greater(zero,growth_rate(efficient_producers,sk2))
| ~ environment(X0)
| ~ subpopulations(efficient_producers,first_movers,X0,sk2) ),
inference(resolution,[status(thm)],[c_71,c_76]) ).
tcf(c_190,plain,
! [X0: $i] :
( greater_or_equal(growth_rate(first_movers,sk2),zero)
| ~ environment(X0)
| ~ subpopulations(efficient_producers,first_movers,X0,sk2) ),
inference(resolution,[status(thm)],[c_70,c_76]) ).
tcf(c_210,plain,
! [X0: $i] :
( ~ environment(X0)
| ~ greater(zero,growth_rate(first_movers,sk2))
| ~ subpopulations(efficient_producers,first_movers,X0,sk2) ),
inference(resolution,[status(thm)],[c_67,c_190]) ).
tcf(c_218,plain,
! [X0: $i] :
( ~ greater(zero,growth_rate(first_movers,sk2))
| ~ subpopulations(efficient_producers,first_movers,X0,sk2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_210,c_65]) ).
tcf(c_351,plain,
! [X0: $i] :
( ~ iPr_def_10
| environment(X0) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_65]) ).
tcf(c_352,plain,
! [X0: $i,X1: $i] :
( ~ iPr_def_11
| ~ greater(zero,growth_rate(X0,X1)) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_11])],[c_65]) ).
tcf(c_353,plain,
( iPr_def_11
| iPr_def_10 ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_65]) ).
tcf(c_354,definition,
iPr_def_12 = growth_rate(first_movers,sk2),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_355,definition,
iPr_def_13 = growth_rate(efficient_producers,sk2),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_356,plain,
! [X0: $i] :
( ~ greater(zero,iPr_def_12)
| ~ subpopulations(efficient_producers,first_movers,X0,sk2) ),
inference(demodulation,[status(thm)],[c_218,c_354]) ).
tcf(c_357,plain,
! [X0: $i] :
( greater(zero,iPr_def_13)
| ~ environment(X0)
| ~ subpopulations(efficient_producers,first_movers,X0,sk2) ),
inference(demodulation,[status(thm)],[c_179,c_355]) ).
tcf(c_358,negated_conjecture,
subpopulations(first_movers,efficient_producers,sk1,sk2),
inference(demodulation,[status(thm)],[c_75]) ).
tcf(c_359,negated_conjecture,
environment(sk1),
inference(demodulation,[status(thm)],[c_74]) ).
tcf(c_585,plain,
! [X0: $i,X1: $i] :
( subpopulations(efficient_producers,X0,X1,sk2)
| ~ greater(zero,iPr_def_13) ),
inference(superposition,[status(thm)],[c_355,c_66]) ).
tcf(c_599,plain,
( subpopulations(efficient_producers,first_movers,sk1,sk2)
| ~ environment(sk1) ),
inference(superposition,[status(thm)],[c_358,c_63]) ).
tcf(c_600,plain,
subpopulations(efficient_producers,first_movers,sk1,sk2),
inference(forward_subsumption_resolution,[status(thm)],[c_599,c_359]) ).
tcf(c_602,plain,
~ greater(zero,iPr_def_12),
inference(superposition,[status(thm)],[c_600,c_356]) ).
tcf(c_603,plain,
( greater(zero,iPr_def_13)
| ~ environment(sk1) ),
inference(superposition,[status(thm)],[c_600,c_357]) ).
tcf(c_604,plain,
greater(zero,iPr_def_13),
inference(forward_subsumption_resolution,[status(thm)],[c_603,c_359]) ).
tcf(c_609,plain,
( ~ iPr_def_11
| ~ greater(zero,iPr_def_13) ),
inference(superposition,[status(thm)],[c_355,c_352]) ).
tcf(c_613,plain,
~ iPr_def_11,
inference(global_subsumption_just,[status(thm)],[c_609,c_604,c_609]) ).
tcf(c_615,plain,
iPr_def_10,
inference(backward_subsumption_resolution,[status(thm)],[c_353,c_613]) ).
tcf(c_616,plain,
! [X0: $i] : environment(X0),
inference(backward_subsumption_resolution,[status(thm)],[c_351,c_615]) ).
tcf(c_617,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subpopulations(X1,X0,X2,X3)
| ~ subpopulations(X0,X1,X2,X3) ),
inference(backward_subsumption_resolution,[status(thm)],[c_63,c_616]) ).
tcf(c_621,plain,
! [X0: $i,X1: $i] : subpopulations(efficient_producers,X0,X1,sk2),
inference(global_subsumption_just,[status(thm)],[c_585,c_585,c_604]) ).
tcf(c_629,plain,
! [X0: $i,X1: $i] : subpopulations(X0,efficient_producers,X1,sk2),
inference(superposition,[status(thm)],[c_621,c_617]) ).
tcf(c_640,plain,
! [X0: $i,X1: $i] :
( greater(zero,growth_rate(X1,sk2))
| ~ greater(zero,growth_rate(X0,sk2))
| ~ greater(resilience(X0),resilience(X1)) ),
inference(superposition,[status(thm)],[c_629,c_170]) ).
tcf(c_650,plain,
( greater(zero,growth_rate(first_movers,sk2))
| ~ greater(zero,growth_rate(efficient_producers,sk2)) ),
inference(superposition,[status(thm)],[c_72,c_640]) ).
tcf(c_651,plain,
( greater(zero,iPr_def_12)
| ~ greater(zero,iPr_def_13) ),
inference(light_normalisation,[status(thm)],[c_650,c_354,c_355]) ).
tcf(c_652,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_651,c_602,c_604]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : MGT036-2 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.35 % Computer : n002.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Thu Sep 24 01:11:18 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.40 Running first-order theorem proving
% 0.12/0.40 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
% 0.12/0.41
% 0.12/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.41
% 0.12/0.41 % Detected problem language: tptp
% 0.12/0.42 % Proving...
% 1.77/1.27 % SZS status Started for theBenchmark.p
% 1.77/1.27 % SZS status Unsatisfiable for theBenchmark.p
% 1.77/1.27
% 1.77/1.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.77/1.27
% 1.77/1.27 % ------ iProver source info
% 1.77/1.27
% 1.77/1.27 % git: date: 2026-07-19 20:42:38 +0200
% 1.77/1.27 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.77/1.27 % git: non_committed_changes: false
% 1.77/1.27
% 1.77/1.27 % ------ Parsing...% successful
% 1.77/1.27
% 1.77/1.27
% 1.77/1.27 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.77/1.27
% 1.77/1.27 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sf_s rm: 0 0s sf_e pe_s pe_e %
% 1.77/1.27
% 1.77/1.27 % ------ Preprocessing... gs_s sp: 2 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.77/1.27
% 1.77/1.27 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.77/1.27 % ------ Proving...
% 1.77/1.27 % ------ Problem Properties
% 1.77/1.27
% 1.77/1.27 %
% 1.77/1.27 % clauses 13
% 1.77/1.27 % conjectures 2
% 1.77/1.27 % EPR 7
% 1.77/1.27 % Horn 12
% 1.77/1.27 % unary 5
% 1.77/1.27 % binary 5
% 1.77/1.27 % lits 25
% 1.77/1.27 % lits eq 2
% 1.77/1.27 % fd_pure 0
% 1.77/1.27 % fd_pseudo 0
% 1.77/1.27 % fd_cond 0
% 1.77/1.27 % fd_pseudo_cond 0
% 1.77/1.27 % AC symbols 0
% 1.77/1.27
% 1.77/1.27 % ------ Schedule dynamic 5 is on
% 1.77/1.27
% 1.77/1.27 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.77/1.27
% 1.77/1.27
% 1.77/1.27 % ------
% 1.77/1.27 % Current options:
% 1.77/1.27 % ------
% 1.77/1.27
% 1.77/1.27
% 1.77/1.27 %
% 1.77/1.27
% 1.77/1.27 % ------ Proving...
% 1.77/1.27 %
% 1.77/1.27
% 1.77/1.27 % SZS status Unsatisfiable for theBenchmark.p
% 1.77/1.27
% 1.77/1.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.77/1.27
% 1.77/1.27
%------------------------------------------------------------------------------