%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : MGT021+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n008.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 02:12:22 PM UTC 2026
% Result : Theorem 1.23s 1.27s
% Output : CNFRefutation 1.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 51 ( 8 unt; 0 def)
% Number of atoms : 172 ( 0 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 226 ( 105 ~; 91 |; 19 &)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 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 : 8 ( 7 usr; 1 prp; 0-4 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 75 ( 0 sgn 71 !; 4 ?; 28 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( ( subpopulations(first_movers,efficient_producers,X0,X1)
& environment(X0) )
=> in_environment(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_time_point_in_environment) ).
fof(f2,axiom,
! [X0,X1] :
( ( subpopulations(first_movers,efficient_producers,X0,X1)
& environment(X0) )
=> greater(number_of_organizations(X0,X1),zero) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_environment_not_empty) ).
fof(f3,axiom,
! [X0] :
( increases(X0)
=> ~ decreases(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_increase_not_decrease) ).
fof(f5,axiom,
! [X0,X1] :
( ( greater(number_of_organizations(X0,X1),zero)
& in_environment(X0,X1)
& environment(X0) )
=> ( ( ~ greater(equilibrium(X0),X1)
=> constant(resources(X0,X1)) )
& ( greater(equilibrium(X0),X1)
=> decreases(resources(X0,X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a3) ).
fof(f6,axiom,
! [X0,X1] :
( ( subpopulations(first_movers,efficient_producers,X0,X1)
& environment(X0) )
=> ( ( constant(resources(X0,X1))
=> ~ decreases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1))) )
& ( decreases(resources(X0,X1))
=> increases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l4) ).
fof(f7,conjecture,
! [X0,X1] :
( ( subpopulations(first_movers,efficient_producers,X0,X1)
& environment(X0) )
=> ~ decreases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l3) ).
fof(f8,negated_conjecture,
~ ! [X0,X1] :
( ( subpopulations(first_movers,efficient_producers,X0,X1)
& environment(X0) )
=> ~ decreases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1))) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f10,plain,
! [X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0)
| in_environment(X0,X1) ),
inference(ennf_transformation,[],[f1]) ).
fof(f11,plain,
! [X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0)
| in_environment(X0,X1) ),
inference(flattening,[],[f10]) ).
fof(f12,plain,
! [X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0)
| greater(number_of_organizations(X0,X1),zero) ),
inference(ennf_transformation,[],[f2]) ).
fof(f13,plain,
! [X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0)
| greater(number_of_organizations(X0,X1),zero) ),
inference(flattening,[],[f12]) ).
fof(f14,plain,
! [X0] :
( ~ increases(X0)
| ~ decreases(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f15,plain,
! [X0,X1] :
( ~ greater(number_of_organizations(X0,X1),zero)
| ~ in_environment(X0,X1)
| ~ environment(X0)
| ( ( greater(equilibrium(X0),X1)
| constant(resources(X0,X1)) )
& ( ~ greater(equilibrium(X0),X1)
| decreases(resources(X0,X1)) ) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f16,plain,
! [X0,X1] :
( ~ greater(number_of_organizations(X0,X1),zero)
| ~ in_environment(X0,X1)
| ~ environment(X0)
| ( ( greater(equilibrium(X0),X1)
| constant(resources(X0,X1)) )
& ( ~ greater(equilibrium(X0),X1)
| decreases(resources(X0,X1)) ) ) ),
inference(flattening,[],[f15]) ).
fof(f17,plain,
! [X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0)
| ( ( ~ constant(resources(X0,X1))
| ~ decreases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1))) )
& ( ~ decreases(resources(X0,X1))
| increases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1))) ) ) ),
inference(ennf_transformation,[],[f6]) ).
fof(f18,plain,
! [X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0)
| ( ( ~ constant(resources(X0,X1))
| ~ decreases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1))) )
& ( ~ decreases(resources(X0,X1))
| increases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1))) ) ) ),
inference(flattening,[],[f17]) ).
fof(f19,plain,
? [X0,X1] :
( subpopulations(first_movers,efficient_producers,X0,X1)
& environment(X0)
& decreases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1))) ),
inference(ennf_transformation,[],[f8]) ).
fof(f20,plain,
? [X0,X1] :
( subpopulations(first_movers,efficient_producers,X0,X1)
& environment(X0)
& decreases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1))) ),
inference(flattening,[],[f19]) ).
fof(f21,plain,
( subpopulations(first_movers,efficient_producers,sK0,sK1)
& environment(sK0)
& decreases(difference(disbanding_rate(first_movers,sK1),disbanding_rate(efficient_producers,sK1))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f20]) ).
fof(f22,plain,
! [X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0)
| in_environment(X0,X1) ),
inference(cnf_transformation,[],[f11]) ).
fof(f23,plain,
! [X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0)
| greater(number_of_organizations(X0,X1),zero) ),
inference(cnf_transformation,[],[f13]) ).
fof(f24,plain,
! [X0] :
( ~ increases(X0)
| ~ decreases(X0) ),
inference(cnf_transformation,[],[f14]) ).
fof(f25,plain,
! [X0,X1] :
( ~ greater(number_of_organizations(X0,X1),zero)
| ~ in_environment(X0,X1)
| ~ environment(X0)
| greater(equilibrium(X0),X1)
| constant(resources(X0,X1)) ),
inference(cnf_transformation,[],[f16]) ).
fof(f26,plain,
! [X0,X1] :
( ~ greater(number_of_organizations(X0,X1),zero)
| ~ in_environment(X0,X1)
| ~ environment(X0)
| ~ greater(equilibrium(X0),X1)
| decreases(resources(X0,X1)) ),
inference(cnf_transformation,[],[f16]) ).
fof(f27,plain,
! [X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0)
| ~ constant(resources(X0,X1))
| ~ decreases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1))) ),
inference(cnf_transformation,[],[f18]) ).
fof(f28,plain,
! [X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0)
| ~ decreases(resources(X0,X1))
| increases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1))) ),
inference(cnf_transformation,[],[f18]) ).
fof(f29,plain,
subpopulations(first_movers,efficient_producers,sK0,sK1),
inference(cnf_transformation,[],[f21]) ).
fof(f30,plain,
environment(sK0),
inference(cnf_transformation,[],[f21]) ).
fof(f31,plain,
decreases(difference(disbanding_rate(first_movers,sK1),disbanding_rate(efficient_producers,sK1))),
inference(cnf_transformation,[],[f21]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] :
( in_environment(X0,X1)
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] :
( greater(number_of_organizations(X0,X1),zero)
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(cnf_transformation,[],[f23]) ).
tcf(c_51,plain,
! [X0: $i] :
( ~ increases(X0)
| ~ decreases(X0) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] :
( decreases(resources(X0,X1))
| ~ environment(X0)
| ~ in_environment(X0,X1)
| ~ greater(equilibrium(X0),X1)
| ~ greater(number_of_organizations(X0,X1),zero) ),
inference(cnf_transformation,[],[f26]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( constant(resources(X0,X1))
| greater(equilibrium(X0),X1)
| ~ environment(X0)
| ~ in_environment(X0,X1)
| ~ greater(number_of_organizations(X0,X1),zero) ),
inference(cnf_transformation,[],[f25]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] :
( increases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1)))
| ~ environment(X0)
| ~ decreases(resources(X0,X1))
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(cnf_transformation,[],[f28]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] :
( ~ environment(X1)
| ~ constant(resources(X1,X0))
| ~ subpopulations(first_movers,efficient_producers,X1,X0)
| ~ decreases(difference(disbanding_rate(first_movers,X0),disbanding_rate(efficient_producers,X0))) ),
inference(cnf_transformation,[],[f27]) ).
tcf(c_56,negated_conjecture,
decreases(difference(disbanding_rate(first_movers,sK1),disbanding_rate(efficient_producers,sK1))),
inference(cnf_transformation,[],[f31]) ).
tcf(c_57,negated_conjecture,
environment(sK0),
inference(cnf_transformation,[],[f30]) ).
tcf(c_58,negated_conjecture,
subpopulations(first_movers,efficient_producers,sK0,sK1),
inference(cnf_transformation,[],[f29]) ).
tcf(c_124,plain,
! [X0: $i,X1: $i] :
( ~ environment(X1)
| ~ decreases(resources(X1,X0))
| ~ subpopulations(first_movers,efficient_producers,X1,X0)
| ~ decreases(difference(disbanding_rate(first_movers,X0),disbanding_rate(efficient_producers,X0))) ),
inference(resolution,[status(thm)],[c_51,c_54]) ).
tcf(c_142,plain,
! [X0: $i,X1: $i] :
( greater(equilibrium(X1),X0)
| ~ environment(X1)
| ~ in_environment(X1,X0)
| ~ greater(number_of_organizations(X1,X0),zero)
| ~ subpopulations(first_movers,efficient_producers,X1,X0)
| ~ decreases(difference(disbanding_rate(first_movers,X0),disbanding_rate(efficient_producers,X0))) ),
inference(resolution,[status(thm)],[c_53,c_55]) ).
tcf(c_156,plain,
! [X0: $i,X1: $i] :
( greater(equilibrium(X1),X0)
| ~ environment(X1)
| ~ subpopulations(first_movers,efficient_producers,X1,X0)
| ~ decreases(difference(disbanding_rate(first_movers,X0),disbanding_rate(efficient_producers,X0))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_142,c_49,c_50]) ).
tcf(c_166,plain,
! [X0: $i,X1: $i] :
( decreases(resources(X0,X1))
| ~ environment(X0)
| ~ greater(equilibrium(X0),X1)
| ~ greater(number_of_organizations(X0,X1),zero)
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(resolution,[status(thm)],[c_49,c_52]) ).
tcf(c_168,plain,
! [X0: $i,X1: $i] :
( decreases(resources(X0,X1))
| ~ environment(X0)
| ~ greater(equilibrium(X0),X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_166,c_49,c_50,c_52]) ).
tcf(c_187,plain,
! [X0: $i] :
( decreases(resources(sK0,X0))
| ~ greater(equilibrium(sK0),X0)
| ~ subpopulations(first_movers,efficient_producers,sK0,X0) ),
inference(resolution,[status(thm)],[c_168,c_57]) ).
tcf(c_206,plain,
! [X0: $i] :
( greater(equilibrium(sK0),X0)
| ~ subpopulations(first_movers,efficient_producers,sK0,X0)
| ~ decreases(difference(disbanding_rate(first_movers,X0),disbanding_rate(efficient_producers,X0))) ),
inference(resolution,[status(thm)],[c_156,c_57]) ).
tcf(c_217,plain,
! [X0: $i] :
( ~ decreases(resources(sK0,X0))
| ~ subpopulations(first_movers,efficient_producers,sK0,X0)
| ~ decreases(difference(disbanding_rate(first_movers,X0),disbanding_rate(efficient_producers,X0))) ),
inference(resolution,[status(thm)],[c_124,c_57]) ).
tcf(c_219,plain,
! [X0: $i] :
( ~ decreases(difference(disbanding_rate(first_movers,X0),disbanding_rate(efficient_producers,X0)))
| ~ subpopulations(first_movers,efficient_producers,sK0,X0) ),
inference(global_subsumption_just,[status(thm)],[c_217,c_187,c_206,c_217]) ).
tcf(c_220,plain,
! [X0: $i] :
( ~ subpopulations(first_movers,efficient_producers,sK0,X0)
| ~ decreases(difference(disbanding_rate(first_movers,X0),disbanding_rate(efficient_producers,X0))) ),
inference(renaming,[status(thm)],[c_219]) ).
tcf(c_235,plain,
~ decreases(difference(disbanding_rate(first_movers,sK1),disbanding_rate(efficient_producers,sK1))),
inference(resolution,[status(thm)],[c_58,c_220]) ).
tcf(c_236,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_235,c_56]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT021+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.36 % Computer : n008.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % 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 01:02:39 UTC 2026
% 0.14/0.37 % CPUTime :
% 0.14/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/0.40 Running first-order theorem proving
% 0.14/0.40 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
% 0.14/0.42
% 0.14/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.42
% 0.14/0.42 % Detected problem language: tptp
% 0.14/0.43 % Proving...
% 1.23/1.27 % SZS status Started for theBenchmark.p
% 1.23/1.27 % SZS status Theorem for theBenchmark.p
% 1.23/1.27
% 1.23/1.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.23/1.27
% 1.23/1.27 % ------ iProver source info
% 1.23/1.27
% 1.23/1.27 % git: date: 2026-07-19 20:42:38 +0200
% 1.23/1.27 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.23/1.27 % git: non_committed_changes: false
% 1.23/1.27
% 1.23/1.27 % ------ Parsing...
% 1.23/1.27 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.23/1.27
% 1.23/1.27 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s%
% 1.23/1.27
% 1.23/1.27 % SZS status Theorem for theBenchmark.p
% 1.23/1.27
% 1.23/1.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.23/1.27
% 1.23/1.27
%------------------------------------------------------------------------------