%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : MGT022+2 : 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 : n019.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 1.59s 1.44s
% Output : CNFRefutation 1.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of formulae : 41 ( 11 unt; 0 def)
% Number of atoms : 124 ( 0 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 139 ( 56 ~; 52 |; 21 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 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 : 7 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 46 ( 0 sgn 42 !; 4 ?; 15 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( constant(X0)
=> ~ decreases(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_constant_not_decrease) ).
fof(f2,axiom,
! [X0,X1,X2,X3] :
( ( greater(resilience(X2),resilience(X1))
& subpopulations(X1,X2,X0,X3)
& environment(X0) )
=> ( ( constant(resources(X0,X3))
=> constant(difference(disbanding_rate(X1,X3),disbanding_rate(X2,X3))) )
& ( decreases(resources(X0,X3))
=> increases(difference(disbanding_rate(X1,X3),disbanding_rate(X2,X3))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a6) ).
fof(f3,axiom,
greater(resilience(efficient_producers),resilience(first_movers)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a2) ).
fof(f4,conjecture,
! [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',prove_l4) ).
fof(f5,negated_conjecture,
~ ! [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(negated_conjecture,[status(cth)],[f4]) ).
fof(f6,plain,
! [X0] :
( ~ constant(X0)
| ~ decreases(X0) ),
inference(ennf_transformation,[],[f1]) ).
fof(f7,plain,
! [X0,X1,X2,X3] :
( ~ greater(resilience(X2),resilience(X1))
| ~ subpopulations(X1,X2,X0,X3)
| ~ environment(X0)
| ( ( ~ constant(resources(X0,X3))
| constant(difference(disbanding_rate(X1,X3),disbanding_rate(X2,X3))) )
& ( ~ decreases(resources(X0,X3))
| increases(difference(disbanding_rate(X1,X3),disbanding_rate(X2,X3))) ) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f8,plain,
! [X0,X1,X2,X3] :
( ~ greater(resilience(X2),resilience(X1))
| ~ subpopulations(X1,X2,X0,X3)
| ~ environment(X0)
| ( ( ~ constant(resources(X0,X3))
| constant(difference(disbanding_rate(X1,X3),disbanding_rate(X2,X3))) )
& ( ~ decreases(resources(X0,X3))
| increases(difference(disbanding_rate(X1,X3),disbanding_rate(X2,X3))) ) ) ),
inference(flattening,[],[f7]) ).
fof(f9,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,[],[f5]) ).
fof(f10,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,[],[f9]) ).
fof(f11,plain,
( subpopulations(first_movers,efficient_producers,sK0,sK1)
& environment(sK0)
& ( ( constant(resources(sK0,sK1))
& decreases(difference(disbanding_rate(first_movers,sK1),disbanding_rate(efficient_producers,sK1))) )
| ( decreases(resources(sK0,sK1))
& ~ increases(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)],[f10]) ).
fof(f12,plain,
! [X0] :
( ~ constant(X0)
| ~ decreases(X0) ),
inference(cnf_transformation,[],[f6]) ).
fof(f13,plain,
! [X2,X3,X0,X1] :
( ~ greater(resilience(X2),resilience(X1))
| ~ subpopulations(X1,X2,X0,X3)
| ~ environment(X0)
| ~ constant(resources(X0,X3))
| constant(difference(disbanding_rate(X1,X3),disbanding_rate(X2,X3))) ),
inference(cnf_transformation,[],[f8]) ).
fof(f14,plain,
! [X2,X3,X0,X1] :
( ~ greater(resilience(X2),resilience(X1))
| ~ subpopulations(X1,X2,X0,X3)
| ~ environment(X0)
| ~ decreases(resources(X0,X3))
| increases(difference(disbanding_rate(X1,X3),disbanding_rate(X2,X3))) ),
inference(cnf_transformation,[],[f8]) ).
fof(f15,plain,
greater(resilience(efficient_producers),resilience(first_movers)),
inference(cnf_transformation,[],[f3]) ).
fof(f16,plain,
subpopulations(first_movers,efficient_producers,sK0,sK1),
inference(cnf_transformation,[],[f11]) ).
fof(f17,plain,
environment(sK0),
inference(cnf_transformation,[],[f11]) ).
fof(f18,plain,
( constant(resources(sK0,sK1))
| decreases(resources(sK0,sK1)) ),
inference(cnf_transformation,[],[f11]) ).
fof(f19,plain,
( decreases(difference(disbanding_rate(first_movers,sK1),disbanding_rate(efficient_producers,sK1)))
| decreases(resources(sK0,sK1)) ),
inference(cnf_transformation,[],[f11]) ).
fof(f20,plain,
( constant(resources(sK0,sK1))
| ~ increases(difference(disbanding_rate(first_movers,sK1),disbanding_rate(efficient_producers,sK1))) ),
inference(cnf_transformation,[],[f11]) ).
fof(f21,plain,
( decreases(difference(disbanding_rate(first_movers,sK1),disbanding_rate(efficient_producers,sK1)))
| ~ increases(difference(disbanding_rate(first_movers,sK1),disbanding_rate(efficient_producers,sK1))) ),
inference(cnf_transformation,[],[f11]) ).
tcf(c_49,plain,
! [X0: $i] :
( ~ constant(X0)
| ~ decreases(X0) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( increases(difference(disbanding_rate(X0,X3),disbanding_rate(X1,X3)))
| ~ environment(X2)
| ~ decreases(resources(X2,X3))
| ~ greater(resilience(X1),resilience(X0))
| ~ subpopulations(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f14]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( constant(difference(disbanding_rate(X0,X3),disbanding_rate(X1,X3)))
| ~ environment(X2)
| ~ constant(resources(X2,X3))
| ~ greater(resilience(X1),resilience(X0))
| ~ subpopulations(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f13]) ).
tcf(c_52,plain,
greater(resilience(efficient_producers),resilience(first_movers)),
inference(cnf_transformation,[],[f15]) ).
tcf(c_53,negated_conjecture,
( decreases(difference(disbanding_rate(first_movers,sK1),disbanding_rate(efficient_producers,sK1)))
| ~ increases(difference(disbanding_rate(first_movers,sK1),disbanding_rate(efficient_producers,sK1))) ),
inference(cnf_transformation,[],[f21]) ).
tcf(c_54,negated_conjecture,
( constant(resources(sK0,sK1))
| ~ increases(difference(disbanding_rate(first_movers,sK1),disbanding_rate(efficient_producers,sK1))) ),
inference(cnf_transformation,[],[f20]) ).
tcf(c_55,negated_conjecture,
( decreases(resources(sK0,sK1))
| decreases(difference(disbanding_rate(first_movers,sK1),disbanding_rate(efficient_producers,sK1))) ),
inference(cnf_transformation,[],[f19]) ).
tcf(c_56,negated_conjecture,
( constant(resources(sK0,sK1))
| decreases(resources(sK0,sK1)) ),
inference(cnf_transformation,[],[f18]) ).
tcf(c_57,negated_conjecture,
environment(sK0),
inference(cnf_transformation,[],[f17]) ).
tcf(c_58,negated_conjecture,
subpopulations(first_movers,efficient_producers,sK0,sK1),
inference(cnf_transformation,[],[f16]) ).
tcf(c_108,plain,
! [X0: $i,X1: $i,X2: $i] :
( constant(difference(disbanding_rate(X0,X2),disbanding_rate(X1,X2)))
| ~ constant(resources(sK0,X2))
| ~ greater(resilience(X1),resilience(X0))
| ~ subpopulations(X0,X1,sK0,X2) ),
inference(resolution,[status(thm)],[c_51,c_57]) ).
tcf(c_122,plain,
! [X0: $i,X1: $i,X2: $i] :
( increases(difference(disbanding_rate(X0,X2),disbanding_rate(X1,X2)))
| ~ decreases(resources(sK0,X2))
| ~ greater(resilience(X1),resilience(X0))
| ~ subpopulations(X0,X1,sK0,X2) ),
inference(resolution,[status(thm)],[c_50,c_57]) ).
tcf(c_144,plain,
( increases(difference(disbanding_rate(first_movers,sK1),disbanding_rate(efficient_producers,sK1)))
| ~ decreases(resources(sK0,sK1))
| ~ greater(resilience(efficient_producers),resilience(first_movers)) ),
inference(resolution,[status(thm)],[c_58,c_122]) ).
tcf(c_145,plain,
( increases(difference(disbanding_rate(first_movers,sK1),disbanding_rate(efficient_producers,sK1)))
| ~ decreases(resources(sK0,sK1)) ),
inference(global_subsumption_just,[status(thm)],[c_144,c_52,c_144]) ).
tcf(c_153,plain,
( constant(difference(disbanding_rate(first_movers,sK1),disbanding_rate(efficient_producers,sK1)))
| ~ constant(resources(sK0,sK1))
| ~ greater(resilience(efficient_producers),resilience(first_movers)) ),
inference(resolution,[status(thm)],[c_58,c_108]) ).
tcf(c_154,plain,
constant(difference(disbanding_rate(first_movers,sK1),disbanding_rate(efficient_producers,sK1))),
inference(global_subsumption_just,[status(thm)],[c_153,c_52,c_56,c_54,c_144,c_153]) ).
tcf(c_168,plain,
( decreases(difference(disbanding_rate(first_movers,sK1),disbanding_rate(efficient_producers,sK1)))
| ~ decreases(resources(sK0,sK1)) ),
inference(resolution,[status(thm)],[c_145,c_53]) ).
tcf(c_169,plain,
decreases(difference(disbanding_rate(first_movers,sK1),disbanding_rate(efficient_producers,sK1))),
inference(global_subsumption_just,[status(thm)],[c_168,c_55,c_168]) ).
tcf(c_176,plain,
~ constant(difference(disbanding_rate(first_movers,sK1),disbanding_rate(efficient_producers,sK1))),
inference(resolution,[status(thm)],[c_49,c_169]) ).
tcf(c_177,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_176,c_154]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : MGT022+2 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.07/0.36 % Computer : n019.cluster.edu
% 0.07/0.36 % Model : x86_64 x86_64
% 0.07/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.36 % Memory : 8046.5625MB
% 0.07/0.36 % OS : Linux 6.8.0-71-generic
% 0.07/0.36 % CPULimit : 300
% 0.07/0.36 % WCLimit : 300
% 0.07/0.36 % DateTime : Thu Sep 24 01:02:19 UTC 2026
% 0.07/0.37 % CPUTime :
% 0.07/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/0.43 Running first-order theorem proving
% 0.14/0.43 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
% 0.14/0.45
% 0.14/0.45 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.45
% 0.14/0.45 % Detected problem language: tptp
% 0.14/0.47 % Proving...
% 1.59/1.44 % SZS status Started for theBenchmark.p
% 1.59/1.44 % SZS status Theorem for theBenchmark.p
% 1.59/1.44
% 1.59/1.44 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.59/1.44
% 1.59/1.44 % ------ iProver source info
% 1.59/1.44
% 1.59/1.44 % git: date: 2026-07-19 20:42:38 +0200
% 1.59/1.44 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.59/1.44 % git: non_committed_changes: false
% 1.59/1.44
% 1.59/1.44 % ------ Parsing...
% 1.59/1.44 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.59/1.44
% 1.59/1.44 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s%
% 1.59/1.44
% 1.59/1.44 % SZS status Theorem for theBenchmark.p
% 1.59/1.44
% 1.59/1.44 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.59/1.44
% 1.59/1.44
%------------------------------------------------------------------------------