%------------------------------------------------------------------------------
% File : SPASS-SCL---0.1.1
% Problem : MGT036+3 : TPTP v9.3.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : /export/starexec/sandbox/solver/bin/SPASS-SCL-FOL -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n004.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 : Tue Sep 8 06:20:09 AM UTC 2026
% Result : Theorem 0.14s 0.37s
% Output : Proof 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of formulae : 29 ( 5 unt; 2 def)
% Number of atoms : 95 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 94 ( 28 ~; 25 |; 31 &)
% ( 5 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-4 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 76 ( 0 sgn 48 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
% FILE RECORD
fof(d2,hypothesis,
! [X1,X2,X3,X4] :
( ( environment(X1)
& subpopulations(X2,X3,X1,X4) )
=> ( ( greater_or_equal(growth_rate(X3,X4),zero)
& greater(zero,growth_rate(X2,X4)) )
<=> outcompetes(X3,X2,X4) ) ),
file('theBenchmark.p',d2) ).
% FOF SIMPLE INFERENCE
fof(d2_elimTB,hypothesis,
! [X1,X2,X3,X4] :
( ( environment(X1)
& subpopulations(X2,X3,X1,X4) )
=> ( ( greater_or_equal(growth_rate(X3,X4),zero)
& greater(zero,growth_rate(X2,X4)) )
<=> outcompetes(X3,X2,X4) ) ),
inference(elimTB,[status(thm)],[inference(variable_rename,[status(thm)],[d2])]) ).
% FOF INTRODUCE RENAMING
fof(ren1_defn,definition,
! [X3,X4,X2] :
( ren1(X3,X4,X2)
<=> ( greater_or_equal(growth_rate(X3,X4),zero)
& greater(zero,growth_rate(X2,X4)) ) ),
introduced(definition,[new_symbols(definition,[ren1])],[d2_elimTB]) ).
% FOF INTRODUCE RENAMING
fof(ren2_defn,definition,
! [X3,X4,X2] :
( ren2(X3,X4,X2)
<=> ( ren1(X3,X4,X2)
<=> outcompetes(X3,X2,X4) ) ),
introduced(definition,[new_symbols(definition,[ren2])],[d2_elimTB]) ).
% FOF RENAMING INFERENCE
fof(d2_renObv,hypothesis,
! [X1,X2,X3,X4] :
( ( environment(X1)
& subpopulations(X2,X3,X1,X4) )
=> ren2(X3,X4,X2) ),
inference(renaming,[status(esa)],[d2_elimTB,ren1_defn,ren2_defn]) ).
% FOF SIMPLE INFERENCE
fof(d2_elimImpEquivPushNegMiniScope,hypothesis,
! [X1,X2,X3,X4] :
( ~ environment(X1)
| ~ subpopulations(X2,X3,X1,X4)
| ren2(X3,X4,X2) ),
inference(elimImpEquivPushNegMiniScope,[status(thm)],[d2_renObv]) ).
% FOF PUSH DISJ SPLITTING.
cnf(c_9,plain,
( ~ environment(X0)
| ~ subpopulations(X1,X2,X0,X3)
| ren2(X2,X3,X1) ),
inference(split_conjunct,[status(thm)],[inference(push_disj,[status(thm)],[d2_elimImpEquivPushNegMiniScope])]) ).
% FILE RECORD
fof(mp_symmetry_of_subpopulations,axiom,
! [X1,X2,X3,X4] :
( ( environment(X1)
& subpopulations(X2,X3,X1,X4) )
=> subpopulations(X3,X2,X1,X4) ),
file('theBenchmark.p',mp_symmetry_of_subpopulations) ).
% FOF SIMPLE INFERENCE
fof(mp_symmetry_of_subpopulations_elimTB,axiom,
! [X1,X2,X3,X4] :
( ( environment(X1)
& subpopulations(X2,X3,X1,X4) )
=> subpopulations(X3,X2,X1,X4) ),
inference(elimTB,[status(thm)],[inference(variable_rename,[status(thm)],[mp_symmetry_of_subpopulations])]) ).
% FOF SIMPLE INFERENCE
fof(mp_symmetry_of_subpopulations_elimImpEquivPushNegMiniScope,axiom,
! [X1,X2,X3,X4] :
( ~ environment(X1)
| ~ subpopulations(X2,X3,X1,X4)
| subpopulations(X3,X2,X1,X4) ),
inference(elimImpEquivPushNegMiniScope,[status(thm)],[mp_symmetry_of_subpopulations_elimTB]) ).
% FOF PUSH DISJ SPLITTING.
cnf(c_1,plain,
( ~ environment(X0)
| ~ subpopulations(X1,X2,X0,X3)
| subpopulations(X2,X1,X0,X3) ),
inference(split_conjunct,[status(thm)],[inference(push_disj,[status(thm)],[mp_symmetry_of_subpopulations_elimImpEquivPushNegMiniScope])]) ).
% FOF SIMPLE INFERENCE
fof(ren2_elimImpEquivPushNegMiniScope,plain,
( ! [X1,X2,X3] :
( ~ ren2(X1,X2,X3)
| ( ( ~ ren1(X1,X2,X3)
| outcompetes(X1,X3,X2) )
& ( ~ outcompetes(X1,X3,X2)
| ren1(X1,X2,X3) ) ) )
& ! [X4,X5,X6] :
( ( ( ~ ren1(X4,X5,X6)
| ~ outcompetes(X4,X6,X5) )
& ( ren1(X4,X5,X6)
| outcompetes(X4,X6,X5) ) )
| ren2(X4,X5,X6) ) ),
inference(elimImpEquivPushNegMiniScope,[status(thm)],[ren2_defn]) ).
% FOF PUSH DISJ SPLITTING.
cnf(c_5,plain,
( ~ ren2(X0,X1,X2)
| ~ ren1(X0,X1,X2)
| outcompetes(X0,X2,X1) ),
inference(split_conjunct,[status(thm)],[inference(push_disj,[status(thm)],[ren2_elimImpEquivPushNegMiniScope])]) ).
% FILE RECORD
fof(prove_t5_star,conjecture,
? [X1,X4] :
( environment(X1)
& subpopulations(first_movers,efficient_producers,X1,X4)
& outcompetes(first_movers,efficient_producers,X4) ),
file('theBenchmark.p',prove_t5_star) ).
% NEGATING CONJECTURE
fof(prove_t5_star_nc,negated_conjecture,
~ ? [X1,X4] :
( environment(X1)
& subpopulations(first_movers,efficient_producers,X1,X4)
& outcompetes(first_movers,efficient_producers,X4) ),
inference(negating_conjecture,[status(cth)],[prove_t5_star]) ).
% FOF SIMPLE INFERENCE
fof(prove_t5_star_nc_elimTB,negated_conjecture,
~ ? [X1,X2] :
( environment(X1)
& subpopulations(first_movers,efficient_producers,X1,X2)
& outcompetes(first_movers,efficient_producers,X2) ),
inference(elimTB,[status(thm)],[inference(variable_rename,[status(thm)],[prove_t5_star_nc])]) ).
% FOF SIMPLE INFERENCE
fof(prove_t5_star_nc_elimImpEquivPushNegMiniScope,negated_conjecture,
! [X1,X2] :
( ~ environment(X1)
| ~ subpopulations(first_movers,efficient_producers,X1,X2)
| ~ outcompetes(first_movers,efficient_producers,X2) ),
inference(elimImpEquivPushNegMiniScope,[status(thm)],[prove_t5_star_nc_elimTB]) ).
% FOF PUSH DISJ SPLITTING.
cnf(c_14,plain,
( ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ outcompetes(first_movers,efficient_producers,X1) ),
inference(split_conjunct,[status(thm)],[inference(push_disj,[status(thm)],[prove_t5_star_nc_elimImpEquivPushNegMiniScope])]) ).
% FOF SIMPLE INFERENCE
fof(ren1_elimImpEquivPushNegMiniScope,plain,
( ! [X1,X2,X3] :
( ~ ren1(X1,X2,X3)
| ( greater_or_equal(growth_rate(X1,X2),zero)
& greater(zero,growth_rate(X3,X2)) ) )
& ! [X4,X5,X6] :
( ~ greater_or_equal(growth_rate(X4,X5),zero)
| ~ greater(zero,growth_rate(X6,X5))
| ren1(X4,X5,X6) ) ),
inference(elimImpEquivPushNegMiniScope,[status(thm)],[ren1_defn]) ).
% FOF PUSH DISJ SPLITTING.
cnf(c_4,plain,
( ~ greater_or_equal(growth_rate(X0,X1),zero)
| ~ greater(zero,growth_rate(X2,X1))
| ren1(X0,X1,X2) ),
inference(split_conjunct,[status(thm)],[inference(push_disj,[status(thm)],[ren1_elimImpEquivPushNegMiniScope])]) ).
% FILE RECORD
fof(a13_star,hypothesis,
? [X1,X4] :
( environment(X1)
& subpopulations(first_movers,efficient_producers,X1,X4)
& greater_or_equal(growth_rate(first_movers,X4),zero)
& greater(zero,growth_rate(efficient_producers,X4)) ),
file('theBenchmark.p',a13_star) ).
% FOF SIMPLE INFERENCE
fof(a13_star_elimTB,hypothesis,
? [X1,X2] :
( environment(X1)
& subpopulations(first_movers,efficient_producers,X1,X2)
& greater_or_equal(growth_rate(first_movers,X2),zero)
& greater(zero,growth_rate(efficient_producers,X2)) ),
inference(elimTB,[status(thm)],[inference(variable_rename,[status(thm)],[a13_star])]) ).
% FOF SIMPLE INFERENCE
fof(a13_star_elimImpEquivPushNegMiniScope,hypothesis,
? [X1,X2] :
( environment(X1)
& subpopulations(first_movers,efficient_producers,X1,X2)
& greater_or_equal(growth_rate(first_movers,X2),zero)
& greater(zero,growth_rate(efficient_producers,X2)) ),
inference(elimImpEquivPushNegMiniScope,[status(thm)],[a13_star_elimTB]) ).
% FOF SKOLEM INFERENCE. WIP!!
fof(a13_star_skol,hypothesis,
( environment(skc1)
& subpopulations(first_movers,efficient_producers,skc1,skc2)
& greater_or_equal(growth_rate(first_movers,skc2),zero)
& greater(zero,growth_rate(efficient_producers,skc2)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[skc1,skc2]),skolemize(X1,skc1),skolemize(X2,skc2)],[a13_star_elimImpEquivPushNegMiniScope]) ).
% FOF PUSH DISJ SPLITTING.
cnf(c_11,plain,
subpopulations(first_movers,efficient_producers,skc1,skc2),
inference(split_conjunct,[status(thm)],[inference(push_disj,[status(thm)],[a13_star_skol])]) ).
% FOF PUSH DISJ SPLITTING.
cnf(c_12,plain,
greater_or_equal(growth_rate(first_movers,skc2),zero),
inference(split_conjunct,[status(thm)],[inference(push_disj,[status(thm)],[a13_star_skol])]) ).
% FOF PUSH DISJ SPLITTING.
cnf(c_13,plain,
greater(zero,growth_rate(efficient_producers,skc2)),
inference(split_conjunct,[status(thm)],[inference(push_disj,[status(thm)],[a13_star_skol])]) ).
% FOF PUSH DISJ SPLITTING.
cnf(c_10,plain,
environment(skc1),
inference(split_conjunct,[status(thm)],[inference(push_disj,[status(thm)],[a13_star_skol])]) ).
% CNF SPASS RESOLUTION.
cnf(c_15,plain,
$false,
inference(resolution,[status(thm)],[c_9,c_1,c_5,c_14,c_4,c_11,c_12,c_13,c_10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : MGT036+3 : TPTP v9.3.0. Released v2.0.0.
% 0.00/0.04 % Command : /export/starexec/sandbox/solver/bin/SPASS-SCL-FOL -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n004.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 7 12:42:00 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running /export/starexec/sandbox/solver/bin/SPASS-SCL-FOL -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.37
% 0.14/0.37 % Input Clauses:
% 0.14/0.37 % 1:3:4:INP:TopTopTopTop: environment(x0),subpopulations(x1,x2,x0,x3) -> subpopulations(x2,x1,x0,x3)
% 0.14/0.37 % 2:2:3:INP:TopTopTop: ren1(x0,x1,x2) -> greater_or_equal(growth_rate(x0,x1),zero)
% 0.14/0.37 % 3:2:3:INP:TopTopTop: ren1(x0,x1,x2) -> greater(zero,growth_rate(x2,x1))
% 0.14/0.37 % 4:3:3:INP:TopTopTop: greater_or_equal(growth_rate(x0,x1),zero),greater(zero,growth_rate(x2,x1)) -> ren1(x0,x1,x2)
% 0.14/0.37 % 5:3:3:INP:TopTopTop: ren2(x0,x1,x2),ren1(x0,x1,x2) -> outcompetes(x0,x2,x1)
% 0.14/0.37 % 6:3:3:INP:TopTopTop: ren2(x0,x1,x2),outcompetes(x0,x2,x1) -> ren1(x0,x1,x2)
% 0.14/0.37 % 7:3:3:INP:TopTopTop: ren1(x0,x1,x2),outcompetes(x0,x2,x1) -> ren2(x0,x1,x2)
% 0.14/0.37 % 8:3:3:INP:TopTopTop: -> ren1(x0,x1,x2),outcompetes(x0,x2,x1),ren2(x0,x1,x2)
% 0.14/0.37 % 9:3:4:INP:TopTopTopTop: environment(x0),subpopulations(x1,x2,x0,x3) -> ren2(x2,x3,x1)
% 0.14/0.37 % 10:1:0:INP:: -> environment(skc1)
% 0.14/0.37 % 11:1:0:INP:: -> subpopulations(first_movers,efficient_producers,skc1,skc2)
% 0.14/0.37 % 12:1:0:INP:: -> greater_or_equal(growth_rate(first_movers,skc2),zero)
% 0.14/0.37 % 13:1:0:INP:: -> greater(zero,growth_rate(efficient_producers,skc2))
% 0.14/0.37 % 14:3:2:INP:TopTop: environment(x0),subpopulations(first_movers,efficient_producers,x0,x1),outcompetes(first_movers,efficient_producers,x1) ->
% 0.14/0.37
% 0.14/0.37 % Predicates: environment subpopulations greater_or_equal greater outcompetes ren1 ren2
% 0.14/0.37 % Fol Constants: zero first_movers efficient_producers skc1 skc2
% 0.14/0.37 % Fol Functions: growth_rate
% 0.14/0.37 % Problem Properties:
% 0.14/0.37 % This is a full first-order problem without equality. The Problem is linear.
% 0.14/0.37
% 0.14/0.37
% 0.14/0.37 % Reduced Input Axiom Clauses:
% 0.14/0.37 % 1:3:4:INP:TopTopTopTop: environment(x0),subpopulations(x1,x2,x0,x3) -> subpopulations(x2,x1,x0,x3)
% 0.14/0.37 % 2:2:3:INP:TopTopTop: ren1(x0,x1,x2) -> greater_or_equal(growth_rate(x0,x1),zero)
% 0.14/0.37 % 3:2:3:INP:TopTopTop: ren1(x0,x1,x2) -> greater(zero,growth_rate(x2,x1))
% 0.14/0.37 % 4:3:3:INP:TopTopTop: greater_or_equal(growth_rate(x0,x1),zero),greater(zero,growth_rate(x2,x1)) -> ren1(x0,x1,x2)
% 0.14/0.37 % 5:3:3:INP:TopTopTop: ren2(x0,x1,x2),ren1(x0,x1,x2) -> outcompetes(x0,x2,x1)
% 0.14/0.37 % 6:3:3:INP:TopTopTop: ren2(x0,x1,x2),outcompetes(x0,x2,x1) -> ren1(x0,x1,x2)
% 0.14/0.37 % 7:3:3:INP:TopTopTop: ren1(x0,x1,x2),outcompetes(x0,x2,x1) -> ren2(x0,x1,x2)
% 0.14/0.37 % 8:3:3:INP:TopTopTop: -> ren1(x0,x1,x2),outcompetes(x0,x2,x1),ren2(x0,x1,x2)
% 0.14/0.37
% 0.14/0.37 % Reduced Input Conjecture Clauses:
% 0.14/0.37 % 9:3:4:INP:TopTopTopTop: environment(x0),subpopulations(x1,x2,x0,x3) -> ren2(x2,x3,x1)
% 0.14/0.37 % 10:1:0:INP:: -> environment(skc1)
% 0.14/0.37 % 11:1:0:INP:: -> subpopulations(first_movers,efficient_producers,skc1,skc2)
% 0.14/0.37 % 12:1:0:INP:: -> greater_or_equal(growth_rate(first_movers,skc2),zero)
% 0.14/0.37 % 13:1:0:INP:: -> greater(zero,growth_rate(efficient_producers,skc2))
% 0.14/0.37 % 14:3:2:INP:TopTop: environment(x0),subpopulations(first_movers,efficient_producers,x0,x1),outcompetes(first_movers,efficient_producers,x1) ->
% 0.14/0.37
% 0.14/0.37
% 0.14/0.37 % === Starting SPASS-SCL-FOL A Little Less Naive, considering 24 atoms initially. Used heuristic: lmodel_grow ===
% 0.14/0.37
% 0.14/0.37
% 0.14/0.37
% 0.14/0.37 % SZS status Theorem
% 0.14/0.37 % Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.37
% 0.14/0.37 % SPASS-SCL-FOL Statistics:
% 0.14/0.37 % Number of learned clauses: 0
% 0.14/0.37 % Number of propagations: 8
% 0.14/0.37 % Number of decisions: 2
% 0.14/0.37 % Number of resolutions: 8
% 0.14/0.37 % Number of condensations: 0
% 0.14/0.37 % Number of sub resolutions: 0
% 0.14/0.37
% 0.14/0.37 % Solver is done. Empty clause found
% 0.14/0.37
% 0.14/0.37 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.14/0.37 % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.37 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.14/0.37
% 0.14/0.37
% 0.14/0.37 % Needed: 0:00:00.00
% 0.14/0.37
% 0.14/0.37 % ###
% 0.14/0.37 % ### Pagesize: 8192
% 0.14/0.37 % ### Marksize: 0
% 0.14/0.37 % ### Memory demanded: 354 KBytes
% 0.14/0.37 % ### Memory freed: 354 KBytes
% 0.14/0.37 % ### Memory remaining: 0 Bytes
% 0.14/0.37 % ### Pages allocated: 132 Pages
% 0.14/0.37 % ###
%------------------------------------------------------------------------------