%------------------------------------------------------------------------------
% File : SPASS-SCL---0.1.1
% Problem : MGT032+2 : 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 : n014.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 06:20:08 AM UTC 2026
% Result : Theorem 0.11s 0.38s
% Output : Proof 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 30 ( 3 unt; 2 def)
% Number of atoms : 109 ( 0 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 112 ( 33 ~; 29 |; 32 &)
% ( 0 <=>; 17 =>; 1 <=; 0 <~>)
% Maximal formula depth : 9 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 1 prp; 0-4 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 75 ( 5 sgn 41 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
% FILE RECORD
fof(l1,hypothesis,
! [X1] :
( ( environment(X1)
& stable(X1) )
=> ? [X5] :
( in_environment(X1,X5)
& ! [X4] :
( ( subpopulations(first_movers,efficient_producers,X1,X4)
& greater_or_equal(X4,X5) )
=> greater(growth_rate(efficient_producers,X4),growth_rate(first_movers,X4)) ) ) ),
file('theBenchmark.p',l1) ).
% FOF SIMPLE INFERENCE
fof(l1_elimTB,hypothesis,
! [X1] :
( ( environment(X1)
& stable(X1) )
=> ? [X2] :
( in_environment(X1,X2)
& ! [X3] :
( ( subpopulations(first_movers,efficient_producers,X1,X3)
& greater_or_equal(X3,X2) )
=> greater(growth_rate(efficient_producers,X3),growth_rate(first_movers,X3)) ) ) ),
inference(elimTB,[status(thm)],[inference(variable_rename,[status(thm)],[l1])]) ).
% FOF INTRODUCE RENAMING
fof(ren1_defn,definition,
! [X1,X2] :
( ren1(X1,X2)
=> ( in_environment(X1,X2)
& ! [X3] :
( ( subpopulations(first_movers,efficient_producers,X1,X3)
& greater_or_equal(X3,X2) )
=> greater(growth_rate(efficient_producers,X3),growth_rate(first_movers,X3)) ) ) ),
introduced(definition,[new_symbols(definition,[ren1])],[l1_elimTB]) ).
% FOF SIMPLE INFERENCE
fof(ren1_elimImpEquivPushNegMiniScope,plain,
! [X1,X2] :
( ~ ren1(X1,X2)
| ( in_environment(X1,X2)
& ! [X3] :
( ~ subpopulations(first_movers,efficient_producers,X1,X3)
| ~ greater_or_equal(X3,X2)
| greater(growth_rate(efficient_producers,X3),growth_rate(first_movers,X3)) ) ) ),
inference(elimImpEquivPushNegMiniScope,[status(thm)],[ren1_defn]) ).
% FOF PUSH DISJ SPLITTING.
cnf(c_3,plain,
( ~ ren1(X0,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ greater_or_equal(X2,X1)
| greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2)) ),
inference(split_conjunct,[status(thm)],[inference(push_disj,[status(thm)],[ren1_elimImpEquivPushNegMiniScope])]) ).
% FILE RECORD
fof(mp1_high_growth_rates,axiom,
! [X1,X2,X3,X4] :
( ( environment(X1)
& subpopulations(X2,X3,X1,X4)
& greater(growth_rate(X3,X4),growth_rate(X2,X4)) )
=> selection_favors(X3,X2,X4) ),
file('theBenchmark.p',mp1_high_growth_rates) ).
% FOF SIMPLE INFERENCE
fof(mp1_high_growth_rates_elimTB,axiom,
! [X1,X2,X3,X4] :
( ( environment(X1)
& subpopulations(X2,X3,X1,X4)
& greater(growth_rate(X3,X4),growth_rate(X2,X4)) )
=> selection_favors(X3,X2,X4) ),
inference(elimTB,[status(thm)],[inference(variable_rename,[status(thm)],[mp1_high_growth_rates])]) ).
% FOF SIMPLE INFERENCE
fof(mp1_high_growth_rates_elimImpEquivPushNegMiniScope,axiom,
! [X1,X2,X3,X4] :
( ~ environment(X1)
| ~ subpopulations(X2,X3,X1,X4)
| ~ greater(growth_rate(X3,X4),growth_rate(X2,X4))
| selection_favors(X3,X2,X4) ),
inference(elimImpEquivPushNegMiniScope,[status(thm)],[mp1_high_growth_rates_elimTB]) ).
% FOF PUSH DISJ SPLITTING.
cnf(c_1,plain,
( ~ environment(X0)
| ~ subpopulations(X1,X2,X0,X3)
| ~ greater(growth_rate(X2,X3),growth_rate(X1,X3))
| selection_favors(X2,X1,X3) ),
inference(split_conjunct,[status(thm)],[inference(push_disj,[status(thm)],[mp1_high_growth_rates_elimImpEquivPushNegMiniScope])]) ).
% FILE RECORD
fof(prove_t1,conjecture,
! [X1] :
( ( environment(X1)
& stable(X1) )
=> ? [X5] :
( in_environment(X1,X5)
& ! [X4] :
( ( subpopulations(first_movers,efficient_producers,X1,X4)
& greater_or_equal(X4,X5) )
=> selection_favors(efficient_producers,first_movers,X4) ) ) ),
file('theBenchmark.p',prove_t1) ).
% NEGATING CONJECTURE
fof(prove_t1_nc,negated_conjecture,
~ ! [X1] :
( ( environment(X1)
& stable(X1) )
=> ? [X5] :
( in_environment(X1,X5)
& ! [X4] :
( ( subpopulations(first_movers,efficient_producers,X1,X4)
& greater_or_equal(X4,X5) )
=> selection_favors(efficient_producers,first_movers,X4) ) ) ),
inference(negating_conjecture,[status(cth)],[prove_t1]) ).
% FOF SIMPLE INFERENCE
fof(prove_t1_nc_elimTB,negated_conjecture,
~ ! [X1] :
( ( environment(X1)
& stable(X1) )
=> ? [X2] :
( in_environment(X1,X2)
& ! [X3] :
( ( subpopulations(first_movers,efficient_producers,X1,X3)
& greater_or_equal(X3,X2) )
=> selection_favors(efficient_producers,first_movers,X3) ) ) ),
inference(elimTB,[status(thm)],[inference(variable_rename,[status(thm)],[prove_t1_nc])]) ).
% FOF INTRODUCE RENAMING
fof(ren2_defn,definition,
! [X1,X3,X2] :
( ren2(X1,X3,X2)
<= ( ( subpopulations(first_movers,efficient_producers,X1,X3)
& greater_or_equal(X3,X2) )
=> selection_favors(efficient_producers,first_movers,X3) ) ),
introduced(definition,[new_symbols(definition,[ren2])],[prove_t1_nc_elimTB]) ).
% FOF SIMPLE INFERENCE
fof(ren2_elimImpEquivPushNegMiniScope,plain,
! [X1,X2,X3] :
( ( subpopulations(first_movers,efficient_producers,X1,X2)
& greater_or_equal(X2,X3)
& ~ selection_favors(efficient_producers,first_movers,X2) )
| ren2(X1,X2,X3) ),
inference(elimImpEquivPushNegMiniScope,[status(thm)],[ren2_defn]) ).
% FOF PUSH DISJ SPLITTING.
cnf(c_5,plain,
( subpopulations(first_movers,efficient_producers,X0,X1)
| ren2(X0,X1,X2) ),
inference(split_conjunct,[status(thm)],[inference(push_disj,[status(thm)],[ren2_elimImpEquivPushNegMiniScope])]) ).
% FOF PUSH DISJ SPLITTING.
cnf(c_7,plain,
( ~ selection_favors(efficient_producers,first_movers,X0)
| ren2(X1,X0,X2) ),
inference(split_conjunct,[status(thm)],[inference(push_disj,[status(thm)],[ren2_elimImpEquivPushNegMiniScope])]) ).
% CNF SPASS RESOLUTION.
cnf(c_11,plain,
( ~ ren1(X0,X1)
| ~ greater_or_equal(X2,X1)
| ~ environment(X0)
| ren2(X0,X2,X3) ),
inference(resolution,[status(thm)],[c_3,c_1,c_5,c_7]) ).
% FOF PUSH DISJ SPLITTING.
cnf(c_6,plain,
( greater_or_equal(X0,X1)
| ren2(X2,X0,X1) ),
inference(split_conjunct,[status(thm)],[inference(push_disj,[status(thm)],[ren2_elimImpEquivPushNegMiniScope])]) ).
% FOF RENAMING INFERENCE
fof(prove_t1_nc_renObv,negated_conjecture,
~ ! [X1] :
( ( environment(X1)
& stable(X1) )
=> ? [X2] :
( in_environment(X1,X2)
& ! [X3] : ren2(X1,X3,X2) ) ),
inference(renaming,[status(esa)],[prove_t1_nc_elimTB,ren2_defn]) ).
% FOF SIMPLE INFERENCE
fof(prove_t1_nc_elimImpEquivPushNegMiniScope,negated_conjecture,
? [X1] :
( environment(X1)
& stable(X1)
& ! [X2] :
( ~ in_environment(X1,X2)
| ? [X3] : ~ ren2(X1,X3,X2) ) ),
inference(elimImpEquivPushNegMiniScope,[status(thm)],[prove_t1_nc_renObv]) ).
% FOF SKOLEM INFERENCE. WIP!!
fof(prove_t1_nc_skol,negated_conjecture,
( environment(skc2)
& stable(skc2)
& ! [X2] :
( ~ in_environment(skc2,X2)
| ~ ren2(skc2,skf3(X2),X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[skc2,skf3]),skolemize(X1,skc2),skolemize(X3,skf3(X2))],[prove_t1_nc_elimImpEquivPushNegMiniScope]) ).
% FOF PUSH DISJ SPLITTING.
cnf(c_10,plain,
( ~ in_environment(skc2,X0)
| ~ ren2(skc2,skf3(X0),X0) ),
inference(split_conjunct,[status(thm)],[inference(push_disj,[status(thm)],[prove_t1_nc_skol])]) ).
% FOF PUSH DISJ SPLITTING.
cnf(c_2,plain,
( ~ ren1(X0,X1)
| in_environment(X0,X1) ),
inference(split_conjunct,[status(thm)],[inference(push_disj,[status(thm)],[ren1_elimImpEquivPushNegMiniScope])]) ).
% FOF RENAMING INFERENCE
fof(l1_renObv,hypothesis,
! [X1] :
( ( environment(X1)
& stable(X1) )
=> ? [X2] : ren1(X1,X2) ),
inference(renaming,[status(esa)],[l1_elimTB,ren1_defn]) ).
% FOF SIMPLE INFERENCE
fof(l1_elimImpEquivPushNegMiniScope,hypothesis,
! [X1] :
( ~ environment(X1)
| ~ stable(X1)
| ? [X2] : ren1(X1,X2) ),
inference(elimImpEquivPushNegMiniScope,[status(thm)],[l1_renObv]) ).
% FOF SKOLEM INFERENCE. WIP!!
fof(l1_skol,hypothesis,
! [X1] :
( ~ environment(X1)
| ~ stable(X1)
| ren1(X1,skf1(X1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[skf1]),skolemize(X2,skf1(X1))],[l1_elimImpEquivPushNegMiniScope]) ).
% FOF PUSH DISJ SPLITTING.
cnf(c_4,plain,
( ~ environment(X0)
| ~ stable(X0)
| ren1(X0,skf1(X0)) ),
inference(split_conjunct,[status(thm)],[inference(push_disj,[status(thm)],[l1_skol])]) ).
% FOF PUSH DISJ SPLITTING.
cnf(c_8,plain,
environment(skc2),
inference(split_conjunct,[status(thm)],[inference(push_disj,[status(thm)],[prove_t1_nc_skol])]) ).
% FOF PUSH DISJ SPLITTING.
cnf(c_9,plain,
stable(skc2),
inference(split_conjunct,[status(thm)],[inference(push_disj,[status(thm)],[prove_t1_nc_skol])]) ).
% CNF SPASS RESOLUTION.
cnf(c_13,plain,
$false,
inference(resolution,[status(thm)],[c_11,c_6,c_10,c_2,c_4,c_8,c_9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT032+2 : 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
% 0.11/0.37 % Computer : n014.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
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 7 12:22:41 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running /export/starexec/sandbox/solver/bin/SPASS-SCL-FOL -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.38
% 0.11/0.38 % Input Clauses:
% 0.11/0.38 % 1:4:4:INP:TopTopTopTop: environment(x0),subpopulations(x1,x2,x0,x3),greater(growth_rate(x2,x3),growth_rate(x1,x3)) -> selection_favors(x2,x1,x3)
% 0.11/0.38 % 2:2:2:INP:TopTop: ren1(x0,x1) -> in_environment(x0,x1)
% 0.11/0.38 % 3:4:3:INP:TopTopTop: ren1(x0,x1),subpopulations(first_movers,efficient_producers,x0,x2),greater_or_equal(x2,x1) -> greater(growth_rate(efficient_producers,x2),growth_rate(first_movers,x2))
% 0.11/0.38 % 4:3:1:INP:Top: environment(x0),stable(x0) -> ren1(x0,skf1(x0))
% 0.11/0.38 % 5:2:3:INP:TopTopTop: -> subpopulations(first_movers,efficient_producers,x0,x1),ren2(x0,x1,x2)
% 0.11/0.38 % 6:2:3:INP:TopTopTop: -> greater_or_equal(x0,x1),ren2(x2,x0,x1)
% 0.11/0.38 % 7:2:3:INP:TopTopTop: selection_favors(efficient_producers,first_movers,x0) -> ren2(x1,x0,x2)
% 0.11/0.38 % 8:1:0:INP:: -> environment(skc2)
% 0.11/0.38 % 9:1:0:INP:: -> stable(skc2)
% 0.11/0.38 % 10:2:1:INP:Top: in_environment(skc2,x0),ren2(skc2,skf3(x0),x0) ->
% 0.11/0.38
% 0.11/0.38 % Predicates: environment subpopulations greater selection_favors stable in_environment greater_or_equal ren1 ren2
% 0.11/0.38 % Fol Constants: first_movers efficient_producers skc2
% 0.11/0.38 % Fol Functions: growth_rate skf1 skf3
% 0.11/0.38 % Problem Properties:
% 0.11/0.38 % This is a full first-order problem without equality. The Problem is non-linear.
% 0.11/0.38
% 0.11/0.38
% 0.11/0.38 % Reduced Input Axiom Clauses:
% 0.11/0.38 % 1:4:4:INP:TopTopTopTop: environment(x0),subpopulations(x1,x2,x0,x3),greater(growth_rate(x2,x3),growth_rate(x1,x3)) -> selection_favors(x2,x1,x3)
% 0.11/0.38 % 2:2:2:INP:TopTop: ren1(x0,x1) -> in_environment(x0,x1)
% 0.11/0.38 % 3:4:3:INP:TopTopTop: ren1(x0,x1),subpopulations(first_movers,efficient_producers,x0,x2),greater_or_equal(x2,x1) -> greater(growth_rate(efficient_producers,x2),growth_rate(first_movers,x2))
% 0.11/0.38 % 5:2:3:INP:TopTopTop: -> subpopulations(first_movers,efficient_producers,x0,x1),ren2(x0,x1,x2)
% 0.11/0.38 % 6:2:3:INP:TopTopTop: -> greater_or_equal(x0,x1),ren2(x2,x0,x1)
% 0.11/0.38 % 7:2:3:INP:TopTopTop: selection_favors(efficient_producers,first_movers,x0) -> ren2(x1,x0,x2)
% 0.11/0.38
% 0.11/0.38 % Reduced Input Conjecture Clauses:
% 0.11/0.38 % 4:3:1:INP:Top: environment(x0),stable(x0) -> ren1(x0,skf1(x0))
% 0.11/0.38 % 8:1:0:INP:: -> environment(skc2)
% 0.11/0.38 % 9:1:0:INP:: -> stable(skc2)
% 0.11/0.38 % 10:2:1:INP:Top: in_environment(skc2,x0),ren2(skc2,skf3(x0),x0) ->
% 0.11/0.38
% 0.11/0.38
% 0.11/0.38 % === Starting SPASS-SCL-FOL A Little Less Naive, considering 22 atoms initially. Used heuristic: lmodel_grow ===
% 0.11/0.38
% 0.11/0.38
% 0.11/0.38
% 0.11/0.38 % SZS status Theorem
% 0.11/0.38 % Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.38
% 0.11/0.38 % SPASS-SCL-FOL Statistics:
% 0.11/0.38 % Number of learned clauses: 2
% 0.11/0.38 % Number of propagations: 34
% 0.11/0.38 % Number of decisions: 22
% 0.11/0.38 % Number of resolutions: 10
% 0.11/0.38 % Number of condensations: 1
% 0.11/0.38 % Number of sub resolutions: 0
% 0.11/0.38
% 0.11/0.38 % Solver is done. Empty clause found
% 0.11/0.38
% 0.11/0.38 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.11/0.38 % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.38 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.11/0.38
% 0.11/0.38
% 0.11/0.38 % Needed: 0:00:00.00
% 0.11/0.38
% 0.11/0.38 % ###
% 0.11/0.38 % ### Pagesize: 8192
% 0.11/0.38 % ### Marksize: 0
% 0.11/0.38 % ### Memory demanded: 553 KBytes
% 0.11/0.38 % ### Memory freed: 553 KBytes
% 0.11/0.38 % ### Memory remaining: 0 Bytes
% 0.11/0.38 % ### Pages allocated: 153 Pages
% 0.11/0.38 % ###
%------------------------------------------------------------------------------