%------------------------------------------------------------------------------
% File : SPASS-SCL---0.1.1
% Problem : MGT022+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 : n005.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 06:20:06 AM UTC 2026
% Result : Theorem 0.09s 0.37s
% Output : Proof 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 39 ( 8 unt; 3 def)
% Number of atoms : 119 ( 0 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 124 ( 44 ~; 30 |; 24 &)
% ( 0 <=>; 24 =>; 2 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 1 prp; 0-4 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 66 ( 2 sgn 43 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
% FILE RECORD
fof(mp_constant_not_decrease,axiom,
! [X1] :
( constant(X1)
=> ~ decreases(X1) ),
file('theBenchmark.p',mp_constant_not_decrease) ).
% FOF SIMPLE INFERENCE
fof(mp_constant_not_decrease_elimTB,axiom,
! [X1] :
( constant(X1)
=> ~ decreases(X1) ),
inference(elimTB,[status(thm)],[inference(variable_rename,[status(thm)],[mp_constant_not_decrease])]) ).
% FOF SIMPLE INFERENCE
fof(mp_constant_not_decrease_elimImpEquivPushNegMiniScope,axiom,
! [X1] :
( ~ constant(X1)
| ~ decreases(X1) ),
inference(elimImpEquivPushNegMiniScope,[status(thm)],[mp_constant_not_decrease_elimTB]) ).
% FOF PUSH DISJ SPLITTING.
cnf(c_1,plain,
( ~ constant(X0)
| ~ decreases(X0) ),
inference(split_conjunct,[status(thm)],[inference(push_disj,[status(thm)],[mp_constant_not_decrease_elimImpEquivPushNegMiniScope])]) ).
% FILE RECORD
fof(prove_l4,conjecture,
! [X2,X5] :
( ( environment(X2)
& subpopulations(first_movers,efficient_producers,X2,X5) )
=> ( ( decreases(resources(X2,X5))
=> increases(difference(disbanding_rate(first_movers,X5),disbanding_rate(efficient_producers,X5))) )
& ( constant(resources(X2,X5))
=> ~ decreases(difference(disbanding_rate(first_movers,X5),disbanding_rate(efficient_producers,X5))) ) ) ),
file('theBenchmark.p',prove_l4) ).
% NEGATING CONJECTURE
fof(prove_l4_nc,negated_conjecture,
~ ! [X2,X5] :
( ( environment(X2)
& subpopulations(first_movers,efficient_producers,X2,X5) )
=> ( ( decreases(resources(X2,X5))
=> increases(difference(disbanding_rate(first_movers,X5),disbanding_rate(efficient_producers,X5))) )
& ( constant(resources(X2,X5))
=> ~ decreases(difference(disbanding_rate(first_movers,X5),disbanding_rate(efficient_producers,X5))) ) ) ),
inference(negating_conjecture,[status(cth)],[prove_l4]) ).
% FOF SIMPLE INFERENCE
fof(prove_l4_nc_elimTB,negated_conjecture,
~ ! [X1,X2] :
( ( environment(X1)
& subpopulations(first_movers,efficient_producers,X1,X2) )
=> ( ( decreases(resources(X1,X2))
=> increases(difference(disbanding_rate(first_movers,X2),disbanding_rate(efficient_producers,X2))) )
& ( constant(resources(X1,X2))
=> ~ decreases(difference(disbanding_rate(first_movers,X2),disbanding_rate(efficient_producers,X2))) ) ) ),
inference(elimTB,[status(thm)],[inference(variable_rename,[status(thm)],[prove_l4_nc])]) ).
% FOF INTRODUCE RENAMING
fof(ren3_defn,definition,
! [X1,X2] :
( ren3(X1,X2)
<= ( constant(resources(X1,X2))
=> ~ decreases(difference(disbanding_rate(first_movers,X2),disbanding_rate(efficient_producers,X2))) ) ),
introduced(definition,[new_symbols(definition,[ren3])],[prove_l4_nc_elimTB]) ).
% FOF SIMPLE INFERENCE
fof(ren3_elimImpEquivPushNegMiniScope,plain,
! [X1,X2] :
( ( constant(resources(X1,X2))
& decreases(difference(disbanding_rate(first_movers,X2),disbanding_rate(efficient_producers,X2))) )
| ren3(X1,X2) ),
inference(elimImpEquivPushNegMiniScope,[status(thm)],[ren3_defn]) ).
% FOF PUSH DISJ SPLITTING.
cnf(c_9,plain,
( decreases(difference(disbanding_rate(first_movers,X0),disbanding_rate(efficient_producers,X0)))
| ren3(X1,X0) ),
inference(split_conjunct,[status(thm)],[inference(push_disj,[status(thm)],[ren3_elimImpEquivPushNegMiniScope])]) ).
% FILE RECORD
fof(a6,hypothesis,
! [X2,X3,X4,X5] :
( ( environment(X2)
& subpopulations(X3,X4,X2,X5)
& greater(resilience(X4),resilience(X3)) )
=> ( ( decreases(resources(X2,X5))
=> increases(difference(disbanding_rate(X3,X5),disbanding_rate(X4,X5))) )
& ( constant(resources(X2,X5))
=> constant(difference(disbanding_rate(X3,X5),disbanding_rate(X4,X5))) ) ) ),
file('theBenchmark.p',a6) ).
% FOF SIMPLE INFERENCE
fof(a6_elimTB,hypothesis,
! [X1,X2,X3,X4] :
( ( environment(X1)
& subpopulations(X2,X3,X1,X4)
& greater(resilience(X3),resilience(X2)) )
=> ( ( decreases(resources(X1,X4))
=> increases(difference(disbanding_rate(X2,X4),disbanding_rate(X3,X4))) )
& ( constant(resources(X1,X4))
=> constant(difference(disbanding_rate(X2,X4),disbanding_rate(X3,X4))) ) ) ),
inference(elimTB,[status(thm)],[inference(variable_rename,[status(thm)],[a6])]) ).
% FOF INTRODUCE RENAMING
fof(ren1_defn,definition,
! [X1,X4,X2,X3] :
( ren1(X1,X4,X2,X3)
=> ( ( decreases(resources(X1,X4))
=> increases(difference(disbanding_rate(X2,X4),disbanding_rate(X3,X4))) )
& ( constant(resources(X1,X4))
=> constant(difference(disbanding_rate(X2,X4),disbanding_rate(X3,X4))) ) ) ),
introduced(definition,[new_symbols(definition,[ren1])],[a6_elimTB]) ).
% FOF SIMPLE INFERENCE
fof(ren1_elimImpEquivPushNegMiniScope,plain,
! [X1,X2,X3,X4] :
( ~ ren1(X1,X2,X3,X4)
| ( ( ~ decreases(resources(X1,X2))
| increases(difference(disbanding_rate(X3,X2),disbanding_rate(X4,X2))) )
& ( ~ constant(resources(X1,X2))
| constant(difference(disbanding_rate(X3,X2),disbanding_rate(X4,X2))) ) ) ),
inference(elimImpEquivPushNegMiniScope,[status(thm)],[ren1_defn]) ).
% FOF PUSH DISJ SPLITTING.
cnf(c_3,plain,
( ~ ren1(X0,X1,X2,X3)
| ~ constant(resources(X0,X1))
| constant(difference(disbanding_rate(X2,X1),disbanding_rate(X3,X1))) ),
inference(split_conjunct,[status(thm)],[inference(push_disj,[status(thm)],[ren1_elimImpEquivPushNegMiniScope])]) ).
% FOF RENAMING INFERENCE
fof(a6_renObv,hypothesis,
! [X1,X2,X3,X4] :
( ( environment(X1)
& subpopulations(X2,X3,X1,X4)
& greater(resilience(X3),resilience(X2)) )
=> ren1(X1,X4,X2,X3) ),
inference(renaming,[status(esa)],[a6_elimTB,ren1_defn]) ).
% FOF SIMPLE INFERENCE
fof(a6_elimImpEquivPushNegMiniScope,hypothesis,
! [X1,X2,X3,X4] :
( ~ environment(X1)
| ~ subpopulations(X2,X3,X1,X4)
| ~ greater(resilience(X3),resilience(X2))
| ren1(X1,X4,X2,X3) ),
inference(elimImpEquivPushNegMiniScope,[status(thm)],[a6_renObv]) ).
% FOF PUSH DISJ SPLITTING.
cnf(c_4,plain,
( ~ environment(X0)
| ~ subpopulations(X1,X2,X0,X3)
| ~ greater(resilience(X2),resilience(X1))
| ren1(X0,X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[inference(push_disj,[status(thm)],[a6_elimImpEquivPushNegMiniScope])]) ).
% FOF INTRODUCE RENAMING
fof(ren2_defn,definition,
! [X1,X2] :
( ren2(X1,X2)
<= ( decreases(resources(X1,X2))
=> increases(difference(disbanding_rate(first_movers,X2),disbanding_rate(efficient_producers,X2))) ) ),
introduced(definition,[new_symbols(definition,[ren2])],[prove_l4_nc_elimTB]) ).
% FOF RENAMING INFERENCE
fof(prove_l4_nc_renObv,negated_conjecture,
~ ! [X1,X2] :
( ( environment(X1)
& subpopulations(first_movers,efficient_producers,X1,X2) )
=> ( ren2(X1,X2)
& ren3(X1,X2) ) ),
inference(renaming,[status(esa)],[prove_l4_nc_elimTB,ren2_defn,ren3_defn]) ).
% FOF SIMPLE INFERENCE
fof(prove_l4_nc_elimImpEquivPushNegMiniScope,negated_conjecture,
? [X1,X2] :
( environment(X1)
& subpopulations(first_movers,efficient_producers,X1,X2)
& ( ~ ren2(X1,X2)
| ~ ren3(X1,X2) ) ),
inference(elimImpEquivPushNegMiniScope,[status(thm)],[prove_l4_nc_renObv]) ).
% FOF SKOLEM INFERENCE. WIP!!
fof(prove_l4_nc_skol,negated_conjecture,
( environment(skc1)
& subpopulations(first_movers,efficient_producers,skc1,skc2)
& ( ~ ren2(skc1,skc2)
| ~ ren3(skc1,skc2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[skc1,skc2]),skolemize(X1,skc1),skolemize(X2,skc2)],[prove_l4_nc_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)],[prove_l4_nc_skol])]) ).
% FILE RECORD
fof(a2,hypothesis,
greater(resilience(efficient_producers),resilience(first_movers)),
file('theBenchmark.p',a2) ).
% FOF SIMPLE INFERENCE
fof(a2_elimTB,hypothesis,
greater(resilience(efficient_producers),resilience(first_movers)),
inference(elimTB,[status(thm)],[inference(variable_rename,[status(thm)],[a2])]) ).
% FOF SIMPLE INFERENCE
fof(a2_elimImpEquivPushNegMiniScope,hypothesis,
greater(resilience(efficient_producers),resilience(first_movers)),
inference(elimImpEquivPushNegMiniScope,[status(thm)],[a2_elimTB]) ).
% FOF PUSH DISJ SPLITTING.
cnf(c_5,plain,
greater(resilience(efficient_producers),resilience(first_movers)),
inference(split_conjunct,[status(thm)],[inference(push_disj,[status(thm)],[a2_elimImpEquivPushNegMiniScope])]) ).
% FOF PUSH DISJ SPLITTING.
cnf(c_8,plain,
( constant(resources(X0,X1))
| ren3(X0,X1) ),
inference(split_conjunct,[status(thm)],[inference(push_disj,[status(thm)],[ren3_elimImpEquivPushNegMiniScope])]) ).
% FOF PUSH DISJ SPLITTING.
cnf(c_10,plain,
environment(skc1),
inference(split_conjunct,[status(thm)],[inference(push_disj,[status(thm)],[prove_l4_nc_skol])]) ).
% FOF PUSH DISJ SPLITTING.
cnf(c_2,plain,
( ~ ren1(X0,X1,X2,X3)
| ~ decreases(resources(X0,X1))
| increases(difference(disbanding_rate(X2,X1),disbanding_rate(X3,X1))) ),
inference(split_conjunct,[status(thm)],[inference(push_disj,[status(thm)],[ren1_elimImpEquivPushNegMiniScope])]) ).
% FOF SIMPLE INFERENCE
fof(ren2_elimImpEquivPushNegMiniScope,plain,
! [X1,X2] :
( ( decreases(resources(X1,X2))
& ~ increases(difference(disbanding_rate(first_movers,X2),disbanding_rate(efficient_producers,X2))) )
| ren2(X1,X2) ),
inference(elimImpEquivPushNegMiniScope,[status(thm)],[ren2_defn]) ).
% FOF PUSH DISJ SPLITTING.
cnf(c_7,plain,
( ~ increases(difference(disbanding_rate(first_movers,X0),disbanding_rate(efficient_producers,X0)))
| ren2(X1,X0) ),
inference(split_conjunct,[status(thm)],[inference(push_disj,[status(thm)],[ren2_elimImpEquivPushNegMiniScope])]) ).
% FOF PUSH DISJ SPLITTING.
cnf(c_6,plain,
( decreases(resources(X0,X1))
| ren2(X0,X1) ),
inference(split_conjunct,[status(thm)],[inference(push_disj,[status(thm)],[ren2_elimImpEquivPushNegMiniScope])]) ).
% FOF PUSH DISJ SPLITTING.
cnf(c_12,plain,
( ~ ren2(skc1,skc2)
| ~ ren3(skc1,skc2) ),
inference(split_conjunct,[status(thm)],[inference(push_disj,[status(thm)],[prove_l4_nc_skol])]) ).
% CNF SPASS RESOLUTION.
cnf(c_13,plain,
( ~ environment(skc1)
| ~ subpopulations(first_movers,efficient_producers,skc1,skc2)
| ~ greater(resilience(efficient_producers),resilience(first_movers))
| ~ ren3(skc1,skc2) ),
inference(resolution,[status(thm)],[c_2,c_7,c_4,c_6,c_12]) ).
% CNF SPASS RESOLUTION.
cnf(c_14,plain,
( ~ subpopulations(first_movers,efficient_producers,skc1,skc2)
| ~ greater(resilience(efficient_producers),resilience(first_movers))
| ~ ren3(skc1,skc2) ),
inference(resolution,[status(thm)],[c_10,c_13]) ).
% CNF SPASS RESOLUTION.
cnf(c_15,plain,
( ~ greater(resilience(efficient_producers),resilience(first_movers))
| ~ ren3(skc1,skc2) ),
inference(resolution,[status(thm)],[c_11,c_14]) ).
% CNF SPASS RESOLUTION.
cnf(c_16,plain,
~ ren3(skc1,skc2),
inference(resolution,[status(thm)],[c_5,c_15]) ).
% CNF SPASS RESOLUTION.
cnf(c_19,plain,
$false,
inference(resolution,[status(thm)],[c_1,c_9,c_3,c_4,c_11,c_5,c_8,c_16,c_10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : MGT022+2 : TPTP v9.3.0. Released v2.0.0.
% 0.00/0.03 % Command : /export/starexec/sandbox/solver/bin/SPASS-SCL-FOL -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n005.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 12:05:35 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
% 0.09/0.37
% 0.09/0.37 % Input Clauses:
% 0.09/0.37 % 1:2:1:INP:Top: constant(x0),decreases(x0) ->
% 0.09/0.37 % 2:3:4:INP:TopTopTopTop: ren1(x0,x1,x2,x3),decreases(resources(x0,x1)) -> increases(difference(disbanding_rate(x2,x1),disbanding_rate(x3,x1)))
% 0.09/0.37 % 3:3:4:INP:TopTopTopTop: ren1(x0,x1,x2,x3),constant(resources(x0,x1)) -> constant(difference(disbanding_rate(x2,x1),disbanding_rate(x3,x1)))
% 0.09/0.37 % 4:4:4:INP:TopTopTopTop: environment(x0),subpopulations(x1,x2,x0,x3),greater(resilience(x2),resilience(x1)) -> ren1(x0,x3,x1,x2)
% 0.09/0.37 % 5:1:0:INP:: -> greater(resilience(efficient_producers),resilience(first_movers))
% 0.09/0.37 % 6:2:2:INP:TopTop: -> decreases(resources(x0,x1)),ren2(x0,x1)
% 0.09/0.37 % 7:2:2:INP:TopTop: increases(difference(disbanding_rate(first_movers,x0),disbanding_rate(efficient_producers,x0))) -> ren2(x1,x0)
% 0.09/0.37 % 8:2:2:INP:TopTop: -> constant(resources(x0,x1)),ren3(x0,x1)
% 0.09/0.37 % 9:2:2:INP:TopTop: -> decreases(difference(disbanding_rate(first_movers,x0),disbanding_rate(efficient_producers,x0))),ren3(x1,x0)
% 0.09/0.37 % 10:1:0:INP:: -> environment(skc1)
% 0.09/0.37 % 11:1:0:INP:: -> subpopulations(first_movers,efficient_producers,skc1,skc2)
% 0.09/0.37 % 12:2:0:INP:: ren2(skc1,skc2),ren3(skc1,skc2) ->
% 0.09/0.37
% 0.09/0.37 % Predicates: constant decreases environment subpopulations greater increases ren1 ren2 ren3
% 0.09/0.37 % Fol Constants: efficient_producers first_movers skc1 skc2
% 0.09/0.37 % Fol Functions: resilience resources disbanding_rate difference
% 0.09/0.37 % Problem Properties:
% 0.09/0.37 % This is a full first-order problem without equality. The Problem is non-linear.
% 0.09/0.37
% 0.09/0.37
% 0.09/0.37 % Reduced Input Axiom Clauses:
% 0.09/0.37 % 1:2:1:INP:Top: constant(x0),decreases(x0) ->
% 0.09/0.37 % 2:3:4:INP:TopTopTopTop: ren1(x0,x1,x2,x3),decreases(resources(x0,x1)) -> increases(difference(disbanding_rate(x2,x1),disbanding_rate(x3,x1)))
% 0.09/0.37 % 3:3:4:INP:TopTopTopTop: ren1(x0,x1,x2,x3),constant(resources(x0,x1)) -> constant(difference(disbanding_rate(x2,x1),disbanding_rate(x3,x1)))
% 0.09/0.37 % 6:2:2:INP:TopTop: -> decreases(resources(x0,x1)),ren2(x0,x1)
% 0.09/0.37 % 7:2:2:INP:TopTop: increases(difference(disbanding_rate(first_movers,x0),disbanding_rate(efficient_producers,x0))) -> ren2(x1,x0)
% 0.09/0.37 % 8:2:2:INP:TopTop: -> constant(resources(x0,x1)),ren3(x0,x1)
% 0.09/0.37 % 9:2:2:INP:TopTop: -> decreases(difference(disbanding_rate(first_movers,x0),disbanding_rate(efficient_producers,x0))),ren3(x1,x0)
% 0.09/0.37
% 0.09/0.37 % Reduced Input Conjecture Clauses:
% 0.09/0.37 % 4:4:4:INP:TopTopTopTop: environment(x0),subpopulations(x1,x2,x0,x3),greater(resilience(x2),resilience(x1)) -> ren1(x0,x3,x1,x2)
% 0.09/0.37 % 5:1:0:INP:: -> greater(resilience(efficient_producers),resilience(first_movers))
% 0.09/0.37 % 10:1:0:INP:: -> environment(skc1)
% 0.09/0.37 % 11:1:0:INP:: -> subpopulations(first_movers,efficient_producers,skc1,skc2)
% 0.09/0.37 % 12:2:0:INP:: ren2(skc1,skc2),ren3(skc1,skc2) ->
% 0.09/0.37
% 0.09/0.37
% 0.09/0.37 % === Starting SPASS-SCL-FOL A Little Less Naive, considering 22 atoms initially. Used heuristic: lmodel_grow ===
% 0.09/0.37
% 0.09/0.37
% 0.09/0.37
% 0.09/0.37 % SZS status Theorem
% 0.09/0.37 % Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37
% 0.09/0.37 % SPASS-SCL-FOL Statistics:
% 0.09/0.37 % Number of learned clauses: 3
% 0.09/0.37 % Number of propagations: 33
% 0.09/0.37 % Number of decisions: 13
% 0.09/0.37 % Number of resolutions: 15
% 0.09/0.37 % Number of condensations: 0
% 0.09/0.37 % Number of sub resolutions: 3
% 0.09/0.37
% 0.09/0.37 % Solver is done. Empty clause found
% 0.09/0.37
% 0.09/0.37 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.09/0.37 % SZS output start Proof for theBenchmark
% See solution above
% 0.09/0.37 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.09/0.37
% 0.09/0.37
% 0.09/0.37 % Needed: 0:00:00.00
% 0.09/0.37
% 0.09/0.37 % ###
% 0.09/0.37 % ### Pagesize: 8192
% 0.09/0.37 % ### Marksize: 0
% 0.09/0.37 % ### Memory demanded: 485 KBytes
% 0.09/0.37 % ### Memory freed: 485 KBytes
% 0.09/0.37 % ### Memory remaining: 0 Bytes
% 0.09/0.37 % ### Pages allocated: 151 Pages
% 0.09/0.37 % ###
%------------------------------------------------------------------------------