%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : MGT032-2 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n011.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 02:11:33 PM UTC 2026
% Result : Unsatisfiable 3.66s 16.09s
% Output : Proof 3.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 48 ( 24 unt; 0 def)
% Number of atoms : 96 ( 17 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 102 ( 54 ~; 48 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-4 aty)
% Number of variables : 50 ( 0 sgn 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f1,hypothesis,
( in_environment(A,sk1(A))
| ~ stable(A)
| ~ environment(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l1_2) ).
fof(f1_nnf,plain,
! [A] :
( in_environment(A,sk1(A))
| ~ stable(A)
| ~ environment(A) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [A] :
( in_environment(A,sk1(A))
| ~ stable(A)
| ~ environment(A) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( in_environment(X0,sk1(X0))
| ~ stable(X0)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(hi1,axiom,
ifeq(environment(X0),true,ifeq(stable(X0),true,in_environment(X0,sk1(X0)),true),true) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(f3,negated_conjecture,
environment(sk2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_t1_4) ).
fof(f3_nnf,plain,
environment(sk2),
inference(nnf_transformation,[status(thm)],[f3]) ).
cnf(c3,plain,
environment(sk2),
inference(cnf_transformation,[status(esa)],[f3_nnf]) ).
cnf(hi3,negated_conjecture,
environment(sk2) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(f4,negated_conjecture,
stable(sk2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_t1_5) ).
fof(f4_nnf,plain,
stable(sk2),
inference(nnf_transformation,[status(thm)],[f4]) ).
cnf(c4,plain,
stable(sk2),
inference(cnf_transformation,[status(esa)],[f4_nnf]) ).
cnf(hi4,negated_conjecture,
stable(sk2) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(h0,plain,
in_environment(sk2,sk1(sk2)) = true,
inference(hyper_resolution,[status(thm)],[hi1,hi3,hi4]) ).
cnf(f6,negated_conjecture,
( greater_or_equal(sk3(A),A)
| ~ in_environment(sk2,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_t1_7) ).
fof(f6_nnf,plain,
! [A] :
( greater_or_equal(sk3(A),A)
| ~ in_environment(sk2,A) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [A] :
( greater_or_equal(sk3(A),A)
| ~ in_environment(sk2,A) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
( greater_or_equal(sk3(X0),X0)
| ~ in_environment(sk2,X0) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(hi6,negated_conjecture,
ifeq(in_environment(sk2,X0),true,greater_or_equal(sk3(X0),X0),true) = true,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(h1,plain,
greater_or_equal(sk3(sk1(sk2)),sk1(sk2)) = true,
inference(hyper_resolution,[status(thm)],[hi6,h0]) ).
cnf(f5,negated_conjecture,
( subpopulations(first_movers,efficient_producers,sk2,sk3(A))
| ~ in_environment(sk2,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_t1_6) ).
fof(f5_nnf,plain,
! [A] :
( subpopulations(first_movers,efficient_producers,sk2,sk3(A))
| ~ in_environment(sk2,A) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [A] :
( subpopulations(first_movers,efficient_producers,sk2,sk3(A))
| ~ in_environment(sk2,A) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
( subpopulations(first_movers,efficient_producers,sk2,sk3(X0))
| ~ in_environment(sk2,X0) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(hi5,negated_conjecture,
ifeq(in_environment(sk2,X0),true,subpopulations(first_movers,efficient_producers,sk2,sk3(X0)),true) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(h2,plain,
subpopulations(first_movers,efficient_producers,sk2,sk3(sk1(sk2))) = true,
inference(hyper_resolution,[status(thm)],[hi5,h0]) ).
cnf(f2,hypothesis,
( greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B))
| ~ greater_or_equal(B,sk1(A))
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ stable(A)
| ~ environment(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l1_3) ).
fof(f2_nnf,plain,
! [A,B] :
( greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B))
| ~ greater_or_equal(B,sk1(A))
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ stable(A)
| ~ environment(A) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [A,B] :
( greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B))
| ~ greater_or_equal(B,sk1(A))
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ stable(A)
| ~ environment(A) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ greater_or_equal(X1,sk1(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ stable(X0)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi2,axiom,
ifeq(environment(X0),true,ifeq(stable(X0),true,ifeq(subpopulations(first_movers,efficient_producers,X0,X1),true,ifeq(greater_or_equal(X1,sk1(X0)),true,greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1)),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(h3,plain,
greater(growth_rate(efficient_producers,sk3(sk1(sk2))),growth_rate(first_movers,sk3(sk1(sk2)))) = true,
inference(hyper_resolution,[status(thm)],[hi2,hi3,hi4,h2,h1]) ).
cnf(f0,axiom,
( selection_favors(C,B,D)
| ~ greater(growth_rate(C,D),growth_rate(B,D))
| ~ subpopulations(B,C,A,D)
| ~ environment(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp1_high_growth_rates_1) ).
fof(f0_nnf,plain,
! [A,B,C,D] :
( selection_favors(C,B,D)
| ~ greater(growth_rate(C,D),growth_rate(B,D))
| ~ subpopulations(B,C,A,D)
| ~ environment(A) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [A,B,C,D] :
( selection_favors(C,B,D)
| ~ greater(growth_rate(C,D),growth_rate(B,D))
| ~ subpopulations(B,C,A,D)
| ~ environment(A) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( selection_favors(X2,X1,X3)
| ~ greater(growth_rate(X2,X3),growth_rate(X1,X3))
| ~ subpopulations(X1,X2,X0,X3)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi0,axiom,
ifeq(environment(X0),true,ifeq(subpopulations(X1,X2,X0,X3),true,ifeq(greater(growth_rate(X2,X3),growth_rate(X1,X3)),true,selection_favors(X2,X1,X3),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(h4,plain,
selection_favors(efficient_producers,first_movers,sk3(sk1(sk2))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi3,h2,h3]) ).
cnf(f7,negated_conjecture,
( ~ selection_favors(efficient_producers,first_movers,sk3(A))
| ~ in_environment(sk2,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_t1_8) ).
fof(f7_nnf,plain,
! [A] :
( ~ selection_favors(efficient_producers,first_movers,sk3(A))
| ~ in_environment(sk2,A) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [A] :
( ~ selection_favors(efficient_producers,first_movers,sk3(A))
| ~ in_environment(sk2,A) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
( ~ selection_favors(efficient_producers,first_movers,sk3(X0))
| ~ in_environment(sk2,X0) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(hi7,negated_conjecture,
ifeq(in_environment(sk2,X0),true,ifeq(selection_favors(efficient_producers,first_movers,sk3(X0)),true,false,true),true) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t0,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi7,h0,h4]) ).
cnf(t44,plain,
false = true,
inference(orient,[status(thm)],[t0]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t44]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT032-2 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.34 % Computer : n011.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/15.61 % CPULimit : 300
% 0.07/15.61 % WCLimit : 300
% 0.07/15.61 % DateTime : Thu Sep 24 01:05:38 UTC 2026
% 0.07/15.62 % CPUTime :
% 0.07/15.62 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 3.66/16.09 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.66/16.09 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------