%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : COM010-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n013.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 : Sun Sep 27 06:59:38 AM UTC 2026
% Result : Unsatisfiable 0.09s 10.78s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 20 ( 20 unt; 0 def)
% Number of atoms : 20 ( 19 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-4 aty)
% Number of variables : 4 ( 0 sgn 2 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_conjecture_0,axiom,
c_UNITY_OInit(v_F,t_a) = c_UNITY_OInit(v_G,t_a),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_1,plain,
c_UNITY_OInit(v_F,t_a) = c_UNITY_OInit(v_G,t_a),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
cnf(c_2,plain,
c_UNITY_OInit(v_G,t_a) = c_UNITY_OInit(v_F,t_a),
inference(copy,[status(thm)],[c_1]) ).
fof(cls_conjecture_1,axiom,
c_UNITY_OActs(v_F,t_a) = c_UNITY_OActs(v_G,t_a),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(c_3,plain,
c_UNITY_OActs(v_F,t_a) = c_UNITY_OActs(v_G,t_a),
inference(clausify,[status(thm)],[cls_conjecture_1]) ).
cnf(c_4,plain,
c_UNITY_OActs(v_G,t_a) = c_UNITY_OActs(v_F,t_a),
inference(copy,[status(thm)],[c_3]) ).
fof(cls_conjecture_2,axiom,
c_UNITY_OAllowedActs(v_F,t_a) = c_UNITY_OAllowedActs(v_G,t_a),
file('theBenchmark.p',cls_conjecture_2) ).
cnf(c_5,plain,
c_UNITY_OAllowedActs(v_F,t_a) = c_UNITY_OAllowedActs(v_G,t_a),
inference(clausify,[status(thm)],[cls_conjecture_2]) ).
cnf(c_6,plain,
c_UNITY_OAllowedActs(v_G,t_a) = c_UNITY_OAllowedActs(v_F,t_a),
inference(copy,[status(thm)],[c_5]) ).
fof(cls_conjecture_3,axiom,
v_F != v_G,
file('theBenchmark.p',cls_conjecture_3) ).
cnf(c_7,plain,
v_F != v_G,
inference(clausify,[status(thm)],[cls_conjecture_3]) ).
cnf(c_8,plain,
v_G != v_F,
inference(copy,[status(thm)],[c_7]) ).
fof(cls_UNITY_Osurjective__mk__program_0,axiom,
! [VAR_0,VAR_1] : c_UNITY_Omk__program(c_Pair(c_UNITY_OInit(VAR_0,VAR_1),c_Pair(c_UNITY_OActs(VAR_0,VAR_1),c_UNITY_OAllowedActs(VAR_0,VAR_1),tc_set(tc_set(tc_prod(VAR_1,VAR_1))),tc_set(tc_set(tc_prod(VAR_1,VAR_1)))),tc_set(VAR_1),tc_prod(tc_set(tc_set(tc_prod(VAR_1,VAR_1))),tc_set(tc_set(tc_prod(VAR_1,VAR_1))))),VAR_1) = VAR_0,
file('theBenchmark.p',cls_UNITY_Osurjective__mk__program_0) ).
cnf(c_9,plain,
c_UNITY_Omk__program(c_Pair(c_UNITY_OInit(A,B),c_Pair(c_UNITY_OActs(A,B),c_UNITY_OAllowedActs(A,B),tc_set(tc_set(tc_prod(B,B))),tc_set(tc_set(tc_prod(B,B)))),tc_set(B),tc_prod(tc_set(tc_set(tc_prod(B,B))),tc_set(tc_set(tc_prod(B,B))))),B) = A,
inference(clausify,[status(thm)],[cls_UNITY_Osurjective__mk__program_0]) ).
cnf(c_12,plain,
c_UNITY_Omk__program(c_Pair(c_UNITY_OInit(v_F,t_a),c_Pair(c_UNITY_OActs(v_G,t_a),c_UNITY_OAllowedActs(v_G,t_a),tc_set(tc_set(tc_prod(t_a,t_a))),tc_set(tc_set(tc_prod(t_a,t_a)))),tc_set(t_a),tc_prod(tc_set(tc_set(tc_prod(t_a,t_a))),tc_set(tc_set(tc_prod(t_a,t_a))))),t_a) = v_G,
inference(paramod,[status(thm)],[c_2,c_9]) ).
cnf(c_13,plain,
c_UNITY_Omk__program(c_Pair(c_UNITY_OInit(v_F,t_a),c_Pair(c_UNITY_OActs(v_F,t_a),c_UNITY_OAllowedActs(v_G,t_a),tc_set(tc_set(tc_prod(t_a,t_a))),tc_set(tc_set(tc_prod(t_a,t_a)))),tc_set(t_a),tc_prod(tc_set(tc_set(tc_prod(t_a,t_a))),tc_set(tc_set(tc_prod(t_a,t_a))))),t_a) = v_G,
inference(paramod,[status(thm)],[c_4,c_12]) ).
cnf(c_14,plain,
c_UNITY_Omk__program(c_Pair(c_UNITY_OInit(v_F,t_a),c_Pair(c_UNITY_OActs(v_F,t_a),c_UNITY_OAllowedActs(v_F,t_a),tc_set(tc_set(tc_prod(t_a,t_a))),tc_set(tc_set(tc_prod(t_a,t_a)))),tc_set(t_a),tc_prod(tc_set(tc_set(tc_prod(t_a,t_a))),tc_set(tc_set(tc_prod(t_a,t_a))))),t_a) = v_G,
inference(paramod,[status(thm)],[c_6,c_13]) ).
cnf(c_15,plain,
v_F = v_G,
inference(paramod,[status(thm)],[c_9,c_14]) ).
cnf(c_10,plain,
v_G = v_F,
inference(copy,[status(thm)],[c_15]) ).
cnf(c_11,plain,
$false,
inference(resolve,[status(thm)],[c_10,c_8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.23 % Problem : COM010-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.24 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/10.75 % Computer : n013.cluster.edu
% 0.09/10.75 % Model : x86_64 x86_64
% 0.09/10.75 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/10.75 % Memory : 8046.5625MB
% 0.09/10.75 % OS : Linux 6.8.0-71-generic
% 0.09/10.76 % CPULimit : 300
% 0.09/10.76 % WCLimit : 300
% 0.09/10.76 % DateTime : Sat Sep 26 23:20:29 UTC 2026
% 0.09/10.76 % CPUTime :
% 0.09/10.76 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/10.76 % Process 3809163 was started by sandbox2 on n013,
% 0.09/10.76 % Sat Sep 26 23:20:29 2026
% 0.09/10.76 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/10.76
% 0.09/10.76 % From the command line: assign(max_seconds, 300).
% 0.09/10.78
% 0.09/10.78 % SZS status Unsatisfiable for theBenchmark
% 0.09/10.78
% 0.09/10.78 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.09/10.78 % Length of proof is 11.
% 0.09/10.78 % Level of proof is 3.
% 0.09/10.78 % Maximum clause weight is 38.000.
% 0.09/10.78 % Given clauses 5.
% 0.09/10.78
% 0.09/10.78 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------