%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : COL102-2 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Apr 9 05:48:04 PM UTC 2025
% Result : Unsatisfiable 2.64s 1.60s
% Output : CNFRefutation 2.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 17 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 27 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 24 ( 14 ~; 10 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-4 aty)
% Number of variables : 24 ( 24 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ c_in > c_Pair > tc_prod > c_Transitive__Closure_Ortrancl > c_Comb_Ocomb_Oop_A_D_D > #nlpp > v_za > v_z > v_y > v_x > tc_Comb_Ocomb > c_Comb_Ocontract
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(v_x,type,
v_x: $i ).
tff(c_Transitive__Closure_Ortrancl,type,
c_Transitive__Closure_Ortrancl: ( $i * $i ) > $i ).
tff(v_y,type,
v_y: $i ).
tff(c_Comb_Ocontract,type,
c_Comb_Ocontract: $i ).
tff(v_z,type,
v_z: $i ).
tff(tc_prod,type,
tc_prod: ( $i * $i ) > $i ).
tff(c_in,type,
c_in: ( $i * $i * $i ) > $o ).
tff(v_za,type,
v_za: $i ).
tff(c_Pair,type,
c_Pair: ( $i * $i * $i * $i ) > $i ).
tff(c_Comb_Ocomb_Oop_A_D_D,type,
c_Comb_Ocomb_Oop_A_D_D: ( $i * $i ) > $i ).
tff(tc_Comb_Ocomb,type,
tc_Comb_Ocomb: $i ).
tff(f_26,axiom,
c_in(c_Pair(v_y,v_za,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Ocontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)),
file(unknown,unknown) ).
tff(f_34,axiom,
! [V_x,V_y,V_z] :
( ~ c_in(c_Pair(V_x,V_y,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Ocontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
| c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_x,V_z),c_Comb_Ocomb_Oop_A_D_D(V_y,V_z),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Ocontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ),
file(unknown,unknown) ).
tff(f_39,axiom,
! [V_p,V_r,T_a] :
( ~ c_in(V_p,V_r,tc_prod(T_a,T_a))
| c_in(V_p,c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)) ),
file(unknown,unknown) ).
tff(f_27,axiom,
c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_x,v_z),c_Comb_Ocomb_Oop_A_D_D(v_y,v_z),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Transitive__Closure_Ortrancl(c_Comb_Ocontract,tc_Comb_Ocomb),tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)),
file(unknown,unknown) ).
tff(f_47,axiom,
! [V_r,V_a,T_a,V_c,V_b] :
( ~ c_in(c_Pair(V_b,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_a,V_b,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| c_in(c_Pair(V_a,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)) ),
file(unknown,unknown) ).
tff(f_29,axiom,
~ c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_x,v_z),c_Comb_Ocomb_Oop_A_D_D(v_za,v_z),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Transitive__Closure_Ortrancl(c_Comb_Ocontract,tc_Comb_Ocomb),tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)),
file(unknown,unknown) ).
tff(c_2,plain,
c_in(c_Pair(v_y,v_za,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Ocontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)),
inference(cnfTransformation,[status(thm)],[f_26]) ).
tff(c_8,plain,
! [V_x_1,V_z_3,V_y_2] :
( c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_x_1,V_z_3),c_Comb_Ocomb_Oop_A_D_D(V_y_2,V_z_3),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Ocontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
| ~ c_in(c_Pair(V_x_1,V_y_2,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Ocontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ),
inference(cnfTransformation,[status(thm)],[f_34]) ).
tff(c_10,plain,
! [V_p_4,V_r_5,T_a_6] :
( c_in(V_p_4,c_Transitive__Closure_Ortrancl(V_r_5,T_a_6),tc_prod(T_a_6,T_a_6))
| ~ c_in(V_p_4,V_r_5,tc_prod(T_a_6,T_a_6)) ),
inference(cnfTransformation,[status(thm)],[f_39]) ).
tff(c_4,plain,
c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_x,v_z),c_Comb_Ocomb_Oop_A_D_D(v_y,v_z),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Transitive__Closure_Ortrancl(c_Comb_Ocontract,tc_Comb_Ocomb),tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)),
inference(cnfTransformation,[status(thm)],[f_27]) ).
tff(c_23,plain,
! [V_a_18,V_r_21,V_c_19,T_a_22,V_b_20] :
( c_in(c_Pair(V_a_18,V_c_19,T_a_22,T_a_22),c_Transitive__Closure_Ortrancl(V_r_21,T_a_22),tc_prod(T_a_22,T_a_22))
| ~ c_in(c_Pair(V_a_18,V_b_20,T_a_22,T_a_22),c_Transitive__Closure_Ortrancl(V_r_21,T_a_22),tc_prod(T_a_22,T_a_22))
| ~ c_in(c_Pair(V_b_20,V_c_19,T_a_22,T_a_22),c_Transitive__Closure_Ortrancl(V_r_21,T_a_22),tc_prod(T_a_22,T_a_22)) ),
inference(cnfTransformation,[status(thm)],[f_47]) ).
tff(c_31,plain,
! [V_c_23] :
( c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_x,v_z),V_c_23,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Transitive__Closure_Ortrancl(c_Comb_Ocontract,tc_Comb_Ocomb),tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
| ~ c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_y,v_z),V_c_23,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Transitive__Closure_Ortrancl(c_Comb_Ocontract,tc_Comb_Ocomb),tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ),
inference(resolution,[status(thm)],[c_4,c_23]) ).
tff(c_36,plain,
! [V_c_24] :
( c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_x,v_z),V_c_24,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Transitive__Closure_Ortrancl(c_Comb_Ocontract,tc_Comb_Ocomb),tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
| ~ c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_y,v_z),V_c_24,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Ocontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ),
inference(resolution,[status(thm)],[c_10,c_31]) ).
tff(c_6,plain,
~ c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_x,v_z),c_Comb_Ocomb_Oop_A_D_D(v_za,v_z),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Transitive__Closure_Ortrancl(c_Comb_Ocontract,tc_Comb_Ocomb),tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)),
inference(cnfTransformation,[status(thm)],[f_29]) ).
tff(c_43,plain,
~ c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_y,v_z),c_Comb_Ocomb_Oop_A_D_D(v_za,v_z),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Ocontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)),
inference(resolution,[status(thm)],[c_36,c_6]) ).
tff(c_46,plain,
~ c_in(c_Pair(v_y,v_za,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Ocontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)),
inference(resolution,[status(thm)],[c_8,c_43]) ).
tff(c_50,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_46]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : COL102-2 : TPTP v9.0.0. Released v3.2.0.
% 0.04/0.13 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.12/0.33 % Computer : n006.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Apr 7 16:05:23 EDT 2025
% 0.12/0.34 % CPUTime :
% 2.64/1.60 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.64/1.61
% 2.64/1.61 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------