%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : COL123-2 : 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/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n022.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 05:48:09 PM UTC 2025
% Result : Unsatisfiable 6.92s 2.80s
% Output : CNFRefutation 7.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 26 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 60 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 74 ( 40 ~; 34 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 4 ( 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 : 11 ( 11 usr; 6 con; 0-4 aty)
% Number of variables : 46 ( 46 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ c_in > c_Pair > v_xa > tc_prod > c_Transitive__Closure_Ortrancl > #nlpp > v_xaa > v_z > v_y > v_xb > v_x > v_r > t_a
%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(t_a,type,
t_a: $i ).
tff(v_z,type,
v_z: $i ).
tff(tc_prod,type,
tc_prod: ( $i * $i ) > $i ).
tff(v_xa,type,
v_xa: ( $i * $i * $i ) > $i ).
tff(c_in,type,
c_in: ( $i * $i * $i ) > $o ).
tff(v_r,type,
v_r: $i ).
tff(c_Pair,type,
c_Pair: ( $i * $i * $i * $i ) > $i ).
tff(v_xb,type,
v_xb: $i ).
tff(v_xaa,type,
v_xaa: $i > $i ).
tff(f_40,axiom,
c_in(c_Pair(v_x,v_xb,t_a,t_a),v_r,tc_prod(t_a,t_a)),
file(unknown,unknown) ).
tff(f_39,axiom,
c_in(c_Pair(v_y,v_z,t_a,t_a),v_r,tc_prod(t_a,t_a)),
file(unknown,unknown) ).
tff(f_50,axiom,
! [V_U] :
( c_in(c_Pair(v_y,v_xaa(V_U),t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_x,V_U,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
file(unknown,unknown) ).
tff(f_72,axiom,
! [V_W,V_U,V_V] :
( c_in(c_Pair(V_W,v_xa(V_U,V_V,V_W),t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(V_U,V_W,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(V_U,V_V,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
file(unknown,unknown) ).
tff(f_64,axiom,
! [V_V,V_U,V_W] :
( c_in(c_Pair(V_V,v_xa(V_U,V_V,V_W),t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(V_U,V_W,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(V_U,V_V,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
file(unknown,unknown) ).
tff(f_30,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_45,axiom,
! [V_U] :
( c_in(c_Pair(V_U,v_xaa(V_U),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_x,V_U,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
file(unknown,unknown) ).
tff(f_38,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_56,axiom,
! [V_U] :
( ~ c_in(c_Pair(v_z,V_U,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_xb,V_U,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
file(unknown,unknown) ).
tff(c_8,plain,
c_in(c_Pair(v_x,v_xb,t_a,t_a),v_r,tc_prod(t_a,t_a)),
inference(cnfTransformation,[status(thm)],[f_40]) ).
tff(c_6,plain,
c_in(c_Pair(v_y,v_z,t_a,t_a),v_r,tc_prod(t_a,t_a)),
inference(cnfTransformation,[status(thm)],[f_39]) ).
tff(c_12,plain,
! [V_U_10] :
( ~ c_in(c_Pair(v_x,V_U_10,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(c_Pair(v_y,v_xaa(V_U_10),t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(cnfTransformation,[status(thm)],[f_50]) ).
tff(c_18,plain,
! [V_U_16,V_V_17,V_W_15] :
( ~ c_in(c_Pair(V_U_16,V_V_17,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(V_U_16,V_W_15,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(c_Pair(V_W_15,v_xa(V_U_16,V_V_17,V_W_15),t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(cnfTransformation,[status(thm)],[f_72]) ).
tff(c_16,plain,
! [V_U_13,V_V_12,V_W_14] :
( ~ c_in(c_Pair(V_U_13,V_V_12,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(V_U_13,V_W_14,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(c_Pair(V_V_12,v_xa(V_U_13,V_V_12,V_W_14),t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(cnfTransformation,[status(thm)],[f_64]) ).
tff(c_2,plain,
! [V_p_1,V_r_2,T_a_3] :
( c_in(V_p_1,c_Transitive__Closure_Ortrancl(V_r_2,T_a_3),tc_prod(T_a_3,T_a_3))
| ~ c_in(V_p_1,V_r_2,tc_prod(T_a_3,T_a_3)) ),
inference(cnfTransformation,[status(thm)],[f_30]) ).
tff(c_10,plain,
! [V_U_9] :
( ~ c_in(c_Pair(v_x,V_U_9,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(c_Pair(V_U_9,v_xaa(V_U_9),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(cnfTransformation,[status(thm)],[f_45]) ).
tff(c_64,plain,
! [V_r_38,V_c_39,V_a_37,V_b_40,T_a_36] :
( c_in(c_Pair(V_a_37,V_c_39,T_a_36,T_a_36),c_Transitive__Closure_Ortrancl(V_r_38,T_a_36),tc_prod(T_a_36,T_a_36))
| ~ c_in(c_Pair(V_a_37,V_b_40,T_a_36,T_a_36),c_Transitive__Closure_Ortrancl(V_r_38,T_a_36),tc_prod(T_a_36,T_a_36))
| ~ c_in(c_Pair(V_b_40,V_c_39,T_a_36,T_a_36),c_Transitive__Closure_Ortrancl(V_r_38,T_a_36),tc_prod(T_a_36,T_a_36)) ),
inference(cnfTransformation,[status(thm)],[f_38]) ).
tff(c_170,plain,
! [V_U_60,V_c_61] :
( c_in(c_Pair(V_U_60,V_c_61,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_xaa(V_U_60),V_c_61,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_x,V_U_60,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(resolution,[status(thm)],[c_10,c_64]) ).
tff(c_195,plain,
! [V_U_62,V_c_63] :
( c_in(c_Pair(V_U_62,V_c_63,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_x,V_U_62,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_xaa(V_U_62),V_c_63,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(resolution,[status(thm)],[c_2,c_170]) ).
tff(c_2461,plain,
! [V_U_247,V_U_248,V_W_249] :
( c_in(c_Pair(V_U_247,v_xa(V_U_248,v_xaa(V_U_247),V_W_249),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_x,V_U_247,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(V_U_248,v_xaa(V_U_247),t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(V_U_248,V_W_249,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(resolution,[status(thm)],[c_16,c_195]) ).
tff(c_14,plain,
! [V_U_11] :
( ~ c_in(c_Pair(v_xb,V_U_11,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_z,V_U_11,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_2514,plain,
! [V_U_248,V_W_249] :
( ~ c_in(c_Pair(v_z,v_xa(V_U_248,v_xaa(v_xb),V_W_249),t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_x,v_xb,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(V_U_248,v_xaa(v_xb),t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(V_U_248,V_W_249,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(resolution,[status(thm)],[c_2461,c_14]) ).
tff(c_2539,plain,
! [V_U_250,V_W_251] :
( ~ c_in(c_Pair(v_z,v_xa(V_U_250,v_xaa(v_xb),V_W_251),t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(V_U_250,v_xaa(v_xb),t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(V_U_250,V_W_251,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_2514]) ).
tff(c_2545,plain,
! [V_U_252] :
( ~ c_in(c_Pair(V_U_252,v_xaa(v_xb),t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(V_U_252,v_z,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(resolution,[status(thm)],[c_18,c_2539]) ).
tff(c_2549,plain,
( ~ c_in(c_Pair(v_y,v_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_x,v_xb,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(resolution,[status(thm)],[c_12,c_2545]) ).
tff(c_2553,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_8,c_6,c_2549]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : COL123-2 : TPTP v9.0.0. Released v3.2.0.
% 0.03/0.12 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.12/0.33 % Computer : n022.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 16:08:05 EDT 2025
% 0.12/0.33 % CPUTime :
% 6.92/2.80 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.92/2.80
% 6.92/2.80 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------