%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET821-2 : 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 : n012.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 08:37:01 AM UTC 2026
% Result : Unsatisfiable 0.08s 10.38s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 10
% Syntax : Number of formulae : 40 ( 20 unt; 0 def)
% Number of atoms : 66 ( 12 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 48 ( 22 ~; 26 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 74 ( 21 sgn 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(clsarity_IntDef__Oint_31,axiom,
class_Orderings_Oorder(tc_IntDef_Oint),
file('theBenchmark.p',clsarity_IntDef__Oint_31) ).
cnf(c_1,plain,
class_Orderings_Oorder(tc_IntDef_Oint),
inference(clausify,[status(thm)],[clsarity_IntDef__Oint_31]) ).
fof(cls_Orderings_Oorder__less__irrefl__iff1_0,axiom,
! [VAR_0,VAR_1] :
( ~ c_less(VAR_1,VAR_1,VAR_0)
| ~ class_Orderings_Oorder(VAR_0) ),
file('theBenchmark.p',cls_Orderings_Oorder__less__irrefl__iff1_0) ).
cnf(c_2,plain,
( ~ c_less(B,B,A)
| ~ class_Orderings_Oorder(A) ),
inference(clausify,[status(thm)],[cls_Orderings_Oorder__less__irrefl__iff1_0]) ).
cnf(c_3,plain,
~ c_less(A,A,tc_IntDef_Oint),
inference(resolve,[status(thm)],[c_1,c_2]) ).
fof(cls_conjecture_2,axiom,
! [VAR_0] :
( c_in(v_a,VAR_0,tc_IntDef_Oint)
| ~ c_in(v_b,VAR_0,tc_IntDef_Oint)
| c_in(v_c,VAR_0,tc_IntDef_Oint) ),
file('theBenchmark.p',cls_conjecture_2) ).
cnf(c_4,plain,
( c_in(v_a,A,tc_IntDef_Oint)
| ~ c_in(v_b,A,tc_IntDef_Oint)
| c_in(v_c,A,tc_IntDef_Oint) ),
inference(clausify,[status(thm)],[cls_conjecture_2]) ).
fof(cls_conjecture_1,axiom,
c_less(v_b,v_c,tc_IntDef_Oint),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(c_5,plain,
c_less(v_b,v_c,tc_IntDef_Oint),
inference(clausify,[status(thm)],[cls_conjecture_1]) ).
fof(cls_conjecture_0,axiom,
c_less(v_a,v_b,tc_IntDef_Oint),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_6,plain,
c_less(v_a,v_b,tc_IntDef_Oint),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
fof(cls_Set_OinsertE_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( VAR_0 = VAR_1
| c_in(VAR_0,VAR_2,VAR_3)
| ~ c_in(VAR_0,c_insert(VAR_1,VAR_2,VAR_3),VAR_3) ),
file('theBenchmark.p',cls_Set_OinsertE_0) ).
cnf(c_7,plain,
( A = B
| c_in(A,C,D)
| ~ c_in(A,c_insert(B,C,D),D) ),
inference(clausify,[status(thm)],[cls_Set_OinsertE_0]) ).
fof(cls_Set_OinsertCI_1,axiom,
! [VAR_0,VAR_1,VAR_2] : c_in(VAR_0,c_insert(VAR_0,VAR_1,VAR_2),VAR_2),
file('theBenchmark.p',cls_Set_OinsertCI_1) ).
cnf(c_8,plain,
c_in(A,c_insert(A,B,C),C),
inference(clausify,[status(thm)],[cls_Set_OinsertCI_1]) ).
fof(cls_Set_OinsertCI_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( c_in(VAR_0,c_insert(VAR_3,VAR_1,VAR_2),VAR_2)
| ~ c_in(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',cls_Set_OinsertCI_0) ).
cnf(c_9,plain,
( c_in(A,c_insert(D,B,C),C)
| ~ c_in(A,B,C) ),
inference(clausify,[status(thm)],[cls_Set_OinsertCI_0]) ).
fof(cls_Set_OComplI_0,axiom,
! [VAR_0,VAR_1,VAR_2] :
( c_in(VAR_0,c_uminus(VAR_1,tc_set(VAR_2)),VAR_2)
| c_in(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',cls_Set_OComplI_0) ).
cnf(c_10,plain,
( c_in(A,c_uminus(B,tc_set(C)),C)
| c_in(A,B,C) ),
inference(clausify,[status(thm)],[cls_Set_OComplI_0]) ).
fof(cls_Set_OComplD__dest_0,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ c_in(VAR_0,c_uminus(VAR_1,tc_set(VAR_2)),VAR_2)
| ~ c_in(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',cls_Set_OComplD__dest_0) ).
cnf(c_11,plain,
( ~ c_in(A,c_uminus(B,tc_set(C)),C)
| ~ c_in(A,B,C) ),
inference(clausify,[status(thm)],[cls_Set_OComplD__dest_0]) ).
cnf(c_13,plain,
c_in(A,c_insert(B,c_insert(A,C,D),D),D),
inference(resolve,[status(thm)],[c_9,c_8]) ).
cnf(c_16,plain,
~ c_in(A,c_uminus(c_insert(A,B,C),tc_set(C)),C),
inference(resolve,[status(thm)],[c_11,c_8]) ).
cnf(c_19,plain,
c_in(A,c_insert(B,c_insert(C,c_insert(A,D,E),E),E),E),
inference(resolve,[status(thm)],[c_13,c_9]) ).
cnf(c_21,plain,
~ c_in(A,c_uminus(c_insert(B,c_insert(A,C,D),D),tc_set(D)),D),
inference(resolve,[status(thm)],[c_11,c_13]) ).
cnf(c_24,plain,
~ c_in(A,c_uminus(c_insert(B,c_insert(C,c_insert(A,D,E),E),E),tc_set(E)),E),
inference(resolve,[status(thm)],[c_11,c_19]) ).
cnf(c_60,plain,
( c_in(v_a,c_uminus(c_insert(v_c,A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)),tc_IntDef_Oint)
| ~ c_in(v_b,c_uminus(c_insert(v_c,A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)),tc_IntDef_Oint) ),
inference(resolve,[status(thm)],[c_4,c_16]) ).
cnf(c_37,plain,
~ c_in(v_b,c_uminus(c_insert(v_c,c_insert(v_a,A,tc_IntDef_Oint),tc_IntDef_Oint),tc_set(tc_IntDef_Oint)),tc_IntDef_Oint),
inference(resolve,[status(thm)],[c_60,c_21]) ).
cnf(c_39,plain,
c_in(v_b,c_insert(v_c,c_insert(v_a,A,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint),
inference(resolve,[status(thm)],[c_37,c_10]) ).
cnf(c_61,plain,
( c_in(v_a,c_uminus(c_insert(A,c_insert(B,c_insert(v_c,C,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint),tc_set(tc_IntDef_Oint)),tc_IntDef_Oint)
| ~ c_in(v_b,c_uminus(c_insert(A,c_insert(B,c_insert(v_c,C,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint),tc_set(tc_IntDef_Oint)),tc_IntDef_Oint) ),
inference(resolve,[status(thm)],[c_4,c_24]) ).
cnf(c_46,plain,
~ c_in(v_b,c_uminus(c_insert(v_a,c_insert(A,c_insert(v_c,B,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint),tc_set(tc_IntDef_Oint)),tc_IntDef_Oint),
inference(resolve,[status(thm)],[c_61,c_16]) ).
cnf(c_62,plain,
( v_b = v_c
| c_in(v_b,c_insert(v_a,A,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(resolve,[status(thm)],[c_39,c_7]) ).
cnf(c_48,plain,
( v_c = v_b
| c_in(v_b,c_insert(v_a,A,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(copy,[status(thm)],[c_62]) ).
cnf(c_63,plain,
( v_b = v_a
| c_in(v_b,A,tc_IntDef_Oint)
| v_c = v_b ),
inference(resolve,[status(thm)],[c_48,c_7]) ).
cnf(c_52,plain,
( v_a = v_b
| c_in(v_b,A,tc_IntDef_Oint)
| v_c = v_b ),
inference(copy,[status(thm)],[c_63]) ).
cnf(c_57,plain,
( v_a = v_b
| v_c = v_b ),
inference(resolve,[status(thm)],[c_52,c_46]) ).
cnf(c_64,plain,
( c_less(v_b,v_b,tc_IntDef_Oint)
| v_a = v_b ),
inference(paramod,[status(thm)],[c_57,c_5]) ).
cnf(c_58,plain,
v_a = v_b,
inference(resolve,[status(thm)],[c_3,c_64]) ).
cnf(c_65,plain,
c_less(v_b,v_b,tc_IntDef_Oint),
inference(paramod,[status(thm)],[c_58,c_6]) ).
cnf(c_59,plain,
$false,
inference(resolve,[status(thm)],[c_3,c_65]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET821-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/10.36 % Computer : n012.cluster.edu
% 0.08/10.36 % Model : x86_64 x86_64
% 0.08/10.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/10.36 % Memory : 8046.5625MB
% 0.08/10.36 % OS : Linux 6.8.0-71-generic
% 0.08/10.36 % CPULimit : 300
% 0.08/10.36 % WCLimit : 300
% 0.08/10.36 % DateTime : Sat Sep 26 08:18:46 UTC 2026
% 0.08/10.36 % CPUTime :
% 0.08/10.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/10.36 % Process 115039 was started by sandbox2 on n012,
% 0.08/10.36 % Sat Sep 26 08:18:46 2026
% 0.08/10.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/10.37
% 0.08/10.37 % From the command line: assign(max_seconds, 300).
% 0.08/10.38
% 0.08/10.38 % SZS status Unsatisfiable for theBenchmark
% 0.08/10.38
% 0.08/10.38 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.08/10.38 % Length of proof is 24.
% 0.08/10.38 % Level of proof is 9.
% 0.08/10.38 % Maximum clause weight is 16.000.
% 0.08/10.38 % Given clauses 31.
% 0.08/10.38
% 0.08/10.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------