%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET831-2 : TPTP v9.2.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n004.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 : Tue May 5 05:08:37 PM UTC 2026
% Result : Unsatisfiable 1.37s 1.74s
% Output : CNFRefutation 1.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 13
% Syntax : Number of clauses : 55 ( 10 unt; 22 nHn; 42 RR)
% Number of literals : 128 ( 22 equ; 56 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-3 aty)
% Number of variables : 82 ( 6 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_Set_OIntE_0,axiom,
( c_in(X1,X3,X4)
| ~ c_in(X1,c_inter(X2,X3,X4),X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OIntE_0) ).
cnf(cls_Set_OsubsetI_0,axiom,
( c_in(c_Main_OsubsetI__1(X1,X2,X3),X1,X3)
| c_lessequals(X1,X2,tc_set(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetI_0) ).
cnf(cls_Set_OIntE_1,axiom,
( c_in(X1,X2,X4)
| ~ c_in(X1,c_inter(X2,X3,X4),X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OIntE_1) ).
cnf(cls_conjecture_0,negated_conjecture,
( v_X = c_inter(v_Y,v_Z,t_a)
| c_lessequals(v_X,v_Y,tc_set(t_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(cls_Set_OsubsetD_0,axiom,
( c_in(X1,X4,X3)
| ~ c_in(X1,X2,X3)
| ~ c_lessequals(X2,X4,tc_set(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetD_0) ).
cnf(cls_Set_OsubsetI_1,axiom,
( c_lessequals(X1,X2,tc_set(X3))
| ~ c_in(c_Main_OsubsetI__1(X1,X2,X3),X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetI_1) ).
cnf(cls_conjecture_1,negated_conjecture,
( v_X = c_inter(v_Y,v_Z,t_a)
| c_lessequals(v_X,v_Z,tc_set(t_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
cnf(cls_conjecture_5,negated_conjecture,
( v_X = c_inter(v_Y,v_Z,t_a)
| c_lessequals(X1,v_X,tc_set(t_a))
| ~ c_lessequals(X1,v_Z,tc_set(t_a))
| ~ c_lessequals(X1,v_Y,tc_set(t_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_5) ).
cnf(cls_Set_OIntI_0,axiom,
( c_in(X1,c_inter(X4,X2,X3),X3)
| ~ c_in(X1,X2,X3)
| ~ c_in(X1,X4,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OIntI_0) ).
cnf(cls_Set_Osubset__antisym_0,axiom,
( X2 = X1
| ~ c_lessequals(X1,X2,tc_set(X3))
| ~ c_lessequals(X2,X1,tc_set(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__antisym_0) ).
cnf(cls_conjecture_2,negated_conjecture,
( c_lessequals(v_x,v_Y,tc_set(t_a))
| ~ c_lessequals(v_X,v_Z,tc_set(t_a))
| ~ c_lessequals(v_X,v_Y,tc_set(t_a))
| v_X != c_inter(v_Y,v_Z,t_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
cnf(cls_conjecture_3,negated_conjecture,
( c_lessequals(v_x,v_Z,tc_set(t_a))
| ~ c_lessequals(v_X,v_Z,tc_set(t_a))
| ~ c_lessequals(v_X,v_Y,tc_set(t_a))
| v_X != c_inter(v_Y,v_Z,t_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
cnf(cls_conjecture_4,negated_conjecture,
( ~ c_lessequals(v_x,v_X,tc_set(t_a))
| ~ c_lessequals(v_X,v_Z,tc_set(t_a))
| ~ c_lessequals(v_X,v_Y,tc_set(t_a))
| v_X != c_inter(v_Y,v_Z,t_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_4) ).
cnf(c_0_13,axiom,
( c_in(X1,X3,X4)
| ~ c_in(X1,c_inter(X2,X3,X4),X4) ),
cls_Set_OIntE_0 ).
cnf(c_0_14,axiom,
( c_in(c_Main_OsubsetI__1(X1,X2,X3),X1,X3)
| c_lessequals(X1,X2,tc_set(X3)) ),
cls_Set_OsubsetI_0 ).
cnf(c_0_15,axiom,
( c_in(X1,X2,X4)
| ~ c_in(X1,c_inter(X2,X3,X4),X4) ),
cls_Set_OIntE_1 ).
cnf(c_0_16,negated_conjecture,
( v_X = c_inter(v_Y,v_Z,t_a)
| c_lessequals(v_X,v_Y,tc_set(t_a)) ),
cls_conjecture_0 ).
cnf(c_0_17,axiom,
( c_in(X1,X4,X3)
| ~ c_in(X1,X2,X3)
| ~ c_lessequals(X2,X4,tc_set(X3)) ),
cls_Set_OsubsetD_0 ).
cnf(c_0_18,axiom,
( c_lessequals(X1,X2,tc_set(X3))
| ~ c_in(c_Main_OsubsetI__1(X1,X2,X3),X2,X3) ),
cls_Set_OsubsetI_1 ).
cnf(c_0_19,plain,
( c_in(c_Main_OsubsetI__1(c_inter(X1,X2,X3),X4,X3),X2,X3)
| c_lessequals(c_inter(X1,X2,X3),X4,tc_set(X3)) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_20,plain,
( c_in(c_Main_OsubsetI__1(c_inter(X1,X2,X3),X4,X3),X1,X3)
| c_lessequals(c_inter(X1,X2,X3),X4,tc_set(X3)) ),
inference(spm,[status(thm)],[c_0_15,c_0_14]) ).
cnf(c_0_21,negated_conjecture,
( c_in(X1,v_Y,t_a)
| c_lessequals(v_X,v_Y,tc_set(t_a))
| ~ c_in(X1,v_X,t_a) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_22,plain,
( c_in(c_Main_OsubsetI__1(X1,X2,X3),X4,X3)
| c_lessequals(X1,X2,tc_set(X3))
| ~ c_lessequals(X1,X4,tc_set(X3)) ),
inference(spm,[status(thm)],[c_0_17,c_0_14]) ).
cnf(c_0_23,plain,
c_lessequals(c_inter(X1,X2,X3),X2,tc_set(X3)),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_24,negated_conjecture,
( v_X = c_inter(v_Y,v_Z,t_a)
| c_lessequals(v_X,v_Z,tc_set(t_a)) ),
cls_conjecture_1 ).
cnf(c_0_25,negated_conjecture,
( v_X = c_inter(v_Y,v_Z,t_a)
| c_lessequals(X1,v_X,tc_set(t_a))
| ~ c_lessequals(X1,v_Z,tc_set(t_a))
| ~ c_lessequals(X1,v_Y,tc_set(t_a)) ),
cls_conjecture_5 ).
cnf(c_0_26,plain,
c_lessequals(c_inter(X1,X2,X3),X1,tc_set(X3)),
inference(spm,[status(thm)],[c_0_18,c_0_20]) ).
cnf(c_0_27,axiom,
( c_in(X1,c_inter(X4,X2,X3),X3)
| ~ c_in(X1,X2,X3)
| ~ c_in(X1,X4,X3) ),
cls_Set_OIntI_0 ).
cnf(c_0_28,negated_conjecture,
( c_in(c_Main_OsubsetI__1(v_X,X1,t_a),v_Y,t_a)
| c_lessequals(v_X,X1,tc_set(t_a)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_14]),c_0_22]) ).
cnf(c_0_29,negated_conjecture,
c_lessequals(v_X,v_Z,tc_set(t_a)),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_30,negated_conjecture,
( c_inter(v_Y,v_Z,t_a) = v_X
| c_lessequals(c_inter(v_Y,X1,t_a),v_X,tc_set(t_a))
| ~ c_lessequals(c_inter(v_Y,X1,t_a),v_Z,tc_set(t_a)) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_31,negated_conjecture,
( c_in(c_Main_OsubsetI__1(v_X,X1,t_a),c_inter(v_Y,X2,t_a),t_a)
| c_lessequals(v_X,X1,tc_set(t_a))
| ~ c_in(c_Main_OsubsetI__1(v_X,X1,t_a),X2,t_a) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_32,negated_conjecture,
( c_in(c_Main_OsubsetI__1(v_X,X1,t_a),v_Z,t_a)
| c_lessequals(v_X,X1,tc_set(t_a)) ),
inference(spm,[status(thm)],[c_0_22,c_0_29]) ).
cnf(c_0_33,axiom,
( X2 = X1
| ~ c_lessequals(X1,X2,tc_set(X3))
| ~ c_lessequals(X2,X1,tc_set(X3)) ),
cls_Set_Osubset__antisym_0 ).
cnf(c_0_34,negated_conjecture,
( c_inter(v_Y,v_Z,t_a) = v_X
| c_lessequals(c_inter(v_Y,v_Z,t_a),v_X,tc_set(t_a)) ),
inference(spm,[status(thm)],[c_0_30,c_0_23]) ).
cnf(c_0_35,negated_conjecture,
( c_in(c_Main_OsubsetI__1(v_X,X1,t_a),c_inter(v_Y,v_Z,t_a),t_a)
| c_lessequals(v_X,X1,tc_set(t_a)) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_36,negated_conjecture,
( c_lessequals(v_x,v_Y,tc_set(t_a))
| ~ c_lessequals(v_X,v_Z,tc_set(t_a))
| ~ c_lessequals(v_X,v_Y,tc_set(t_a))
| v_X != c_inter(v_Y,v_Z,t_a) ),
cls_conjecture_2 ).
cnf(c_0_37,negated_conjecture,
c_lessequals(v_X,v_Y,tc_set(t_a)),
inference(spm,[status(thm)],[c_0_18,c_0_28]) ).
cnf(c_0_38,negated_conjecture,
( c_inter(v_Y,v_Z,t_a) = v_X
| ~ c_lessequals(v_X,c_inter(v_Y,v_Z,t_a),tc_set(t_a)) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_39,negated_conjecture,
c_lessequals(v_X,c_inter(v_Y,v_Z,t_a),tc_set(t_a)),
inference(spm,[status(thm)],[c_0_18,c_0_35]) ).
cnf(c_0_40,negated_conjecture,
( c_lessequals(v_x,v_Y,tc_set(t_a))
| c_inter(v_Y,v_Z,t_a) != v_X ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_37])]),c_0_29])]) ).
cnf(c_0_41,negated_conjecture,
c_inter(v_Y,v_Z,t_a) = v_X,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_38,c_0_39])]) ).
cnf(c_0_42,negated_conjecture,
( c_lessequals(v_x,v_Z,tc_set(t_a))
| ~ c_lessequals(v_X,v_Z,tc_set(t_a))
| ~ c_lessequals(v_X,v_Y,tc_set(t_a))
| v_X != c_inter(v_Y,v_Z,t_a) ),
cls_conjecture_3 ).
cnf(c_0_43,negated_conjecture,
c_lessequals(v_x,v_Y,tc_set(t_a)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_40,c_0_41])]) ).
cnf(c_0_44,negated_conjecture,
( c_lessequals(v_x,v_Z,tc_set(t_a))
| c_inter(v_Y,v_Z,t_a) != v_X ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_37])]),c_0_29])]) ).
cnf(c_0_45,negated_conjecture,
( ~ c_lessequals(v_x,v_X,tc_set(t_a))
| ~ c_lessequals(v_X,v_Z,tc_set(t_a))
| ~ c_lessequals(v_X,v_Y,tc_set(t_a))
| v_X != c_inter(v_Y,v_Z,t_a) ),
cls_conjecture_4 ).
cnf(c_0_46,negated_conjecture,
( c_in(c_Main_OsubsetI__1(v_x,X1,t_a),v_Y,t_a)
| c_lessequals(v_x,X1,tc_set(t_a)) ),
inference(spm,[status(thm)],[c_0_22,c_0_43]) ).
cnf(c_0_47,negated_conjecture,
c_lessequals(v_x,v_Z,tc_set(t_a)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_44,c_0_41])]) ).
cnf(c_0_48,negated_conjecture,
( c_inter(v_Y,v_Z,t_a) != v_X
| ~ c_lessequals(v_X,v_Z,tc_set(t_a))
| ~ c_lessequals(v_x,v_X,tc_set(t_a)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_45,c_0_37])]) ).
cnf(c_0_49,negated_conjecture,
( c_in(c_Main_OsubsetI__1(v_x,X1,t_a),c_inter(v_Y,X2,t_a),t_a)
| c_lessequals(v_x,X1,tc_set(t_a))
| ~ c_in(c_Main_OsubsetI__1(v_x,X1,t_a),X2,t_a) ),
inference(spm,[status(thm)],[c_0_27,c_0_46]) ).
cnf(c_0_50,negated_conjecture,
( c_in(c_Main_OsubsetI__1(v_x,X1,t_a),v_Z,t_a)
| c_lessequals(v_x,X1,tc_set(t_a)) ),
inference(spm,[status(thm)],[c_0_22,c_0_47]) ).
cnf(c_0_51,negated_conjecture,
( c_inter(v_Y,v_Z,t_a) != v_X
| ~ c_lessequals(v_x,v_X,tc_set(t_a)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_48,c_0_29])]) ).
cnf(c_0_52,negated_conjecture,
( c_in(c_Main_OsubsetI__1(v_x,X1,t_a),v_X,t_a)
| c_lessequals(v_x,X1,tc_set(t_a)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_41]) ).
cnf(c_0_53,negated_conjecture,
~ c_lessequals(v_x,v_X,tc_set(t_a)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_51,c_0_41])]) ).
cnf(c_0_54,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_52]),c_0_53]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SET831-2 : TPTP v9.2.1. Released v3.2.0.
% 0.00/0.10 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.14/0.31 % Computer : n004.cluster.edu
% 0.14/0.31 % Model : x86_64 x86_64
% 0.14/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.31 % Memory : 8042.1875MB
% 0.14/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.31 % CPULimit : 300
% 0.14/0.31 % WCLimit : 300
% 0.14/0.31 % DateTime : Tue May 5 02:36:32 EDT 2026
% 0.14/0.31 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 1.37/1.74 % Version : CSE_E---1.7
% 1.37/1.74 % Problem : theBenchmark.p
% 1.37/1.74 % SZS status Unsatisfiable for theBenchmark.p
% 1.37/1.74 % SZS output start CNFRefutation
% See solution above
% 1.37/1.74 % Total time : 1.372s
%------------------------------------------------------------------------------