%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : COM011-2 : 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 : n005.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 5.38s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of formulae : 38 ( 11 unt; 0 def)
% Number of atoms : 75 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 68 ( 31 ~; 37 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 4 con; 0-3 aty)
% Number of variables : 85 ( 3 sgn 27 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_UNITY_Oconstrains__weaken__L_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] :
( c_in(VAR_0,c_UNITY_Oconstrains(VAR_4,VAR_2,VAR_3),tc_UNITY_Oprogram(VAR_3))
| ~ c_lessequals(VAR_4,VAR_1,tc_set(VAR_3))
| ~ c_in(VAR_0,c_UNITY_Oconstrains(VAR_1,VAR_2,VAR_3),tc_UNITY_Oprogram(VAR_3)) ),
file('theBenchmark.p',cls_UNITY_Oconstrains__weaken__L_0) ).
cnf(c_1,plain,
( c_in(A,c_UNITY_Oconstrains(E,C,D),tc_UNITY_Oprogram(D))
| ~ c_lessequals(E,B,tc_set(D))
| ~ c_in(A,c_UNITY_Oconstrains(B,C,D),tc_UNITY_Oprogram(D)) ),
inference(clausify,[status(thm)],[cls_UNITY_Oconstrains__weaken__L_0]) ).
fof(cls_Set_OsubsetI_1,axiom,
! [VAR_0,VAR_1,VAR_2] :
( c_lessequals(VAR_0,VAR_1,tc_set(VAR_2))
| ~ c_in(c_Main_OsubsetI__1(VAR_0,VAR_1,VAR_2),VAR_1,VAR_2) ),
file('theBenchmark.p',cls_Set_OsubsetI_1) ).
cnf(c_2,plain,
( c_lessequals(A,B,tc_set(C))
| ~ c_in(c_Main_OsubsetI__1(A,B,C),B,C) ),
inference(clausify,[status(thm)],[cls_Set_OsubsetI_1]) ).
fof(cls_Set_OsubsetI_0,axiom,
! [VAR_0,VAR_1,VAR_2] :
( c_lessequals(VAR_0,VAR_1,tc_set(VAR_2))
| c_in(c_Main_OsubsetI__1(VAR_0,VAR_1,VAR_2),VAR_0,VAR_2) ),
file('theBenchmark.p',cls_Set_OsubsetI_0) ).
cnf(c_3,plain,
( c_lessequals(A,B,tc_set(C))
| c_in(c_Main_OsubsetI__1(A,B,C),A,C) ),
inference(clausify,[status(thm)],[cls_Set_OsubsetI_0]) ).
fof(cls_WFair_Otransient__strengthen_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( c_in(VAR_0,c_WFair_Otransient(VAR_3,VAR_2),tc_UNITY_Oprogram(VAR_2))
| ~ c_lessequals(VAR_3,VAR_1,tc_set(VAR_2))
| ~ c_in(VAR_0,c_WFair_Otransient(VAR_1,VAR_2),tc_UNITY_Oprogram(VAR_2)) ),
file('theBenchmark.p',cls_WFair_Otransient__strengthen_0) ).
cnf(c_4,plain,
( c_in(A,c_WFair_Otransient(D,C),tc_UNITY_Oprogram(C))
| ~ c_lessequals(D,B,tc_set(C))
| ~ c_in(A,c_WFair_Otransient(B,C),tc_UNITY_Oprogram(C)) ),
inference(clausify,[status(thm)],[cls_WFair_Otransient__strengthen_0]) ).
cnf(c_5,plain,
( c_in(c_Main_OsubsetI__1(D,B,C),D,C)
| c_in(A,c_WFair_Otransient(D,C),tc_UNITY_Oprogram(C))
| ~ c_in(A,c_WFair_Otransient(B,C),tc_UNITY_Oprogram(C)) ),
inference(resolve,[status(thm)],[c_4,c_3]) ).
cnf(c_6,plain,
( ~ c_in(c_Main_OsubsetI__1(D,B,C),B,C)
| c_in(A,c_WFair_Otransient(D,C),tc_UNITY_Oprogram(C))
| ~ c_in(A,c_WFair_Otransient(B,C),tc_UNITY_Oprogram(C)) ),
inference(resolve,[status(thm)],[c_4,c_2]) ).
cnf(c_7,plain,
( c_in(c_Main_OsubsetI__1(E,B,D),E,D)
| c_in(A,c_UNITY_Oconstrains(E,C,D),tc_UNITY_Oprogram(D))
| ~ c_in(A,c_UNITY_Oconstrains(B,C,D),tc_UNITY_Oprogram(D)) ),
inference(resolve,[status(thm)],[c_1,c_3]) ).
cnf(c_8,plain,
( ~ c_in(c_Main_OsubsetI__1(E,B,D),B,D)
| c_in(A,c_UNITY_Oconstrains(E,C,D),tc_UNITY_Oprogram(D))
| ~ c_in(A,c_UNITY_Oconstrains(B,C,D),tc_UNITY_Oprogram(D)) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
fof(cls_WFair_OleadsTo__Basis_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( c_in(VAR_0,c_WFair_OleadsTo(VAR_1,VAR_2,VAR_3),tc_UNITY_Oprogram(VAR_3))
| ~ c_in(VAR_0,c_WFair_Oensures(VAR_1,VAR_2,VAR_3),tc_UNITY_Oprogram(VAR_3)) ),
file('theBenchmark.p',cls_WFair_OleadsTo__Basis_0) ).
cnf(c_9,plain,
( c_in(A,c_WFair_OleadsTo(B,C,D),tc_UNITY_Oprogram(D))
| ~ c_in(A,c_WFair_Oensures(B,C,D),tc_UNITY_Oprogram(D)) ),
inference(clausify,[status(thm)],[cls_WFair_OleadsTo__Basis_0]) ).
fof(cls_WFair_OensuresI_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( c_in(VAR_0,c_WFair_Oensures(VAR_1,VAR_2,VAR_3),tc_UNITY_Oprogram(VAR_3))
| ~ c_in(VAR_0,c_WFair_Otransient(c_minus(VAR_1,VAR_2,tc_set(VAR_3)),VAR_3),tc_UNITY_Oprogram(VAR_3))
| ~ c_in(VAR_0,c_UNITY_Oconstrains(c_minus(VAR_1,VAR_2,tc_set(VAR_3)),c_union(VAR_1,VAR_2,VAR_3),VAR_3),tc_UNITY_Oprogram(VAR_3)) ),
file('theBenchmark.p',cls_WFair_OensuresI_0) ).
cnf(c_10,plain,
( c_in(A,c_WFair_Oensures(B,C,D),tc_UNITY_Oprogram(D))
| ~ c_in(A,c_WFair_Otransient(c_minus(B,C,tc_set(D)),D),tc_UNITY_Oprogram(D))
| ~ c_in(A,c_UNITY_Oconstrains(c_minus(B,C,tc_set(D)),c_union(B,C,D),D),tc_UNITY_Oprogram(D)) ),
inference(clausify,[status(thm)],[cls_WFair_OensuresI_0]) ).
fof(cls_Set_ODiffE_1,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( c_in(VAR_0,VAR_1,VAR_3)
| ~ c_in(VAR_0,c_minus(VAR_1,VAR_2,tc_set(VAR_3)),VAR_3) ),
file('theBenchmark.p',cls_Set_ODiffE_1) ).
cnf(c_11,plain,
( c_in(A,B,D)
| ~ c_in(A,c_minus(B,C,tc_set(D)),D) ),
inference(clausify,[status(thm)],[cls_Set_ODiffE_1]) ).
fof(cls_conjecture_2,axiom,
~ c_in(v_F,c_WFair_OleadsTo(v_A,v_B,t_a),tc_UNITY_Oprogram(t_a)),
file('theBenchmark.p',cls_conjecture_2) ).
cnf(c_12,plain,
~ c_in(v_F,c_WFair_OleadsTo(v_A,v_B,t_a),tc_UNITY_Oprogram(t_a)),
inference(clausify,[status(thm)],[cls_conjecture_2]) ).
fof(cls_conjecture_1,axiom,
c_in(v_F,c_WFair_Otransient(v_A,t_a),tc_UNITY_Oprogram(t_a)),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(c_13,plain,
c_in(v_F,c_WFair_Otransient(v_A,t_a),tc_UNITY_Oprogram(t_a)),
inference(clausify,[status(thm)],[cls_conjecture_1]) ).
fof(cls_conjecture_0,axiom,
c_in(v_F,c_UNITY_Oconstrains(v_A,c_union(v_A,v_B,t_a),t_a),tc_UNITY_Oprogram(t_a)),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_14,plain,
c_in(v_F,c_UNITY_Oconstrains(v_A,c_union(v_A,v_B,t_a),t_a),tc_UNITY_Oprogram(t_a)),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
cnf(c_16,plain,
~ c_in(v_F,c_WFair_Oensures(v_A,v_B,t_a),tc_UNITY_Oprogram(t_a)),
inference(resolve,[status(thm)],[c_9,c_12]) ).
cnf(c_17,plain,
( ~ c_in(c_Main_OsubsetI__1(A,v_A,t_a),v_A,t_a)
| c_in(v_F,c_WFair_Otransient(A,t_a),tc_UNITY_Oprogram(t_a)) ),
inference(resolve,[status(thm)],[c_13,c_6]) ).
cnf(c_18,plain,
( c_in(c_Main_OsubsetI__1(A,v_A,t_a),A,t_a)
| c_in(v_F,c_WFair_Otransient(A,t_a),tc_UNITY_Oprogram(t_a)) ),
inference(resolve,[status(thm)],[c_13,c_5]) ).
cnf(c_19,plain,
( ~ c_in(c_Main_OsubsetI__1(A,v_A,t_a),v_A,t_a)
| c_in(v_F,c_UNITY_Oconstrains(A,c_union(v_A,v_B,t_a),t_a),tc_UNITY_Oprogram(t_a)) ),
inference(resolve,[status(thm)],[c_14,c_8]) ).
cnf(c_20,plain,
( c_in(c_Main_OsubsetI__1(A,v_A,t_a),A,t_a)
| c_in(v_F,c_UNITY_Oconstrains(A,c_union(v_A,v_B,t_a),t_a),tc_UNITY_Oprogram(t_a)) ),
inference(resolve,[status(thm)],[c_14,c_7]) ).
cnf(c_27,plain,
( c_in(c_Main_OsubsetI__1(c_minus(A,B,tc_set(t_a)),v_A,t_a),A,t_a)
| c_in(v_F,c_WFair_Otransient(c_minus(A,B,tc_set(t_a)),t_a),tc_UNITY_Oprogram(t_a)) ),
inference(resolve,[status(thm)],[c_18,c_11]) ).
cnf(c_28,plain,
( c_in(c_Main_OsubsetI__1(c_minus(A,B,tc_set(t_a)),v_A,t_a),A,t_a)
| c_in(v_F,c_UNITY_Oconstrains(c_minus(A,B,tc_set(t_a)),c_union(v_A,v_B,t_a),t_a),tc_UNITY_Oprogram(t_a)) ),
inference(resolve,[status(thm)],[c_20,c_11]) ).
cnf(c_42,plain,
( c_in(v_F,c_WFair_Otransient(c_minus(v_A,A,tc_set(t_a)),t_a),tc_UNITY_Oprogram(t_a))
| c_in(v_F,c_WFair_Otransient(c_minus(v_A,A,tc_set(t_a)),t_a),tc_UNITY_Oprogram(t_a)) ),
inference(resolve,[status(thm)],[c_27,c_17]) ).
cnf(c_30,plain,
c_in(v_F,c_WFair_Otransient(c_minus(v_A,A,tc_set(t_a)),t_a),tc_UNITY_Oprogram(t_a)),
inference(copy,[status(thm)],[c_42]) ).
cnf(c_43,plain,
( c_in(v_F,c_WFair_Oensures(v_A,A,t_a),tc_UNITY_Oprogram(t_a))
| ~ c_in(v_F,c_UNITY_Oconstrains(c_minus(v_A,A,tc_set(t_a)),c_union(v_A,A,t_a),t_a),tc_UNITY_Oprogram(t_a)) ),
inference(resolve,[status(thm)],[c_10,c_30]) ).
cnf(c_35,plain,
~ c_in(v_F,c_UNITY_Oconstrains(c_minus(v_A,v_B,tc_set(t_a)),c_union(v_A,v_B,t_a),t_a),tc_UNITY_Oprogram(t_a)),
inference(resolve,[status(thm)],[c_43,c_16]) ).
cnf(c_44,plain,
( c_in(v_F,c_UNITY_Oconstrains(c_minus(v_A,A,tc_set(t_a)),c_union(v_A,v_B,t_a),t_a),tc_UNITY_Oprogram(t_a))
| c_in(v_F,c_UNITY_Oconstrains(c_minus(v_A,A,tc_set(t_a)),c_union(v_A,v_B,t_a),t_a),tc_UNITY_Oprogram(t_a)) ),
inference(resolve,[status(thm)],[c_28,c_19]) ).
cnf(c_40,plain,
c_in(v_F,c_UNITY_Oconstrains(c_minus(v_A,A,tc_set(t_a)),c_union(v_A,v_B,t_a),t_a),tc_UNITY_Oprogram(t_a)),
inference(copy,[status(thm)],[c_44]) ).
cnf(c_41,plain,
$false,
inference(resolve,[status(thm)],[c_40,c_35]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM011-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/5.36 % Computer : n005.cluster.edu
% 0.09/5.36 % Model : x86_64 x86_64
% 0.09/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.36 % Memory : 8046.5625MB
% 0.09/5.36 % OS : Linux 6.8.0-71-generic
% 0.09/5.36 % CPULimit : 300
% 0.09/5.36 % WCLimit : 300
% 0.09/5.36 % DateTime : Sat Sep 26 23:20:52 UTC 2026
% 0.09/5.37 % CPUTime :
% 0.09/5.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/5.37 % Process 3360813 was started by sandbox2 on n005,
% 0.09/5.37 % Sat Sep 26 23:20:52 2026
% 0.09/5.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/5.37
% 0.09/5.37 % From the command line: assign(max_seconds, 300).
% 0.09/5.38
% 0.09/5.38 % SZS status Unsatisfiable for theBenchmark
% 0.09/5.38
% 0.09/5.38 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.09/5.38 % Length of proof is 25.
% 0.09/5.38 % Level of proof is 6.
% 0.09/5.38 % Maximum clause weight is 54.000.
% 0.09/5.38 % Given clauses 26.
% 0.09/5.38
% 0.09/5.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------