%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : COM011-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n004.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 : Fri Sep 25 01:03:29 PM UTC 2026
% Result : Unsatisfiable 4.78s 6.11s
% Output : Proof 4.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of formulae : 49 ( 16 unt; 0 def)
% Number of atoms : 94 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 88 ( 43 ~; 45 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 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 : 122 ( 5 sgn 54 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f4,axiom,
( c_lessequals(V_A,V_B,tc_set(T_a))
| c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_A,T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetI_0) ).
fof(f4_nnf,plain,
! [V_A,V_B,T_a] :
( c_lessequals(V_A,V_B,tc_set(T_a))
| c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_A,T_a) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [V_A,V_B,T_a] :
( c_lessequals(V_A,V_B,tc_set(T_a))
| c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_A,T_a) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
( c_lessequals(X0,X1,tc_set(X2))
| c_in(c_Main_OsubsetI__1(X0,X1,X2),X0,X2) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(f3,axiom,
( c_in(V_c,V_A,T_a)
| ~ c_in(V_c,c_minus(V_A,V_B,tc_set(T_a)),T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiffE_1) ).
fof(f3_nnf,plain,
! [V_c,V_A,V_B,T_a] :
( c_in(V_c,V_A,T_a)
| ~ c_in(V_c,c_minus(V_A,V_B,tc_set(T_a)),T_a) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [V_c,V_A,V_B,T_a] :
( c_in(V_c,V_A,T_a)
| ~ c_in(V_c,c_minus(V_A,V_B,tc_set(T_a)),T_a) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
( c_in(X0,X1,X3)
| ~ c_in(X0,c_minus(X1,X2,tc_set(X3)),X3) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p10,plain,
( c_in(c_Main_OsubsetI__1(c_minus(X0,X1,tc_set(X2)),X3,X2),X0,X2)
| c_lessequals(c_minus(X0,X1,tc_set(X2)),X3,tc_set(X2)) ),
inference(resolution,[status(thm)],[c4,c3]) ).
cnf(f5,axiom,
( c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_B,T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetI_1) ).
fof(f5_nnf,plain,
! [V_A,V_B,T_a] :
( c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_B,T_a) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [V_A,V_B,T_a] :
( c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_B,T_a) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
( c_lessequals(X0,X1,tc_set(X2))
| ~ c_in(c_Main_OsubsetI__1(X0,X1,X2),X1,X2) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p19,plain,
( c_lessequals(c_minus(X0,X1,tc_set(X2)),X0,tc_set(X2))
| c_lessequals(c_minus(X0,X1,tc_set(X2)),X0,tc_set(X2)) ),
inference(resolution,[status(thm)],[p10,c5]) ).
cnf(p25,plain,
c_lessequals(c_minus(X0,X1,tc_set(X2)),X0,tc_set(X2)),
inference(factoring,[status(thm)],[p19]) ).
cnf(f6,axiom,
( c_in(V_F,c_UNITY_Oconstrains(V_B,V_A_H,T_a),tc_UNITY_Oprogram(T_a))
| ~ c_lessequals(V_B,V_A,tc_set(T_a))
| ~ c_in(V_F,c_UNITY_Oconstrains(V_A,V_A_H,T_a),tc_UNITY_Oprogram(T_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UNITY_Oconstrains__weaken__L_0) ).
fof(f6_nnf,plain,
! [V_F,V_A,V_A_H,T_a,V_B] :
( c_in(V_F,c_UNITY_Oconstrains(V_B,V_A_H,T_a),tc_UNITY_Oprogram(T_a))
| ~ c_lessequals(V_B,V_A,tc_set(T_a))
| ~ c_in(V_F,c_UNITY_Oconstrains(V_A,V_A_H,T_a),tc_UNITY_Oprogram(T_a)) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [V_F,V_A,V_A_H,T_a,V_B] :
( c_in(V_F,c_UNITY_Oconstrains(V_B,V_A_H,T_a),tc_UNITY_Oprogram(T_a))
| ~ c_lessequals(V_B,V_A,tc_set(T_a))
| ~ c_in(V_F,c_UNITY_Oconstrains(V_A,V_A_H,T_a),tc_UNITY_Oprogram(T_a)) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
( c_in(X0,c_UNITY_Oconstrains(X4,X2,X3),tc_UNITY_Oprogram(X3))
| ~ c_lessequals(X4,X1,tc_set(X3))
| ~ c_in(X0,c_UNITY_Oconstrains(X1,X2,X3),tc_UNITY_Oprogram(X3)) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(f0,negated_conjecture,
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('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f0_nnf,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(nnf_transformation,[status(thm)],[f0]) ).
cnf(c0,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(cnf_transformation,[status(esa)],[f0_nnf]) ).
cnf(p14,plain,
( c_in(v_F,c_UNITY_Oconstrains(X0,c_union(v_A,v_B,t_a),t_a),tc_UNITY_Oprogram(t_a))
| ~ c_lessequals(X0,v_A,tc_set(t_a)) ),
inference(resolution,[status(thm)],[c6,c0]) ).
cnf(p26,plain,
c_in(v_F,c_UNITY_Oconstrains(c_minus(v_A,X0,tc_set(t_a)),c_union(v_A,v_B,t_a),t_a),tc_UNITY_Oprogram(t_a)),
inference(resolution,[status(thm)],[p25,p14]) ).
cnf(f7,axiom,
( c_in(V_F,c_WFair_Oensures(V_A,V_B,T_a),tc_UNITY_Oprogram(T_a))
| ~ c_in(V_F,c_WFair_Otransient(c_minus(V_A,V_B,tc_set(T_a)),T_a),tc_UNITY_Oprogram(T_a))
| ~ 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)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WFair_OensuresI_0) ).
fof(f7_nnf,plain,
! [V_F,V_A,V_B,T_a] :
( c_in(V_F,c_WFair_Oensures(V_A,V_B,T_a),tc_UNITY_Oprogram(T_a))
| ~ c_in(V_F,c_WFair_Otransient(c_minus(V_A,V_B,tc_set(T_a)),T_a),tc_UNITY_Oprogram(T_a))
| ~ 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(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [V_F,V_A,V_B,T_a] :
( c_in(V_F,c_WFair_Oensures(V_A,V_B,T_a),tc_UNITY_Oprogram(T_a))
| ~ c_in(V_F,c_WFair_Otransient(c_minus(V_A,V_B,tc_set(T_a)),T_a),tc_UNITY_Oprogram(T_a))
| ~ 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(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
( c_in(X0,c_WFair_Oensures(X1,X2,X3),tc_UNITY_Oprogram(X3))
| ~ c_in(X0,c_WFair_Otransient(c_minus(X1,X2,tc_set(X3)),X3),tc_UNITY_Oprogram(X3))
| ~ c_in(X0,c_UNITY_Oconstrains(c_minus(X1,X2,tc_set(X3)),c_union(X1,X2,X3),X3),tc_UNITY_Oprogram(X3)) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p30,plain,
( c_in(v_F,c_WFair_Oensures(v_A,v_B,t_a),tc_UNITY_Oprogram(t_a))
| ~ c_in(v_F,c_WFair_Otransient(c_minus(v_A,v_B,tc_set(t_a)),t_a),tc_UNITY_Oprogram(t_a)) ),
inference(resolution,[status(thm)],[p26,c7]) ).
cnf(f9,axiom,
( c_in(V_F,c_WFair_Otransient(V_B,T_a),tc_UNITY_Oprogram(T_a))
| ~ c_lessequals(V_B,V_A,tc_set(T_a))
| ~ c_in(V_F,c_WFair_Otransient(V_A,T_a),tc_UNITY_Oprogram(T_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WFair_Otransient__strengthen_0) ).
fof(f9_nnf,plain,
! [V_F,V_A,T_a,V_B] :
( c_in(V_F,c_WFair_Otransient(V_B,T_a),tc_UNITY_Oprogram(T_a))
| ~ c_lessequals(V_B,V_A,tc_set(T_a))
| ~ c_in(V_F,c_WFair_Otransient(V_A,T_a),tc_UNITY_Oprogram(T_a)) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [V_F,V_A,T_a,V_B] :
( c_in(V_F,c_WFair_Otransient(V_B,T_a),tc_UNITY_Oprogram(T_a))
| ~ c_lessequals(V_B,V_A,tc_set(T_a))
| ~ c_in(V_F,c_WFair_Otransient(V_A,T_a),tc_UNITY_Oprogram(T_a)) ),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
( c_in(X0,c_WFair_Otransient(X3,X2),tc_UNITY_Oprogram(X2))
| ~ c_lessequals(X3,X1,tc_set(X2))
| ~ c_in(X0,c_WFair_Otransient(X1,X2),tc_UNITY_Oprogram(X2)) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(f1,negated_conjecture,
c_in(v_F,c_WFair_Otransient(v_A,t_a),tc_UNITY_Oprogram(t_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f1_nnf,plain,
c_in(v_F,c_WFair_Otransient(v_A,t_a),tc_UNITY_Oprogram(t_a)),
inference(nnf_transformation,[status(thm)],[f1]) ).
cnf(c1,plain,
c_in(v_F,c_WFair_Otransient(v_A,t_a),tc_UNITY_Oprogram(t_a)),
inference(cnf_transformation,[status(esa)],[f1_nnf]) ).
cnf(p16,plain,
( c_in(v_F,c_WFair_Otransient(X0,t_a),tc_UNITY_Oprogram(t_a))
| ~ c_lessequals(X0,v_A,tc_set(t_a)) ),
inference(resolution,[status(thm)],[c9,c1]) ).
cnf(p27,plain,
c_in(v_F,c_WFair_Otransient(c_minus(v_A,X0,tc_set(t_a)),t_a),tc_UNITY_Oprogram(t_a)),
inference(resolution,[status(thm)],[p25,p16]) ).
cnf(p34,plain,
c_in(v_F,c_WFair_Oensures(v_A,v_B,t_a),tc_UNITY_Oprogram(t_a)),
inference(resolution,[status(thm)],[p30,p27]) ).
cnf(f8,axiom,
( c_in(V_F,c_WFair_OleadsTo(V_A,V_B,T_a),tc_UNITY_Oprogram(T_a))
| ~ c_in(V_F,c_WFair_Oensures(V_A,V_B,T_a),tc_UNITY_Oprogram(T_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WFair_OleadsTo__Basis_0) ).
fof(f8_nnf,plain,
! [V_F,V_A,V_B,T_a] :
( c_in(V_F,c_WFair_OleadsTo(V_A,V_B,T_a),tc_UNITY_Oprogram(T_a))
| ~ c_in(V_F,c_WFair_Oensures(V_A,V_B,T_a),tc_UNITY_Oprogram(T_a)) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [V_F,V_A,V_B,T_a] :
( c_in(V_F,c_WFair_OleadsTo(V_A,V_B,T_a),tc_UNITY_Oprogram(T_a))
| ~ c_in(V_F,c_WFair_Oensures(V_A,V_B,T_a),tc_UNITY_Oprogram(T_a)) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
( c_in(X0,c_WFair_OleadsTo(X1,X2,X3),tc_UNITY_Oprogram(X3))
| ~ c_in(X0,c_WFair_Oensures(X1,X2,X3),tc_UNITY_Oprogram(X3)) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p35,plain,
c_in(v_F,c_WFair_OleadsTo(v_A,v_B,t_a),tc_UNITY_Oprogram(t_a)),
inference(resolution,[status(thm)],[p34,c8]) ).
cnf(f2,negated_conjecture,
~ c_in(v_F,c_WFair_OleadsTo(v_A,v_B,t_a),tc_UNITY_Oprogram(t_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f2_nnf,plain,
~ c_in(v_F,c_WFair_OleadsTo(v_A,v_B,t_a),tc_UNITY_Oprogram(t_a)),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
~ c_in(v_F,c_WFair_OleadsTo(v_A,v_B,t_a),tc_UNITY_Oprogram(t_a)),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
~ c_in(v_F,c_WFair_OleadsTo(v_A,v_B,t_a),tc_UNITY_Oprogram(t_a)),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p37,plain,
$false,
inference(resolution,[status(thm)],[p35,c2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM011-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/5.39 % Computer : n004.cluster.edu
% 0.09/5.39 % Model : x86_64 x86_64
% 0.09/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.39 % Memory : 8046.5625MB
% 0.09/5.39 % OS : Linux 6.8.0-71-generic
% 0.09/5.39 % CPULimit : 300
% 0.09/5.39 % WCLimit : 300
% 0.09/5.39 % DateTime : Fri Sep 25 07:46:03 UTC 2026
% 0.09/5.39 % CPUTime :
% 0.09/5.39 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 4.78/6.11 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.78/6.11 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------