%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SWX228-1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n008.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 03:32:10 PM UTC 2026
% Result : Unsatisfiable 7.88s 1.62s
% Output : Proof 7.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 17
% Syntax : Number of formulae : 121 ( 117 unt; 0 def)
% Number of atoms : 125 ( 124 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 14 ( 10 ~; 4 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 6 con; 0-4 aty)
% Number of variables : 212 ( 53 sgn 54 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f25,negated_conjecture,
eq3(prop_union_comm(X,Y),bfalse) != btrue,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal) ).
fof(f25_nnf,plain,
! [X,Y] : eq3(prop_union_comm(X,Y),bfalse) != btrue,
inference(nnf_transformation,[status(thm)],[f25]) ).
fof(f25_sk,plain,
! [X,Y] : eq3(prop_union_comm(X,Y),bfalse) != btrue,
inference(skolemisation,[status(esa)],[f25_nnf]) ).
cnf(c25,plain,
eq3(prop_union_comm(X0,X1),bfalse) != btrue,
inference(cnf_transformation,[status(esa)],[f25_sk]) ).
cnf(t21,plain,
eqq(eq3(prop_union_comm(X1,X2),bfalse),btrue) = efalse,
inference(equality_encoding,[status(esa)],[c25]) ).
cnf(t101,plain,
eqq(eq3(prop_union_comm(X1,X2),bfalse),btrue) = efalse,
inference(orient,[status(thm)],[t21]) ).
cnf(f12,axiom,
prop_union_comm(X,Y) = eq(union(X,Y),union(Y,X)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_012) ).
fof(f12_nnf,plain,
! [X,Y] : prop_union_comm(X,Y) = eq(union(X,Y),union(Y,X)),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [X,Y] : prop_union_comm(X,Y) = eq(union(X,Y),union(Y,X)),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c12,plain,
prop_union_comm(X0,X1) = eq(union(X0,X1),union(X1,X0)),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(t26,plain,
eq(union(X1,X2),union(X2,X1)) = prop_union_comm(X1,X2),
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(t77,plain,
eq(union(X1,X2),union(X2,X1)) = prop_union_comm(X1,X2),
inference(orient,[status(thm)],[t26]) ).
cnf(f11,axiom,
union(cons(Z,Xs),Y) = aux(Y,Z,Xs,elem(Z,Y)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_011) ).
fof(f11_nnf,plain,
! [Z,Xs,Y] : union(cons(Z,Xs),Y) = aux(Y,Z,Xs,elem(Z,Y)),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [Z,Xs,Y] : union(cons(Z,Xs),Y) = aux(Y,Z,Xs,elem(Z,Y)),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
union(cons(X0,X1),X2) = aux(X2,X0,X1,elem(X0,X2)),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(t27,plain,
aux(X1,X2,X3,elem(X2,X1)) = union(cons(X2,X3),X1),
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(t92,plain,
aux(X1,X2,X3,elem(X2,X1)) = union(cons(X2,X3),X1),
inference(orient,[status(thm)],[t27]) ).
cnf(f9,axiom,
elem(X,cons(Z,Xs)) = barbar(eqNat(X,Z),elem(X,Xs)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_009) ).
fof(f9_nnf,plain,
! [X,Z,Xs] : elem(X,cons(Z,Xs)) = barbar(eqNat(X,Z),elem(X,Xs)),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [X,Z,Xs] : elem(X,cons(Z,Xs)) = barbar(eqNat(X,Z),elem(X,Xs)),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
elem(X0,cons(X1,X2)) = barbar(eqNat(X0,X1),elem(X0,X2)),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(t28,plain,
barbar(eqNat(X1,X2),elem(X1,X3)) = elem(X1,cons(X2,X3)),
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(t94,plain,
barbar(eqNat(X1,X2),elem(X1,X3)) = elem(X1,cons(X2,X3)),
inference(orient,[status(thm)],[t28]) ).
cnf(f7,axiom,
eqNat(z,z) = btrue,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_007) ).
fof(f7_nnf,plain,
eqNat(z,z) = btrue,
inference(nnf_transformation,[status(thm)],[f7]) ).
cnf(c7,plain,
eqNat(z,z) = btrue,
inference(cnf_transformation,[status(esa)],[f7_nnf]) ).
cnf(t8,plain,
eqNat(z,z) = btrue,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t84,plain,
eqNat(z,z) = btrue,
inference(orient,[status(thm)],[t8]) ).
cnf(t98,plain,
elem(z,cons(z,X1)) = barbar(btrue,elem(z,X1)),
inference(cp,[status(thm)],[t94,t84]) ).
cnf(f2,axiom,
barbar(btrue,Y) = btrue,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_002) ).
fof(f2_nnf,plain,
! [Y] : barbar(btrue,Y) = btrue,
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [Y] : barbar(btrue,Y) = btrue,
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
barbar(btrue,X0) = btrue,
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(t1,plain,
barbar(btrue,X1) = btrue,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t86,plain,
barbar(btrue,X1) = btrue,
inference(orient,[status(thm)],[t1]) ).
cnf(t639,plain,
elem(z,cons(z,X1)) = btrue,
inference(step,[status(thm)],[t98,t86]) ).
cnf(t105,plain,
elem(z,cons(z,X1)) = btrue,
inference(orient,[status(thm)],[t639]) ).
cnf(t108,plain,
union(cons(z,X1),cons(z,X2)) = aux(cons(z,X2),z,X1,btrue),
inference(cp,[status(thm)],[t92,t105]) ).
cnf(f0,axiom,
aux(Y,Z,Xs,btrue) = union(Xs,Y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom) ).
fof(f0_nnf,plain,
! [Y,Z,Xs] : aux(Y,Z,Xs,btrue) = union(Xs,Y),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [Y,Z,Xs] : aux(Y,Z,Xs,btrue) = union(Xs,Y),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
aux(X0,X1,X2,btrue) = union(X2,X0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t18,plain,
aux(X1,X2,X3,btrue) = union(X3,X1),
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t91,plain,
aux(X1,X2,X3,btrue) = union(X3,X1),
inference(orient,[status(thm)],[t18]) ).
cnf(t651,plain,
union(cons(z,X1),cons(z,X2)) = union(X1,cons(z,X2)),
inference(step,[status(thm)],[t108,t91]) ).
cnf(t183,plain,
union(cons(z,X1),cons(z,X2)) = union(X1,cons(z,X2)),
inference(orient,[status(thm)],[t651]) ).
cnf(t186,plain,
prop_union_comm(cons(z,X1),cons(z,X2)) = eq(union(X1,cons(z,X2)),union(cons(z,X2),cons(z,X1))),
inference(cp,[status(thm)],[t77,t183]) ).
cnf(t679,plain,
prop_union_comm(cons(z,X1),cons(z,X2)) = eq(union(X1,cons(z,X2)),union(X2,cons(z,X1))),
inference(step,[status(thm)],[t186,t183]) ).
cnf(t497,plain,
eq(union(X1,cons(z,X2)),union(X2,cons(z,X1))) = prop_union_comm(cons(z,X1),cons(z,X2)),
inference(orient,[status(thm)],[t679]) ).
cnf(f10,axiom,
union(nil,Y) = Y,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_010) ).
fof(f10_nnf,plain,
! [Y] : union(nil,Y) = Y,
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [Y] : union(nil,Y) = Y,
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
union(nil,X0) = X0,
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(t10,plain,
union(nil,X1) = X1,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(t31,plain,
union(nil,X1) = X1,
inference(orient,[status(thm)],[t10]) ).
cnf(t504,plain,
prop_union_comm(cons(z,X1),cons(z,nil)) = eq(union(X1,cons(z,nil)),cons(z,X1)),
inference(cp,[status(thm)],[t497,t31]) ).
cnf(t515,plain,
eq(union(X1,cons(z,nil)),cons(z,X1)) = prop_union_comm(cons(z,X1),cons(z,nil)),
inference(orient,[status(thm)],[t504]) ).
cnf(f5,axiom,
eqNat(s(Z),z) = bfalse,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_005) ).
fof(f5_nnf,plain,
! [Z] : eqNat(s(Z),z) = bfalse,
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [Z] : eqNat(s(Z),z) = bfalse,
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
eqNat(s(X0),z) = bfalse,
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(t13,plain,
eqNat(s(X1),z) = bfalse,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t40,plain,
eqNat(s(X1),z) = bfalse,
inference(orient,[status(thm)],[t13]) ).
cnf(t95,plain,
elem(s(X1),cons(z,X2)) = barbar(bfalse,elem(s(X1),X2)),
inference(cp,[status(thm)],[t94,t40]) ).
cnf(f3,axiom,
barbar(bfalse,Y) = Y,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_003) ).
fof(f3_nnf,plain,
! [Y] : barbar(bfalse,Y) = Y,
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [Y] : barbar(bfalse,Y) = Y,
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
barbar(bfalse,X0) = X0,
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(t0,plain,
barbar(bfalse,X1) = X1,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t32,plain,
barbar(bfalse,X1) = X1,
inference(orient,[status(thm)],[t0]) ).
cnf(t645,plain,
elem(s(X1),cons(z,X2)) = elem(s(X1),X2),
inference(step,[status(thm)],[t95,t32]) ).
cnf(t156,plain,
elem(s(X1),cons(z,X2)) = elem(s(X1),X2),
inference(orient,[status(thm)],[t645]) ).
cnf(t159,plain,
union(cons(s(X1),X2),cons(z,X3)) = aux(cons(z,X3),s(X1),X2,elem(s(X1),X3)),
inference(cp,[status(thm)],[t92,t156]) ).
cnf(t588,plain,
aux(cons(z,X1),s(X2),X3,elem(s(X2),X1)) = union(cons(s(X2),X3),cons(z,X1)),
inference(orient,[status(thm)],[t159]) ).
cnf(f8,axiom,
elem(X,nil) = bfalse,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_008) ).
fof(f8_nnf,plain,
! [X] : elem(X,nil) = bfalse,
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [X] : elem(X,nil) = bfalse,
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
elem(X0,nil) = bfalse,
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(t2,plain,
elem(X1,nil) = bfalse,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t44,plain,
elem(X1,nil) = bfalse,
inference(orient,[status(thm)],[t2]) ).
cnf(t616,plain,
union(cons(s(X1),X2),cons(z,nil)) = aux(cons(z,nil),s(X1),X2,bfalse),
inference(cp,[status(thm)],[t588,t44]) ).
cnf(t617,plain,
union(cons(s(X1),X2),cons(z,nil)) = aux(cons(z,nil),s(X1),X2,bfalse),
inference(orient,[status(thm)],[t616]) ).
cnf(t624,plain,
prop_union_comm(cons(z,cons(s(X1),X2)),cons(z,nil)) = eq(aux(cons(z,nil),s(X1),X2,bfalse),cons(z,cons(s(X1),X2))),
inference(cp,[status(thm)],[t515,t617]) ).
cnf(f21,axiom,
( eq(cons(X,Y),cons(Z,X2)) = bfalse
| eq2(X,Z) != bfalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_021) ).
fof(f21_nnf,plain,
! [X,Z,Y,X2] :
( eq(cons(X,Y),cons(Z,X2)) = bfalse
| eq2(X,Z) != bfalse ),
inference(nnf_transformation,[status(thm)],[f21]) ).
fof(f21_sk,plain,
! [X,Z,Y,X2] :
( eq(cons(X,Y),cons(Z,X2)) = bfalse
| eq2(X,Z) != bfalse ),
inference(skolemisation,[status(esa)],[f21_nnf]) ).
cnf(c21,plain,
( eq(cons(X0,X2),cons(X1,X3)) = bfalse
| eq2(X0,X1) != bfalse ),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(hi20,axiom,
ifeq(eq2(X0,X1),bfalse,eq(cons(X0,X2),cons(X1,X3)),bfalse) = bfalse,
inference(equality_encoding,[status(esa)],[c21]) ).
cnf(f16,axiom,
eq2(s(X),z) = bfalse,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_016) ).
fof(f16_nnf,plain,
! [X] : eq2(s(X),z) = bfalse,
inference(nnf_transformation,[status(thm)],[f16]) ).
fof(f16_sk,plain,
! [X] : eq2(s(X),z) = bfalse,
inference(skolemisation,[status(esa)],[f16_nnf]) ).
cnf(c16,plain,
eq2(s(X0),z) = bfalse,
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(hi15,axiom,
eq2(s(X0),z) = bfalse,
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(t22,plain,
eq(cons(s(X1),X2),cons(z,X3)) = bfalse,
inference(hyper_resolution,[status(thm)],[hi20,hi15]) ).
cnf(t35,plain,
eq(cons(s(X1),X2),cons(z,X3)) = bfalse,
inference(orient,[status(thm)],[t22]) ).
cnf(f1,axiom,
aux(Y,Z,Xs,bfalse) = cons(Z,union(Xs,Y)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_001) ).
fof(f1_nnf,plain,
! [Y,Z,Xs] : aux(Y,Z,Xs,bfalse) = cons(Z,union(Xs,Y)),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [Y,Z,Xs] : aux(Y,Z,Xs,bfalse) = cons(Z,union(Xs,Y)),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
aux(X0,X1,X2,bfalse) = cons(X1,union(X2,X0)),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(t24,plain,
cons(X1,union(X2,X3)) = aux(X3,X1,X2,bfalse),
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t46,plain,
cons(X1,union(X2,X3)) = aux(X3,X1,X2,bfalse),
inference(orient,[status(thm)],[t24]) ).
cnf(t50,plain,
bfalse = eq(aux(X1,s(X2),X3,bfalse),cons(z,X4)),
inference(cp,[status(thm)],[t35,t46]) ).
cnf(t160,plain,
eq(aux(X1,s(X2),X3,bfalse),cons(z,X4)) = bfalse,
inference(orient,[status(thm)],[t50]) ).
cnf(t681,plain,
prop_union_comm(cons(z,cons(s(X1),X2)),cons(z,nil)) = bfalse,
inference(step,[status(thm)],[t624,t160]) ).
cnf(t628,plain,
prop_union_comm(cons(z,cons(s(X1),X2)),cons(z,nil)) = bfalse,
inference(orient,[status(thm)],[t681]) ).
cnf(t632,plain,
efalse = eqq(eq3(bfalse,bfalse),btrue),
inference(cp,[status(thm)],[t101,t628]) ).
cnf(f20,axiom,
eq3(X,X) = btrue,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_020) ).
fof(f20_nnf,plain,
! [X] : eq3(X,X) = btrue,
inference(nnf_transformation,[status(thm)],[f20]) ).
fof(f20_sk,plain,
! [X] : eq3(X,X) = btrue,
inference(skolemisation,[status(esa)],[f20_nnf]) ).
cnf(c20,plain,
eq3(X0,X0) = btrue,
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(t5,plain,
eq3(X1,X1) = btrue,
inference(equality_encoding,[status(esa)],[c20]) ).
cnf(t85,plain,
eq3(X1,X1) = btrue,
inference(orient,[status(thm)],[t5]) ).
cnf(t682,plain,
efalse = eqq(btrue,btrue),
inference(step,[status(thm)],[t632,t85]) ).
cnf(t9,plain,
eqq(X1,X1) = etrue,
introduced(definition) ).
cnf(t100,plain,
eqq(X1,X1) = etrue,
inference(orient,[status(thm)],[t9]) ).
cnf(t683,plain,
efalse = etrue,
inference(step,[status(thm)],[t682,t100]) ).
cnf(t633,plain,
efalse = etrue,
inference(orient,[status(thm)],[t683]) ).
cnf(goal_0,negated_conjecture,
etrue != efalse,
introduced(definition) ).
cnf(g0_0,plain,
etrue != etrue,
inference(rw,[status(thm)],[goal_0,t633]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX228-1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n008.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Thu Sep 24 23:45:24 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 7.88/1.62 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.88/1.62 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------