%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SWX186-1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n006.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 03:32:03 PM UTC 2026
% Result : Unsatisfiable 3.42s 0.88s
% Output : Proof 3.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 10
% Syntax : Number of formulae : 66 ( 66 unt; 0 def)
% Number of atoms : 66 ( 65 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 6 ( 6 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 5 con; 0-3 aty)
% Number of variables : 113 ( 38 sgn 30 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f18,negated_conjecture,
eq3(prop_drop_inj2(X,Y,Z),bfalse) != btrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal) ).
fof(f18_nnf,plain,
! [X,Y,Z] : eq3(prop_drop_inj2(X,Y,Z),bfalse) != btrue,
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
! [X,Y,Z] : eq3(prop_drop_inj2(X,Y,Z),bfalse) != btrue,
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c18,plain,
eq3(prop_drop_inj2(X0,X1,X2),bfalse) != btrue,
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(t19,plain,
eqq(eq3(prop_drop_inj2(X1,X2,X3),bfalse),btrue) = efalse,
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(t77,plain,
eqq(eq3(prop_drop_inj2(X1,X2,X3),bfalse),btrue) = efalse,
inference(orient,[status(thm)],[t19]) ).
cnf(f5,axiom,
prop_drop_inj2(X,Y,Z) = impl(eq(drop(X,Y),drop(X,Z)),eq(Y,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_005) ).
fof(f5_nnf,plain,
! [X,Y,Z] : prop_drop_inj2(X,Y,Z) = impl(eq(drop(X,Y),drop(X,Z)),eq(Y,Z)),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [X,Y,Z] : prop_drop_inj2(X,Y,Z) = impl(eq(drop(X,Y),drop(X,Z)),eq(Y,Z)),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
prop_drop_inj2(X0,X1,X2) = impl(eq(drop(X0,X1),drop(X0,X2)),eq(X1,X2)),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(t22,plain,
impl(eq(drop(X1,X2),drop(X1,X3)),eq(X2,X3)) = prop_drop_inj2(X1,X2,X3),
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t62,plain,
impl(eq(drop(X1,X2),drop(X1,X3)),eq(X2,X3)) = prop_drop_inj2(X1,X2,X3),
inference(orient,[status(thm)],[t22]) ).
cnf(f2,axiom,
drop(s(Z),nil) = nil,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_002) ).
fof(f2_nnf,plain,
! [Z] : drop(s(Z),nil) = nil,
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [Z] : drop(s(Z),nil) = nil,
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
drop(s(X0),nil) = nil,
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(t9,plain,
drop(s(X1),nil) = nil,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t61,plain,
drop(s(X1),nil) = nil,
inference(orient,[status(thm)],[t9]) ).
cnf(t66,plain,
prop_drop_inj2(s(X1),nil,X2) = impl(eq(nil,drop(s(X1),X2)),eq(nil,X2)),
inference(cp,[status(thm)],[t62,t61]) ).
cnf(t112,plain,
impl(eq(nil,drop(s(X1),X2)),eq(nil,X2)) = prop_drop_inj2(s(X1),nil,X2),
inference(orient,[status(thm)],[t66]) ).
cnf(f3,axiom,
drop(s(Z),cons(X2,X3)) = drop(Z,X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_003) ).
fof(f3_nnf,plain,
! [Z,X2,X3] : drop(s(Z),cons(X2,X3)) = drop(Z,X3),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [Z,X2,X3] : drop(s(Z),cons(X2,X3)) = drop(Z,X3),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
drop(s(X0),cons(X1,X2)) = drop(X0,X2),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(t16,plain,
drop(s(X1),cons(X2,X3)) = drop(X1,X3),
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t60,plain,
drop(s(X1),cons(X2,X3)) = drop(X1,X3),
inference(orient,[status(thm)],[t16]) ).
cnf(t113,plain,
prop_drop_inj2(s(X1),nil,cons(X2,X3)) = impl(eq(nil,drop(X1,X3)),eq(nil,cons(X2,X3))),
inference(cp,[status(thm)],[t112,t60]) ).
cnf(f16,axiom,
eq(nil,cons(X,Y)) = bfalse,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_016) ).
fof(f16_nnf,plain,
! [X,Y] : eq(nil,cons(X,Y)) = bfalse,
inference(nnf_transformation,[status(thm)],[f16]) ).
fof(f16_sk,plain,
! [X,Y] : eq(nil,cons(X,Y)) = bfalse,
inference(skolemisation,[status(esa)],[f16_nnf]) ).
cnf(c16,plain,
eq(nil,cons(X0,X1)) = bfalse,
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(t13,plain,
eq(nil,cons(X1,X2)) = bfalse,
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(t30,plain,
eq(nil,cons(X1,X2)) = bfalse,
inference(orient,[status(thm)],[t13]) ).
cnf(t155,plain,
prop_drop_inj2(s(X1),nil,cons(X2,X3)) = impl(eq(nil,drop(X1,X3)),bfalse),
inference(step,[status(thm)],[t113,t30]) ).
cnf(t126,plain,
prop_drop_inj2(s(X1),nil,cons(X2,X3)) = impl(eq(nil,drop(X1,X3)),bfalse),
inference(orient,[status(thm)],[t155]) ).
cnf(t130,plain,
prop_drop_inj2(s(s(X1)),nil,cons(X2,nil)) = impl(eq(nil,nil),bfalse),
inference(cp,[status(thm)],[t126,t61]) ).
cnf(f11,axiom,
eq(X,X) = btrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_011) ).
fof(f11_nnf,plain,
! [X] : eq(X,X) = btrue,
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [X] : eq(X,X) = btrue,
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
eq(X0,X0) = btrue,
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(t1,plain,
eq(X1,X1) = btrue,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(t49,plain,
eq(X1,X1) = btrue,
inference(orient,[status(thm)],[t1]) ).
cnf(t156,plain,
prop_drop_inj2(s(s(X1)),nil,cons(X2,nil)) = impl(btrue,bfalse),
inference(step,[status(thm)],[t130,t49]) ).
cnf(f0,axiom,
impl(btrue,Q) = Q,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom) ).
fof(f0_nnf,plain,
! [Q] : impl(btrue,Q) = Q,
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [Q] : impl(btrue,Q) = Q,
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
impl(btrue,X0) = X0,
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t8,plain,
impl(btrue,X1) = X1,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t25,plain,
impl(btrue,X1) = X1,
inference(orient,[status(thm)],[t8]) ).
cnf(t157,plain,
prop_drop_inj2(s(s(X1)),nil,cons(X2,nil)) = bfalse,
inference(step,[status(thm)],[t156,t25]) ).
cnf(t132,plain,
prop_drop_inj2(s(s(X1)),nil,cons(X2,nil)) = bfalse,
inference(orient,[status(thm)],[t157]) ).
cnf(t133,plain,
efalse = eqq(eq3(bfalse,bfalse),btrue),
inference(cp,[status(thm)],[t77,t132]) ).
cnf(f13,axiom,
eq3(X,X) = btrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_013) ).
fof(f13_nnf,plain,
! [X] : eq3(X,X) = btrue,
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [X] : eq3(X,X) = btrue,
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c13,plain,
eq3(X0,X0) = btrue,
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(t3,plain,
eq3(X1,X1) = btrue,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(t55,plain,
eq3(X1,X1) = btrue,
inference(orient,[status(thm)],[t3]) ).
cnf(t158,plain,
efalse = eqq(btrue,btrue),
inference(step,[status(thm)],[t133,t55]) ).
cnf(t6,plain,
eqq(X1,X1) = etrue,
introduced(definition) ).
cnf(t76,plain,
eqq(X1,X1) = etrue,
inference(orient,[status(thm)],[t6]) ).
cnf(t159,plain,
efalse = etrue,
inference(step,[status(thm)],[t158,t76]) ).
cnf(t134,plain,
efalse = etrue,
inference(orient,[status(thm)],[t159]) ).
cnf(goal_0,negated_conjecture,
etrue != efalse,
introduced(definition) ).
cnf(g0_0,plain,
etrue != etrue,
inference(rw,[status(thm)],[goal_0,t134]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWX186-1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.35 % Computer : n006.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Thu Sep 24 23:32:28 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 3.42/0.88 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.42/0.88 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------