%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN646-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n012.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 03:35:24 PM UTC 2026
% Result : Unsatisfiable 53.86s 7.16s
% Output : Proof 53.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 11
% Syntax : Number of formulae : 57 ( 49 unt; 0 def)
% Number of atoms : 81 ( 18 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 58 ( 34 ~; 24 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 10 ( 3 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 6 con; 0-4 aty)
% Number of variables : 30 ( 0 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f27,negated_conjecture,
( ~ p2(X16,X18)
| ~ p2(X16,X17)
| p2(X17,X18) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_28) ).
fof(f27_nnf,plain,
! [X17,X18,X16] :
( ~ p2(X16,X18)
| ~ p2(X16,X17)
| p2(X17,X18) ),
inference(nnf_transformation,[status(thm)],[f27]) ).
fof(f27_sk,plain,
! [X17,X18,X16] :
( ~ p2(X16,X18)
| ~ p2(X16,X17)
| p2(X17,X18) ),
inference(skolemisation,[status(esa)],[f27_nnf]) ).
cnf(c27,plain,
( ~ p2(X2,X1)
| ~ p2(X2,X0)
| p2(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f27_sk]) ).
cnf(hi25,negated_conjecture,
ifeq(p2(X0,X1),true,ifeq(p2(X0,X2),true,p2(X1,X2),true),true) = true,
inference(equality_encoding,[status(esa)],[c27]) ).
cnf(f34,negated_conjecture,
p2(f13(f11(c23)),f7(f8(f9(f8(f9(f9(f9(f9(f8(c24)))))))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_35) ).
fof(f34_nnf,plain,
p2(f13(f11(c23)),f7(f8(f9(f8(f9(f9(f9(f9(f8(c24)))))))))),
inference(nnf_transformation,[status(thm)],[f34]) ).
cnf(c34,plain,
p2(f13(f11(c23)),f7(f8(f9(f8(f9(f9(f9(f9(f8(c24)))))))))),
inference(cnf_transformation,[status(esa)],[f34_nnf]) ).
cnf(hi32,negated_conjecture,
p2(f13(f11(c23)),f7(f8(f9(f8(f9(f9(f9(f9(f8(c24)))))))))) = true,
inference(equality_encoding,[status(esa)],[c34]) ).
cnf(f13,negated_conjecture,
p2(f13(f11(c23)),f13(f11(c22))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_14) ).
fof(f13_nnf,plain,
p2(f13(f11(c23)),f13(f11(c22))),
inference(nnf_transformation,[status(thm)],[f13]) ).
cnf(c13,plain,
p2(f13(f11(c23)),f13(f11(c22))),
inference(cnf_transformation,[status(esa)],[f13_nnf]) ).
cnf(hi11,negated_conjecture,
p2(f13(f11(c23)),f13(f11(c22))) = true,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(h75,plain,
p2(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f13(f11(c22))) = true,
inference(hyper_resolution,[status(thm)],[hi25,hi32,hi11]) ).
cnf(f35,negated_conjecture,
p2(f13(f11(c25)),f7(f8(f9(f8(f9(f9(f9(f9(f8(c24)))))))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_36) ).
fof(f35_nnf,plain,
p2(f13(f11(c25)),f7(f8(f9(f8(f9(f9(f9(f9(f8(c24)))))))))),
inference(nnf_transformation,[status(thm)],[f35]) ).
cnf(c35,plain,
p2(f13(f11(c25)),f7(f8(f9(f8(f9(f9(f9(f9(f8(c24)))))))))),
inference(cnf_transformation,[status(esa)],[f35_nnf]) ).
cnf(hi33,negated_conjecture,
p2(f13(f11(c25)),f7(f8(f9(f8(f9(f9(f9(f9(f8(c24)))))))))) = true,
inference(equality_encoding,[status(esa)],[c35]) ).
cnf(f4,negated_conjecture,
p2(X16,X16),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_5) ).
fof(f4_nnf,plain,
! [X16] : p2(X16,X16),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [X16] : p2(X16,X16),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
p2(X0,X0),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(hi4,negated_conjecture,
p2(X0,X0) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(h94,plain,
p2(f7(f8(f9(f8(f9(f9(f9(f9(f8(c24))))))))),f13(f11(c25))) = true,
inference(hyper_resolution,[status(thm)],[hi25,hi33,hi4]) ).
cnf(h6206,plain,
p2(f13(f11(c25)),f13(f11(c22))) = true,
inference(hyper_resolution,[status(thm)],[hi25,h94,h75]) ).
cnf(f39,negated_conjecture,
( ~ p20(f14(f11(X39)),f14(f11(X40)))
| ~ p2(f13(f11(X39)),f13(f11(X40)))
| ~ p2(f12(f11(X40)),f7(c24))
| ~ p2(f12(f11(X39)),f7(c24))
| p21(f17(X39),f17(X40)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p21_40) ).
fof(f39_nnf,plain,
! [X39,X40] :
( ~ p20(f14(f11(X39)),f14(f11(X40)))
| ~ p2(f13(f11(X39)),f13(f11(X40)))
| ~ p2(f12(f11(X40)),f7(c24))
| ~ p2(f12(f11(X39)),f7(c24))
| p21(f17(X39),f17(X40)) ),
inference(nnf_transformation,[status(thm)],[f39]) ).
fof(f39_sk,plain,
! [X39,X40] :
( ~ p20(f14(f11(X39)),f14(f11(X40)))
| ~ p2(f13(f11(X39)),f13(f11(X40)))
| ~ p2(f12(f11(X40)),f7(c24))
| ~ p2(f12(f11(X39)),f7(c24))
| p21(f17(X39),f17(X40)) ),
inference(skolemisation,[status(esa)],[f39_nnf]) ).
cnf(c39,plain,
( ~ p20(f14(f11(X0)),f14(f11(X1)))
| ~ p2(f13(f11(X0)),f13(f11(X1)))
| ~ p2(f12(f11(X1)),f7(c24))
| ~ p2(f12(f11(X0)),f7(c24))
| p21(f17(X0),f17(X1)) ),
inference(cnf_transformation,[status(esa)],[f39_sk]) ).
cnf(hi37,negated_conjecture,
ifeq(p2(f12(f11(X0)),f7(c24)),true,ifeq(p2(f12(f11(X1)),f7(c24)),true,ifeq(p2(f13(f11(X0)),f13(f11(X1))),true,ifeq(p20(f14(f11(X0)),f14(f11(X1))),true,p21(f17(X0),f17(X1)),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c39]) ).
cnf(f9,negated_conjecture,
p2(f12(f11(c25)),f7(c24)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_10) ).
fof(f9_nnf,plain,
p2(f12(f11(c25)),f7(c24)),
inference(nnf_transformation,[status(thm)],[f9]) ).
cnf(c9,plain,
p2(f12(f11(c25)),f7(c24)),
inference(cnf_transformation,[status(esa)],[f9_nnf]) ).
cnf(hi7,negated_conjecture,
p2(f12(f11(c25)),f7(c24)) = true,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(f8,negated_conjecture,
p2(f12(f11(c22)),f7(c24)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_9) ).
fof(f8_nnf,plain,
p2(f12(f11(c22)),f7(c24)),
inference(nnf_transformation,[status(thm)],[f8]) ).
cnf(c8,plain,
p2(f12(f11(c22)),f7(c24)),
inference(cnf_transformation,[status(esa)],[f8_nnf]) ).
cnf(hi6,negated_conjecture,
p2(f12(f11(c22)),f7(c24)) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(f11,negated_conjecture,
p20(f14(f11(c25)),f14(f11(c22))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p20_12) ).
fof(f11_nnf,plain,
p20(f14(f11(c25)),f14(f11(c22))),
inference(nnf_transformation,[status(thm)],[f11]) ).
cnf(c11,plain,
p20(f14(f11(c25)),f14(f11(c22))),
inference(cnf_transformation,[status(esa)],[f11_nnf]) ).
cnf(hi9,negated_conjecture,
p20(f14(f11(c25)),f14(f11(c22))) = true,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(h20321,plain,
p21(f17(c25),f17(c22)) = true,
inference(hyper_resolution,[status(thm)],[hi37,hi7,hi6,h6206,hi9]) ).
cnf(f6,negated_conjecture,
~ p21(f17(c25),f17(c22)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_p21_7) ).
fof(f6_nnf,plain,
~ p21(f17(c25),f17(c22)),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
~ p21(f17(c25),f17(c22)),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
~ p21(f17(c25),f17(c22)),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(hi42,negated_conjecture,
ifeq(p21(f17(c25),f17(c22)),true,false,true) = true,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t0,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi42,h20321]) ).
cnf(t1008,plain,
false = true,
inference(orient,[status(thm)],[t0]) ).
cnf(f7,negated_conjecture,
~ p21(f17(c22),f17(c23)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_p21_8) ).
fof(f7_nnf,plain,
~ p21(f17(c22),f17(c23)),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
~ p21(f17(c22),f17(c23)),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
~ p21(f17(c22),f17(c23)),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c6,c7]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t1008]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SYN646-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.02 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.03/0.30 % Computer : n012.cluster.edu
% 0.03/0.30 % Model : x86_64 x86_64
% 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30 % Memory : 8046.5625MB
% 0.03/0.30 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Fri Sep 25 01:58:20 UTC 2026
% 0.03/0.31 % CPUTime :
% 0.03/0.31 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 53.86/7.16 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 53.86/7.16 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------