%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : KRS015-1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n009.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 01:52:54 PM UTC 2026
% Result : Unsatisfiable 4.37s 1.40s
% Output : Proof 4.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 11
% Syntax : Number of formulae : 68 ( 28 unt; 0 def)
% Number of atoms : 128 ( 24 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 126 ( 66 ~; 60 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-4 aty)
% Number of variables : 75 ( 0 sgn 30 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f13,axiom,
( ~ e(X1)
| r(X1,u4r4(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_14) ).
fof(f13_nnf,plain,
! [X1] :
( ~ e(X1)
| r(X1,u4r4(X1)) ),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [X1] :
( ~ e(X1)
| r(X1,u4r4(X1)) ),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c13,plain,
( ~ e(X0)
| r(X0,u4r4(X0)) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(hi12,axiom,
ifeq(e(X0),true,r(X0,u4r4(X0)),true) = true,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(f0,negated_conjecture,
e(exist),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1) ).
fof(f0_nnf,plain,
e(exist),
inference(nnf_transformation,[status(thm)],[f0]) ).
cnf(c0,plain,
e(exist),
inference(cnf_transformation,[status(esa)],[f0_nnf]) ).
cnf(hi0,negated_conjecture,
e(exist) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(h0,plain,
r(exist,u4r4(exist)) = true,
inference(hyper_resolution,[status(thm)],[hi12,hi0]) ).
cnf(f17,axiom,
( ~ r(X1,X2)
| ~ e(X1)
| c(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_18) ).
fof(f17_nnf,plain,
! [X2,X1] :
( ~ r(X1,X2)
| ~ e(X1)
| c(X2) ),
inference(nnf_transformation,[status(thm)],[f17]) ).
fof(f17_sk,plain,
! [X2,X1] :
( ~ r(X1,X2)
| ~ e(X1)
| c(X2) ),
inference(skolemisation,[status(esa)],[f17_nnf]) ).
cnf(c17,plain,
( ~ r(X1,X0)
| ~ e(X1)
| c(X0) ),
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
cnf(hi16,axiom,
ifeq(e(X0),true,ifeq(r(X0,X1),true,c(X1),true),true) = true,
inference(equality_encoding,[status(esa)],[c17]) ).
cnf(h1,plain,
c(u4r4(exist)) = true,
inference(hyper_resolution,[status(thm)],[hi16,hi0,h0]) ).
cnf(f1,axiom,
( ~ c(X1)
| t2least(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_2) ).
fof(f1_nnf,plain,
! [X1] :
( ~ c(X1)
| t2least(X1) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X1] :
( ~ c(X1)
| t2least(X1) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( ~ c(X0)
| t2least(X0) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(hi1,axiom,
ifeq(c(X0),true,t2least(X0),true) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(h3,plain,
t2least(u4r4(exist)) = true,
inference(hyper_resolution,[status(thm)],[hi1,h1]) ).
cnf(f4,axiom,
( ~ t2least(X1)
| t(X1,u1r1(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_5) ).
fof(f4_nnf,plain,
! [X1] :
( ~ t2least(X1)
| t(X1,u1r1(X1)) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [X1] :
( ~ t2least(X1)
| t(X1,u1r1(X1)) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
( ~ t2least(X0)
| t(X0,u1r1(X0)) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(hi3,axiom,
ifeq(t2least(X0),true,t(X0,u1r1(X0)),true) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(h5,plain,
t(u4r4(exist),u1r1(u4r4(exist))) = true,
inference(hyper_resolution,[status(thm)],[hi3,h3]) ).
cnf(f5,axiom,
( ~ t2least(X1)
| t(X1,u1r2(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_6) ).
fof(f5_nnf,plain,
! [X1] :
( ~ t2least(X1)
| t(X1,u1r2(X1)) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [X1] :
( ~ t2least(X1)
| t(X1,u1r2(X1)) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
( ~ t2least(X0)
| t(X0,u1r2(X0)) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(hi4,axiom,
ifeq(t2least(X0),true,t(X0,u1r2(X0)),true) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(h4,plain,
t(u4r4(exist),u1r2(u4r4(exist))) = true,
inference(hyper_resolution,[status(thm)],[hi4,h3]) ).
cnf(f14,axiom,
( ~ r(X1,X4)
| ~ e(X1)
| s(X1,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_15) ).
fof(f14_nnf,plain,
! [X1,X4] :
( ~ r(X1,X4)
| ~ e(X1)
| s(X1,X4) ),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [X1,X4] :
( ~ r(X1,X4)
| ~ e(X1)
| s(X1,X4) ),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c14,plain,
( ~ r(X0,X1)
| ~ e(X0)
| s(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(hi13,axiom,
ifeq(e(X0),true,ifeq(r(X0,X1),true,s(X0,X1),true),true) = true,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(h2,plain,
s(exist,u4r4(exist)) = true,
inference(hyper_resolution,[status(thm)],[hi13,hi0,h0]) ).
cnf(f16,axiom,
( ~ s(X1,X3)
| ~ e(X1)
| d(X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_17) ).
fof(f16_nnf,plain,
! [X3,X1] :
( ~ s(X1,X3)
| ~ e(X1)
| d(X3) ),
inference(nnf_transformation,[status(thm)],[f16]) ).
fof(f16_sk,plain,
! [X3,X1] :
( ~ s(X1,X3)
| ~ e(X1)
| d(X3) ),
inference(skolemisation,[status(esa)],[f16_nnf]) ).
cnf(c16,plain,
( ~ s(X1,X0)
| ~ e(X1)
| d(X0) ),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(hi15,axiom,
ifeq(e(X0),true,ifeq(s(X0,X1),true,d(X1),true),true) = true,
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(h6,plain,
d(u4r4(exist)) = true,
inference(hyper_resolution,[status(thm)],[hi15,hi0,h2]) ).
cnf(f7,axiom,
( ~ d(X1)
| t1most(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_8) ).
fof(f7_nnf,plain,
! [X1] :
( ~ d(X1)
| t1most(X1) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [X1] :
( ~ d(X1)
| t1most(X1) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
( ~ d(X0)
| t1most(X0) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(hi6,axiom,
ifeq(d(X0),true,t1most(X0),true) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(h7,plain,
t1most(u4r4(exist)) = true,
inference(hyper_resolution,[status(thm)],[hi6,h6]) ).
cnf(f9,axiom,
( ~ t(X1,X2)
| ~ t(X1,X3)
| ~ t1most(X1)
| equalish(X3,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_10) ).
fof(f9_nnf,plain,
! [X3,X2,X1] :
( ~ t(X1,X2)
| ~ t(X1,X3)
| ~ t1most(X1)
| equalish(X3,X2) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [X3,X2,X1] :
( ~ t(X1,X2)
| ~ t(X1,X3)
| ~ t1most(X1)
| equalish(X3,X2) ),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
( ~ t(X2,X1)
| ~ t(X2,X0)
| ~ t1most(X2)
| equalish(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(hi8,axiom,
ifeq(t1most(X0),true,ifeq(t(X0,X1),true,ifeq(t(X0,X2),true,equalish(X1,X2),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(h11,plain,
equalish(u1r2(u4r4(exist)),u1r1(u4r4(exist))) = true,
inference(hyper_resolution,[status(thm)],[hi8,h7,h4,h5]) ).
cnf(f3,axiom,
( ~ equalish(u1r2(X1),u1r1(X1))
| ~ t2least(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_4) ).
fof(f3_nnf,plain,
! [X1] :
( ~ equalish(u1r2(X1),u1r1(X1))
| ~ t2least(X1) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [X1] :
( ~ equalish(u1r2(X1),u1r1(X1))
| ~ t2least(X1) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
( ~ equalish(u1r2(X0),u1r1(X0))
| ~ t2least(X0) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(hi25,axiom,
ifeq(t2least(X0),true,ifeq(equalish(u1r2(X0),u1r1(X0)),true,false,true),true) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t0,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi25,h3,h11]) ).
cnf(t153,plain,
false = true,
inference(orient,[status(thm)],[t0]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t153]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS015-1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.12/0.38 % Computer : n009.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Wed Sep 23 19:14:58 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 4.37/1.40 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.37/1.40 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------