%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : PUZ040-1 : TPTP v9.3.1. Bugfixed v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n014.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 02:31:57 PM UTC 2026
% Result : Unsatisfiable 6.52s 6.39s
% Output : Proof 6.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 12
% Syntax : Number of formulae : 70 ( 38 unt; 0 def)
% Number of atoms : 102 ( 30 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 70 ( 38 ~; 32 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 15 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-12 aty)
% Number of functors : 21 ( 21 usr; 5 con; 0-4 aty)
% Number of variables : 548 ( 44 sgn 214 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f42,negated_conjecture,
~ state(bb(o,o),V1,V2,V3,V4,H,S1,S2,S3,S4,E1,E2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal_state) ).
fof(f42_nnf,plain,
! [V1,V2,V3,V4,H,S1,S2,S3,S4,E1,E2] : ~ state(bb(o,o),V1,V2,V3,V4,H,S1,S2,S3,S4,E1,E2),
inference(nnf_transformation,[status(thm)],[f42]) ).
fof(f42_sk,plain,
! [V1,V2,V3,V4,H,S1,S2,S3,S4,E1,E2] : ~ state(bb(o,o),V1,V2,V3,V4,H,S1,S2,S3,S4,E1,E2),
inference(skolemisation,[status(esa)],[f42_nnf]) ).
cnf(c42,plain,
~ state(bb(o,o),X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10),
inference(cnf_transformation,[status(esa)],[f42_sk]) ).
cnf(t1,plain,
eq(ap2(ap2(ap2(ap2(ap2(ap2(ap2(ap2(ap2(ap2(ap2(ap2(state,bb(o,o)),X1),X2),X3),X4),X5),X6),X7),X8),X9),X10),X11),true) = efalse,
inference(equality_encoding,[status(esa)],[c42]) ).
cnf(t431,plain,
eq(ap2(ap2(ap2(ap2(ap2(ap2(ap2(ap2(ap2(ap2(ap2(ap2(state,bb(o,o)),X1),X2),X3),X4),X5),X6),X7),X8),X9),X10),X11),true) = efalse,
inference(orient,[status(thm)],[t1]) ).
cnf(f9,axiom,
( state(B,V1,V2,V3,V4,H,S1,S2,s3(X,Y),S4,e1(X,s(Y)),E2)
| ~ state(B,V1,V2,V3,V4,H,S1,S2,s3(X,s(Y)),S4,e1(X,Y),E2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s3_left) ).
fof(f9_nnf,plain,
! [B,V1,V2,V3,V4,H,S1,S2,X,Y,S4,E2] :
( state(B,V1,V2,V3,V4,H,S1,S2,s3(X,Y),S4,e1(X,s(Y)),E2)
| ~ state(B,V1,V2,V3,V4,H,S1,S2,s3(X,s(Y)),S4,e1(X,Y),E2) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [B,V1,V2,V3,V4,H,S1,S2,X,Y,S4,E2] :
( state(B,V1,V2,V3,V4,H,S1,S2,s3(X,Y),S4,e1(X,s(Y)),E2)
| ~ state(B,V1,V2,V3,V4,H,S1,S2,s3(X,s(Y)),S4,e1(X,Y),E2) ),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
( state(X0,X1,X2,X3,X4,X5,X6,X7,s3(X8,X9),X10,e1(X8,s(X9)),X11)
| ~ state(X0,X1,X2,X3,X4,X5,X6,X7,s3(X8,s(X9)),X10,e1(X8,X9),X11) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(hi9,axiom,
ifeq(state(X0,X1,X2,X3,X4,X5,X6,X7,s3(X8,s(X9)),X10,e1(X8,X9),X11),true,state(X0,X1,X2,X3,X4,X5,X6,X7,s3(X8,X9),X10,e1(X8,s(X9)),X11),true) = true,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(f41,hypothesis,
state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(o)),o),v4(s(s(o)),s(s(s(o)))),h(s(s(o)),s(o)),s1(s(s(s(o))),s(o)),s2(s(s(s(o))),s(s(o))),s3(s(s(s(s(o)))),s(o)),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(s(s(o)))),o),e2(s(s(s(s(o)))),s(s(s(o))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',initial_state) ).
fof(f41_nnf,plain,
state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(o)),o),v4(s(s(o)),s(s(s(o)))),h(s(s(o)),s(o)),s1(s(s(s(o))),s(o)),s2(s(s(s(o))),s(s(o))),s3(s(s(s(s(o)))),s(o)),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(s(s(o)))),o),e2(s(s(s(s(o)))),s(s(s(o))))),
inference(nnf_transformation,[status(thm)],[f41]) ).
cnf(c41,plain,
state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(o)),o),v4(s(s(o)),s(s(s(o)))),h(s(s(o)),s(o)),s1(s(s(s(o))),s(o)),s2(s(s(s(o))),s(s(o))),s3(s(s(s(s(o)))),s(o)),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(s(s(o)))),o),e2(s(s(s(s(o)))),s(s(s(o))))),
inference(cnf_transformation,[status(esa)],[f41_nnf]) ).
cnf(hi41,axiom,
state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(o)),o),v4(s(s(o)),s(s(s(o)))),h(s(s(o)),s(o)),s1(s(s(s(o))),s(o)),s2(s(s(s(o))),s(s(o))),s3(s(s(s(s(o)))),s(o)),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(s(s(o)))),o),e2(s(s(s(s(o)))),s(s(s(o))))) = true,
inference(equality_encoding,[status(esa)],[c41]) ).
cnf(h2,plain,
state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(o)),o),v4(s(s(o)),s(s(s(o)))),h(s(s(o)),s(o)),s1(s(s(s(o))),s(o)),s2(s(s(s(o))),s(s(o))),s3(s(s(s(s(o)))),o),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(s(s(o)))),s(o)),e2(s(s(s(s(o)))),s(s(s(o))))) = true,
inference(hyper_resolution,[status(thm)],[hi9,hi41]) ).
cnf(f2,axiom,
( state(B,V1,V2,V3,V4,H,s1(s(X),Y),S2,S3,S4,e1(X,Y),E2)
| ~ state(B,V1,V2,V3,V4,H,s1(X,Y),S2,S3,S4,e1(s(X),Y),E2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_down) ).
fof(f2_nnf,plain,
! [B,V1,V2,V3,V4,H,X,Y,S2,S3,S4,E2] :
( state(B,V1,V2,V3,V4,H,s1(s(X),Y),S2,S3,S4,e1(X,Y),E2)
| ~ state(B,V1,V2,V3,V4,H,s1(X,Y),S2,S3,S4,e1(s(X),Y),E2) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [B,V1,V2,V3,V4,H,X,Y,S2,S3,S4,E2] :
( state(B,V1,V2,V3,V4,H,s1(s(X),Y),S2,S3,S4,e1(X,Y),E2)
| ~ state(B,V1,V2,V3,V4,H,s1(X,Y),S2,S3,S4,e1(s(X),Y),E2) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( state(X0,X1,X2,X3,X4,X5,s1(s(X6),X7),X8,X9,X10,e1(X6,X7),X11)
| ~ state(X0,X1,X2,X3,X4,X5,s1(X6,X7),X8,X9,X10,e1(s(X6),X7),X11) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi2,axiom,
ifeq(state(X0,X1,X2,X3,X4,X5,s1(X6,X7),X8,X9,X10,e1(s(X6),X7),X11),true,state(X0,X1,X2,X3,X4,X5,s1(s(X6),X7),X8,X9,X10,e1(X6,X7),X11),true) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(h10,plain,
state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(o)),o),v4(s(s(o)),s(s(s(o)))),h(s(s(o)),s(o)),s1(s(s(s(s(o)))),s(o)),s2(s(s(s(o))),s(s(o))),s3(s(s(s(s(o)))),o),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(s(o))),s(o)),e2(s(s(s(s(o)))),s(s(s(o))))) = true,
inference(hyper_resolution,[status(thm)],[hi2,h2]) ).
cnf(f40,axiom,
( state(B,V1,V2,V3,V4,H,S1,S2,S3,S4,e1(Q,W),e2(X,Y))
| ~ state(B,V1,V2,V3,V4,H,S1,S2,S3,S4,e1(X,Y),e2(Q,W)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',swap_blanks) ).
fof(f40_nnf,plain,
! [B,V1,V2,V3,V4,H,S1,S2,S3,S4,X,Y,Q,W] :
( state(B,V1,V2,V3,V4,H,S1,S2,S3,S4,e1(Q,W),e2(X,Y))
| ~ state(B,V1,V2,V3,V4,H,S1,S2,S3,S4,e1(X,Y),e2(Q,W)) ),
inference(nnf_transformation,[status(thm)],[f40]) ).
fof(f40_sk,plain,
! [B,V1,V2,V3,V4,H,S1,S2,S3,S4,X,Y,Q,W] :
( state(B,V1,V2,V3,V4,H,S1,S2,S3,S4,e1(Q,W),e2(X,Y))
| ~ state(B,V1,V2,V3,V4,H,S1,S2,S3,S4,e1(X,Y),e2(Q,W)) ),
inference(skolemisation,[status(esa)],[f40_nnf]) ).
cnf(c40,plain,
( state(X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,e1(X12,X13),e2(X10,X11))
| ~ state(X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,e1(X10,X11),e2(X12,X13)) ),
inference(cnf_transformation,[status(esa)],[f40_sk]) ).
cnf(hi40,axiom,
ifeq(state(X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,e1(X10,X11),e2(X12,X13)),true,state(X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,e1(X12,X13),e2(X10,X11)),true) = true,
inference(equality_encoding,[status(esa)],[c40]) ).
cnf(h31,plain,
state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(o)),o),v4(s(s(o)),s(s(s(o)))),h(s(s(o)),s(o)),s1(s(s(s(s(o)))),s(o)),s2(s(s(s(o))),s(s(o))),s3(s(s(s(s(o)))),o),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(s(s(o)))),s(s(s(o)))),e2(s(s(s(o))),s(o))) = true,
inference(hyper_resolution,[status(thm)],[hi40,h10]) ).
cnf(f30,axiom,
( state(B,V1,V2,V3,v4(s(X),Y),H,S1,S2,S3,S4,e1(X,Y),E2)
| ~ state(B,V1,V2,V3,v4(X,Y),H,S1,S2,S3,S4,e1(s(s(X)),Y),E2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v4_down) ).
fof(f30_nnf,plain,
! [B,V1,V2,V3,X,Y,H,S1,S2,S3,S4,E2] :
( state(B,V1,V2,V3,v4(s(X),Y),H,S1,S2,S3,S4,e1(X,Y),E2)
| ~ state(B,V1,V2,V3,v4(X,Y),H,S1,S2,S3,S4,e1(s(s(X)),Y),E2) ),
inference(nnf_transformation,[status(thm)],[f30]) ).
fof(f30_sk,plain,
! [B,V1,V2,V3,X,Y,H,S1,S2,S3,S4,E2] :
( state(B,V1,V2,V3,v4(s(X),Y),H,S1,S2,S3,S4,e1(X,Y),E2)
| ~ state(B,V1,V2,V3,v4(X,Y),H,S1,S2,S3,S4,e1(s(s(X)),Y),E2) ),
inference(skolemisation,[status(esa)],[f30_nnf]) ).
cnf(c30,plain,
( state(X0,X1,X2,X3,v4(s(X4),X5),X6,X7,X8,X9,X10,e1(X4,X5),X11)
| ~ state(X0,X1,X2,X3,v4(X4,X5),X6,X7,X8,X9,X10,e1(s(s(X4)),X5),X11) ),
inference(cnf_transformation,[status(esa)],[f30_sk]) ).
cnf(hi30,axiom,
ifeq(state(X0,X1,X2,X3,v4(X4,X5),X6,X7,X8,X9,X10,e1(s(s(X4)),X5),X11),true,state(X0,X1,X2,X3,v4(s(X4),X5),X6,X7,X8,X9,X10,e1(X4,X5),X11),true) = true,
inference(equality_encoding,[status(esa)],[c30]) ).
cnf(h70,plain,
state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(o)),o),v4(s(s(s(o))),s(s(s(o)))),h(s(s(o)),s(o)),s1(s(s(s(s(o)))),s(o)),s2(s(s(s(o))),s(s(o))),s3(s(s(s(s(o)))),o),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(o)),s(s(s(o)))),e2(s(s(s(o))),s(o))) = true,
inference(hyper_resolution,[status(thm)],[hi30,h31]) ).
cnf(f32,axiom,
( state(B,V1,V2,V3,V4,h(X,s(Y)),S1,S2,S3,S4,e1(X,Y),E2)
| ~ state(B,V1,V2,V3,V4,h(X,Y),S1,S2,S3,S4,e1(X,s(s(Y))),E2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',h_right) ).
fof(f32_nnf,plain,
! [B,V1,V2,V3,V4,X,Y,S1,S2,S3,S4,E2] :
( state(B,V1,V2,V3,V4,h(X,s(Y)),S1,S2,S3,S4,e1(X,Y),E2)
| ~ state(B,V1,V2,V3,V4,h(X,Y),S1,S2,S3,S4,e1(X,s(s(Y))),E2) ),
inference(nnf_transformation,[status(thm)],[f32]) ).
fof(f32_sk,plain,
! [B,V1,V2,V3,V4,X,Y,S1,S2,S3,S4,E2] :
( state(B,V1,V2,V3,V4,h(X,s(Y)),S1,S2,S3,S4,e1(X,Y),E2)
| ~ state(B,V1,V2,V3,V4,h(X,Y),S1,S2,S3,S4,e1(X,s(s(Y))),E2) ),
inference(skolemisation,[status(esa)],[f32_nnf]) ).
cnf(c32,plain,
( state(X0,X1,X2,X3,X4,h(X5,s(X6)),X7,X8,X9,X10,e1(X5,X6),X11)
| ~ state(X0,X1,X2,X3,X4,h(X5,X6),X7,X8,X9,X10,e1(X5,s(s(X6))),X11) ),
inference(cnf_transformation,[status(esa)],[f32_sk]) ).
cnf(hi32,axiom,
ifeq(state(X0,X1,X2,X3,X4,h(X5,X6),X7,X8,X9,X10,e1(X5,s(s(X6))),X11),true,state(X0,X1,X2,X3,X4,h(X5,s(X6)),X7,X8,X9,X10,e1(X5,X6),X11),true) = true,
inference(equality_encoding,[status(esa)],[c32]) ).
cnf(h133,plain,
state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(o)),o),v4(s(s(s(o))),s(s(s(o)))),h(s(s(o)),s(s(o))),s1(s(s(s(s(o)))),s(o)),s2(s(s(s(o))),s(s(o))),s3(s(s(s(s(o)))),o),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(o)),s(o)),e2(s(s(s(o))),s(o))) = true,
inference(hyper_resolution,[status(thm)],[hi32,h70]) ).
cnf(f24,axiom,
( state(B,V1,V2,v3(X,s(Y)),V4,H,S1,S2,S3,S4,e1(X,Y),e2(s(X),Y))
| ~ state(B,V1,V2,v3(X,Y),V4,H,S1,S2,S3,S4,e1(X,s(Y)),e2(s(X),s(Y))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v3_right) ).
fof(f24_nnf,plain,
! [B,V1,V2,X,Y,V4,H,S1,S2,S3,S4] :
( state(B,V1,V2,v3(X,s(Y)),V4,H,S1,S2,S3,S4,e1(X,Y),e2(s(X),Y))
| ~ state(B,V1,V2,v3(X,Y),V4,H,S1,S2,S3,S4,e1(X,s(Y)),e2(s(X),s(Y))) ),
inference(nnf_transformation,[status(thm)],[f24]) ).
fof(f24_sk,plain,
! [B,V1,V2,X,Y,V4,H,S1,S2,S3,S4] :
( state(B,V1,V2,v3(X,s(Y)),V4,H,S1,S2,S3,S4,e1(X,Y),e2(s(X),Y))
| ~ state(B,V1,V2,v3(X,Y),V4,H,S1,S2,S3,S4,e1(X,s(Y)),e2(s(X),s(Y))) ),
inference(skolemisation,[status(esa)],[f24_nnf]) ).
cnf(c24,plain,
( state(X0,X1,X2,v3(X3,s(X4)),X5,X6,X7,X8,X9,X10,e1(X3,X4),e2(s(X3),X4))
| ~ state(X0,X1,X2,v3(X3,X4),X5,X6,X7,X8,X9,X10,e1(X3,s(X4)),e2(s(X3),s(X4))) ),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
cnf(hi24,axiom,
ifeq(state(X0,X1,X2,v3(X3,X4),X5,X6,X7,X8,X9,X10,e1(X3,s(X4)),e2(s(X3),s(X4))),true,state(X0,X1,X2,v3(X3,s(X4)),X5,X6,X7,X8,X9,X10,e1(X3,X4),e2(s(X3),X4)),true) = true,
inference(equality_encoding,[status(esa)],[c24]) ).
cnf(h234,plain,
state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(o)),s(o)),v4(s(s(s(o))),s(s(s(o)))),h(s(s(o)),s(s(o))),s1(s(s(s(s(o)))),s(o)),s2(s(s(s(o))),s(s(o))),s3(s(s(s(s(o)))),o),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(o)),o),e2(s(s(s(o))),o)) = true,
inference(hyper_resolution,[status(thm)],[hi24,h133]) ).
cnf(f18,axiom,
( state(B,v1(s(X),Y),V2,V3,V4,H,S1,S2,S3,S4,e1(X,Y),E2)
| ~ state(B,v1(X,Y),V2,V3,V4,H,S1,S2,S3,S4,e1(s(s(X)),Y),E2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v1_down) ).
fof(f18_nnf,plain,
! [B,X,Y,V2,V3,V4,H,S1,S2,S3,S4,E2] :
( state(B,v1(s(X),Y),V2,V3,V4,H,S1,S2,S3,S4,e1(X,Y),E2)
| ~ state(B,v1(X,Y),V2,V3,V4,H,S1,S2,S3,S4,e1(s(s(X)),Y),E2) ),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
! [B,X,Y,V2,V3,V4,H,S1,S2,S3,S4,E2] :
( state(B,v1(s(X),Y),V2,V3,V4,H,S1,S2,S3,S4,e1(X,Y),E2)
| ~ state(B,v1(X,Y),V2,V3,V4,H,S1,S2,S3,S4,e1(s(s(X)),Y),E2) ),
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c18,plain,
( state(X0,v1(s(X1),X2),X3,X4,X5,X6,X7,X8,X9,X10,e1(X1,X2),X11)
| ~ state(X0,v1(X1,X2),X3,X4,X5,X6,X7,X8,X9,X10,e1(s(s(X1)),X2),X11) ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(hi18,axiom,
ifeq(state(X0,v1(X1,X2),X3,X4,X5,X6,X7,X8,X9,X10,e1(s(s(X1)),X2),X11),true,state(X0,v1(s(X1),X2),X3,X4,X5,X6,X7,X8,X9,X10,e1(X1,X2),X11),true) = true,
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(h368,plain,
state(bb(o,s(o)),v1(s(o),o),v2(o,s(s(s(o)))),v3(s(s(o)),s(o)),v4(s(s(s(o))),s(s(s(o)))),h(s(s(o)),s(s(o))),s1(s(s(s(s(o)))),s(o)),s2(s(s(s(o))),s(s(o))),s3(s(s(s(s(o)))),o),s4(s(s(s(s(o)))),s(s(o))),e1(o,o),e2(s(s(s(o))),o)) = true,
inference(hyper_resolution,[status(thm)],[hi18,h234]) ).
cnf(h375,plain,
state(bb(o,s(o)),v1(s(o),o),v2(o,s(s(s(o)))),v3(s(s(o)),s(o)),v4(s(s(s(o))),s(s(s(o)))),h(s(s(o)),s(s(o))),s1(s(s(s(s(o)))),s(o)),s2(s(s(s(o))),s(s(o))),s3(s(s(s(s(o)))),o),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(s(o))),o),e2(o,o)) = true,
inference(hyper_resolution,[status(thm)],[hi40,h368]) ).
cnf(h380,plain,
state(bb(o,s(o)),v1(s(s(o)),o),v2(o,s(s(s(o)))),v3(s(s(o)),s(o)),v4(s(s(s(o))),s(s(s(o)))),h(s(s(o)),s(s(o))),s1(s(s(s(s(o)))),s(o)),s2(s(s(s(o))),s(s(o))),s3(s(s(s(s(o)))),o),s4(s(s(s(s(o)))),s(s(o))),e1(s(o),o),e2(o,o)) = true,
inference(hyper_resolution,[status(thm)],[hi18,h375]) ).
cnf(h384,plain,
state(bb(o,s(o)),v1(s(s(o)),o),v2(o,s(s(s(o)))),v3(s(s(o)),s(o)),v4(s(s(s(o))),s(s(s(o)))),h(s(s(o)),s(s(o))),s1(s(s(s(s(o)))),s(o)),s2(s(s(s(o))),s(s(o))),s3(s(s(s(s(o)))),o),s4(s(s(s(s(o)))),s(s(o))),e1(o,o),e2(s(o),o)) = true,
inference(hyper_resolution,[status(thm)],[hi40,h380]) ).
cnf(f37,axiom,
( state(bb(X,Y),V1,V2,V3,V4,H,S1,S2,S3,S4,e1(X,s(s(Y))),e2(s(X),s(s(Y))))
| ~ state(bb(X,s(Y)),V1,V2,V3,V4,H,S1,S2,S3,S4,e1(X,Y),e2(s(X),Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_left) ).
fof(f37_nnf,plain,
! [X,Y,V1,V2,V3,V4,H,S1,S2,S3,S4] :
( state(bb(X,Y),V1,V2,V3,V4,H,S1,S2,S3,S4,e1(X,s(s(Y))),e2(s(X),s(s(Y))))
| ~ state(bb(X,s(Y)),V1,V2,V3,V4,H,S1,S2,S3,S4,e1(X,Y),e2(s(X),Y)) ),
inference(nnf_transformation,[status(thm)],[f37]) ).
fof(f37_sk,plain,
! [X,Y,V1,V2,V3,V4,H,S1,S2,S3,S4] :
( state(bb(X,Y),V1,V2,V3,V4,H,S1,S2,S3,S4,e1(X,s(s(Y))),e2(s(X),s(s(Y))))
| ~ state(bb(X,s(Y)),V1,V2,V3,V4,H,S1,S2,S3,S4,e1(X,Y),e2(s(X),Y)) ),
inference(skolemisation,[status(esa)],[f37_nnf]) ).
cnf(c37,plain,
( state(bb(X0,X1),X2,X3,X4,X5,X6,X7,X8,X9,X10,e1(X0,s(s(X1))),e2(s(X0),s(s(X1))))
| ~ state(bb(X0,s(X1)),X2,X3,X4,X5,X6,X7,X8,X9,X10,e1(X0,X1),e2(s(X0),X1)) ),
inference(cnf_transformation,[status(esa)],[f37_sk]) ).
cnf(hi37,axiom,
ifeq(state(bb(X0,s(X1)),X2,X3,X4,X5,X6,X7,X8,X9,X10,e1(X0,X1),e2(s(X0),X1)),true,state(bb(X0,X1),X2,X3,X4,X5,X6,X7,X8,X9,X10,e1(X0,s(s(X1))),e2(s(X0),s(s(X1)))),true) = true,
inference(equality_encoding,[status(esa)],[c37]) ).
cnf(t109,plain,
ap2(ap2(ap2(ap2(ap2(ap2(ap2(ap2(ap2(ap2(ap2(ap2(state,bb(o,o)),v1(s(s(o)),o)),v2(o,s(s(s(o))))),v3(s(s(o)),s(o))),v4(s(s(s(o))),s(s(s(o))))),h(s(s(o)),s(s(o)))),s1(s(s(s(s(o)))),s(o))),s2(s(s(s(o))),s(s(o)))),s3(s(s(s(s(o)))),o)),s4(s(s(s(s(o)))),s(s(o)))),e1(o,s(s(o)))),e2(s(o),s(s(o)))) = true,
inference(hyper_resolution,[status(thm)],[hi37,h384]) ).
cnf(t429,plain,
ap2(ap2(ap2(ap2(ap2(ap2(ap2(ap2(ap2(ap2(ap2(ap2(state,bb(o,o)),v1(s(s(o)),o)),v2(o,s(s(s(o))))),v3(s(s(o)),s(o))),v4(s(s(s(o))),s(s(s(o))))),h(s(s(o)),s(s(o)))),s1(s(s(s(s(o)))),s(o))),s2(s(s(s(o))),s(s(o)))),s3(s(s(s(s(o)))),o)),s4(s(s(s(s(o)))),s(s(o)))),e1(o,s(s(o)))),e2(s(o),s(s(o)))) = true,
inference(orient,[status(thm)],[t109]) ).
cnf(t432,plain,
efalse = eq(true,true),
inference(cp,[status(thm)],[t431,t429]) ).
cnf(t0,plain,
eq(X1,X1) = etrue,
introduced(definition) ).
cnf(t430,plain,
eq(X1,X1) = etrue,
inference(orient,[status(thm)],[t0]) ).
cnf(t436,plain,
efalse = etrue,
inference(step,[status(thm)],[t432,t430]) ).
cnf(t433,plain,
efalse = etrue,
inference(orient,[status(thm)],[t436]) ).
cnf(goal_0,negated_conjecture,
etrue != efalse,
introduced(definition) ).
cnf(g0_0,plain,
etrue != etrue,
inference(rw,[status(thm)],[goal_0,t433]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PUZ040-1 : TPTP v9.3.1. Bugfixed v2.6.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/5.36 % Computer : n014.cluster.edu
% 0.09/5.36 % Model : x86_64 x86_64
% 0.09/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.36 % Memory : 8046.5625MB
% 0.09/5.36 % OS : Linux 6.8.0-71-generic
% 0.09/5.36 % CPULimit : 300
% 0.09/5.36 % WCLimit : 300
% 0.09/5.36 % DateTime : Thu Sep 24 06:46:12 UTC 2026
% 0.09/5.37 % CPUTime :
% 0.09/5.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 6.52/6.39 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.52/6.39 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------