%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : PUZ039-10 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 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 : Sun Sep 27 08:22:10 AM UTC 2026
% Result : Unsatisfiable 45.82s 7.22s
% Output : CNFRefutation 45.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 9
% Syntax : Number of clauses : 33 ( 33 unt; 0 nHn; 19 RR)
% Number of literals : 33 ( 32 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 2 con; 0-12 aty)
% Number of variables : 174 ( 24 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(ifeq_axiom,axiom,
ifeq(X0,X0,X1,X2) = X1 ).
cnf(s2_down,axiom,
ifeq(state(X0,X1,X2,X3,X4,X5,X6,s2(X7,X8),X9,X10,e1(s(X7),X8),X11),true,state(X0,X1,X2,X3,X4,X5,X6,s2(s(X7),X8),X9,X10,e1(X7,X8),X11),true) = true ).
cnf(s4_right,axiom,
ifeq(state(X0,X1,X2,X3,X4,X5,X6,X7,X8,s4(X9,X10),e1(X9,s(X10)),X11),true,state(X0,X1,X2,X3,X4,X5,X6,X7,X8,s4(X9,s(X10)),e1(X9,X10),X11),true) = true ).
cnf(v3_down,axiom,
ifeq(state(X0,X1,X2,v3(X3,X4),X5,X6,X7,X8,X9,X10,e1(s(s(X3)),X4),X11),true,state(X0,X1,X2,v3(s(X3),X4),X5,X6,X7,X8,X9,X10,e1(X3,X4),X11),true) = true ).
cnf(v4_left,axiom,
ifeq(state(X0,X1,X2,X3,v4(X4,s(X5)),X6,X7,X8,X9,X10,e1(X4,X5),e2(s(X4),X5)),true,state(X0,X1,X2,X3,v4(X4,X5),X6,X7,X8,X9,X10,e1(X4,s(X5)),e2(s(X4),s(X5))),true) = true ).
cnf(h_left,axiom,
ifeq(state(X0,X1,X2,X3,X4,h(X5,s(X6)),X7,X8,X9,X10,e1(X5,X6),X11),true,state(X0,X1,X2,X3,X4,h(X5,X6),X7,X8,X9,X10,e1(X5,s(s(X6))),X11),true) = true ).
cnf(swap_blanks,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 ).
cnf(initial_state,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))))) = true ).
cnf(goal_state,negated_conjecture,
state(X0,X1,X2,X3,v4(s(s(o)),s(s(o))),X4,X5,X6,X7,X8,X9,X10) != true ).
cnf(c0,plain,
ifeq(X0,X0,X1,X2) = X1,
inference(clausification,[status(esa)],[ifeq_axiom]) ).
cnf(c7,plain,
ifeq(state(X0,X1,X2,X3,X4,X5,X6,s2(X7,X8),X9,X10,e1(s(X7),X8),X11),true,state(X0,X1,X2,X3,X4,X5,X6,s2(s(X7),X8),X9,X10,e1(X7,X8),X11),true) = true,
inference(clausification,[status(esa)],[s2_down]) ).
cnf(c13,plain,
ifeq(state(X0,X1,X2,X3,X4,X5,X6,X7,X8,s4(X9,X10),e1(X9,s(X10)),X11),true,state(X0,X1,X2,X3,X4,X5,X6,X7,X8,s4(X9,s(X10)),e1(X9,X10),X11),true) = true,
inference(clausification,[status(esa)],[s4_right]) ).
cnf(c27,plain,
ifeq(state(X0,X1,X2,v3(X3,X4),X5,X6,X7,X8,X9,X10,e1(s(s(X3)),X4),X11),true,state(X0,X1,X2,v3(s(X3),X4),X5,X6,X7,X8,X9,X10,e1(X3,X4),X11),true) = true,
inference(clausification,[status(esa)],[v3_down]) ).
cnf(c30,plain,
ifeq(state(X0,X1,X2,X3,v4(X4,s(X5)),X6,X7,X8,X9,X10,e1(X4,X5),e2(s(X4),X5)),true,state(X0,X1,X2,X3,v4(X4,X5),X6,X7,X8,X9,X10,e1(X4,s(X5)),e2(s(X4),s(X5))),true) = true,
inference(clausification,[status(esa)],[v4_left]) ).
cnf(c34,plain,
ifeq(state(X0,X1,X2,X3,X4,h(X5,s(X6)),X7,X8,X9,X10,e1(X5,X6),X11),true,state(X0,X1,X2,X3,X4,h(X5,X6),X7,X8,X9,X10,e1(X5,s(s(X6))),X11),true) = true,
inference(clausification,[status(esa)],[h_left]) ).
cnf(c41,plain,
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(clausification,[status(esa)],[swap_blanks]) ).
cnf(c42,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))))) = true,
inference(clausification,[status(esa)],[initial_state]) ).
cnf(c43,plain,
state(X0,X1,X2,X3,v4(s(s(o)),s(s(o))),X4,X5,X6,X7,X8,X9,X10) != true,
inference(clausification,[status(esa)],[goal_state]) ).
cnf(d0,plain,
ifeq(true,true,state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(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(o)),o),e2(s(s(s(s(o)))),s(s(s(o))))),true) = true,
inference(superposition,[status(thm)],[c42,c27]) ).
cnf(d1,plain,
state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(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(o)),o),e2(s(s(s(s(o)))),s(s(s(o))))) = true,
inference(demodulation,[status(thm)],[d0,c0]) ).
cnf(d2,plain,
ifeq(true,true,state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(s(o))),o),v4(s(s(o)),s(s(s(o)))),h(s(s(o)),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(o)),s(s(o))),e2(s(s(s(s(o)))),s(s(s(o))))),true) = true,
inference(superposition,[status(thm)],[d1,c34]) ).
cnf(d3,plain,
state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(s(o))),o),v4(s(s(o)),s(s(s(o)))),h(s(s(o)),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(o)),s(s(o))),e2(s(s(s(s(o)))),s(s(s(o))))) = true,
inference(demodulation,[status(thm)],[d2,c0]) ).
cnf(d4,plain,
ifeq(true,true,state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(s(o))),o),v4(s(s(o)),s(s(s(o)))),h(s(s(o)),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)))),s(s(s(o)))),e2(s(s(o)),s(s(o)))),true) = true,
inference(superposition,[status(thm)],[d3,c41]) ).
cnf(d5,plain,
state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(s(o))),o),v4(s(s(o)),s(s(s(o)))),h(s(s(o)),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)))),s(s(s(o)))),e2(s(s(o)),s(s(o)))) = true,
inference(demodulation,[status(thm)],[d4,c0]) ).
cnf(d6,plain,
ifeq(true,true,state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(s(o))),o),v4(s(s(o)),s(s(s(o)))),h(s(s(o)),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(s(o)))),e1(s(s(s(s(o)))),s(s(o))),e2(s(s(o)),s(s(o)))),true) = true,
inference(superposition,[status(thm)],[d5,c13]) ).
cnf(d7,plain,
state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(s(o))),o),v4(s(s(o)),s(s(s(o)))),h(s(s(o)),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(s(o)))),e1(s(s(s(s(o)))),s(s(o))),e2(s(s(o)),s(s(o)))) = true,
inference(demodulation,[status(thm)],[d6,c0]) ).
cnf(d8,plain,
ifeq(true,true,state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(s(o))),o),v4(s(s(o)),s(s(s(o)))),h(s(s(o)),o),s1(s(s(s(o))),s(o)),s2(s(s(s(s(o)))),s(s(o))),s3(s(s(s(s(o)))),s(o)),s4(s(s(s(s(o)))),s(s(s(o)))),e1(s(s(s(o))),s(s(o))),e2(s(s(o)),s(s(o)))),true) = true,
inference(superposition,[status(thm)],[d7,c7]) ).
cnf(d9,plain,
state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(s(o))),o),v4(s(s(o)),s(s(s(o)))),h(s(s(o)),o),s1(s(s(s(o))),s(o)),s2(s(s(s(s(o)))),s(s(o))),s3(s(s(s(s(o)))),s(o)),s4(s(s(s(s(o)))),s(s(s(o)))),e1(s(s(s(o))),s(s(o))),e2(s(s(o)),s(s(o)))) = true,
inference(demodulation,[status(thm)],[d8,c0]) ).
cnf(d10,plain,
ifeq(true,true,state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(s(o))),o),v4(s(s(o)),s(s(s(o)))),h(s(s(o)),o),s1(s(s(s(o))),s(o)),s2(s(s(s(s(o)))),s(s(o))),s3(s(s(s(s(o)))),s(o)),s4(s(s(s(s(o)))),s(s(s(o)))),e1(s(s(o)),s(s(o))),e2(s(s(s(o))),s(s(o)))),true) = true,
inference(superposition,[status(thm)],[d9,c41]) ).
cnf(d11,plain,
state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(s(o))),o),v4(s(s(o)),s(s(s(o)))),h(s(s(o)),o),s1(s(s(s(o))),s(o)),s2(s(s(s(s(o)))),s(s(o))),s3(s(s(s(s(o)))),s(o)),s4(s(s(s(s(o)))),s(s(s(o)))),e1(s(s(o)),s(s(o))),e2(s(s(s(o))),s(s(o)))) = true,
inference(demodulation,[status(thm)],[d10,c0]) ).
cnf(d12,plain,
ifeq(true,true,state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(s(o))),o),v4(s(s(o)),s(s(o))),h(s(s(o)),o),s1(s(s(s(o))),s(o)),s2(s(s(s(s(o)))),s(s(o))),s3(s(s(s(s(o)))),s(o)),s4(s(s(s(s(o)))),s(s(s(o)))),e1(s(s(o)),s(s(s(o)))),e2(s(s(s(o))),s(s(s(o))))),true) = true,
inference(superposition,[status(thm)],[d11,c30]) ).
cnf(d13,plain,
state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(s(o))),o),v4(s(s(o)),s(s(o))),h(s(s(o)),o),s1(s(s(s(o))),s(o)),s2(s(s(s(s(o)))),s(s(o))),s3(s(s(s(s(o)))),s(o)),s4(s(s(s(s(o)))),s(s(s(o)))),e1(s(s(o)),s(s(s(o)))),e2(s(s(s(o))),s(s(s(o))))) = true,
inference(demodulation,[status(thm)],[d12,c0]) ).
cnf(d14,plain,
$false,
inference(resolution,[status(thm)],[c43,d13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PUZ039-10 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n006.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 26 05:07:11 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 45.82/7.22 % SZS status Unsatisfiable for theBenchmark.p
% 45.82/7.22 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------