%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWX222-1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 05:34:46 PM UTC 2026
% Result : Unsatisfiable 1.38s 1.76s
% Output : CNFRefutation 1.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 12
% Syntax : Number of clauses : 28 ( 28 unt; 0 nHn; 6 RR)
% Number of literals : 28 ( 27 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 20 ( 20 usr; 6 con; 0-4 aty)
% Number of variables : 48 ( 13 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(axiom_019,axiom,
tc(X1,var(X2),X3) = aux(X1,X3,X2,index(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_019) ).
cnf(axiom_005,axiom,
index(cons(X1,X2),zero) = just(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_005) ).
cnf(axiom_001,axiom,
aux(X1,X2,X3,just(X4)) = eq(X4,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_001) ).
cnf(axiom_015,axiom,
tc(X1,lam(X2),arr(X3,X4)) = tc(cons(X3,X1),X2,X4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_015) ).
cnf(goal,negated_conjecture,
eq4(sat_synth_nf_k(X1),bfalse) != btrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal) ).
cnf(axiom_020,axiom,
sat_synth_nf_k(X1) = notb(andb(nf(X1),tc(nil,X1,arr(a,arr(b,b))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_020) ).
cnf(axiom_012,axiom,
nf(lam(X1)) = nf(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_012) ).
cnf(axiom_013,axiom,
nf(var(X1)) = btrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_013) ).
cnf(axiom_051,axiom,
eq(X1,X1) = btrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_051) ).
cnf(axiom_007,axiom,
andb(btrue,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_007) ).
cnf(axiom_002,axiom,
notb(btrue) = bfalse,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_002) ).
cnf(axiom_054,axiom,
eq4(X1,X1) = btrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_054) ).
cnf(c_0_12,axiom,
tc(X1,var(X2),X3) = aux(X1,X3,X2,index(X1,X2)),
axiom_019 ).
cnf(c_0_13,axiom,
index(cons(X1,X2),zero) = just(X1),
axiom_005 ).
cnf(c_0_14,axiom,
aux(X1,X2,X3,just(X4)) = eq(X4,X2),
axiom_001 ).
cnf(c_0_15,axiom,
tc(X1,lam(X2),arr(X3,X4)) = tc(cons(X3,X1),X2,X4),
axiom_015 ).
cnf(c_0_16,negated_conjecture,
eq4(sat_synth_nf_k(X1),bfalse) != btrue,
goal ).
cnf(c_0_17,axiom,
sat_synth_nf_k(X1) = notb(andb(nf(X1),tc(nil,X1,arr(a,arr(b,b))))),
axiom_020 ).
cnf(c_0_18,plain,
tc(X1,lam(var(zero)),arr(X2,X3)) = eq(X2,X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14]),c_0_15]) ).
cnf(c_0_19,negated_conjecture,
eq4(notb(andb(nf(X1),tc(nil,X1,arr(a,arr(b,b))))),bfalse) != btrue,
inference(rw,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_20,plain,
tc(X1,lam(lam(var(zero))),arr(X2,arr(X3,X4))) = eq(X3,X4),
inference(spm,[status(thm)],[c_0_15,c_0_18]) ).
cnf(c_0_21,axiom,
nf(lam(X1)) = nf(X1),
axiom_012 ).
cnf(c_0_22,axiom,
nf(var(X1)) = btrue,
axiom_013 ).
cnf(c_0_23,axiom,
eq(X1,X1) = btrue,
axiom_051 ).
cnf(c_0_24,axiom,
andb(btrue,X1) = X1,
axiom_007 ).
cnf(c_0_25,axiom,
notb(btrue) = bfalse,
axiom_002 ).
cnf(c_0_26,axiom,
eq4(X1,X1) = btrue,
axiom_054 ).
cnf(c_0_27,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]),c_0_21]),c_0_22]),c_0_23]),c_0_24]),c_0_25]),c_0_26])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWX222-1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33 % Computer : n008.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 07:59:13 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.38/1.76 % Version : CSE_E---1.7
% 1.38/1.76 % Problem : theBenchmark.p
% 1.38/1.76 % SZS status Unsatisfiable for theBenchmark.p
% 1.38/1.76 % SZS output start CNFRefutation
% See solution above
% 1.38/1.76 % Total time : 1.372s
%------------------------------------------------------------------------------