%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWX199-1 : 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 : n015.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 05:34:42 PM UTC 2026
% Result : Unsatisfiable 1.33s 1.74s
% Output : CNFRefutation 1.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 17
% Syntax : Number of clauses : 49 ( 45 unt; 0 nHn; 8 RR)
% Number of literals : 53 ( 52 equ; 11 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 4 con; 0-5 aty)
% Number of variables : 114 ( 19 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(axiom_010,axiom,
prop_merge_comm(X1,X2,X3) = impl(eq(merge(X1,X2),merge(X2,X1)),impl(eq(merge(X1,X3),merge(X3,X1)),eq(merge(X2,X3),merge(X3,X2)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_010) ).
cnf(axiom_006,axiom,
merge(cons(X1,X2),nil) = cons(X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_006) ).
cnf(axiom_005,axiom,
merge(nil,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_005) ).
cnf(axiom_016,axiom,
eq(X1,X1) = btrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_016) ).
cnf(axiom_008,axiom,
impl(btrue,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_008) ).
cnf(axiom_007,axiom,
merge(cons(X1,X2),cons(X3,X4)) = aux(X1,X2,X3,X4,leqNat(X1,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_007) ).
cnf(axiom_002,axiom,
leqNat(z,X1) = btrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_002) ).
cnf(axiom,axiom,
aux(X1,X2,X3,X4,btrue) = cons(X1,merge(X2,cons(X3,X4))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom) ).
cnf(axiom_020,axiom,
( eq(cons(X1,X3),cons(X2,X4)) = eq(X3,X4)
| eq2(X1,X2) != btrue ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_020) ).
cnf(axiom_017,axiom,
eq2(X1,X1) = btrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_017) ).
cnf(goal,negated_conjecture,
eq3(prop_merge_comm(X1,X2,X3),bfalse) != btrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal) ).
cnf(axiom_003,axiom,
leqNat(s(X1),z) = bfalse,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_003) ).
cnf(axiom_001,axiom,
aux(X1,X2,X3,X4,bfalse) = cons(X3,merge(cons(X1,X2),X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_001) ).
cnf(axiom_004,axiom,
leqNat(s(X1),s(X2)) = leqNat(X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_004) ).
cnf(axiom_019,axiom,
( eq(cons(X1,X3),cons(X2,X4)) = bfalse
| eq2(X1,X2) != bfalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_019) ).
cnf(axiom_014,axiom,
eq2(z,s(X1)) = bfalse,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_014) ).
cnf(axiom_018,axiom,
eq3(X1,X1) = btrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_018) ).
cnf(c_0_17,axiom,
prop_merge_comm(X1,X2,X3) = impl(eq(merge(X1,X2),merge(X2,X1)),impl(eq(merge(X1,X3),merge(X3,X1)),eq(merge(X2,X3),merge(X3,X2)))),
axiom_010 ).
cnf(c_0_18,axiom,
merge(cons(X1,X2),nil) = cons(X1,X2),
axiom_006 ).
cnf(c_0_19,axiom,
merge(nil,X1) = X1,
axiom_005 ).
cnf(c_0_20,axiom,
eq(X1,X1) = btrue,
axiom_016 ).
cnf(c_0_21,axiom,
impl(btrue,X1) = X1,
axiom_008 ).
cnf(c_0_22,axiom,
merge(cons(X1,X2),cons(X3,X4)) = aux(X1,X2,X3,X4,leqNat(X1,X3)),
axiom_007 ).
cnf(c_0_23,axiom,
leqNat(z,X1) = btrue,
axiom_002 ).
cnf(c_0_24,axiom,
aux(X1,X2,X3,X4,btrue) = cons(X1,merge(X2,cons(X3,X4))),
axiom ).
cnf(c_0_25,plain,
impl(eq(X1,merge(X1,nil)),eq(merge(X1,cons(X2,X3)),merge(cons(X2,X3),X1))) = prop_merge_comm(nil,X1,cons(X2,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]),c_0_19]),c_0_20]),c_0_21]) ).
cnf(c_0_26,plain,
merge(cons(z,X1),cons(X2,X3)) = cons(z,merge(X1,cons(X2,X3))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]) ).
cnf(c_0_27,axiom,
( eq(cons(X1,X3),cons(X2,X4)) = eq(X3,X4)
| eq2(X1,X2) != btrue ),
axiom_020 ).
cnf(c_0_28,axiom,
eq2(X1,X1) = btrue,
axiom_017 ).
cnf(c_0_29,plain,
eq(merge(cons(X1,X2),cons(z,X3)),cons(z,merge(X3,cons(X1,X2)))) = prop_merge_comm(nil,cons(X1,X2),cons(z,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_18]),c_0_20]),c_0_21]) ).
cnf(c_0_30,plain,
eq(cons(X1,X2),cons(X1,X3)) = eq(X2,X3),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_31,negated_conjecture,
eq3(prop_merge_comm(X1,X2,X3),bfalse) != btrue,
goal ).
cnf(c_0_32,plain,
eq(merge(X1,cons(z,X2)),merge(X2,cons(z,X1))) = prop_merge_comm(nil,cons(z,X1),cons(z,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_26]),c_0_30]) ).
cnf(c_0_33,axiom,
leqNat(s(X1),z) = bfalse,
axiom_003 ).
cnf(c_0_34,axiom,
aux(X1,X2,X3,X4,bfalse) = cons(X3,merge(cons(X1,X2),X4)),
axiom_001 ).
cnf(c_0_35,axiom,
leqNat(s(X1),s(X2)) = leqNat(X1,X2),
axiom_004 ).
cnf(c_0_36,negated_conjecture,
eq3(eq(merge(X1,cons(z,X2)),merge(X2,cons(z,X1))),bfalse) != btrue,
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_37,plain,
merge(cons(s(X1),X2),cons(z,X3)) = cons(z,merge(cons(s(X1),X2),X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_33]),c_0_34]) ).
cnf(c_0_38,plain,
aux(s(X1),X2,s(X3),X4,leqNat(X1,X3)) = merge(cons(s(X1),X2),cons(s(X3),X4)),
inference(spm,[status(thm)],[c_0_22,c_0_35]) ).
cnf(c_0_39,negated_conjecture,
eq3(eq(merge(X1,cons(z,cons(s(X2),X3))),cons(z,merge(cons(s(X2),X3),X1))),bfalse) != btrue,
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_40,plain,
merge(cons(s(z),X1),cons(s(X2),X3)) = cons(s(z),merge(X1,cons(s(X2),X3))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_23]),c_0_24]) ).
cnf(c_0_41,negated_conjecture,
eq3(eq(merge(cons(s(X1),X2),cons(s(z),X3)),cons(s(z),merge(X3,cons(s(X1),X2)))),bfalse) != btrue,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_37]),c_0_30]) ).
cnf(c_0_42,negated_conjecture,
eq3(eq(merge(X1,cons(s(z),X2)),merge(X2,cons(s(z),X1))),bfalse) != btrue,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_40]),c_0_30]) ).
cnf(c_0_43,axiom,
( eq(cons(X1,X3),cons(X2,X4)) = bfalse
| eq2(X1,X2) != bfalse ),
axiom_019 ).
cnf(c_0_44,axiom,
eq2(z,s(X1)) = bfalse,
axiom_014 ).
cnf(c_0_45,negated_conjecture,
eq3(eq(merge(X1,cons(s(z),nil)),cons(s(z),X1)),bfalse) != btrue,
inference(spm,[status(thm)],[c_0_42,c_0_19]) ).
cnf(c_0_46,plain,
eq(cons(z,X1),cons(s(X2),X3)) = bfalse,
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_47,axiom,
eq3(X1,X1) = btrue,
axiom_018 ).
cnf(c_0_48,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_26]),c_0_46]),c_0_47])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWX199-1 : 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
% 0.16/0.32 % Computer : n015.cluster.edu
% 0.16/0.32 % Model : x86_64 x86_64
% 0.16/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.32 % Memory : 8042.1875MB
% 0.16/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 07:55:46 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.33/1.74 % Version : CSE_E---1.7
% 1.33/1.74 % Problem : theBenchmark.p
% 1.33/1.74 % SZS status Unsatisfiable for theBenchmark.p
% 1.33/1.74 % SZS output start CNFRefutation
% See solution above
% 1.33/1.74 % Total time : 1.373s
%------------------------------------------------------------------------------