%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWX228-1 : 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 : n028.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 05:34:47 PM UTC 2026
% Result : Unsatisfiable 1.26s 1.71s
% Output : CNFRefutation 1.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 12
% Syntax : Number of clauses : 32 ( 30 unt; 0 nHn; 10 RR)
% Number of literals : 34 ( 33 equ; 9 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 4 con; 0-4 aty)
% Number of variables : 55 ( 13 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(axiom_009,axiom,
elem(X1,cons(X2,X3)) = barbar(eqNat(X1,X2),elem(X1,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_009) ).
cnf(axiom_007,axiom,
eqNat(z,z) = btrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_007) ).
cnf(axiom_002,axiom,
barbar(btrue,X1) = btrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_002) ).
cnf(goal,negated_conjecture,
eq3(prop_union_comm(X1,X2),bfalse) != btrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal) ).
cnf(axiom_012,axiom,
prop_union_comm(X1,X2) = eq(union(X1,X2),union(X2,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_012) ).
cnf(axiom_011,axiom,
union(cons(X1,X2),X3) = aux(X3,X1,X2,elem(X1,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_011) ).
cnf(axiom,axiom,
aux(X1,X2,X3,btrue) = union(X3,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom) ).
cnf(axiom_010,axiom,
union(nil,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_010) ).
cnf(axiom_022,axiom,
( eq(cons(X1,X3),cons(X2,X4)) = eq(X3,X4)
| eq2(X1,X2) != btrue ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_022) ).
cnf(axiom_023,axiom,
eq(nil,cons(X1,X2)) = bfalse,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_023) ).
cnf(axiom_020,axiom,
eq3(X1,X1) = btrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_020) ).
cnf(axiom_019,axiom,
eq2(X1,X1) = btrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_019) ).
cnf(c_0_12,axiom,
elem(X1,cons(X2,X3)) = barbar(eqNat(X1,X2),elem(X1,X3)),
axiom_009 ).
cnf(c_0_13,axiom,
eqNat(z,z) = btrue,
axiom_007 ).
cnf(c_0_14,axiom,
barbar(btrue,X1) = btrue,
axiom_002 ).
cnf(c_0_15,negated_conjecture,
eq3(prop_union_comm(X1,X2),bfalse) != btrue,
goal ).
cnf(c_0_16,axiom,
prop_union_comm(X1,X2) = eq(union(X1,X2),union(X2,X1)),
axiom_012 ).
cnf(c_0_17,axiom,
union(cons(X1,X2),X3) = aux(X3,X1,X2,elem(X1,X3)),
axiom_011 ).
cnf(c_0_18,plain,
elem(z,cons(z,X1)) = btrue,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14]) ).
cnf(c_0_19,axiom,
aux(X1,X2,X3,btrue) = union(X3,X1),
axiom ).
cnf(c_0_20,negated_conjecture,
eq3(eq(union(X1,X2),union(X2,X1)),bfalse) != btrue,
inference(rw,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_21,plain,
union(cons(z,X1),cons(z,X2)) = union(X1,cons(z,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]) ).
cnf(c_0_22,negated_conjecture,
eq3(eq(union(X1,cons(z,X2)),union(X2,cons(z,X1))),bfalse) != btrue,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_21]) ).
cnf(c_0_23,axiom,
union(nil,X1) = X1,
axiom_010 ).
cnf(c_0_24,negated_conjecture,
eq3(eq(union(X1,cons(z,nil)),cons(z,X1)),bfalse) != btrue,
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_25,negated_conjecture,
eq3(eq(union(X1,cons(z,nil)),cons(z,cons(z,X1))),bfalse) != btrue,
inference(spm,[status(thm)],[c_0_24,c_0_21]) ).
cnf(c_0_26,negated_conjecture,
eq3(eq(cons(z,nil),cons(z,cons(z,nil))),bfalse) != btrue,
inference(spm,[status(thm)],[c_0_25,c_0_23]) ).
cnf(c_0_27,axiom,
( eq(cons(X1,X3),cons(X2,X4)) = eq(X3,X4)
| eq2(X1,X2) != btrue ),
axiom_022 ).
cnf(c_0_28,axiom,
eq(nil,cons(X1,X2)) = bfalse,
axiom_023 ).
cnf(c_0_29,axiom,
eq3(X1,X1) = btrue,
axiom_020 ).
cnf(c_0_30,axiom,
eq2(X1,X1) = btrue,
axiom_019 ).
cnf(c_0_31,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28]),c_0_29]),c_0_30])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWX228-1 : 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
% 0.15/0.32 % Computer : n028.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Tue May 5 07:59:45 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.26/1.71 % Version : CSE_E---1.7
% 1.26/1.71 % Problem : theBenchmark.p
% 1.26/1.71 % SZS status Unsatisfiable for theBenchmark.p
% 1.26/1.71 % SZS output start CNFRefutation
% See solution above
% 1.26/1.71 % Total time : 1.373s
%------------------------------------------------------------------------------