%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWX185-1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n011.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 05:34:39 PM UTC 2026
% Result : Unsatisfiable 36.96s 21.88s
% Output : CNFRefutation 37.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 13
% Syntax : Number of clauses : 43 ( 41 unt; 0 nHn; 12 RR)
% Number of literals : 45 ( 44 equ; 7 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 : 16 ( 16 usr; 6 con; 0-2 aty)
% Number of variables : 67 ( 26 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(axiom_006,axiom,
assoc(x2(X1,X2)) = x2(assoc(X1),assoc(X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_006) ).
cnf(axiom_008,axiom,
assoc(eY) = eY,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_008) ).
cnf(axiom_016,axiom,
lin(x2(X1,X2)) = append(lin(X1),append(cons(mul,nil),lin(X2))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_016) ).
cnf(axiom_010,axiom,
append(cons(X1,X2),X3) = cons(X1,append(X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_010) ).
cnf(axiom_009,axiom,
append(nil,X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_009) ).
cnf(axiom_056,axiom,
( eq3(x2(X1,X3),x2(X2,X4)) = bfalse
| eq3(X1,X2) != bfalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_056) ).
cnf(axiom_067,axiom,
eq3(eY,x2(X1,X2)) = bfalse,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_067) ).
cnf(axiom_018,axiom,
lin(eY) = cons(y,nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_018) ).
cnf(goal,negated_conjecture,
eq4(prop_unambig(X1,X2),bfalse) != btrue,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal) ).
cnf(axiom_019,axiom,
prop_unambig(X1,X2) = impl(eq(lin(X1),lin(X2)),eq3(assoc(X1),assoc(X2))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_019) ).
cnf(axiom_068,axiom,
eq(X1,X1) = btrue,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_068) ).
cnf(axiom,axiom,
impl(btrue,X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom) ).
cnf(axiom_071,axiom,
eq4(X1,X1) = btrue,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_071) ).
cnf(c_0_13,axiom,
assoc(x2(X1,X2)) = x2(assoc(X1),assoc(X2)),
axiom_006 ).
cnf(c_0_14,axiom,
assoc(eY) = eY,
axiom_008 ).
cnf(c_0_15,axiom,
lin(x2(X1,X2)) = append(lin(X1),append(cons(mul,nil),lin(X2))),
axiom_016 ).
cnf(c_0_16,axiom,
append(cons(X1,X2),X3) = cons(X1,append(X2,X3)),
axiom_010 ).
cnf(c_0_17,axiom,
append(nil,X1) = X1,
axiom_009 ).
cnf(c_0_18,axiom,
( eq3(x2(X1,X3),x2(X2,X4)) = bfalse
| eq3(X1,X2) != bfalse ),
axiom_056 ).
cnf(c_0_19,axiom,
eq3(eY,x2(X1,X2)) = bfalse,
axiom_067 ).
cnf(c_0_20,plain,
x2(assoc(X1),eY) = assoc(x2(X1,eY)),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_21,plain,
append(lin(X1),cons(mul,lin(X2))) = lin(x2(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_16]),c_0_17]) ).
cnf(c_0_22,axiom,
lin(eY) = cons(y,nil),
axiom_018 ).
cnf(c_0_23,plain,
eq3(x2(eY,X1),x2(x2(X2,X3),X4)) = bfalse,
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_24,plain,
x2(eY,assoc(X1)) = assoc(x2(eY,X1)),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_25,plain,
assoc(x2(eY,eY)) = x2(eY,eY),
inference(spm,[status(thm)],[c_0_20,c_0_14]) ).
cnf(c_0_26,plain,
append(lin(X1),cons(mul,cons(y,nil))) = lin(x2(X1,eY)),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_27,negated_conjecture,
eq4(prop_unambig(X1,X2),bfalse) != btrue,
goal ).
cnf(c_0_28,axiom,
prop_unambig(X1,X2) = impl(eq(lin(X1),lin(X2)),eq3(assoc(X1),assoc(X2))),
axiom_019 ).
cnf(c_0_29,plain,
eq3(assoc(x2(eY,X1)),x2(x2(X2,X3),X4)) = bfalse,
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_30,plain,
x2(x2(eY,eY),assoc(X1)) = assoc(x2(x2(eY,eY),X1)),
inference(spm,[status(thm)],[c_0_13,c_0_25]) ).
cnf(c_0_31,plain,
cons(y,cons(mul,cons(y,nil))) = lin(x2(eY,eY)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_22]),c_0_16]),c_0_17]) ).
cnf(c_0_32,negated_conjecture,
eq4(impl(eq(lin(X1),lin(X2)),eq3(assoc(X1),assoc(X2))),bfalse) != btrue,
inference(rw,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_33,plain,
eq3(assoc(x2(eY,X1)),assoc(x2(x2(eY,eY),X2))) = bfalse,
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_34,plain,
append(lin(x2(eY,eY)),X1) = cons(y,cons(mul,cons(y,X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_31]),c_0_16]),c_0_16]),c_0_17]) ).
cnf(c_0_35,plain,
cons(y,cons(mul,lin(X1))) = lin(x2(eY,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_16]),c_0_17]) ).
cnf(c_0_36,negated_conjecture,
eq4(impl(eq(lin(x2(eY,X1)),lin(x2(x2(eY,eY),X2))),bfalse),bfalse) != btrue,
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_37,plain,
lin(x2(x2(eY,eY),X1)) = lin(x2(eY,x2(eY,X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_34]),c_0_35]),c_0_35]) ).
cnf(c_0_38,negated_conjecture,
eq4(impl(eq(lin(x2(eY,X1)),lin(x2(eY,x2(eY,X2)))),bfalse),bfalse) != btrue,
inference(rw,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_39,axiom,
eq(X1,X1) = btrue,
axiom_068 ).
cnf(c_0_40,axiom,
impl(btrue,X1) = X1,
axiom ).
cnf(c_0_41,axiom,
eq4(X1,X1) = btrue,
axiom_071 ).
cnf(c_0_42,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40]),c_0_41])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWX185-1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33 % Computer : n011.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 07:54:17 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 36.96/21.88 % Version : CSE_E---1.7
% 36.96/21.88 % Problem : theBenchmark.p
% 36.96/21.88 % SZS status Unsatisfiable for theBenchmark.p
% 36.96/21.88 % SZS output start CNFRefutation
% See solution above
% 37.19/22.03 % Total time : 16.400s
%------------------------------------------------------------------------------